 Contents

Click on one of the topics to display information about it.

Learning the Program

Accessing and Using Files

Working with Data and DataSheets

Working with Graphs and Graphics Options

Printing

Using Special Features

Using Standard Edition Analyses

Using OLE

Using the Analyses in the Plot Menu

Using the Analyses in the Describe Menu

Using Analyses in the Compare Menu

Using Analyses for Quality Control

Using Analyses for Experimental Design

Using Analyses for Advanced Regression

Using Analyses for Multivariate Methods

Using Analyses for Time Series

Reference Information

Technical Support

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Learning the Program

Accessing and Using Files

Working with Data and DataSheets

Working with Graphs and Graphics Options

Printing

Using Special Features

Using Standard Edition Analyses

Using Analyses for Quality Control

Using Analyses for Experimental Design

Using Analyses for Advanced Regression

Using Analyses for Multivariate Methods

Using Analyses for Time Series

Reference Information

Technical Support


Variable l

The term l represents a single numeric value.  The examples use this term with m and n when the example needs three single values.


Variable m

The term m represents a single numeric value.  The examples use this term with n when the example needs two single values.


Variable n

The term n represents a single numeric value.


Variable x

The term x represents a numeric variable or constant.


Variable y

The term y represents a numeric variable or constant.  The examples use this term with x when the example needs two numeric variables or constants.


Variable charvar

The term charvar represents any character variable.


Variable logical

The term logical represents a variable that contains only 0's and 1's.


Variable numvar

The term numvar represents any numeric variable.


Variable var

The term var represents any variable.


Dataset sample1

sample1 = 1  2  3  4  5


Dataset sample2

sample2 = 5  6  7  8  9


Dataset sample3

sample3 = -5  -4  -3  -2  -1


Dataset sample4

sample4 = 72  41  93  10  72


Dataset sample5

sample5 = a  c  e  g  i


Dataset sample6

sample6 = b  d  f  h  j


Dataset sample7

sample7 = Ford  Chrysler  Chevrolet  Mazda  Acura


Dataset sample8

sample8 = Ford    Mustang (a single row with extraneous blanks)


ABS

Take the Absolute Value (ABS)

Type:	ABS  (-20)

Result:	20

Type:	ABS  (sample3)

Result:	5  4  3  2  1


ACOS

Calculate the Inverse Cosine of an Angle in Degrees (ACOS)

Type:	ACOS  (.7)

Result:	45.572996

Type:	ACOS  (sample2 * .01)

Result:	87.134016  86.560187  85.986012  85.411434  84.836393


ACOSR

Calculate the Inverse Cosine of an Angle in Radians (ACOSR)

Type:	ACOSR  (.7)

Result:	.795399

Type:	ACOSR  (sample2 * .01)

Result:	1.520775  1.510760  1.500739  1.490710  1.480674


ADD

Add (+)

Type:	2  +  4

Result:	6

Type:	sample1  +  sample2

Result:	6  8  10 12 14


AND

Both of Two Conditions Must Be True (&)

Type:	(40  >  10)  &  (10  =  50)

Result:	0.  The result of the first condition (40 > 10) is 1.  The result of the second condition (10 = 50) is 0.  The value meets only one condition, so the system returns a 0 (false).

Type:	(sample1  =  3)  & (sample2  >  5)

Result:	The system returns a 1 for cases where a data value in the variable sample1 is equal to 3 and the corresponding data value in sample2 is greater than 5.  For cases that meet only one or neither of these conditions, the system returns a 0.


ASIN

Calculate the Inverse Sine of an Angle in Degrees (ASIN)

Type:	ASIN  (.7)

Result:	44.427004

Type:	ASIN  (sample2 * .01)

Result:	2.865983  3.439812  4.013987  4.588565  5.163607


ASINR

Calculate the Inverse Sine of an Angle in Radians (ASINR)

Type:	ASINR  (.7)

Result:	.775397

Type:	ASINR  (sample2 * .01)

Result:	0.050020  0.060036  0.070057  0.080085  0.090121


ATAN

Calculate the Inverse Tangent of an Angle in Degrees (ATAN)

Type:	ATAN  (.7)

Result:	34.992020

Type:	ATAN  (sample2 * .01)

Result:	2.862405  3.433630  4.004172  4.573921  5.142764


ATANR

Calculate the Inverse Tangent of an Angle in Radians (ATANR)

Type:	ATANR  (.7)

Result:	0.610725

Type:	ATANR  (sample2 * .01)

Result:	0.049958  0.059928  0.069886  0.079829  0.089758


AVG

Calculate the Average (AVG)

Type:	AVG  (sample1)

Result:	3


BETA

Calculate the Probability of the Cumulative Beta Distribution (BETA)

Type:	BETA (0.5,2,5)

Result:	0.890624


CELL

Select Specified Row (CELL)

Type:	CELL  (sample2,3)

Result:	7


CHISQUARE

Calculate the Probability of the Cumulative Chi-Square Distribution (CHISQUARE)

Type:	CHISQUARE (30,20)

Result:	0.930146


COMPRESS

Select Rows that Meet a Condition (COMPRESS)

Type:	COMPRESS  (sample2,sample1 > 2)

Result:	7  8  9

Type:	COMPRESS (sample2,sample7 > "Acura" )

Result:	5


COS

Calculate the Cosine of an Angle in Degrees (COS)

Type:	COS  (40.0)

Result:	0.766044

Type:	COS  (sample1)

Result:	0.999847  0.999390  0.998629  0.997564  0.996194


COSR

Calculate the Cosine of an Angle in Radians (COSR)

Type:	COSR (40.0)

Result:	-0.6669380

Type:	COSR (sample1)

Result:	0.540302  -0.416146  -0.989992  -0.653643  0.283662


COUNT

Create a Sequential Numeric Vector (COUNT)

Type:	COUNT  (10,20,2)

Result:	10  12  14  16  18  20

Type:	10  +  (COUNT  (1,5,1))

Result:	11  12  13  14  15


CV

Calculate the Coefficient of Variation (CV)

Type:	CV (sample1)

Result:	52.704627


DIFF

Calculate Differences between Consecutive Values (DIFF)

Type:	DIFF  (sample1)

Result:	(missing)  1  1  1  1

Type:	DIFF  (sample1*sample2)

Result:	(missing)  7  9  11  13


DIVIDE

Divide (/)

Type:	32  /  8

Result:	4

Type:	sample2  /  sample1

Result:	5.0  3.0  2.333333  2.0  1.8


DROP

Select All but First n Rows (DROP)

Type:	DROP  (sample1,2)

Result:	3  4  5


DROPLAST

Select All but Last n Rows (DROPLAST)

Type:	DROPLAST  (sample2,2)

Result:	5  6  7


EQUAL TO

Equal To (=)

Type:	sample1  =  1

Result:	1  0  0  0  0

Type:	sample1  =  sample2

Result:	0  0  0  0  0


EXP

Raise e to a Power (EXP)

Type:	EXP  (2)

Result:	7.38905

Type:	EXP (sample1)

Result:	2.718281  7.389056  20.085536  54.598150  148.413159


EXP10

Raise 10 to a Power (EXP10)

Type:	EXP10  (2)

Result:	100

Type:	EXP10 (sample1)

Result:	10  100  1000  10000  100000


FACT

Calculate the Factorial (FACT)

Type:	FACT  (3)

Result:	6

Type:	FACT (sample1)

Result:	1  2  6  24  120


FIRST

Generate a 1 for the First n Rows (FIRST)

Type:	FIRST  (3)

Result:	In a file with four rows, the system generates three 1's followed by one 0.


FIRSTROWS

Select the First n Rows, Using Missing Values for Other Rows (FIRSTROWS)

Type:	FIRSTROWS  (sample2,4)

Result:	5  6  7  8  (missing)


GREATER THAN OR EQUAL TO

Greater Than or Equal To (>=)

Type:	sample1  >=  3

Result:	0  0  1  1  1

Type:	sample2  >=  sample1

Result:	1  1  1  1  1


GEOMEAN

Calculate the Geometric Mean (GEOMEAN)

Type:	GEOMEAN  (sample2)

Result:	6.853467


GREATER THAN

Greater Than (>)

Type:	sample1  >  3

Result:	0  0  0  1  1

Type:	sample2  >  sample1

Result:	1  1  1  1  1


INVBETA

Calculate the Critical Value of the Beta Distribution (INVBETA)

Type:	INVBETA (0.9,2,5)

Result:	0.510318


INVCHISQUARE

Calculate the Critical Value of the Chi-Square Distribution (INVCHISQUARE)

Type:	INVCHISQUARE (.9,20)

Result:	28.3989


INVNORMAL

Calculate the Critical Value of the Normal Distribution (INVNORMAL)

Type:	INVNORMAL (.9,0,1)

Result:	1.28155


INVSNEDECOR

Calculate the Critical Value of the Snedecor's-F Distribution (INVSNEDECOR)

Type:	INVSNEDECOR (.9,3,20)

Result:	2.38053


INVSTUDENT

Calculate the Critical Value of the Student's-t Distribution (INVSTUDENT)

Type:	INVSTUDENT (.9,20)

Result:	1.32534


IQR

Calculate the Interquartile Range (IQR)

Type:	IQR  (sample2)

Result:	2


JOIN

Join Columns End to End (JOIN)

Type:	JOIN (sample1,sample2)

Result:	1  2  3  4  5  5  6  7  8  9


JUXTAPOSE

Join Character Variables Side by Side (JUXTAPOSE)

Type:	JUXTAPOSE (sample5,sample6)

Result:	ab  cd  ef  gh  ij


KURTOSIS

Calculate the Coefficient of Kurtosis (KURTOSIS)

Type:	KURTOSIS  (sample2)

Result:	-1.2


LAG

Shift Values n Positions Forward or Backward (LAG)

Type:	LAG  (sample1,2)

Result:	The system inserts two missing values at the beginning of the variable sample1 and moves the first nonmissing value in sample1 to the third position.

Type:	LAG  (sample1,-2)

Result:	The system drops the first two data values (observations) in sample1 and moves the third value to the first position.


LAST

Generate a 1 for the Last n Rows (LAST)

Type:	LAST  (3)

Result:	In a file with four rows, the system generates one 0 followed by three 1's.


LASTROWS

Select the Last n Rows, Using Missing Values for Other Rows (LASTROWS)

Type:	LASTROWS  (sample2,4)

Result:	(missing)  6  7  8  9


LESS THAN OR EQUAL TO

Less Than or Equal To (<=)

Type:	sample1  <=  3

Result:	1  1  1  0  0

Type:	sample1  <=  sample2

Result:	1  1  1  1  1


LOG

Take the Natural Logarithm (LOG)

Type:	LOG (100)

Result:	4.60517

Type:	LOG (sample1)

Result:	0  0.693147  1.098612  1.386294  1.609437


LOG10

Take the Base-Ten Logarithm (LOG10)

Type:	LOG10 (100)

Result:	2

Type:	LOG10  (sample1)

Result:	0  0.301029  0.477121  0.602059  0.698970


LESS THAN

Less Than (<)

Type:	sample1  <  3

Result:	1  1  0  0  0

Type:	sample1  <  sample2

Result:	1  1  1  1  1


MAX

Find the Largest Value (MAX)

Type:	MAX  (sample2)

Result:	9


MDIFF

Calculate Multiple Backward Differences (MDIFF)

Type:	MDIFF  (sample4,2)

Result:	(missing)  (missing)  83.0  -135.0  145.0


MEDIAN

Calculate the Median (MEDIAN)

Type:	MEDIAN  (sample2)

Result:	7


MIN

Find the Smallest Value (MIN)

Type:	MIN  (sample1)

Result:	1


MODE

Find the Most Frequent Observation (MODE)

Type:	MODE  (sample4)

Result:	72


MULTIPLY

Multiply (*)

Type:	4  *  10

Result:	40

Type:	sample1  *  sample2

Result:	5  12  21  32  45


NOT EQUAL

Not Equal (<>)

Type:	sample1  <>  1

Result:	0  1  1  1  1

Type:	sample1  <>  sample2

Result:	1  1  1  1  1


NORMAL

Calculate the Probability of the Cumulative Normal Distribution (NORMAL)

Type:	NORMAL (2,0,1)

Result:	0.97725


NOT

Negate a Boolean Constant or Variable (~)

Type:	~ 0

Result:	1

Type:	~ (sample1 = 4)

Result:	The system evaluates the statement in parentheses, returning a 1 (true) for every data value in the sample1 variable that meets the condition and a 0 (false) for every data value that does not meet the condition.  Then the system negates the Boolean result, in effect returning a 1 for every data value in the sample1 variable that is not equal to 4.


OR

Either of Two Conditions Must be True (|)

Type:	(40  >  10)  |  (40  =  20)

Result:	The result of the first condition (40 > 10) is 1.  The result of the second condition (40 = 20) is 0.  The value meets one condition, so the system returns a 1 (true).

Type:	(sample2  =  7)  |  (sample1  >  2)

Result:	The system returns a 1 for cases where a data value in the variable sample2 is equal to 7 or the corresponding data value in sample1 is greater than 2.  For cases that meet neither condition, the system returns a 0.


PERCENTILE

Calculate a Percentile (PERCENTILE)

Type:	PERCENTILE (sample1,25)

Result:	2


Q25

Calculate the Lower Quartile (Q25)

Type:	Q25 (sample2)

Result:	6


Q75

Calculate the Upper Quartile (Q75)

Type:	Q75 (sample2)

Result:	8


RAISE TO A POWER

Raise to a Power (^)

Type:	9  ^  2

Result:	81

Type:	sample2  ^  sample1

Result:	5  36  343  4096  59049


RANDOM

Generate a 1 for n Randomly Selected Rows (RANDOM)

Type:	RANDOM  (3)

Result:	In a file with four rows, the system generates three 1's in random rows and 0's in all the other rows.


RANGE

Calculate the Range (RANGE)

Type:	RANGE (sample2)

Result:	4


RECODE

Recode Numeric or Character Values to Integers (RECODE)

Type:	RECODE  (sample4)

Result:	3  2  4  1  3

Type:	RECODE  (sample7)

Result:	4  3  2  5  1


REP

Repeat Each Value n Times (REP)

Type:	REP  (sample1,2)

Result:	1  1  2  2  3  3  4  4  5  5


RESHAPE

Expand or Compress a Constant or Variable (RESHAPE)

Type:	RESHAPE  (COUNT (1,5,1),12)

Result:	1  2  3  4  5  1  2  3  4  5  1  2

Type:	RESHAPE  (sample2,3)

Result:	5  6  7


REXPONENTIAL

Generate Random Numbers from an Exponential Distribution (REXPONENTIAL)

Type:	REXPONENTIAL  (5,20)

Result:	35.445269  42.880350  48.049617  18.078479  2.923928


RGAMMA

Generate Random Numbers from a Gamma Distribution (RGAMMA)

Type:	RGAMMA  (5,1,3)

Result:	2.231758  2.729751  3.263105  1.364058  2.697922


RINTEGER

Generate Random Numbers (Integer Values) from a Discrete Uniform Distribution (RINTEGER)

Type:	RINTEGER  (5,10,15)

Result:	15  15  14  13  11


RLOGNORMAL

Generate Random Numbers from a Lognormal Distribution (RLOGNORMAL)

Type:	RLOGNORMAL  (5,7,9)

Result:	51372.3221  0.002422  2156.244872  8.874807  0.000172


RNORMAL

Generate Random Numbers from a Normal Distribution (RNORMAL)

Type:	RNORMAL  (5,3.2,4.9)

Result:	-2.957235  6.426126  -0.497581  9.598366  -3.141531


ROUND

Round to the Nearest Integer (ROUND)

Type:	ROUND  1234.5678

Result:	1235

Type:	ROUND  (sample1 + .6)

Result:	2  3  4  5  6


ROWS

Generate a 1 for Rows n to m (ROWS)

Type:	ROWS  (2,4)

Result:	In a file with 10 rows, the system generates one 0, followed by three 1's and six 0's


RUNIFORM

Generate Random Numbers from a Continuous Uniform Distribution (RUNIFORM)

Type:	RUNIFORM  (5,20,100)

Result:	39.514873  59.491310  35.746625  79.181132  51.351437


RWEIBULL

Generate Random Numbers from a Weibull Distribution (RWEIBULL)

Type:	RWEIBULL  (5,.2,.4)

Result:	0.000016  2.331905  0.000462  2.183750  81.772798


SD

Calculate the Standard Deviation (SD)

Type:	SD  (sample2)

Result:	1.581138


SDIFF

Calculate Seasonal Differences (SDIFF)

Type:	SDIFF  (sample4,2)

Result:	(missing)  (missing)  21.0  -31.0  -21.0


SELECT

Select Rows that Meet a Condition (SELECT)

Type:	SELECT  (sample1,sample2 =  6)

Result:	The system selects the values from sample1 for cases where the corresponding values in sample2 are greater than or equal to 6.  For cases where the corresponding values in sample2 are not greater than or equal to 6, the system returns a missing value.  The variables you use in this type of expression must contain the same number of data values.

Type:	SELECT  (sample1,(sample2  <  7)  |  (sample2  >  8)

Result:	The system selects values from sample1 for cases where the corresponding values in sample2 are less than 7 or greater than 8.  For cases that do not meet the conditions, the system returns a missing value.


SERROR

Calculate the Standard Error (SERROR)

Type:	SERROR  (sample1)

Result:	0.707106


SIN

Calculate the Sine of an Angle in Degrees (SIN)

Type:	SIN  (30.0)

Result:	.5

Type:	SIN (sample1)

Result:	0.017452  0.034899  0.052335  0.069756  0.087155


SINR

Calculate the Sine of an Angle in Radians (SINR)

Type:	SINR  (30.0)

Result:	-0.988032

Type:	SINR (sample1)

Result:	0.841470  0.909297  0.141120  -0.756802  -0.958924


SIZE

Count the Number of Nonmissing Observations (SIZE)

Type:	SIZE  (sample1)

Result:	5


SKEWNESS

Calculate the Coefficient of Skewness (SKEWNESS)

Type:	SKEWNESS  (sample4)

Result:	-.757888


SKURT

Calculate the Standardized Kurtosis (SKURT)

Type:	SKURT  (sample1)

Result:	-0.547723


SNEDECOR

Calculate the Probability of the Cumulative Snedecor's F Distribution (SNEDECOR)

Type:	SNEDECOR (4,3,20)

Result:	0.977923


SQRT

Calculate the Square Root (SQRT)

Type:	SQRT  10000

Result:	100

Type:	SQRT  (sample1)

Result:	1  1.414213  1.732050  2  2.236067


SSKEW

Calculate the Standardized Skewness (SSKEW)

Type:	SSKEW  (sample4)

Result:	-.691854


STRIPBLANKS

Remove Double Blanks (STRIPBLANKS)

Type:	STRIPBLANKS  (sample8)

Result:	Ford Mustang


STUDENT

Calculate the Probability of the Cumulative Student's t Distribution (STUDENT)

Type:	STUDENT (2,20)

Result:	0.970367


SUBTRACT

Subtract (-)

Type:	10  -  4

Result:	6

Type:	sample2  -  sample1

Result:	4  4  4  4  4


SUM

Calculate the Sum of the Observations (SUM)

Type:	SUM  (sample1)

Result:	15


TAKE

Select the First n Rows (TAKE)

Type:	TAKE  (sample2,3)

Result:	5  6  7


TAKELAST

Select the Last n Rows (TAKELAST)

Type:	TAKELAST  (sample2,3)

Result:	7  8  9


TAN

Calculate the Tangent of an Angle in Degrees (TAN)

Type:	TAN  (30.0)

Result:	0.577350

Type:	TAN (sample1)

Result:	0.017455  0.034920  0.052407  0.069926  0.087488


TANR

Calculate the Tangent of an Angle in Radians (TANR)

Type:	TANR  (30.0)

Result:	-6.405331

Type:	TANR (sample1)

Result:	1.557407  -2.185039  -0.142546  1.157821  -3.380515


TRUNCATE

Find the Largest Integer (TRUNCATE)

Type:	TRUNCATE  (4.98315)

Result:	4

Type:	TRUNCATE  (sample1 + .06)

Result:	1  2  3  4  5


VARIANCE

Calculate the Variance (VARIANCE)

Type:	VARIANCE  (sample2)

Result:	2.5


VV RUNTOT
RUNTOT

Calculate a running total (RUNTOT)

Type:	RUNTOT  (sample1)

Result:	1 3 6 10 15


VV STANDARDIZE
STANDARDIZE

Use this operator to subtract the average from each value and then divide by the standard deviation.

Type:	STANDARDIZE  (sample1)

Result:	-1.26491 -0.632456 0.632456 1.26491


VV DATENUM
DATENUM

Use this operator to make it easier to use dates in a calculation.  It converts the data to a STATGRAPHICS Plus date code.  The right argument must be a date variable.  The DATENUM operator converts the values to counting numbers that are equivalent to changing the date type in the editor to integer

Type:	DATENUM (sample9)

Result:	16710 16711 16712


Dataset sample9

sample9 = 10/1/95  10/2/95  10/3/95


VV datevar
datevar

The term datevar represents any date variable.


VV JOIN3
JOIN3

Use this operator to join three numeric or three character variables end to end.

Type:	JOIN3 (sample1,sample2,sample3)

Result:	1 2 3 4 5 5 6 7 8 9 -5 -4 -3 -2 -1


VV JOIN4
JOIN4

Use this operator to join four numeric or four character variables end to end.

Type:	JOIN4 (sample1,sample3,sample1,sample3)

Result:	1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -5 -4 -3 -2 -1


RANK

Calculate the rank of each row (RANK)

Type:	RANK (sample4)

Result:	3.5 2 5 1 3.5


REPLACE

Replace all occurrences of a number with a different number (REPLACE)

Type:	REPLACE (sample1,5,6)

Result:	1 2 3 4 6


ROUNDTO

Round to the specified number of decimal places (ROUNDTO)

Type:	ROUNDTO (sample10,4)

Result:	1.1111 2.2222 3.3333 4.4444 5.5556


Dataset sample10

sample10 = 1.111111 2.222222 3.333333 4.444444 5.555555


Buttons

On dialog boxes, buttons perform a command, cancel a command, or present additional options.  On the Application toolbar, buttons give you quick access to the most common system-wide features and analyses.  On the Analysis toolbar, buttons allow you to redisplay the Analysis or Plot dialog box, access additional tabular and graphical options, and save the results of certain statistical analyses. See also command button.


Cascade

To display windows in an overlapping format.


Case

In STATGRAPHICS Plus, the observations that correspond across variables.


Cell

In the Spreadsheet window, the intersection of a row and a column.


Character Variable

A variable that contains characters and/or numbers that are treated as characters.  You cannot run calculations on character variables.


Check Boxes

On a dialog box, small square boxes that allow you to select as many options as you like from a list of options.  When the option is on, the box contains an X.  When the option is off, the box is blank.


Clear

To turn off an option by removing the X from a check box.  You clear an option by clicking on it, or by selecting it and pressing the space bar.


Click

To press and release a mouse button quickly.


Click and Drag

To move an item on the screen by holding down the left mouse button while moving the mouse.


Clipboard

A temporary storage area for information you cut and copy using the Cut and Copy commands.


Combo Box

A text box with an attached list.  Combo boxes provide a list of possible responses you can select.


Command

A word or phrase you choose to carry out an action.


Command Button

A button on a dialog box that carries out or cancels an action, such as OK and Cancel.


Data File

A file that contains variables that you store on a hard disk or a diskette.


Date Variable

A variable that contains numbers in mm/dd/yy format or the format you set on the Windows Control Panel.


Default Value

A value the program uses when you do not provide an explicit choice.  Also known as the default.


Delimiter

A character that marks the beginning and ending of a record or command.


Dialog Box

A window with command options you can review or change, or with warnings or explanations that inform you about certain actions.  Dialog boxes are the primary tool the program uses to interact with you.


DIF

An acronym for Data Interchange Format.  A specially formatted ASCII file designed to be easily transported between software packages.


Directory

A storage area on a hard disk or a diskette.


Distribution Operators

Operators that calculate the cumulative probability for a distribution at a given point, or the critical value from a distribution given a probability.


Double-Click

To press and release the mouse button twice in rapid succession without moving the mouse.


Driver

A software program that lets your computer communicate with a peripheral unit (such as a printer).


dropdown list
Drop-Down List

On a dialog box, a box with a downward arrow to the right of a hidden list of options.  You must select the drop-down list and click on the downward arrow to see the options.


Dynamic Data Exchange (DDE)

A channel through which applications pass information to each other.  For example, when you link a variable in STATGRAPHICS Plus to data in Microsoft Excel, STATGRAPHICS Plus uses DDE to update the results when you change the corresponding data in Excel.


Error Message

A message the program produces when it encounters data it cannot process.


Exit

A menu option that closes the active application and all the windows associated with it.


Expression

A formula composed of one or more phrases.  A phrase always contains at least one operator and a right argument (values or phrases to the right of the operator).  It may also contain a left argument (values or phrases to the left of the operator), depending on the operator you use.


Extension

A synonym for file extension.


File

A data structure that can contain variables.


File Extension

An additional one to three characters that appear after a file name to further identify the file.


File Name

In versions of Windows prior to 95, a name of up to eight characters that identifies a file.  File names should begin with a letter.  You can use upper- and lowercase letters as well as numbers.


Fixed-Decimal Variable

A variable that contains only numbers that have a fixed number of decimal places.


Font

A complete assortment of type of one style and size that determines how material you view or print will look.


Formula

A mathematical expression or statement.


Function Keys

The keys F1 through F12 on your keyboard that are predefined in the program to perform certain operations you frequently use.


Generation Operators

Operators that let you generate data values quickly, such as a variable that contains random numbers or consecutive numbers.


Graphics Adapter

A hardware device that allows you to display information on your computer's screen.


Graphics Pane

The viewing area of an Analysis window that contains graphical output.


Group Box

On a dialog box, a visual grouping of related controls.


Hardware

The physical equipment or devices (for example, CPU and disk drives) that together make up a computer system.


Icon

A small picture that represents a program, function, or file in a meaningful way.


Import

The process of converting data you create in other software programs into a format the program understands so you can analyze the data using the analyses available in STATGRAPHICS Plus.


Inactive

A window or icon you are not currently using.  You activate an inactive window or icon by clicking it.


Input

Data you want to process, and the instructions to control the processing, that you enter into the program.


Integer Variable

A variable that contains numbers with no decimal digits.


List Box

On a dialog box, a box that lists all the available choices.  If all the available choices do not fit the list box, it has a vertical scroll bar.


Logical Operators

Operators that let you select values that meet both or either of two conditions, or that negate a variable that contains only zeros and ones.  You use logical operators in conjunction with relational operators (see Relational Operators).


math co-processor
Math Coprocessor

An integrated circuit that enhances the execution speed of floating-point mathematical computations.


Mathematical Operators

Operators that perform standard mathematical operations on constants and the values in numeric variables; for example, addition, subtraction, division, and multiplication.


Menu

A list of commands, files, or other actions you access by selecting the menu name then choosing the associated item from the list.


Menu Bar

A horizontal bar at the top of a window that contains the main headings for all the menu items available for that window.


Metafile

A graphics format that many graphics software programs can read.


Missing Value

An observation for which there is no data.


Monitor

A computer device that displays information.  The display can appear in either one color (on a monochrome monitor) or in many colors (on a color monitor).


Month Variable

A variable that contains numbers entered in mm/yy format or the format you set on the Windows Control Panel.


Multiple-Selection List

Displays the choices from which you can select more than one option at a time.  The options have check boxes preceding them from which you make your selections.


Numeric Variable

A variable that contains only numbers and has a floating decimal place; you can type as many numbers as you want after the decimal.  You can also create numeric variables that contain numbers you use as codes.  You use these codes to divide data into classes for certain statistical analyses.


Operators

Functions that let you perform complex mathematical calculations, generate and transform data, and otherwise manipulate data.  See also Generation Operators, Logical Operators, Mathematical Operators, Relational Operators, Selection Operators, and Transformation Operators.


Options

The choices on a dialog box.


Option Buttons

In a dialog box, circles that represent a set of mutually exclusive choices; for example, on and off.  When you select the option, the program places a black dot in the button.  Also called radio buttons.


Output

Data the program transfers from your computer's internal storage unit to a computer screen, printer, or some storage device for later processing.


Output Device

Any device you attach to your computer that displays information; for example, a monitor or a printer.


Pane

The viewing area of a window.  Analysis windows can have text in a single pane, graphics in a single pane, or both text and graphics in multiple panes.


Path

A specification that indicates a directory on a hard disk or diskette.  The path consists of the drive, directory, and file name.


Point Size

The size of a typographical element, such as the points displayed on a graph.


Prompt

A line of text that the program displays in a dialog box that asks you to enter information.


pulldown, single-selection list
Pull-Down, Single-Selection List

A list of varying lengths that displays options.  You  can select only one option at a time.  When closed, the list displays only one item.  A closed list has downward pointing arrow.  When you click on the arrow, you open the list, which then displays from three to eight items.


RAM

An acronym for random-access memory; a memory chip that can be read from and written to.


Relational Operators

Operators that determine whether an expression is true or false.  The program matches each value in the left argument to a value in the right argument.  If the calculation for that pair of values is true, the program returns a 1; if it is false, the program returns a 0.  If one of the values is missing, the program returns the missing value.


Scroll Bars

Bars along the right and/or bottom sides of a window or list box that allow you to scroll through a document vertically and horizontally.  The length of the scroll bar represents the entire document.  Dragging the scroll box to a different position on the scroll bar and releasing the mouse button displays the part of the document that is in that position.


Scroll Box

In a scroll bar, a small box that shows the relative position of the information that is currently visible in the window or list box.


Select-All Button

In a Spreadsheet window, the button in the upper left corner of the window that selects all the rows and columns in the spreadsheet.


Select-Column Buttons

In a Spreadsheet window, the buttons at the top of each column that contain the names of the columns and allow you to select all the rows in the corresponding column in the spreadsheet.


Select-Row Buttons

In a Spreadsheet window, the buttons along the left side of the window that contain the numbers of the rows and allow you to select all the columns in the corresponding row in the spreadsheet.


Selection Operators

Operators that let you select certain values from the variables.  For example, the CELL operator selects a specified row from a numeric or character variable.


Session

The period of time between starting and leaving STATGRAPHICS Plus.


Slider

On a dialog box, a horizontal bar that allows you to set a value on a continuous scale.  For example, you can use a slider that ranges from smallest to largest to set the size of the points on a graph.


Spreadsheet Window

A window that displays an open data file.  If no data file is open, the Spreadsheet window contains blank rows and columns you use to enter data.


Standard, Single-Selection List Box

In a dialog box, a list box that displays options.  You can select only one option at a time.


StatFolio

Similar to a statistical project; a file in which you can save data, analyses, and comments.


Comments Window

A window you can use to record pertinent information about the StatFolio.


Status Bar

In STATGRAPHICS Plus a bar at the bottom of the Application window that displays information about the current state of the program.


Subdirectory

A directory you create within another directory.  Subdirectories can contain files or other subdirectories.


Text Box

In a dialog box, an area in which you can type, edit, or replace information.


Text Pane

The viewing area of an Analysis window that contains text.


Tickmark

A small line that intersects an axis like a division on a ruler.  Tickmarks are considered part of the axis.


Time Series Operators

Operators that calculate seasonal and backward differences.


Transformation Operators

Operators used to manipulate variables.  For example, the JOIN operator joins variables end to end to form one continuous column of values.


Variable

A named collection of data; a column in a Spreadsheet window.  A variable in STATGRAPHICS Plus has two characteristics:  Name and type.


Variable Name

The name you use to access a variable you created.  In STATGRAPHICS Plus, variable names can contain up to 10 characters, can consist of upper- and lowercase letters and numbers, and must begin with a letter.


Variable Type

In STATGRAPHICS Plus, identifies a variable as containing either character data or specific types of numeric data.


Window

A portion of a computer screen enclosed by a border and in which you view an application.  There are six distinct types of window STATGRAPHICS Plus:  The Application window, the Comments window, the Spreadsheet window, the Analysis window, a StatAdvisor window, and a StatGallery window.


Statistical Glossary Alphalist
Statistical Glossary

To quickly move to a portion of the statistical glossary, select one of the following letters.  Or click the Search button to use the Search feature in Windows Help.

#    A    B    C    D    E    F    G    H    I    K    L    M    N    O    P    Q    R    S    T    U    V    W    X    Y    Z


#

2-Level Design

3-Level Design

3 RSR

3 RSS

3 RSSH

5 RSS

5 RSSH


A

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

Agglomerative Methods

Alias Pattern

Aliased Effects

Aliases

Aliasing

Alpha Error

Alpha Level

Alpha Risk

Alternative Hypothesis

Analysis of Covariance

Analysis of Variance

Analysis Sample

ANOVA

ANOVA Table

Appraiser Variation

Area of Opportunity

ARIMA

Asymmetric Matrix

Asymptotic Normality

Attribute

Attributes Control Chart

Autocorrelated Residuals

Autocorrelation

Autocorrelation Coefficient

Autocorrelation Function Plot

Auto Regressive (AR)

Autoregressive Moving Average (ARMA) Scheme

Average

Average Linkage

Axial Distance


B

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

Backward Selection

Balanced Design

Balanced Experimental Design

Balanced Incomplete Block Design

Balanced Nested Design

Balanced One-Way Design

Balanced Randomized Block Design

Barchart

Bartlett's Test

Baseline

Baseline Value

Bernoulli Distribution

Best-Fitting Normal Distribution

Beta Distribution

Beta Error

Beta Risk

Beta Value

Bias

Biased Estimate

Binomial Distribution

Biplot

Bivariate Normal Distribution

Block

Block Effect

Blocked Design

Blocking Variable

Bonferroni Method

Boxcar Method

Box-and-Whisker Plot

Box-Behnken Design

Box-Cox Transformation

Box-Jenkins Methodology

Box-Pierce Test

Brown's Linear Exponential Smoothing

Brushing

Bubble Chart Analysis


C

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

C (Count)

C Chart

Calibration Line

Calibration Problem

Canonical Correlations Analysis

Capable Process

Capability Indices

Casement Plot

Catagorical Data

Categorical Factor

Categorical Variable

Causality

CDF (Cumulative Distribution Function)

Censored Data

Censored Data Analysis

Censoring

Censoring Indicator

Censoring Time

Centerpoint

Central Composite Design

Central Tendency

Centroid

Centroid Method

Chance Models

Character Variable

Chart

Chi-Square Distribution

Chi-Square Statistic

Chi-Square Test

City-Block Distance

Class (of Data)

Classical Decomposition

Classical Factor Analysis

Classification

Classification Codes

Classification Data

Classification Factor

Classification Function Coefficients

Classification Matrix

Classification Variable

Cluster

Cluster Analysis

Cluster Centroid

Cluster Seeds

Clustered Barchart

Clustering Method

Cochran's C Test

Coded Scatterplot

Coefficient

Coefficient Correlation Matrix

Coefficient of Kurtosis

Coefficient of Skewness

Coefficient of Variation

Collinear Independent Variables

Comments Window

Communality

Comparison of Alternative Models

Comparison of Means

Comparison of Medians

Comparison of Regression Lines

Comparison of Standard Deviation

Complete Linkage

Component Analysis

Component Effects Plot

Component-plus-Residuals Plot

Computational Method

Conditional Gamma

Conditional Sums of Squares

Confidence Bands

Confidence Interval

Confidence Level

Confidence Limits

Confidence Limits for Forecast Means

Confidence Limits for Individual Forecasts

Confounded Effects

Confounding

Constant Term

Constants

Contingency Coefficient

Contingency Tables Analysis

Continuous Data

Continuous Factor

Contour Plot

Control Chart

Control Limits

Control Mean

Control to Standard

Controllable Factors

Convergence

Cook's Distance

Coordinate

Correlated

Correlation

Correlation Coefficient

Correlation Matrix

Cosine Method

Count Data

Covariance

Covariance Matrix

Covariate

Cp

Cpk

Cpm

Cr

Critical Region

Critical Value

Cross Operator

Crosscorrelation

Crossed Factors

Crosstabulation Analysis

Cube Plot

Cumulative Density Function

Cumulative Distribution Function (cdf)

Cumulative Forecasting

Cumulative Frequency

Cumulative Frequency Polygon

Cumulative Hazard Function Plot

Cumulative Normal Distribution

Cumulative Plot

Cumulative Relative Frequency

Cumulative Relative Frequency Polygon

Cumulative Sum

Cumulative Sum chart

Cumulative Survival Probability

Curvature

Curvature Check

Curve

Curvilinear Model

Curvilinear Trend

Cutting Score

Custom Chart

Custom Chart Analysis

CuSum Chart


D

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

Daniel Plot

Data

Date Variable

Death Density Function Plot

Decomposition

Defining Relationship

Definite Integral

Degrees of Freedom

Dendrogram

Density/Mass Function Plot

Density Trace

Dependent Variable

Derivative

Design

Design Centerpoint

Design Generators

Design Matrix

Design Point

Design Resolution (III, IV, V, or V+)

DFITS Statistic

Differencing

Discrete Data

Discrete Uniform Distribution

Discriminant Analysis

Discriminant Function

Discriminant Loadings

Discriminant Score

Discriminant Weight

Dispersion

Distribution

Distribution Curve

Distribution Fitting Analysis

Distribution-Free Tolerance Limits

Distribution Function

Distribution Functions 1 and 2

Divisive

Dot Diagram Analysis

Double Reciprocal Model

Draftsman Plot

Draper-Lin Small Composite Design

Dummy Variable

Duncan Method

Dunnett

Durbin-Watson Statistic

Dynamic Data Exchange (DDE)


E

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

Effect

Eigenvalue

Eigenvector

Empirical Data

Empirical Model

Endpoint

Entropy Group

Entry Time

Equipment Variation

Erlang Distribution

Error

Error Bars

Error Sum of Squares

Error Term

Estimate

Estimator

Eta

Event

Event Probability

EWMA

EWMA Chart

Exit Time

Expected Frequency

Experimental Condition

Experimental Design

Experimental Factor

Experimental Region

Exploratory Data Analysis

Exponential Distribution

Exponential Model

Exponential Power Curve

Exponential Smoothing

Exponential Value Distribution

Exponentially Weighted Moving Average (EWMA)

Exponentially Weighted Moving Averages (EWMA) Chart

Extrapolate

Extreme Value

Extreme Value Distribution


F

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

F Distribution

F Ratio

F (Variance Ratio) Distribution

F Statistic

Face-Centered Design

Factor Analysis

Factor Effects

Factor Level

Factor Loadings

Factor Matrix

Factor Rotation

Factor Score

Factor Variable

Factorial Design

Factors

Failure

Failure-Censored Data

First-Degree Polynomial Function

Fisher's Exact Test

Fitted Curve

Fitted Line

Fitted Model

Fitted Normal Curve

Fitted Value

Fixed-Decimal Variable

Floating-Point Numeric Variable

Foldover Design

Forecast

Forecasting

Forward Selection

Fractional Factorial Design

Frequency

Frequency Distribution

Frequency Histogram

Frequency Polygon

Frequency Table

Frequency Tabulation

Full Factorial Design

Function


G

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

gage repeatability

Gage Reproducibility

Gamma Distribution

Gaussian Distribution

General Linear Model (GLM)

Geometric Distribution

Geometric Mean

Geometric Moving Average Chart

Glyph

Goodness-of-Fit

Goodness-of-Fit Tests

Gradient

Grand Mean

Group Comparisons


H

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

Half-Normal Plot

Hartley's Test

Hazard Function Plot

Hazard Function

Hazard Plot

Henderson’s Weighted Moving Average

Heteroscedasticity

Hierarchical Clustering

Hierarchical Data

Hierarchical Model

Higher-Order Derivative

Hit Ratio

Histogram

Hold-Out Sample

Holt's Linear Exponential Smoothing

Homogeneous Group

Homoscedasticity

Hotelling T-squared statistic

Hypothesis

Hypothesis Test

Hypothesis Tests (Compare Analysis)

Hypothesis Tests (Describe) Analysis

Hypothesized Value


I

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

Icicle Plot

Identity Matrix

Independent Samples

Independent Variable

Independent (X) Variable

Indicator Variable

Individuals Chart

Influential Points

Initial Study

Integer Variable

Integrated Time-Series Models

Interaction

Interaction Effect

Iteraction Plot

Intercept

Internal Standard Error

Interpretation Stage

Interpolate

Interquartile Range

Interval

Interval Data

Interval Depth

Interval Estimate

Interval Limits

Interval Plot

Intervening Variable


K

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

K

K-Means Procedure

Kendall 's Rank Correlation Coefficient

Kendall's Tau b and c

Key Glyph

Kolmogorov-Smirnov One-Sample Test

Kolmogorov-Smirnov Two-Sample Test

Kruskal-Wallis Test

Kurtosis

Kurtosis Coefficient


L

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

Labels

Lack-of-Fit Test

Lag

Lambda

Lambda Values

Laplace Distribution

Latin Square Design

LCL

Least Significant Difference (LSD) Test

Least Squares

Least Squares Equations

Least Squares Regression

Left-Sided (LT) Test

Level

Level Code

Levels of Variable

Leverage

Life Tables (Intervals) Analysis

Life Tables (Times) Analysis

Likelihood Ratio Chi-Square

Limit

Limits

Line Plot

Linear Combination

Linear Equation

Linear Forecast

Linear Model

Linear Regression

Linear Regression Model

Locally Weighted Regression

Log (Logarithmic) Scaling

Log Plot

Log Probit Model

Log Survival Function Plot

Log Survivor Function Plot

Log-Likelihood Ratio

Logarithmic Transformation

Logarithmic-X Model

Logistic Distribution

Logistic Model

Lognormal Distribution

Lower Bound Interval

Lower Capability Indices

Lower Control Limit (LCL)

Lower Quartile

Lower Specification Limit (LSL)

LSD (Least Significant Differences) Method

LSL


M

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

MA Chart

MAE (Mean Absolute Error)

Mahalanobis Distance

Main Effect

Mallows' Cp

Mann-Whitney (Wilcoxon) U Test

MANOVA

MAPE (Mean Absolute Percentage Error)

Marquardt Algorithm

Matrix

Maximum

Maximum Likelihood

Maximum Likelihood Estimate

ME (Mean Error)

Mean

Mean Absolute Error (MAE)

Mean Absolute Percentage Error (MAPE)

Mean Error (ME)

Mean Marker

Mean Percentage Error (MPE)

Mean Range

Mean Sigma

Mean Square

Mean Square for Rows

Mean Squared Error (MSE)

Mean Variance

Means Plot

Means Table

Means Test

Median

Median Notch

Median Plot

Metric Variable

Midpoint

Minima

Minimum

Missing Value

Mixed Model

Mixture Experiment

Mode

Model

Model Fitting

Month Variable

Mosaic Plot

Moving Average

Moving Averages (MA) Chart

Moving Range (MR)

Moving Range (MR) Chart

MPE (Mean Percentage Error)

MR Chart

MR(2)

MR(2) Chart

MSE (Mean Square Error)

Multicollinearity

Multifactor ANOVA Analysis

Multiple Barchart Analysis

Multiple Box-and-Whisker Plot

Multiple Discriminant Analysis

Multiple Range Test

Multiple Regression

Multiple-Sample Comparison Analysis

Multiple-Variable Analysis

Multiple X-Y Plot

Multiple X-Y-Z Plot

Multiplicative Model

Multivariate

Multivariate Control Chart

Multivariate Data

Multivariate Normal Data

Multivariate Normal Distribution

Multivariate t

Multiway Table

Mutual Similarity Procedures


N

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

Natural Logarithm

Negative Binomial Distribution

Negative Correlation

Nest Operator

Nested Data

Nested Design

Nested Factor

Nested Model

Newman-Keuls Method

Newton-Raphson Algorithm

Noise

Nominal (Target) Value

Nonhierarchical Procedures

Nonlinear Model

Nonlinear Regression

Nonmetric Variable

Nonparametric

Nonstationary

Normal Distribution

Normal Equations

Normalized Distance Function

Number of Defectives per Item Chart

Number of Defectives per Sample Chart

Numeric Variable


O

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

Object Linking and Embedding (OLE)

Oblique Factor Solutions

Observation

Observed Frequency

Observed Value

Observed versus Predicted Plot

OC Curve

Offset

One-Ahead Forecast

One-Factor-At-a-Time Experimentation

One-Tailed Test

One-Variable Analysis

One-Way Analysis of Variance

One-Way Design

Open Database Connectivity (ODBC)

Operating Characteristic Curve

Operator Variation

Order of Polynomial

Ordinate

Orthogonal

Orthogonal Design

Orthogonal Factor Solutions

Orthogonal Transformation

Out-of-Control Process

Outliers


P

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

p Chart

p-Level

p-Value

Paired-Sample Test

Paired Samples

Paired-Sample Comparison Analysis

Pairwise Comparison

Pairwise Means Comparison

Parameter

Parametric

Pareto Chart

Pareto Distribution

Partial Autocorrelation

Partial Confounding

Partial Correlations

Partial Correlation Coefficient

Partial Derivative

Partially Nested Design

Partitioning Stage

Path of Steepest Ascent

Path of Steepest Descent

Pearson Correlation Coefficient

Pearson's  Product-Moment Correlation

Pearson's R

Percentage Barchart

Percentage of Variance Criterion

Percentile

Percentiles

Periodicity

Periodogram

Physical Acceleration Model

Piechart

Plackett-Burman Design

Plot of Fitted Model

Poisson Distribution

Polynomial

Polynomial Function

Polynomial Regression Analysis

Pooled Data

Pooled Estimate

Pooled Samples

Pooled Standard Error

Pooled Variance

Pooling

Population Mean

Population Standard Deviation

Population Variance

Portmanteau Statistic

Portmanteau Test

Positive Correlation

Power

Power Curve

Power Function

Predicted Value

Prediction Capability Plot

Prediction Histogram

Prediction Limits

Predictor Variable

Prime Number

Principal Components

Probability

Probability Density Function

Probability Distribution

Probability Distributions

Probability Level (P-Level)

Probability Plot

Process Capability

Process Fallout

Process Mean

Process Sigma

Product-Moment Correlation Coefficient

Profiling Stage

Pure Error


Q

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

Quadratic Line

Quadratic Model

Quadratic Exponential Smoothing

Qualitative Factor

Qualitative Variable

Quality

Quality Control

Quality Improvement

Quantile Plot

Quantile-Quantile Plot

Quantitative Variable

Quartile


R

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

R Chart

R-Squared (Coefficient of Determination) Statistic

R-Squared Statistic

Random Number

Random Sample

Random Seed

Random Variable

Random Walk

Randomization

Randomized Block Design

Randomness

Range

Range Chart

Range Plot

Rank

Rank Correlation Coefficient

Rank Correlations

Rank Regression

Rank Test

Ratio-Scaled Data

Raw Data

Raw Mean

Readout/Interval Data

Reciprocal

Reciprocal Model

Reciprocal-X Model

Reciprocal-Y Model

Recode Data

Regression

Regression Analysis

Regression Line

Rejection Region

Relative Frequency

Relative Frequency Polygon

Repeatability

Repeated Measures Design

Replication

Replicated Design

Reproducibility

Residual

Residual Average

Residual Mean Square

Residual Plot

Residual Standard Deviation

Residual Sum of Squares

Residuals versus Factor Levels Plot

Residuals versus Level Codes Plot

Residuals versus Observations Plot

Residuals versus Predicted Plot

Residuals versus Row Numbers Plot

Residuals versus Samples Plot

Residuals versus X Plot

Resolution

Response

Response Surface

Response Surface Methodology

Response Surface Plot

Response Surfaces Analysis

Response Variable

Ridge Parameter

Ridge Regression

Ridge Trace Plot

Right-Sided (GT) Test

Risk

Robust Lowess

Rotatability

Rotatable Design

Rotation

Rough

Row Sum of Squares

Row-Wise Statistics Analysis

Running Lines

Running Means

Runs Test


S

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

s Chart

S-Curve Model

S-Squared Chart

Sample

Sample Mean

Sample Median

Sample Size

Sample Size Determination (Compare) Analysis

Sample Size Determination (Describe) Analysis

Sample Standard Deviation

Sample Variance

Samples

Sampling

Sampling Interval

Sampling Plan

Scatterplot

Scatterplot Matrix

Scheffe Method

Scree Test Criterion

Screening

SE

Seasonality

Second-Degree Polynomial Function

Second Factor Plot

Second-Order Model

Sequential Sampling

Shape of Data

Shewhart Control Chart

Sigma

Sigma Chart

Sigma Limits

Sigma Plot

Significance Level

Signs Test

Simple Exponential Smoothing

Simple Linear Regression

Simple Moving Average

Simple Regression Analysis

Simultaneous Method

Single Linkage Method

Sinusoid

Skewed

Skewed Left

Skewed Right

Skewness

Skewness Coefficient

Skychart

Slope

Smoothing

Somer's D Statistic

Spearman Rank Correlation Coefficient

Specification Limits

Spencer’s 15-Term/21-Term Moving Averages

Split Plot Design

Spread of Data

Square Plot

Square Root

Square Root-X Model

Square Root-Y Model

Stacked Barchart

Standard Deviation

Standard Error

Standard Error Bars

Standard Error of Estimate

Standard Errors for Forecasts Statistic

Standard Mean

Standard Order

Standard Sigma

Standardize

Standardized Kurtosis

Standardized Pareto Chart

Standardized Residual

Standard Regression Coefficient

Standardized Skewness

Standardized Value

Star Plots

StatAdvisor

StatFolio

StatGallery

Stationary

Statistic

Statistical Tolerances

Steepest Descent

Stem-and-Leaf Display

Stepwise Method

Stepwise Variable Selection

Stopping Criterion

Strip Plot Design

Studentized Residuals

Studentized Residuals Plot

Student's t Distribution

subgroup

Subgroup Size

Subgroup Statistics

Subset Analysis

Sum

Sum of Squares

Sum of Squares between Groups

Sum of Squares within Groups

Summary Statistics

Sun Ray Plot

Surface Plot

Survival Function Plot

Survival Probability

Survivor Function

Symmetric Distribution

Symmetric Matrix

Symmetry Plot


T

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

t Distribution

t-Statistic

t-Test

t-Value

Table

Table of Frequencies

Tabulate

Tabulated Data

Tail Area

Taper

Tests for Normality

Test Statistic

Three-Dimensional Frequency Histogram

Three-Dimensional Scatterplot

Three-Level Factorial Design

Time-Censored Data

Time Series

Time-Series Data

Time Series Operators

Time-Weighted Charts

Tolerance

Tolerance Interval

Tolerance Limits

Tolerance Width

Total Sum of Squares

Trace

Trading Day

Transform Data

Transformation

Trend

Triangular Distribution

Trial

Tukey's Honestly Significant Difference (HSD) Test

Two-Level Factorial Design

Two-Sample Comparison Analysis

Two-Sided Interval

Two-Sided (NE) Test

Two-Tailed Test

Two-Way Analysis of Variance

Two-Way Design

Two-Way Table

Type I Data

Type I Sums of Squares

Type II Sums of Squares

Type II Data

Type II Error

Type III Sums of Squares


U

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

u (Count per Unit)

u Chart

UCL

Unbalanced Design

Unbalanced Nested Design

Unbalanced One-Way Design

Unblocked Design

Uncensored Data

Uncertainty

Uncertainty Coefficient

Uniform Distribution

Unit Normal

Univariate Data

Univariate Plot

Unsaturated Model

Unspecified Values

Unusual Residuals

Upper Bound Interval

Upper Capability Indices

Upper Control Limit (UCL)

Upper Quartile

Upper Specification Limit

User-Defined Design

User-Specified Comparison

USL


V

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

v-Mask

Validation

Variables Control Chart

Variance Chart

Variance Check

Variance Components Analysis

Variance Inflation Factors (VIFs)

Variation

Vector


W

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

Ward's Method

Warning Limits

Weibull Analysis

Weibull Distribution

Weibull Plot

Weighted Average

Weights

Whisker

White Noise

Wilcoxon Signed-Rank Test


X

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

X-Axis

X-Bar

X-Bar and R Chart

X-Bar and S Chart

X-Bar and S-Squared Chart

X-Bar Chart


Y

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

Y-Axis

Y-Intercept


Z

Click on a term in the scrolling list to display a pop-up definition of the term.  Or click on the Search button to use the Search feature in Windows Help.

Z-Axis

z-Score

z-Score for Kurtosis

z-Score for Skewness

z-Statistic

Zero Correlation


Visual Glossary

Icons

STATGRAPHICS Application Icon

Clicking this icon opens a STATGRAPHICS session.  Under the Windows 95 operating system, this icon also displays on the Taskbar button.

Data Icon

When you first start the program, the Application window contains the Data icon.  As you work with the program, this icon is identified with an open data file.

StatFolio Comments Icon

When you first start the program, the Application window contains the StatFolio Comments icon.  As you work with the program, this icon is identified with an open StatFolio.

Analysis Icon

Each time you use a statistical analysis, the program displays an Analysis window.  When you click the Minimize button on an Analysis window, the program shrinks the window to an Analysis icon.  The title of the icon represents the name of the statistical analysis and may include the variables the analysis uses.

StatGallery Icon

Clicking this icon enables a function that places multiple text and graphics images on one page for viewing or printing.

StatAdvisor Icon

Clicking this icon is one way to open the StatAdvisor, which provides a statistical interpretation of the active analysis.

Buttons on the Application Toolbar

Open StatFolio Button

Clicking this button is equivalent to choosing FILE... OPEN… OPEN STATFOLIO… from the Menu bar.  For more information, see Accessing and Using Files, and Using Special Features.

Save StatFolio Button

Clicking this button is equivalent to choosing FILE… SAVE… SAVE STATFOLIO… from the Menu bar (if the current StatFolio has a title) or FILE… SAVE… SAVE STATFOLIO AS… (if the current StatFolio does not have a title).  For more information, see Accessing and Using Files and Using Special Features.

Open Data File Button

Clicking this button is equivalent to choosing FILE… OPEN… OPEN DATA FILE from the Menu bar.  For more information, see Accessing and Using Files and Using Special Features.

Save Data File Button

Clicking this button is equivalent to choosing FILE… SAVE DATA FILE… from the Menu bar (if the current data file has a title) or FILE… SAVE… SAVE DATA FILE AS… (if the current data file does not have a title).  For more information, see Accessing and Using Files and Using Special Features.

Cut Button

Clicking this button is equivalent to choosing EDIT… CUT… from the Menu bar.  For more information, see Accessing and Using Files and Using Special Features.

Copy Button

Clicking this button is equivalent to choosing EDIT… COPY… from the menu bar.  For more information, see Accessing and Using Files and Using Special Features.

Paste Button

Clicking this button is equivalent to choosing EDIT… PASTE… from the Menu bar.  For more information, see Accessing and Using Files and Using Special Features.

Print Button

Clicking this button is equivalent to choosing FILE… PRINT… from the Menu bar.  For more information, see Accessing and Using Files and Using Special Features.

X-Y Plot Button

Clicking this button is equivalent to choosing PLOT… SCATTERPLOTS… X-Y PLOT… from the Menu bar.  For more information, see Using Analyses in the Base System.

Box-and-Whisker Plot Button

Clicking this button is equivalent to choosing PLOT… EXPLORATORY PLOTS… BOX-AND-WHISKER PLOT… from the Menu bar. For more information, see Using Analyses in the Base System.

Frequency Histogram Button

Clicking this button is equivalent to choosing PLOT… EXPLORATORY PLOTS… FREQUENCY HISTOGRAM… from the Menu bar. For more information, see Using Analyses in the Base System.

Multiple-Variable Analysis Button

Clicking this button is equivalent to choosing DESCRIBE… NUMERIC DATA… MULTIPLE-VARIABLE ANALYSIS… from the Menu bar.  For more information, see Using Analyses in the Base System.

Multiple Regression Button

Clicking this button is equivalent to choosing RELATE… MULTIPLE REGRESSION… from the Menu bar.  For more information, see Using Analyses in the Base System.

X-bar and R Charts Button

Clicking this button is equivalent to choosing SPECIAL… QUALITY CONTROL… VARIABLES CONTROL CHARTS… from the Menu bar.  For more information on performing an X-bar and R Charts Analysis, see Using Analyses for Quality Control

Process Capability Analysis Button

Clicking this button is equivalent to choosing SPECIAL… QUALITY CONTROL… PROCESS CAPABILITY… from the Menu bar.  For more information on the Process Capability Analysis, see Using Analyses for Quality Control.

Forecast Analysis Button

Clicking this button is equivalent to choosing SPECIAL… TIME-SERIES ANALYSIS… FORECASTING… from the Menu bar.  For more information on the Forecasting Analysis, see Using Analyses for Time Series.

Experimental Design Button

Clicking this button is equivalent to choosing SPECIAL… EXPERIMENTAL DESIGN… OPEN DESIGN… from the Menu bar.  For more information on Experimental Designs, see Using Analyses for Experimental Design.

Multivariate Methods Button

Clicking this button is equivalent to choosing SPECIAL… MULTIVARIATE METHODS… CLUSTER ANALYSIS… from the Menu bar.  For more information on Cluster Analysis, see Using Analyses for Multivariate Methods.

Advanced Regression Button

Clicking this button is equivalent to choosing SPECIAL… ADVANCED REGRESSION… GENERAL LINEAR MODELS… from the Menu bar.  For additional information on the General Linear Models Analysis, see Using Analyses for Advanced Regression.

StatAdvisor Button

Clicking this button opens the StatAdvisor for the currently active analysis.  The StatAdvisor provides a statistical interpretation of the analysis.

StatWizard Button

Clicking this button opens the StatWizard.  If the datasheet is empty, the StatWizard will open to a screen that will direct you towards obtaining data or running an analysis that does not need data.  If there is data in the datasheet, the StatWizard will guide you in selecting an analysis for that data.

Help Button

Clicking this button accesses Help about the panes in an Analysis window.  Online Help allows you to learn about STATGRAPHICS Plus without referencing manuals.

Buttons on the Analysis Toolbar

Return to Data Input Dialog Box Button

Clicking this button redisplays the Analysis dialog box for the current analysis.  If you modify the dialog box and click OK, a revised pane displays in the Analysis window.

Tabular Options Button

Clicking this button displays the Tabular Options dialog box for the current analysis.  This dialog box lists all the available options for text panes.  If you modify the dialog box and click OK, a text pane with your modifications displays in the Analysis window.

Graphical Options Button

Clicking this button displays the Graphical Options dialog box for the current analysis.  This dialog box lists all the available options for graphics panes.  If you modify the dialog box and click OK, a graphics pane with your modifications displays in the Analysis window.

Save Results Button

Clicking this button displays the Save Results Options dialog box for the current analysis.  This dialog box lists all the results you can save and the names of the corresponding target variables.  If you modify the dialog box and click OK, the results as you modified them are saved.

Add Text Button

(This button is not available until you maximize a graph in the Analysis window.)  Clicking this button displays the Text Options dialog box.  This dialog box allows you to choose the text you want to add and the direction (horizontal or vertical) in which you want it to display.  If you modify the dialog box and click OK, the specified text is added above the graph.  For more information, see Working with Graphs and Graphics Options.

Jittering Button

(This button is not available until you maximize a scatterplot in the Analysis window.)  Clicking this button displays the Jittering dialog box.  This dialog box allows you to adjust the amount of horizontal and/or vertical jittering that will be applied to the points.  If you modify the dialog box and click OK, your changes are processed and the graph redisplayed.  For more information, see working with Graphs and Graphics Options.

Brushing Button

(This button is not available until you maximize a scatterplot in the Analysis window.)  Clicking this button displays the Brushing dialog box.  This dialog box allows you to choose the variable that will be used for brushing.  If you modify the dialog box and click OK, a scroll bar displays on the Analysis toolbar.  You then use the scroll bar to add or remove color from additional points as the corresponding value of the variable increases or decreases.  For more information, see Working with Graphs and Graphics Options.

Exclude/Include Button

(This button is not available until you maximize a scatterplot in the Analysis window.)  Clicking this button excludes from the analysis the point you choose on the scatterplot.  When you choose a point and click the Exclude/Include button, the point is marked with a red X.  You can exclude as many points as you like.  If you choose a point that was previously excluded, then click the Exclude/Include button, it is included in the analysis.

Smooth/Rotate Button

(This button is not available until you maximize a two-dimensional or three-dimensional graph in an Analysis window.) Clicking this button when a two-dimensional graph is maximized displays a dialog box that allows you to select the type of smoothing that will be applied to the graph.  Clicking this button when a three-dimensional graph is maximized displays a slidebar/button combination that rotates the graph horizontally or vertically.

Set Point Labels Button

(This button is not available until you maximize a scatterplot in the Analysis window.)  Clicking this button displays the Point Identification dialog box.  This dialog box allows you to choose the variable that will be used to identify points.  If you modify the dialog box and click OK, the program activates the graphics point identification fields and buttons on the Analysis toolbar. For more information, see Working with Graphs and Graphics Options.

Locate Labels Button

(This button is not available until you follow the process described above for the Set Point Labels button.)  If you modify the Label field on the Analysis toolbar, clicking the Locate Labels button changes the color of all the corresponding points on the graph. For more information, see Working with Graphs and Graphics Options.

Locate Row Button

(This button is not available until you maximize a scatterplot in the Analysis window.)  If you modify the Row field on the Analysis toolbar, clicking the Locate Row button changes the color of the corresponding point on the graph.  For more information, see Working with Graphs and Graphics Options.


When You Have a Question

Manugistics offers a variety of customer support options to help you get the most from STATGRAPHICS Plus.

When you have a question about STATGRAPHICS Plus:

-	check the Online Help or look in the printed documentation

-	check the "Answers to Common Questions" topic in the Online Help

-	check the README file that is installed in the SGWIN program directory.

You can also check several other sources, including an automated information telephone line, our Web Page, and our HelpLine.

See also:

Using the Information Line

Using the Web Page

Answers to Common Questions

Calling Manugistics' HelpLine in the U.S.

Calling Manugistics' HelpLine Worldwide


Using the Information Line
Using the 24-Hour Information Line

301-984-LINE  (301-984-5463)

The Information Line contains recorded answers to frequently asked technical questions and is available 24 hours a day.  To use this service, you must have a touch-tone telephone.


Calling Manugistics' HelpLine in the U.S.

301-984-5489 (voice)

301-255-8406 (fax)

Telephone assistance is provided free for 90 days to all registered users of the current version of the software.  Your free 90-day support period begins with date of purchase.  The HelpLine is available 10:00 a.m. to 5:30 p.m., Eastern time, Monday through Friday (excluding holidays).

See also:

Registering for Product Support

Using Software Support Services

Requesting Technical Assistance

Requesting Replacement Items

Using the 24-Hour Information Line

Manugistics' HelpLine can:

-	Answer general questions about the use of the software

-	Answer questions about hardware and software compatibility

-	Help you install the software

-	Investigate software errors

-	Explain error messages.

Information We Need When You Contact Us

When you contact us, please have the following information ready:

-	Serial number of your copy of the software

-	Your name

-	Your company's name

-	Your telephone or fax number

-	Name of the software product you are using

-	Version number of the software

-	A complete description of your problem or question.

The software version number appears on the label of the original media and in the About STATGRAPHICS Plus window.  To display the About window, select HELP... ABOUT... from the Menu bar.


Calling Manugistics' HelpLine Worldwide

If you need help with a problem, contact your dealer for the most current information on the available software support and services.  If you purchased STATGRAPHICS Plus directly from Manugistics, you can get help by calling the HelpLine at:

301-984-5489 (voice)

301-255-8406 (fax)

by writing to:

Manugistics, Inc.

Attn:  STATGRAPHICS HelpLine

2115 East Jefferson Street

Rockville, Maryland  20852

U.S.A

or by sending an e-mail message to:

answer@manu.com

The HelpLine is available 10:00 a.m. to 5:30 p.m., Eastern time, Monday through Friday (excluding holidays).

Information We Need When You Contact Us

When you contact us, please have the following information ready:

-	Serial number of your copy of the software

-	Your name

-	Your company's name

-	Your telephone or fax number

-	Name of the software product you are using

-	Version number of the software

-	A complete description of your problem or question.

The software version number appears on the label of the original media and in the About STATGRAPHICS Plus window.  To display the About window, select HELP... ABOUT... from the Menu bar.


Requesting Replacement Items

301-984-5489

Manugistics can provide you with replacement software or manuals.  If you are an international user and you purchased your software through a dealer, check with that dealer for replacement items.

If documentation or disks are missing from your order, please call for a replacement.

If you believe that the software media (disks) that you received are defective, first check the media in another computer or try to read the media using another method.  Then, if you still receive an error, call our HelpLine at the telephone number shown above.  Please have your software serial number ready when you call.


Providing Feedback

We welcome your evaluation of our manuals and online Help.  Your comments and suggestions help us improve our documentation.  For your convenience, the manuals contain a postage-paid Reader Comment Card.  Please use this card to provide your comments.  If the card is missing, send your comments to:

Manugistics, Inc.

ATTN:  Manager, STATGRAPHICS Documentation

2115 East Jefferson Street

Rockville, MD  20852-4999  U.S.A.


Using the Web Page
Using the STATGRAPHICS Plus Web Site

http://www.statgraphics.com

The STATGRAPHICS Plus Resource Center web tool is available to enhance your productivity when you are using STATGRAPHICS Plus.  The goal of the web site is to provide you with additional information and a variety of related sources that let you maximize your use of the product.

Information on the site includes statistics-related resources, information about our training courses, technical specifications that list the recommendations for the current version of the software, software patches, sample StatFolios, and tutorials from our manuals and from other web sites.

Start your visit by checking What’s New with STATGRAPHICS.  Then proceed to the detailed descriptions of the base program and its modules, then access demo versions of the product, and contact information for domestic and international users.

In addition, there are sample data files, sample StatFolios.  The Resource Center links you to other statistical resources available on the Internet.  You will also find e-mail links to staff for STATGRAPHICS sales, support, and training.


Registering for Product Support

To receive product support services for STATGRAPHICS Plus you should complete and return the Registration Card attached to the Warranty and License Agreement.

Users outside the United States should contact the dealer from whom they purchased their software.


Using Software Support Services

Support services are available to help you gain the most benefit from your STATGRAPHICS Plus product.  Every user receives Basic Support at no cost for ninety (90) days.  The service begins with your first call to our Technical Support HelpLine.  You must be using the current version of STATGRAPHICS Plus.  The “STATGRAPHICS Software Support Plan” brochure included with your software package outlines the available services.

Manugistics also offers HelpLine Plus, an alternative support plan that includes all the benefits of Basic Support but provides even more support services, such as priority telephone service and free software patches.  This fee-for-service plan ensures fast technical assistance.  The “Software Support Plan” brochure also outlines the services available when you sign up for HelpLine Plus.

In addition to showing how to get support, the “How to Get Help” card included with your package also explains how you order replacement items, lists the information we need when you contact us, and instructs you on how to use our 24-hour Information Line.


Registering for Product Training

To Register for a Course or Receive Training Information

•	Complete and return the Training Registration form

•	Send us a fax at 301-255-8406

•	Call us at 1-800-592-0050

Improving productivity is only one benefit you get when you sign up for product training.  Most users who complete training courses have a high degree of appreciation for the power of STATGRAPHICS Plus.  Many believe that the courses provide skills they can immediately apply to their job.

Public or customized on-site courses are available.  The “STATGRAPHICS Plus Training Card” included with your package includes a course schedule with locations and dates.


Using the STATGRAPHICS Plus Documentation Set

The documentation set supports STATGRAPHICS Plus running in a Windows 32-bit environment and contains several different types of documentation:

•	Printed and bound manuals

•	Electronic manuals

•	Online help.

Printed and Bound Manuals

A printed User Manual describes the features in the base product.  Online Manuals are available for Quality Control, Design of Experiments, Time Series, Multivariate Methods, and Advanced Regression analyses.  The manuals provide step-by-step instructions for using the features of the product and for using the statistical analyses and their options.  They are intended for users of all experience levels.

Electronic Manuals

Online manuals for Quality Control, Design of Experiments, Time Series, Multivariate Methods and Advanced Regression are provided in an Adobe Acrobat format; the Adobe Acrobat Reader is included with STATGRAPHICS Plus.


Descriptive Methods Data Input Dialog Box
Descriptive Methods Analysis Dialog Box

The Descriptive Methods Analysis provide various techniques you can use to adjust or transform data to improve the results of an analysis.  The analysis allows you to perform statistical calculations that reveal correlations in the data, to test for nonrandomness of the data, and to produce various plots that reveal trends and cycles as well as data errors and outliers.

Data

Once Every

Starting At

(Seasonality)

Trading Days Adjustment

Select

Sort

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left mouse button on either Pane Options or Analysis Options.

See also

Using the Descriptive Methods Analysis

Adjustment Options

Autocorrelation Function Options

Partial Autocorrelation Function Options

Periodogram Table Options

Crosscorrelation Function Dialog Box

Horizontal Time Sequence Plot Options

Vertical Time Sequence Plot Options

Periodogram Options

Integrated Periodogram Options


Once Every:

This text box allows you to enter a unit of time — calendar or clock — and to indicate the type of sampling interval the program will use to analyze the data.


Starting At:

This text box displays the start time for the sampling interval you choose.  You can override the default.


Seasonality

This text box allows you to enter the number of periods the program will analyze each season.  Enter an integer greater than 1.


Trading Days Adjustment

This optional text box allows you to enter the name of the variable that contains the number of trading days for each value and for each period you want to forecast.  The program divides the data by this variable before it performs the calculations.  You should use this adjustment when each period has a different number of trading days.


Descriptive Methods - Tabular Options Dialog Box
Descriptive Methods Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the Descriptive Methods Analysis.

Analysis Summary (Descriptive Methods)

Data Table (Descriptive Methods)

Autocorrelations (Descriptive Methods)

Partial Autocorrelations (Descriptive Methods)

Periodogram Table (Descriptive Methods)

Tests for Randomness (Descriptive Methods)

Crosscorrelations (Descriptive Methods)


Descriptive Methods Analysis Summary
Analysis Summary (Descriptive Methods)

The Analysis Summary displays the name of the variable, the number of observations, the start index, and the sampling interval.  If the program provided estimates for missing values, the Analysis Summary also displays those values.  If you make adjustments to the data, the summary lists those adjustments.

To choose options for the analysis, use the Adjustment Options dialog box.


Descriptive Methods Data Table
Data Table (Descriptive Methods)

The Data Table tabular option displays the values for the original data and for the adjusted values for each period.  The program adjusts the values according to the sampling interval you choose on the Descriptive Methods Analysis dialog box and the options you choose on the Adjustment Options dialog box.

Use the Trading Days Adjustment text box on the analysis dialog box and the Adjustment Options dialog box if you want to choose other options.


Autocorrelations
Autocorrelations (Descriptive Methods)

The Autocorrelations tabular option displays the correlation coefficients between a time-series variable and the values for earlier time periods.  The table shows the estimated autocorrelations, the standard errors, and the upper and lower probability limits for each lag.  You can use the correlation coefficients to test for seasonal patterns or as a preliminary step in determining an appropriate model for the data.

To choose options for this table, use the Autocorrelation Function Options dialog box.


Partial Autocorrelations

The Partial Autocorrelations tabular option displays the partial correlation coefficients between a time-series variable and the values for earlier time periods.  The table shows the partial autocorrelations, the standard errors, and the upper and lower probability limits for each lag.  You can use the partial correlation coefficients to test for seasonal patterns, or as a preliminary step in determining an appropriate ARIMA model for forecasting the data.

To choose options for this table, use the Partial Autocorrelation Function Options dialog box.


Periodogram Table
Periodogram Table (Descriptive Methods)

The Periodogram Table tabular option displays the frequency and ordinate pairs for a period.  The program uses these pairs to plot the amplitudes and frequencies estimated from the data.  It also displays the cumulative sum and integrated periodograms for each period.

To choose options for this table, use the Periodogram Table Options dialog box.


Tests for Randomness
Tests for Randomness (Descriptive Methods)

The Tests for Randomness tabular option displays the results of two runs tests and a Box-Pierce test.  You can use the results to determine if the time-series data have significant autocorrelation.

Runs Above and Below the Median

This test counts the number of runs that are completely above or completely below the median and ignores the values that are equal to the median.  The test is sensitive to trends in the data.  If the test statistic is large (corresponds to a p-value less than .05), you can conclude that the values occur in nonrandom order.

Runs Up and Down

This test counts the number of times a sequence rises or falls.  The test is sensitive to long-term cycles.  If the test statistic is small (corresponds to a p-value less than .05), you can conclude that the values occur in nonrandom order.

Box-Pierce Test

This test determines if the autocorrelation is equal to 0.  If the test statistic is large (corresponds to a p-value less than .05), the autocorrelation is not equal to 0.  To choose options for this test, use the Box-Pierce Test Options dialog box.


Crosscorrelations
Crosscorrelations (Descriptive Methods)

The Crosscorrelations tabular option allows the program to estimate the correlation between a time-series variable at a specific period and a second time-series variable at a specific period.  Use crosscorrelations to determine whether two time series are correlated and, if so, whether one series leads to the other.  The results do not display until you complete the Crosscorrelation Function dialog box.

To choose options for this table, use the Crosscorrelation Function dialog box.


Descriptive Methods - Graphical Options Dialog Box
Descriptive Methods Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the Descriptive Methods Analysis.

Horizontal Time Sequence Plot (Descriptive Methods)

Vertical Time Sequence Plot (Descriptive Methods)

Autocorrelation Function (Descriptive Methods)

Partial Autocorrelation Function (Descriptive Methods)

Periodogram (Descriptive Methods)

Integrated Periodogram (Descriptive Methods)

Crosscorrelation Function (Descriptive Methods)


Horizontal Time Sequence Plot
Horizontal Time Sequence Plot (Descriptive Methods)

The Horizontal Time Sequence Plot graphical option displays a connected line plot for the variable against time.  The plot shows important features such as trend, seasonality, discontinuity, and outliers.

To choose options for this plot, use the Horizontal Time Sequence Plot Options dialog box.


Vertical Time Sequence Plot (Descriptive Methods)

The Vertical Time Sequence Plot graphical option displays a plot of a time-series variable in relation to a baseline.  The plot contains a vertical line that extends from the baseline to each value.  Use this plot to identify the values that are above and below the baseline.

To choose options for this plot, use the Vertical Time Sequence Plot Options dialog box.


Autocorrelation Function
Autocorrelation Function (Descriptive Methods)

The Autocorrelation Function graphical option displays a plot of the autocorrelation estimates.  The plot contains vertical bars that represent the coefficient for each lag and a pair of dotted lines at a distance from the baseline that are a multiple of the standard error at each lag.  The plot is useful for testing seasonality or other cycles.  Statistically significant coefficients appear as bars that extend beyond either line.

To choose options for this plot, use the Autocorrelation Function Options dialog box.


Partial Autocorrelation Function
Partial Autocorrelation Function (Descriptive Methods)

The Partial Autocorrelation Function graphical option displays a plot of each coefficient using a bar whose height is proportional to the value of the coefficient.  The program, by default, plots probability limits as dashed lines at plus or minus 2 divided by the square root of the number of observations in the time series.  The bounds are useful for indicating partial autocorrelations that are significantly different from 0.  Bars that extend beyond either line indicate significant correlations.

To choose options for this plot, use the Partial Autocorrelation Function Options dialog box.


Periodogram
Periodogram (Descriptive Methods)

The Periodogram graphical option displays a plot of the ordinates to construct a frequency spectrum.  The program plots the amplitudes of the sinusoids for various frequencies against the frequencies.  It scales the Periodogram so that, if the mean of the series is 0, the sum of the ordinates equals the sum of the squared values.  This is also known as the Line Spectrum.

To choose options for this plot, use the Periodogram Options dialog box.


Integrated Periodogram
Integrated Periodogram (Descriptive Methods)

The Integrated Periodogram graphical option displays a plot of the normalized cumulative sum of the periodogram ordinates against the frequencies from 0.0 to 0.5.

To choose options for this plot, use the Integrated Periodogram Options dialog box.


Crosscorrelation Function
Crosscorrelation Function (Descriptive Methods)

The Crosscorrelation Function graphical option displays a plot of the estimated correlations between a time-series variable at time t and a second time-series variable at time t + k as a function of the lag or time differential k.  The program does not display the results until you complete the Crosscorrelation Function Analysis dialog box.

To choose options for this plot, use the Crosscorrelation Function dialog box.


Adjustment Options Dialog Box

This dialog box allows you to make various types of adjustments to data to make it more appropriate for a model:  Math, Seasonal, Trend, Differencing, and Inflation.

Math (Descriptive Methods)

Seasonal (Descriptive Methods)

Trend (Descriptive Methods)

Differencing (Descriptive Methods)

Inflation (Descriptive Methods)


None (No Mathematical Adjustment)

This option instructs the program not to make a mathematical adjustment to the data.


Natural Log

This option instructs the program to apply a natural log transformation to the data.


Base 10 Log

This option instructs the program to apply a base 10 log transformation to the data.


Square Root

This option instructs the program to apply a square root transformation to the data.


Reciprocal

This option instructs the program to apply this reciprocal transformation to the data:  (1/t).


Power

This option instructs the program to raise the data to a power.  Use the text box to enter the power.  For example, if you choose this option and enter 10 in the text box, the program raises each value to the power of 10.  Enter any numeric value except 0.


Box-Cox

This option instructs the program to scale the values by the geometric mean, which stabilizes the variance of the time-series data and makes the distribution closer to normal.  Use the Power text box to choose the strength of the transformation.  Enter any numeric value except 0.  A power of 1 corresponds to the original data.  Use the Addend text box to choose the value you want the program to add to the original data before it raises it to the power you specify.


None (No Seasonal Adjustment)

This option instructs the program not to make a seasonal adjustment.


Method

These options allow you to choose the method the program will use to combine the component factors.

Multiplicative

Uses the multiplicative ratio-to-moving-average method to make a seasonal adjustment.  The program assumes that the components of the data (trend, seasonal, and random effects) cause proportional changes in the series, and expresses the result as a product of the components.

Additive

Uses the additive difference-from-the-moving-average method.  The program simply adds or subtracts given amounts and expresses the result as a sum of the components.


Additive

This option instructs the program to use the additive difference-from-the-moving-average method.  The program simply adds or subtracts given amounts and expresses the result as a sum of the components.


None (No Trend Adjustment)

This option instructs the program not to fit a function to the data.


Linear Trend Adjustment
Linear

This option allows the program to estimate a linear trend.


Quadratic Trend Adjustment
Quadratic

This option instructs the program to estimate a quadratic trend.


Exponential Trend Adjustment
Exponential

This option instructs the program to estimate an exponential power curve.


S-Curve

This option instructs the program to estimate the S-Curve trend.


Nonseasonal Order Differencing
Differencing

A differencing adjustment removes a trend from the data, which enables you to analyze local fluctuations.  This method makes the data stationary and, therefore, more appropriate for most methods of analysis.  The program subtracts the difference of the original value from a value you enter in the data series.  Use the following text boxes to enter the order of differencing the program will apply to the data.

Nonseasonal Order

Allows you to enter the order of nonseasonal differencing the program will apply to the model.  Enter any integer greater than or equal to 0.  The program assumes a seasonality of 1; for example, for this time-series data:

2.8  2.6  2.7  2.9  3.0  2.2  4.3  5.7  2.5

enter 1  into the text box.  The program subtracts the value 2.8 from the next value, 2.6.  If you enter 2, the program subtracts 2.8 from the value that is two places from the original value, 2.7.

Seasonal Order

Allows you to enter the order of seasonal differencing the program will apply to the model.  Enter any integer greater than or equal to 0.  The program accounts for the seasonality you choose in the Analysis dialog box.  For example, if the time-series data above are quarterly data and you enter 1 into the text box, the program subtracts 2.8 from the value that is four places from the original value, 3.0.  This option is available only when you choose seasonality on the Analysis dialog box.


Seasonal Order Differencing
Seasonal Order

This text box allows you to choose the order of seasonal differencing you want the program to apply to the model.  Enter any integer greater than or equal to 0.  The program subtracts the difference of the original value from the value you choose in the series.  The program takes into account the seasonality you choose in the Descriptive Methods Analysis dialog box.  This option is available only when you choose seasonality on the analysis dialog box.


Inflation:  Apply at End of Period
End of Period

This option allows you to adjust the data for a constant rate of inflation.


Inflation:  Apply at Middle of Period
Middle of Period

This option allows you to adjust the data for a constant rate of inflation.


Inflation:  Rate
Rate

This text box allows you to enter the rate you want the program to use for inflation for one entire cycle.


Autocorrelation Function Options Dialog Box

Allows you to choose the number of lags and the confidence level that will be used to calculate the autocorrelations.

Number of Lags

Confidence Level (for Probability Limits)


Number of Lags

This text box allows you to enter the maximum number of lags for which the program should calculate the crosscorrelations.  Enter any positive integer.


Partial Autocorrelation Function Options Dialog Box

This dialog box allows you to choose the number of lags and confidence level the program will use to calculate the partial autocorrelations.

Number of Lags

Confidence Level (for Probability Limits)


Periodogram Table Options Dialog Box

This dialog box allows you to remove the mean from the Periodogram Table and to choose a value for the taper.

Remove Mean

Taper


Remove Mean

This option instructs the program to subtract the mean from each observation.  When the dialog box displays, this option is chosen; that is, the mean will be subtracted.


Taper

This text box instructs the program to taper the beginning and end of the time-series data using a split cosine-bell window.  For example, if you enter a value of 10, the program tapers the first and last 5 percent of the data.  Enter a number from 0 to 50; common values are 10 or 20 percent.


Box-Pierce Test Options Dialog Box

This dialog box allows you to choose the number of lags the program will use for the Box-Pierce Test.

Number of Lags


Crosscorrelation Function Data Input Dialog Box
Crosscorrelations

The Crosscorrelations tabular option displays the estimates for the correlation between a time-series variable at a specific period and a second time-series variable at a specific period.  Use the values to determine if two time series are correlated and, if so, whether one series leads to the other.

Second Time Series

Number of Lags


Second Time Series

This text box allows you to enter the variable that contains the second set of time-series data.


Horizontal Time Sequence Plot Options Dialog Box

Allows you to indicate if you want to plot points and/or lines.

Plot (Points or Lines)


Plot (Points or Lines)

Determines what will appear on the plot.

Points

Plots points; it is the default.

Lines

Plots lines.


Lines

This option allows you plot lines that connect the observations.


Vertical Time Sequence Plot Options Dialog Box

This dialog box allows you to indicate where on the Vertical Time Sequence Plot the program should draw the baseline.

Baseline


Baseline

This text box allows you to enter the point at which the program should draw the baseline.  Enter any number; the default is 0.


Periodogram Options Dialog Box

This dialog box allows you to remove the mean from the Periodogram and to choose a value for the taper.  You can also indicate if the program should plot points and/or lines.

Remove Mean

Points

Lines

Taper


Integrated Periodogram Options Dialog Box

This dialog box allows you to remove the mean from the Integrated Periodogram and to choose a value for the taper.

Remove Mean

Taper


Descriptive Methods Save Results Options Dialog Box
Save Results Options Dialog Box (Descriptive Methods)

The Save Results Options dialog box allows you to choose the results you want to save.  There are seven selections:  Data, Adjusted Data, Autocorrelations, Partial Autocorrelations, Crosscorrelations, Periodogram Ordinates, and Fourier Frequencies.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Fourier Frequencies

This option allows you to save the Fourier frequencies.


Descriptive Methods Analysis Summary
Analysis Summary (Descriptive Methods)

The Analysis Summary displays the name of the variable, the number of observations, the start index, and the sampling interval.  If the program provided estimates for missing values, the Analysis Summary also displays those values.  If you make adjustments to the data, the summary lists those adjustments.

To choose options for the analysis, use the Adjustment Options dialog box.


Descriptive Methods Data Table
Data Table (Descriptive Methods)

The Data Table tabular option displays the values for the original data and the adjusted values for the data for each period.  The program adjusts the values according to the sampling interval you choose on the Analysis dialog box and the options you choose on the Adjustment Options dialog box.  Use the Trading Days Adjustment text box on the Analysis dialog box and the Adjustment Options dialog box if you want to choose other options.


Autocorrelations
Autocorrelations (Descriptive Methods)

The Autocorrelations tabular option displays the correlation coefficients between a time-series variable and the values for earlier time periods.  The table shows the estimated autocorrelations, the standard errors, and the upper and lower probability limits for each lag.  You can use the correlation coefficients to test for seasonal patterns or as a preliminary step in determining an appropriate model for the data.

To choose options for this table, use the Autocorrelation Function Options dialog box.


Partial Autocorrelations

The Partial Autocorrelations tabular option displays the partial correlation coefficients between a time-series variable and the values for earlier time periods.  The table shows the partial autocorrelations, the standard errors, and the upper and lower probability limits for each lag.  You can use the partial correlation coefficients to test for seasonal patterns, or as a preliminary step in determining an appropriate ARIMA model for forecasting the data.

To choose options for this table, use the Partial Autocorrelation Function Options dialog box.


Periodogram Table
Periodogram Table (Descriptive Methods)

The Periodogram Table tabular option displays the values for the frequency and ordinate pairs for a period.  The program uses these pairs to plot the amplitudes and frequencies estimated from the data.  The program also displays the cumulative sum and integrated periodograms for each period.

To choose options for this table, use the Periodogram Table Options dialog box.


Tests for Randomness
Tests for Randomness (Descriptive Methods)

The Tests for Randomness tabular option displays the results of two runs tests and a Box-Pierce test.  You can use the results to determine if the time-series data have significant autocorrelation.


Crosscorrelations
Crosscorrelations (Descriptive Methods)

The Crosscorrelations tabular option displays the estimates for the correlation between a time-series variable at a specific period and a second time-series variable at a specific period.  Use crosscorrelations to determine whether two time series are correlated and, if so, whether one series leads to the other.

To choose options for this table, use the Crosscorrelation Function dialog box.


Horizontal Time Sequence Plot
Horizontal Time Sequence Plot (Descriptive Methods)

The Horizontal Time Sequence Plot graphical option displays a connected line plot for the variable against time.  The plot shows important features such as trend, seasonality, discontinuity, and outliers.

To choose options for this plot, use the Horizontal Time Sequence Plot Options dialog box.


Vertical Time Sequence Plot
Vertical Time Sequence Plot (Descriptive Methods)

The Vertical Time Sequence Plot graphical option displays a plot of a time-series variable in relation to a baseline.  The plot contains a vertical line that extends from the baseline to each value.  Use this plot to identify the values that are above and below the baseline.

To choose options for this plot, use the Vertical Time Sequence Plot Options dialog box.


Autocorrelation Function
Autocorrelation Function (Descriptive Methods)

The Autocorrelation Function graphical option displays a plot of the autocorrelation estimates.  The plot contains vertical bars that represent the coefficient for each lag and a pair of dotted lines at a distance from the baseline that are a multiple of the standard error at each lag.  The plot is useful for testing seasonality or other cycles.  Statistically significant coefficients appear as bars that extend beyond either line.

To choose options for this plot, use the Autocorrelation Function Options dialog box.


Partial Autocorrelation Function
Partial Autocorrelation Function (Descriptive Methods)

The Partial Autocorrelation Function graphical option displays a plot of each coefficient represented by a bar whose height is proportional to the value of the coefficient.  By default, the probability limits are plotted as dashed lines at plus or minus 2 divided by the square root of the number of observations in the time series.  The bounds are useful for indicating partial autocorrelations that are significantly different from 0.  Bars that extend beyond either line indicate significant correlations.

To choose options for this plot, use the Partial Autocorrelation Function Options dialog box.


Periodogram
Periodogram (Descriptive Methods)

The Periodogram graphical option displays a plot of the ordinates that construct a frequency spectrum.  The program plots the amplitudes of the sinusoids for various frequencies against the frequencies.  It also scales the Periodogram so that, if the mean of the series is 0, the sum of the ordinates equals the sum of the squared values.  This is also known as the Line Spectrum.

To choose options for this plot, use the Periodogram Options dialog box.


Integrated Periodogram
Integrated Periodogram (Descriptive Methods)

The Integrated Periodogram graphical option displays a plot of the normalized cumulative sum of the periodogram ordinates against the frequencies from 0.0 to 0.5.

To choose options for this plot, use the Integrated Periodogram Options dialog box.


Crosscorrelation Function
Crosscorrelation Function (Descriptive Methods)

The Crosscorrelation Function graphical option displays a plot of the estimated correlations between a time-series variable at time t and a second time-series variable at time t + k as a function of the lag or time differential k.  The program does not display the results until you complete the Crosscorrelation Function Analysis dialog box.

To choose options for this plot, use the Crosscorrelation Function dialog box.


Smoothing Data Input Dialog Box
Smoothing Analysis Dialog Box

Smoothing methods move through the known data, period by period, as opposed to using all the past data in one model-fitting exercise.  When you smooth data you combine observations, which tends to reduce randomness by allowing the positive and negative random effects to partially offset each other.  To eliminate the randomness in the data pattern, you can combine two or more observations from periods during which the causal factors were in effect to achieve a smoothed value.  The plot you create after you smooth the data will produce a curve that more clearly shows the general pattern of the data.

The Smoothing Analysis allows you to apply up to two consecutive smoothing methods to a time-series variable.  After you apply smoothing methods to your data, the program plots the data to reveal trends and cycles as well as data errors and outliers; it also plots residuals.  The Smoothing Analysis also provides several methods you can use to adjust or transform data to make it more appropriate for your evaluation.

Data

Once Every

Starting At

(Seasonality)

Trading Days Adjustment

Select

Sort

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left mouse button on either Pane Options or Analysis Options.

See also

Using the Smoothing Analysis

Adjustment Options

Smoothing Analysis


Smoothing - Tabular Options Dialog Box
Smoothing Analysis Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the Smoothing Analysis.

Analysis Summary (Smoothing)

Data Table (Smoothing)


Smoothing Analysis Summary
Analysis Summary (Smoothing)

The Analysis Summary displays the name of the variable, the number of observations, the start index, the sampling interval, and the names of the two smoothers you specified on the Analysis dialog box.  If you make adjustments to the data, the summary lists those adjustments.

There are five type of data adjustments.  If you choose more than one adjustment, the program adjusts the data in this order:  Inflation, Math, Seasonal, Trend, and Differencing.

To choose options for this analysis, use the Adjustment Options dialog box.


Smoothing Data Table
Data Table (Smoothing)

The Data Table tabular option displays the values of the original data, and the smoothed and rough values (the residuals) for the data for each period.  The program smoothes the values using the default smoothing method, Simple Moving Average with Five Terms.

Use the Smoothing Options dialog box to change the first smoother and to choose a second smoothing method.  The smoothing methods you choose from this dialog box will also affect the Time Sequence Plot.


Smoothing - Graphical Options Dialog Box
Smoothing Analysis Graphical Options Dialog Box

This dialog box allows you to choose the graphical options for the Smoothing Analysis.

Time Sequence Plot (Smoothing)

Residual Plot (Smoothing)


Time Sequence Plot

The Time Sequence Plot graphical option displays a connected line plot for the variable against time.  The plot shows important features such as trend, seasonality, discontinuity, and outliers.


Residual Plot
Residual Plot (Smoothing)

The Residual Plot graphical option displays a plot of the residuals that is calculated as a result of the smoothing.  The residuals are the points that fall outside a smooth curve (the roughs).


Smoothing Options Dialog Box

This dialog box allows you to choose a first and second smoothing method for the data.

Smoother 1

Smoother 2

Length of Moving Average

EWMA Smoothing Constant


Smoother 1

These options allow you to choose the first smoothing option.

Simple Moving Average

Uses a moving average to smooth the data.  The program computes a new average for each period by adding a new observation to the calculation and dropping the oldest observation from the calculation.  Doing this ensures that the number of points in each average is always the same.  If you choose this option, you must complete the Length of Moving Average text box.

Spencer’s 15-Term MA (Moving Average)

Uses a weighted moving average with 15 observations to smooth the data.

Spencer’s 21-Term MA (Moving Average)

Uses a weighted moving average with 21 observations to smooth the data.

Henderson’s Weighted MA (Moving Average)

Uses Henderson's weighted moving average to smooth the data.

EWMA

Uses an Exponentially Weighted Moving Average (EWMA) to smooth the data.

3 RSS

Uses a nonlinear smoothing method that calculates the median for a value and three points around it.  The program performs a resmoothing (R) and a special splitting operation that eliminates plateaus in the data sequence (as the first S denotes; the second S indicates that the program will perform a second splitting.)

3 RSSH

Uses a nonlinear smoothing method that calculates the median for a value and three points around it.  The program performs a resmoothing (R) and a special splitting operation that eliminates plateaus in the data sequence (as the first S denotes; the second S indicates that the program will perform a second splitting).  The program also performs a Hanning (H), which is a running weighted average with weights at one-fourth, one-half, and one-fourth.

5 RSS

Uses a nonlinear smoothing method that calculates the median for a value and five points around it.  The program performs a resmoothing (R) and a special splitting operation that eliminates plateaus in the data sequence (as the first S denotes; the second S indicates that the program will perform a second splitting).

5 RSSH

Uses a nonlinear smoothing method that calculates the median for a value and five points around it.  The program performs a resmoothing (R) and a special splitting operation that eliminates plateaus in the data sequence (as the S denotes; the second S indicates that the program will perform a second splitting).  The program also performs a Hanning (H), which is a running weighted average with weights at one-fourth, one-half, and one-fourth.

3 RSR

Uses a nonlinear smoothing method that calculates the median for a value and three points around it.  The program performs two resmoothings (as denoted by the R) and a special splitting operation to eliminate plateaus in the data sequence (as the R denotes).


Spencer's 15-Term MA

This option uses a weighted moving average with 15 observations to smooth the data.


Spencer's 21-Term MA

This option uses a weighted moving average with 21 observations to smooth the data.


Henderson's Weighted MA

This option uses Henderson's weighted moving average to smooth the data.


EWMA

This option uses an exponentially weighted moving average (EWMA) to smooth the data.  If you choose this option, you must complete the EWMA Smoothing Constant text box.


3 RSS Option

This option uses a nonlinear smoothing method that calculates the median for a value and three points around it.  The program performs a resmoothing (R) and a special splitting operation that eliminates plateaus in the data sequence (as the first S denotes; the second S indicates that the program will perform a second splitting).


3 RSSH Option

This option uses a nonlinear smoothing method that calculates the median for a value and three points around it.  The program performs a resmoothing (R) and a special splitting operation that eliminates plateaus in the data sequence (as the first S denotes; the second S indicates that the program will perform a second splitting).  The program also performs a Hanning (H), which is a running weighted average with weights at one-fourth, one-half, and one-fourth.


5 RSS Option

This option uses a nonlinear smoothing method that calculates the median for a value and five points around it.  The program performs a resmoothing (R) and a special splitting operation that eliminates plateaus in the data sequence (as the first S denotes; the second S indicates that the program will perform a second splitting).


5 RSSH Option

This option uses a nonlinear smoothing method that calculates the median for a value and five points around it.  The program performs a resmoothing (R) and a special splitting operation that eliminates plateaus in the data sequence (as the S denotes; the second S indicates that the program will perform a second splitting).  The program also performs a Hanning (H), which is a running weighted average with weights at one-fourth, one-half, and one-fourth.


3 RSR Option

This option uses a nonlinear smoothing method that calculates the median for a value and three points around it.  The program performs two resmoothings (as denoted by the R) and a special splitting operation to eliminate plateaus in the data sequence (as the R denotes).


Length of Moving Average

This text box allows you to choose the number of points you want the program to use for each average when it applies the Simple Moving Average smoothing method to the data.  Enter an integer greater than 0.  The larger the number you enter, the greater the smoothing effect.  This text box is active only when you choose the Simple Moving Average option.


EWMA Smoothing Constant

This text box allows you to choose the number of points you want the program to use for each exponentially weighted average when it applies the EWMA smoothing method to the data.  A larger value gives more weight to the more recent data.  Enter a number greater than 0 and less than 1.  This text box is active only when you choose the EWMA option.


Smoothing Save Results Options Dialog Box
Save Results Options Dialog Box (Smoothing)

The Save Results Options dialog box allows you to choose the results you want to save.  There are four selections:  Data, Adjusted Data, Smooth, Rough.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Smoothing Analysis Summary
Analysis Summary (Smoothing)

The Analysis Summary displays the name of the variable, the number of observations, the start index, the sampling interval, and the names of the two smoothers you specified on the Analysis dialog box.  If you make adjustments to the data, the summary lists those adjustments.

There are five type of data adjustments.  If you choose more than one adjustment, the program adjusts the data in this order:  Inflation, Math, Seasonal, Trend, and Differencing.

To choose options for this analysis, use the Adjustment Options dialog box.


Smoothing Data Table
Data Table (Smoothing)

The Data Table tabular option displays the values of the original data, and the smoothed and rough values (the residuals) for the data for each period.  The program smoothes the values using the default smoothing method, Simple Moving Average with Five Terms.

Use the Smoothing Options dialog box to change the first smoother and to choose a second smoothing method.  The smoothing methods you choose from this dialog box will also affect the Time Sequence Plot.


Time Sequence Plot
Time Sequence Plot (Smoothing)

The Time Sequence Plot graphical option displays a connected line plot for the variable against time.  The plot shows important features such as trend, seasonality, discontinuity, and outliers.

To choose options for the plot, use the Smoothing Options dialog box.


Residual Plot
Residual Plot (Smoothing)

The Residual Plot graphical option displays a plot of the residuals that the program calculates as a result of the smoothing.  The residuals are the points that fall outside a smooth curve (the roughs).


Seasonal Decomposition Data Input Dialog Box
Seasonal Decomposition Analysis Dialog Box

The Seasonal Decomposition Analysis allows you to perform a classical decomposition of the data.  Classical decomposition breaks the time-series data into four components:  Trend, Seasonality, Cycle, and Irregular movement.  You can use a multiplicative or additive model, adjust or transform the data to make it more appropriate for the analysis you are performing, and specify the unit of time and seasonality of the data.

Data

Once Every

Starting At

(Seasonality)

Trading Days Adjustment

Select

Sort

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left mouse button on either Pane Options or Analysis

Options.

See also

Using the Seasonal Decomposition Analysis

Adjustment Options

Seasonal Decomposition Options

Annual Subseries Plot Options


Seasonal Decomposition - Tabular Options Dialog Box
Seasonal Decomposition Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the Seasonal Decomposition Analysis.

Analysis Summary (Seasonal Decomposition)

Data Table (Seasonal Decomposition)

Seasonal Indices (Seasonal Decomposition)


Seasonal Decomposition Analysis Summary
Analysis Summary (Seasonal Decomposition)

The Analysis Summary displays the name of the variable, the number of observations, the start index, the sampling interval, and the method of decomposition you are using on the data.  If the program provided estimates for missing values, it also displays those values.  If you make adjustments to the data, the summary lists those adjustments.

There are two types of adjustments:  Math and Inflation.  If you choose more than one adjustment, the program adjusts the data in that order.

To choose options for the analysis, use the Adjustment Options dialog box.


Seasonal Decomposition Data Table
Data Table (Seasonal Decomposition)

The Data Table tabular option displays the values for the original data and the seasonally adjusted values for each period and for each component of the decomposition:  Trend-Cycle, Seasonality, and Irregular.

The program breaks the values down according to the decomposition method you choose on the Seasonal Decomposition Options dialog box and the options you choose on the Adjustment Options dialog box.  Use the Trading Days Adjustment text box on the analysis dialog box and the Adjustment Options dialog box if you want to choose other options.


Seasonal Indices
Seasonal Indices (Seasonal Decomposition)

The Seasonal Indices tabular option displays the seasonal indices for the data.  The program uses these indices to calculate seasonally adjusted values for the data on the Data Table.  A seasonally adjusted value is the actual value divided by the seasonal index.


Seasonal Decomposition - Graphical Options Dialog Box
Seasonal Decomposition Graphical Options Dialog Box

This dialog box allows you to choose the graphical options for the Seasonal Decomposition Analysis.

Trend-Cycle (Seasonal Decomposition)

Seasonal Indices (Seasonal Decomposition)

Irregular Component (Seasonal Decomposition)

Seasonally Adjusted Data (Seasonal Decomposition)

Seasonal Subseries Plot (Seasonal Decomposition)

Annual Subseries Plot (Seasonal Decomposition)


Trend-Cycle
Trend-Cycle Plot (Seasonal Decomposition)

The Trend Cycle Plot graphical option displays a plot of the trend and cycle components for seasonal decomposition.  The plot shows the long-term behavior of the data and reveals any trends.


Seasonal Indices
Seasonal Indices Plot (Seasonal Decomposition)

The Seasonal Indices Plot graphical option displays a plot of the seasonal indices for each period.  If you choose the Multiplicative Method on the Seasonal Decomposition Options dialog box, the program bases the indices on the average ratios to the moving average.  If you choose the Additive Method, the program bases the indices on the average differences.


Irregular Component
Irregular Component Plot (Seasonal Decomposition)

The Irregular Component Plot graphical option displays a plot of the data with the trend and seasonality removed.  Depending on the method you choose (Multiplicative or Additive), the program either divides each value by its index or subtracts the index from each value.  The resulting spikes represent the irregular or residual component of the data; in other words, movement you cannot attribute to trend, seasonality, or cycles.


Seasonally Adjusted Data
Seasonally Adjusted Data Plot (Seasonal Decomposition)

The Seasonally Adjusted Data Plot graphical option displays a plot of the seasonally adjusted values from the Data Table, which are the actual values divided by the seasonality indices.


Seasonal Subseries Plot
Seasonal Subseries Plot (Seasonal Decomposition)

The Seasonal Subseries Plot graphical option displays a plot of the values for the time-series data arranged by season.  The horizontal lines represent the average values of the observations for each season.  The vertical lines represent the actual values in the season.


Annual Subseries Plot
Annual Subseries Plot (Seasonal Decomposition)

The Annual Subseries Plot graphical option displays the values for the time-series data arranged by series.  If the data are monthly with a seasonality length of 12, each series represents one year.

To choose options for the plot, use the Annual Subseries Plot Options dialog box.


Seasonal Decomposition Adjustment Options Dialog Box
Adjustment Options Dialog Box (Seasonal Decomposition)

This dialog box allows you to make various types of adjustments to data to make it more appropriate for a model.

Math (Seasonal Decomposition)

Inflation


Seasonal Decomposition Options Dialog Box

This dialog box allows you to choose the method you want the program to use to combine the seasonal decomposition factors.

Method


Seasonal Subseries Plot Options Dialog Box

This dialog box allows you to indicate how the plot will display the seasonal periods.

Plot (Vertical Line or Connected Scatterplot)


Vertical Line

Plots the periods as vertical lines.


Connected Scatterplots

Plots the periods as points, then connect the periods within each season.


Annual Subseries Plot Options Dialog Box

This dialog box allows you to indicate if the program should plot the cumulative values for each series.


Seasonal Decomposition Save Results Options Dialog Box
Save Results Options Dialog Box (Seasonal Decomposition)

The Save Results Options dialog box allows you to choose the results you want to save.  There are five selections:  Data, Adjusted Data, Trend-Cycle, Seasonal Indices, Irregular, and Seasonally Adjusted Data.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Seasonal Decomposition Analysis Summary
Analysis Summary (Seasonal Decomposition)

The Analysis Summary displays the name of the variable, the number of observations, the start index, the sampling interval, and the method of decomposition you are using on the data.  If the program provided estimates for missing values, it also displays those values.  If you make adjustments to the data, the summary lists those adjustments.

There are two types of adjustments:  Math and Inflation.  If you choose more than one adjustment, the program adjusts the data in that order.

To choose options for the analysis, use the Adjustment Options dialog box.


Seasonal Decomposition Data Table
Data Table (Seasonal Decomposition)

The Data Table tabular option displays the values for the original data and the seasonally adjusted values for each period and for each component of the decomposition:  Trend-Cycle, Seasonality, and Irregular.

The program breaks the values down according to the decomposition method you choose on the Seasonal Decomposition Options dialog box and the options you choose on the Adjustment Options dialog box.  Use the Trading Days Adjustment text box on the analysis dialog box and the Adjustment Options dialog box if you want to choose other options.


Seasonal Indices
Seasonal Indices (Seasonal Decomposition)

The Seasonal Indices tabular option displays the seasonal indices for the data.  The program uses these indices to calculate seasonally adjusted values for the data in the Data Table.  A seasonally adjusted value is the actual value divided by the seasonal index.


Trend-Cycle
Trend-Cycle Plot (Seasonal Decomposition)

The Trend-Cycle Plot graphical option displays a plot of the trend and cycle components of the seasonal decomposition.  The plot shows the long-term behavior of the data and reveals any trends.


Seasonal Indices
Seasonal Indices Plot (Seasonal Decomposition)

The Seasonal Indices Plot graphical option displays a plot of the seasonal indices for each period.

If you choose the Multiplicative Method on the Seasonal Decomposition Options dialog box, the program bases the average ratio indices with the moving average.

If you choose the Additive Method, the program bases the indices on the average differences.


Irregular Component
Irregular Component Plot (Seasonal Decomposition)

The Irregular Component Plot graphical option displays a plot of the data with the trend and seasonality removed.  Depending on the method you choose (Multiplicative or Additive), the program either divides each value by its index or subtracts the index from each value.  The resulting spikes represent the irregular or residual component of the data; in other words, movement you cannot attribute to trend, seasonality, or cycles.


Seasonally Adjusted Data
Seasonally Adjusted Data Plot (Seasonal Decomposition)

The Seasonally Adjusted Data Plot graphical option displays a plot of the seasonally adjusted values from the Data Table, which are the actual values divided by the seasonality indices.


Seasonal Subseries Plot
Seasonal Subseries Plot (Seasonal Decomposition)

The Seasonal Subseries Plot graphical option displays a plot of the values for the time-series data arranged by season.  The horizontal lines represent the average values of the observations for each season.  The vertical lines represent the actual values in the season.


Annual Subseries Plot
Annual Subseries Plot (Seasonal Decomposition)

The Annual Subseries Plot graphical option displays a plot of the values for the time-series data arranged by series.  If the data are monthly with a seasonality length of 12, each series represents one year.


Forecasting Data Input Dialog Box
Forecasting Analysis Dialog Box

Forecasting is based on fitting a model to past observations in a given time series.  The Forecasting Analysis in STATGRAPHICS Plus includes 13 forecasting models you can modify by changing the parameters.  You can choose up to five models.  With each model you can transform the data or apply a constant rate of inflation.

Depending on the model you choose, the program also allows you to optimize the parameters or include a constant term.  If the data are seasonal, you can apply differencing and choose a seasonal adjustment.  You can also choose the unit of time and seasonality you want to use to perform the time-series analysis.

Data

Once Every

Starting At

(Seasonality)

Trading Days Adjustment

Select

Sort

Number of Forecasts

Withhold for Validation

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left mouse button on either Pane Options or Analysis Options.

See also

Using the Forecasting Analysis

Model Specification Options

Estimation Options

Autocorrelation Function Options

Partial Autocorrelation Function Options

Periodogram Table Options

Forecast Limits Options

Forecasting Residual Plots Options

Periodogram Options

Crosstabulation Function Dialog Box


Number of Forecasts

This text box allows you to enter the number of periods the program will forecast.  Enter a numeric integer greater than or equal to 0; the default is 10.


Withhold for Validation

This option allows you to include a check for the validity of a model.  Enter the number of values the program should remove from the end of the time-series variable before it validates the model.  The program fits the estimated model to the withheld data and calculates separate forecast error statistics.


Forecasting - Tabular Options Dialog Box
Forecasting Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the Forecasting Analysis.

Forecasting Analysis Summary

Forecast Table (Forecasting)

Model Comparisons (Forecasting)

Residual Autocorrelations (Forecasting)

Residual Partial Autocorrelations (Forecasting)

Residual Periodogram Table (Forecasting)

Residual Tests for Randomness (Forecasting)


Forecasting Analysis Summary
Analysis Summary (Forecasting)

The Analysis Summary displays the name of the variable, the number of observations, the start index, and the sampling interval.  If the program provided estimates for missing values, it also displays those values.  If you make adjustments to the data, the summary lists those adjustments.

The Analysis Summary also displays a summary of the forecast statistics:  The name of the forecast model you chose, the number of forecasts generated, and the number of periods withheld for validation.  A table at the bottom of the summary shows the results of the validation.

MSE (Mean Square Error)

A measure of accuracy computed by squaring the individual error for each item in a dataset, then finding the average or mean value for the sum of those squares.  If the result is a small value, you can predict performance more accurately; if the result is a large value, you may want to use a different forecasting model.

MAE (Mean Absolute Error)

The average of the absolute values of the residuals; appropriate for linear and symmetric data.  If the result is a small value, you can predict performance more accurately; if the result is a large value, you may want to use a different forecasting model.

MAPE (Mean Absolute Percentage Error)

The mean or average of the sum of all the percentage errors for a given dataset without regard to sign (that is, their absolute values are summed and the average is computed).  Unlike the ME, MSE, and MAE, the size of the MAPE is independent of scale.

ME (Mean Error)

The average of the residuals.  The closer the ME is to 0, the less biased, or more accurate, the forecast.

MPE (Mean Percentage Error)

The average of the absolute values of the residuals divided by the corresponding estimates.  The program divides the one-ahead forecast errors by the actual values.  Like MAPE, it is independent of scale.


Forecast Table
Forecast Table (Forecasting)

The Forecast Table tabular option displays the values for the original and forecasted data, and the residual for each period.  Scroll to the bottom of the table to view future forecasts and their corresponding upper and lower confidence limits.


Model Comparisons
Model Comparisons (Forecasting)

The Model Comparisons tabular option displays statistics that compare the accuracy of five models.  In general, the better model has smaller MSE and MAE values and values for ME and MPE that are closer to 0.


Residual Autocorrelations
Residual Autocorrelations (Forecasting)

The Residual Autocorrelations tabular option displays correlation coefficients between the actual values and the forecasted values.  The table shows the estimated residual autocorrelations, the standard errors, and the upper and lower probability limits for each lag.

You can use the residual autocorrelations to determine if the model you choose is appropriate for the data.

To choose options for this table, use the Autocorrelation Function Options dialog box.


Residual Partial Autocorrelations
Residual Partial Autocorrelations (Forecasting)

The Residual Partial Autocorrelations tabular option displays partial correlation coefficients between the actual values and forecasted values.  The table shows the partial autocorrelations, the standard errors, and the upper and lower probability limits for each lag.

You can use the residual coefficients to determine an appropriate model for the data.

To choose options for the table, use the Partial Autocorrelation Function Options dialog box.


Residual Periodogram Table
Residual Periodogram Table (Forecasting)

The Residual Periodogram Table tabular option displays the frequency and ordinate pairs for a period.  The program uses these pairs to plot the amplitudes and frequencies estimated from the data.  The program also displays the cumulative sum and integrated periodograms for each period.

To choose options for the table, use the Periodogram Table Options dialog box.


Residual Tests for Randomness
Residual Tests for Randomness (Forecasting)

The Residual Tests for Randomness tabular option displays the results of two runs tests and a Box-Pierce test.  You can use the results to determine if the time-series data have significant autocorrelation.

Runs Above and Below the Median

This test counts the number of runs that are completely above or completely below the median and ignores the values that are equal to the median.  The test is sensitive to trends in the data.  If the test statistic is large (corresponds to a p-value less than .05), you can conclude that the values occur in nonrandom order.

Runs Up and Down

This test counts the number of times a sequence rises or falls.  The test is sensitive to long-term cycles.  If the test statistic is small (corresponds to a p-value less than .05), you can conclude that the values occur in nonrandom order.

Box-Pierce Test

This test determines if the autocorrelation is equal to 0.  If the test statistic is large (corresponds to a p-value less than .05), the autocorrelation is not equal to 0.  To choose options for this test, use the Box-Pierce Test Options dialog box.

To choose options for the Box-Pierce Test, use the Box-Pierce Test Options dialog box.


Forecasting - Graphical Options Dialog Box
Forecasting Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the Forecasting Analysis.

Time Sequence Plot (Forecasting)

Forecast Plot (Forecasting)

Residual Plots (Forecasting)

Residual Autocorrelation Function Plot (Forecasting)

Residual Partial Autocorrelation Function Plot (Forecasting)

Residual Periodogram (Forecasting)

Residual Crosscorrelation Function Plot (Forecasting)


Forecasting Time Sequence Plot
Time Sequence Plot (Forecasting)

The Time Sequence Plot graphical option displays a connected line plot of the forecasted values against time.

To choose options for the plot, use the Forecast Limits Options dialog box.


Forecast Plot
Forecast Plot (Forecasting)

The Forecast Plot graphical option displays a plot of the forecasts using the fitted model with the confidence limits you choose.

To choose options for this plot, use the Forecast Limits Options dialog box.


Residual Plot
Residual Plots (Forecasting)

The Residual Plots graphical option displays a connected line plot of the model residuals.

To choose options for this plot, use the Forecasting Residual Plots Options dialog box.


Residual Autocorrelation Function
Residual Autocorrelation Function Plot (Forecasting)

The Residual Autocorrelation Function Plot graphical option displays a plot of the autocorrelation estimates for the residuals.  The plot contains vertical bars that represent the coefficient for each lag and a pair of dotted lines at a distance from the baseline that are a multiple of the standard error at each lag.  Significant autocorrelations extend above or below the confidence limits.

To choose options for this plot, use the Autocorrelation Function Options dialog box.


Residual Partial Autocorrelation Function
Residual Partial Autocorrelation Function Plot (Forecasting)

The Residual Partial Autocorrelation Function Plot graphical option displays a plot of each coefficient using a bar whose height is proportional to the value of the coefficient.  By default, the program plots probability limits as dashed lines at plus or minus 2 divided by the square root of the number of observations in the time series.

The bounds are useful for indicating partial autocorrelations that are significantly different from 0.  Bars that extend beyond either line indicate significant correlations.

To choose options for this plot, use the Partial Autocorrelation Function Options dialog box.


Residual Periodogram
Residual Periodogram (Forecasting)

The Residual Periodogram graphical option displays a plot of the ordinates you use to construct a frequency spectrum.  The program plots the amplitudes of the sinusoids for various frequencies against the frequencies.

The program scales the Residual Periodogram so that, if the mean of the series is 0, the sum of the ordinates equals the sum of the squared values.

To choose options for this plot, use the Periodogram Options dialog box.


Residual Crosscorrelation Function
Residual Crosscorrelation Function Plot (Forecasting)

The Residual Crosscorrelation Function Plot graphical option displays a plot of the estimated correlations between the residuals at time t and a second time-series variable at time t + k as a function of the lag or time differential k.

To choose options for this plot, use the Crosscorrelation Function dialog box.


Model Specification Options Dialog Box

Because model types require different parameters and terms, the available options and text boxes depend on the model you choose.  For example, if you choose the Moving Average option, you must complete the Order text box.  If you choose the Simple Exponential Smoothing option, you must complete the Alpha text box.  In addition, if you complete the Seasonality text box on the Forecasting Analysis dialog box, the Seasonality option buttons and text boxes are active on the Model Specification Options dialog box.  Math transformation options and Inflation options are always available no matter which model you choose.

Model

Math (Forecasting)

Inflation

Type

Parameters and Terms

Seasonal (Forecasting)

Differencing

Estimation... Command

Regression... Command


Model

These options allow you to choose which of the forecasting models the program will use to fit the data.  You can choose up to five models.  Before you choose any model, the defaults are:  Model A = Random Walk, Model B = Mean, Model C = Linear Trend, Model D = Moving Average, Model E = Simple Exponential Smoothing.

To choose a model, first click one of the option buttons (A through E), then choose a model from the Type options.  Depending on the model you choose, the program either weights or smoothes past observations and fits a deterministic model or an ARIMA model to obtain a forecast for future values.


None (No Model)

This option allows you to indicate that you do not want to apply a forecasting model.  Use this option if you want to compare less than five models.  For example, if you want to compare four models, choose Model E, then click the None option button.  The program will not forecast values for Model E.


Random Walk

This option allows you to randomly forecast the next observation, based on the current observation and the mean and standard deviation for the difference of the values.


Mean Model
Mean

This option allows you to simply estimate the model by using the average.  The model is Z(t) = mean.


Linear Trend Model
Linear Trend

This option allows you to fit a straight line through the data and into the forecast periods.  The program bases the linear trend on the function:  Z(t) = a + bt, where t represents the time index.  It estimates the coefficients by least squares.  This method is useful when the actual values follow a straight line.


Quadratic Trend Model
Quadratic Trend

This option allows you to fit a quadratic curve (second-order polynomial) through the data and into the forecast periods.  The program bases the quadratic curve on the function:  Z(t) = a + bt + ct2, where t represents the time index.  The program estimates the coefficients by least squares.  This method is useful when the actual values follow a quadratic curve.


Exponential Trend Model
Exponential Trend

This option allows you to fit an exponential curve through the data and into the forecast periods.  The program first takes the natural logarithm of the Z(t) function and then uses least squares estimates.  The exponential curve is based on the function:  Z(t) = exp(a + bt).  This method is useful for data that are increasing or decreasing at a nonconstant rate.


S-Curve Model

This option allows you to fit an S-shaped curve through the data and into the forecast periods.  The program first takes the natural logarithm of the Z(t) function and the reciprocal of t, and then uses least squares estimates.  The exponential curve is based on the function:  Z(t) = exp(a + b/t).  This method is useful only if the actual values follow the S-shaped curve.


Moving Average

This option allows you to use the moving average to smooth the data and predict future values.  The program computes a new average for each period by adding the next observation to the calculation and dropping the oldest observation.  This ensures that the number of points in each average is always the same.  When you choose this option, you must complete the Order text box, which determines the number of observations in each average.


Simple Exponential Smoothing

This option allows you to smooth the data and predict future values by exponentially weighting the past values.  In this method, the program gives recent values relatively more weight than older observations.  When you choose this option, you must complete the Alpha text box.


Brown's Linear Exponential Smoothing

This option allows you to smooth the data and predict future values by applying a double-smoothing formula to the data using one parameter, alpha.  In other words, the program will smooth the data twice using the alpha parameter.  This type of smoothing is useful for nonseasonal data.  When you choose this option, you must complete the Alpha text box.


Holt's Linear Exponential Smoothing

This option allows you to apply a double-smoothing formula to the data using two smoothing parameters, alpha and beta.  The program uses alpha to smooth the estimate of the level, and beta to smooth the estimate of the trend.  This type of smoothing is useful for nonseasonal data, but provides more flexibility than Brown's Linear Exponential Smoothing.  When you choose this option, you must complete the Alpha and Beta text boxes.


Quadratic Exponential Smoothing

This option allows you to assume that the data follow a trend that is characterized as a second-order polynomial.  The program uses three levels of smoothing with one parameter, alpha, to remove the quadratic trend.  This method is also known as Brown's quadratic exponential smoothing.  When you choose this option, you must complete the Alpha text box.


Winter's Exponential Smoothing

This option allows you to apply three separate smoothing parameters (alpha, beta, and gamma) to estimate the level of the series (stationarity), linear trend, and seasonality.  This method is appropriate for seasonal data; however, it is sensitive to values for the three smoothing parameters and may give poor results for some values.  Experiment using different combinations of values until you are satisfied with the numerical results and the graph you produce shows reasonable performance tracking.  If the best results occur for values of alpha and beta that are larger than 0.5, this model may not be appropriate for the data.  When you choose this option, you must complete the Alpha, Beta, and Gamma text boxes.


ARIMA Model

This option allows you to estimate and forecast models using the methods prescribed by Box and Jenkins (1976).  The ARIMA (Auto Regressive Integrated Moving Average) analysis allows you to model a discrete time series as a function of a constant autoregressive term (AR), and a moving-average (MA) term.  You can apply one seasonal (SAR or SMA) and one nonseasonal (AR or MA) parameter of each type.  When you choose this option, you must complete the AR, SAR, MA, SMA, Nonseasonal Order, and Seasonal Order text boxes.


Alpha Parameter
Alpha

This text box allows you to choose the value you want to use as the first smoothing constant.  This parameter smoothes the estimates of the level of the time series.  Enter a number greater than 0 and less than 1.  The larger the value, the more weight the program gives to the most recent observations.  This text box is active when you choose Simple Exponential Smoothing, Brown's Linear Exponential Smoothing, Holt's Linear Exponential Smoothing, Quadratic Exponential Smoothing, or Winter's Exponential Smoothing.


Beta Parameter
Beta

This text box allows you to choose the value you want to use as the second smoothing constant.  This parameter smoothes the estimates of the linear trend.  Enter a number greater than 0 and less than 1.  The larger the value, the more weight the program gives to the most recent observations.  This text box is active when you choose Holt's Linear Exponential Smoothing or Winter's Exponential Smoothing.


Gamma Parameter
Gamma

Use this text box to specify the value you want the system to use as the third smoothing constant.  This parameter smoothes the estimates of the seasonal index.  Enter a number greater than 0 and less than 1.  The larger the value, the more weight the system gives to the most recent observations.  This text box is active when you specify Winter's Exponential Smoothing.


Order

This text box allows you to choose the number of points the program will use for each average when it applies a moving average.  Enter an integer greater than 0;  the larger the number, the greater the smoothing effect.  This text box is active when you choose Moving Average.


AR

This text box allows you to choose the number of nonseasonal autoregressive parameters you want to estimate.  Enter an integer from 0 to 6.  This text box is active when you choose an ARIMA Model.


SAR

This text box allows you to choose the number of seasonal autoregressive parameters you want to estimate.  Enter an integer from 0 to 6.  This text box is active when you complete the Seasonality text box on the Forecast Analysis dialog box and choose an ARIMA Model.


MA

This text box allows you to choose the number of nonseasonal moving-average parameters you want to estimate.  Enter an integer from 0 to 6.  This text box is active when you choose an ARIMA Model.


SMA

This text box allows you to choose the number of seasonal moving-average parameters you want to estimate.  Enter an integer from 0 to 6. This text box is active when you complete the Seasonality text box on the Forecasting Analysis dialog box and choose an ARIMA Model.


Optimize

This check box allows the program to search for a value(s) that minimizes the mean square error.  The program uses the value(s) as a starting point and performs an iterative search to find the optimum value(s).  The check box is active when you choose Simple Exponential Smoothing, Brown's Linear Exponential Smoothing, Holt's Linear Exponential Smoothing, Quadratic Exponential Smoothing, or Winter's Exponential Smoothing.  Note:  The program may find a local optimum rather than a global optimum; you should try different starting values for the parameter(s) to obtain the best results.


Constant

This check box allows you to use a constant term in the model.  The check box is active when you choose an ARIMA Model.


Estimation Options Dialog Box

This dialog box allows you to limit and stop the model-estimation process.

Estimation


Stopping Criterion 1

This text box allows you to enter the number of iterations the program will use to stop the estimation process.  The program stops the process when the change in the residual sum of squares between the iterations reaches the minimal change you choose.  Enter a number greater than or equal to 0.


Stopping Criterion 2

This text box allows you to enter the number of iterations the program will use to stop the estimation process.  The program stops the process when the change in all the parameter estimates between the iterations reaches the minimal relative change you choose.  Enter a number greater than or equal to 0.


Maximum Iterations

This text box allows you to enter the maximum number of iterations the program will use to perform the estimation.  Enter an integer between 1 and 1000.


Backforecasting

This check box allows you to indicate whether or not you want the program to backforecast to obtain starting values for the modeling errors.  After you choose a forecasting method, the program applies it to the time series, starting at the last value and moving to the beginning of the data.


Regression...

This command displays the Regression Variable(s) dialog box.  Use the dialog box to choose the one or more independent variables you want to use in the regression analysis.

This command is available when you choose any of these models:  Mean, Linear Trend, Quadratic Trend, Exponential Trend, S-Curve, or ARIMA.

Variable(s)

Sort


Variable(s)

This text box allows you to choose one or more independent numeric variables for a regression analysis.


Forecast Limits Options Dialog Box

Allows you to enter a value (in percentages) that will be used to calculate the probability limits for the Forecast plot.  Enter a number greater than 0 and less than 100; common levels are 90, 95, or 99 percent.


Forecasting Residual Plots Options Dialog Box

This dialog box allows you to choose the type of plot the program will create.

Type


Time Sequence Plot
Time Sequence Plot for the Forecasting Analysis

The Time Sequence Plot graphical option displays a plot of the forecast residuals.  The graph is a connected line plot for the residuals against time.


Probability Plot (Horizontal)
Probability Plot (Horizontal) for the Forecasting Analysis

The Probability Plot (Horizontal) graphical option displays a horizontal probability plot of residuals.  The program plots the residuals on the Y-axis from smallest to largest.  The X-axis is a normal probability scale (it “straightens out” the plot of a cumulative normal distribution).  If the residuals do not fall approximately along a straight line, they are not from a normal distribution, which suggests that you may not have used the best model.


Probability Plot (Vertical)
Probability Plot (Vertical) for the Forecasting Analysis

The Probability Plot (Vertical) graphical option displays a vertical probability plot of the residuals.  The program plots the residuals on the X-axis from smallest to largest.  The Y-axis is a normal probability scale (it “straightens out” the plot of a cumulative normal distribution).  If the residuals do not fall approximately along a straight line, they are not from a normal distribution.  This suggests that you may not have used the best model for the data.


Forecasting Save Results Options Dialog Box
Save Results Options Dialog Box (Forecasting)

The Save Results Options dialog box allows you to choose the results you want to save.  There are 11 selections:  Data, Adjusted Data, Forecasts, Upper Forecast Limits, Lower Forecast Limits, Residuals, Autocorrelations, Partial Autocorrelations, Residual Periodogram Ordinates, Crosscorrelations and Fourier Frequencies.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


TSSave Forecasts
Forecasts

This option saves the forecasted values.


Forecasting Analysis Summary
Analysis Summary (Forecasting)

The Analysis Summary displays the name of the variable, the number of observations, the start index, and the sampling interval.  If the program provided estimates for missing values, it also displays those values.  If you make adjustments to the data, the summary lists those adjustments.

The Analysis Summary also displays a summary of the forecast statistics:  The name of the forecast model you chose, the number of forecasts generated, and the number of periods withheld for validation.  A table at the bottom of the summary shows the results of the validation.

MSE (Mean Square Error)

A measure of accuracy computed by squaring the individual error for each item in a dataset, then finding the average or mean value for the sum of those squares.  If the result is a small value, you can predict performance more accurately; if the result is a large value, you may want to use a different forecasting model.

MAE (Mean Absolute Error)

The average of the absolute values of the residuals; appropriate for linear and symmetric data.  If the result is a small value, you can predict performance more accurately; if the result is a large value, you may want to use a different forecasting model.

MAPE (Mean Absolute Percentage Error)

The mean or average of the sum of all the percentage errors for a given dataset without regard to sign (that is, their absolute values are summed and the average is computed).  Unlike the ME, MSE, and MAE, the size of the MAPE is independent of scale.

ME (Mean Error)

The average of the residuals.  The closer the ME is to 0, the less biased, or more accurate, the forecast.

MPE (Mean Percentage Error)

The average of the absolute values of the residuals divided by the corresponding estimates.  The program divides the one-ahead forecast errors by the actual values.  Like MAPE, it is independent of scale.


Forecast Table
Forecast Table (Forecasting)

The Forecast Table tabular option displays the values for the original and forecasted data, and the residual for each period.  Scroll to the bottom of the table to view future forecasts and their corresponding upper and lower confidence limits.


Model Comparisons
Model Comparisons (Forecasting)

The Model Comparisons tabular option displays comparison statistics that compare the accuracy of five models.  In general, the better model has smaller MSE and MAE values and values for ME and MPE that are closer to 0.


Residual Autocorrelations
Residual Autocorrelations (Forecasting)

The Residual Autocorrelations tabular option displays correlation coefficients between the actual values and the forecasted values.  The table shows the estimated residual autocorrelations, the standard errors, and the upper and lower probability limits for each lag.

You can use the residual autocorrelations to determine if the model you choose is appropriate for the data.

To choose options for this table, use the Autocorrelation Function Options dialog box.


Residual Partial Autocorrelations
Residual Partial Autocorrelations (Forecasting)

The Residual Partial Autocorrelations tabular option displays partial correlation coefficients between the actual values and forecasted values.  The table shows the partial autocorrelations, the standard errors, and the upper and lower probability limits for each lag.

You can use the residual coefficients to determine an appropriate model for the data.

To choose options for the table, use the Partial Autocorrelation Function Options dialog box.


Residual Periodogram Table
Residual Periodogram Table (Forecasting)

The Residual Periodogram Table tabular option displays the frequency and ordinate pairs for a period.  The program uses these pairs to plot the amplitudes and frequencies estimated from the data.  The program also displays the cumulative sum and integrated periodograms for each period.

To choose options for the table, use the Periodogram Table Options dialog box.


Residual Tests for Randomness
Residual Tests for Randomness (Forecasting)

The Residual Tests for Randomness tabular option displays the results of two runs tests and a Box-Pierce test.  You can use the results to determine if the time-series data have significant autocorrelation.

Runs Above and Below the Median

This test counts the number of runs that are completely above or completely below the median and ignores the values that are equal to the median.  The test is sensitive to trends in the data.  If the test statistic is large (corresponds to a p-value less than .05), you can conclude that the values occur in nonrandom order.

Runs Up and Down

This test counts the number of times a sequence rises or falls.  The test is sensitive to long-term cycles.  If the test statistic is small (corresponds to a p-value less than .05), you can conclude that the values occur in nonrandom order.

Box-Pierce Test

This test determines if the autocorrelation is equal to 0.  If the test statistic is large (corresponds to a p-value less than .05), the autocorrelation is not equal to 0.  To choose options for this test, use the Box-Pierce Test Options dialog box.

To choose options for the Box-Pierce Test, use the Box-Pierce Test Options dialog box.


Time Sequence Plot for Forecasting
Time Sequence Plot (Forecasting)

The Time Sequence Plot graphical option displays a connected line plot of the forecasted values against time.

To choose options for the plot, use the Forecast Limits Options dialog box.


Forecast Plot
Forecast Plot (Forecasting)

The Forecast Plot graphical option displays a plot of the forecasts using the fitted model with the confidence limits you choose.

To choose options for the plot, use the Forecast Limits Options dialog box.


Residual Plots
Residual Plots (Forecasting)

The Residual Plots graphical option displays a connected line plot of the model residuals.

To choose options for this plot, use the Forecasting Residual Plots Options dialog box.


Residual Autocorrelation Function
Residual Autocorrelation Function Plot (Forecasting)

The Residual Autocorrelation Function Plot graphical option displays a plot of the autocorrelation estimates for the residuals.  The plot contains vertical bars that represent the coefficient for each lag and a pair of dotted lines at a distance from the baseline that are a multiple of the standard error at each lag.  Significant autocorrelations extend above or below the confidence limits.


Residual Partial Autocorrelation Function
Residual Partial Autocorrelation Function Plot (Forecasting)

The Residual Partial Autocorrelation Function Plot graphical option displays a plot of each coefficient using a bar whose height is proportional to the value of the coefficient.  By default, the program plots probability limits as dashed lines at plus or minus 2 divided by the square root of the number of observations in the time series.

The bounds are useful for indicating partial autocorrelations that are significantly different from 0.  Bars that extend beyond either line indicate significant correlations.

To choose options for this plot, use the Partial Autocorrelation Function Options dialog box.


Residual Periodogram
Residual Periodogram (Forecasting)

The Residual Periodogram graphical option displays a plot of the ordinates you use to construct a frequency spectrum.  The program plots the amplitudes of the sinusoids for various frequencies against the frequencies.

The program scales the Residual Periodogram so that, if the mean of the series is 0, the sum of the ordinates equals the sum of the squared values.

To choose options for this plot, use the Periodogram Options dialog box.


Residual Crosscorrelation Function
Residual Crosscorrelation Function Plot (Forecasting)

The Residual Crosscorrelation Function Plot graphical option displays a plot of the estimated correlations between the residuals at time t and a second time-series variable at time t + k as a function of the lag or time differential k.

To choose options for this plot, use the Crosscorrelation Function dialog box.


Runs Above and Below the Median

This test counts the number of runs that are completely above or completely below the median and ignores the values that are equal to the median.  The test is sensitive to trends in the data.  If the test statistic is large (corresponds to a p-value less than .05), you can conclude that the values occur in nonrandom order.


Runs Up and Down

This test counts the number of times a sequence rises or falls.  The test is sensitive to long-term cycles.  If the test statistic is small (corresponds to a p-value less than .05), you can conclude that the values occur in nonrandom order.


Box-Pierce Test

This test determines whether the autocorrelation is equal to 0.  If the test statistic is large (corresponds to a p-value less than .05), the autocorrelation is not equal to 0.


Nonseasonal Order

This text box allows you to specify the order of nonseasonal differencing you want the program to apply to the model.  Enter any integer greater than or equal to 0.  The program assumes a seasonality of 1.  For example, for this time-series data

2.8 	2.6  2.7  2.9  3.0  2.2  4.3  5.7  2.5

enter 1 in the text box.  The program subtracts the value 2.8 from the next value, 2.6.  If you enter 2, the program subtracts 2.8 from the value that is two places from the original value, 2.7.


Seasonal Order

This text box allows you to specify the order of seasonal differencing the program should apply to the model.  Enter any integer greater than or equal to 0.  The program takes into account the seasonality you specify in the Descriptive Methods Analysis dialog box.  For example, if the time-series data above are quarterly and you enter 1 in the text box, the program subtracts 2.8 from the value that is four places from the original value, 3.0.

This option is available only when you choose seasonality on the Descriptive Methods Analysis dialog box.


Math (Descriptive Methods)
Math

These options instruct the program to apply a mathematical transformation to the data.

None

No mathematical transformation is applied to the data.

Natural Log

A natural log transformation is applied to the data.

Base 10 Log

A base 10 log transformation is applied to the data.

Square Root

A square-root transformation is applied to the data.

Reciprocal

This reciprocal transformation is applied to the data:  (1/t).

Power

The program raises the data to a power.  Use the text box to enter the power.  For example, if you choose this option and enter 10 into the text box, the program raises each value to the power of 10.  Enter any numeric value except 0.

Box-Cox

The program scales the values by the geometric mean, which stabilizes the variance of the time-series data and makes the distribution closer to normal.

Use the Power text box to enter a value for the strength of the transformation.  Enter any numeric value except 0.  A power of 1 corresponds to the original data.

Use the Addend text box to enter a value the program will add to the original data before it raises the value to the power you choose.  For example, before taking the log, you might add (shift the data) one value so all the observations are positive.  Enter any numeric value.


Seasonal (Descriptive Methods)
Seasonal

In a seasonal adjustment, the program performs a multiplicative or additive seasonal adjustment.  Choose one of the three the methods the program will use to perform the seasonal adjustment, which determines how the terms will be combined.

The Seasonal option is available only if you choose Seasonality on the Descriptive Methods Analysis dialog box.

None

No seasonal adjustment is made to the data.

Multiplicative

The program uses the multiplicative ratio-to-moving-average method to make the seasonal adjustment.  The program assumes that the components of the data (trend, seasonal, and random effects) cause proportional changes in the series, and therefore expresses the result as a product of the components.

Additive

The program uses the additive difference from the moving-average method to make the seasonal adjustment.  It simply adds or subtracts given amounts and expresses the result as a sum of the components.


Trend (Descriptive Methods)
Trend

In this type of adjustment, the program estimates and removes the trend using the unweighted regression analysis.  The program fits a linear or quadratic line, exponential power curve, or an S-Curve through the time-series data.  Each of the four fitted models estimates a function Z(t), where t represents the time index.

None

No function will be fit to the data.

Linear

The program estimates a linear trend based on Z(t) = a + bt, which fits a straight line through the data.

Quadratic

The program estimates a quadratic trend based on Z(t) = a + bt + ct2, which fits a curved line through the data.

Exponential

The program estimates an exponential power curve based on Z(t) = exp(a + bt), which fits an exponential growth curve through the data.

S-Curve

The program estimates an S-curve trend based on Z(t) = exp(a + b/t), which first takes the natural logarithm of the Z(t) function and then uses least-squares estimates.


Differencing (Descriptive Methods)
Differencing

A differencing adjustment removes a trend from the data, which enables you to analyze local fluctuations.  This method makes the data stationary and, therefore, more appropriate for most methods of analysis.  The program subtracts the difference of the original value from a value you enter in the data series.  Use the following text boxes to enter the order of differencing the program will apply to the data.

Nonseasonal Order

Allows you to enter the order of nonseasonal differencing the program will apply to the model.  Enter any integer greater than or equal to 0.  The program assumes a seasonality of 1; for example, for this time-series data:

2.8  2.6  2.7  2.9  3.0  2.2  4.3  5.7  2.5

enter 1  into the text box.  The program subtracts the value 2.8 from the next value, 2.6.  If you enter 2, the program subtracts 2.8 from the value that is two places from the original value, 2.7.

Seasonal Order

Allows you to enter the order of seasonal differencing the program will apply to the model.  Enter any integer greater than or equal to 0.  The program accounts for the seasonality you choose in the Analysis dialog box.  For example, if the time-series data above are quarterly data and you enter 1 into the text box, the program subtracts 2.8 from the value that is four places from the original value, 3.0.  This option is available only when you choose seasonality on the Analysis dialog box.

Nonseasonal Order

Seasonal Order


Inflation (Descriptive Methods)
Inflation

These options allow you to indicate how the program should adjust the data for a constant rate of inflation.

Apply at End of Period

The program applies data/(1 + ratet) to the data.

Apply at Middle of Period

The program applies data/(1 + ratet - .5) to the data.

Rate

Enter the rate the program will use for inflation for one entire cycle.


Crosscorrelation Function Dialog Box

This dialog box allows you to enter the name of the variable and the maximum number of lags for the crosscorrelations.

Second Time Series

Number of Lags


Smoother 1

These options allow you to choose the first smoothing method the program will use to smooth the data.

Simple Moving Average

Spencer's 15-Term MA

Spencer's 21-Term MA

Henderson's Weighted MA

EWMA

3  RSS

3 RSSH

5  RSS

5  RSSH

3  RSR


Smoother 2

These options allow you to indicate if you want to apply a second smoothing method, and if so, to choose the method the program will use.

Simple Moving Average

Uses a moving average to smooth the data.  The program computes a new average for each period by adding a new observation to the calculation and dropping the oldest observation from the calculation.  Doing this ensures that the number of points in each average is always the same.  If you choose this option, you must complete the Length of Moving Average text box.

Spencer’s 15-Term MA (Moving Average)

Uses a weighted moving average with 15 observations to smooth the data.

Spencer’s 21-Term MA (Moving Average)

Uses a weighted moving average with 21 observations to smooth the data.

Henderson’s Weighted MA (Moving Average)

Uses Henderson's weighted moving average to smooth the data.

EWMA

Uses an Exponentially Weighted Moving Average (EWMA) to smooth the data.

3 RSS

Uses a nonlinear smoothing method that calculates the median for a value and three points around it.  The program performs a resmoothing (R) and a special splitting operation that eliminates plateaus in the data sequence (as the first S denotes; the second S indicates that the program will perform a second splitting.)

3 RSSH

Uses a nonlinear smoothing method that calculates the median for a value and three points around it.  The program performs a resmoothing (R) and a special splitting operation that eliminates plateaus in the data sequence (as the first S denotes; the second S indicates that the program will perform a second splitting).  The program also performs a Hanning (H), which is a running weighted average with weights at one-fourth, one-half, and one-fourth.

5 RSS

Uses a nonlinear smoothing method that calculates the median for a value and five points around it.  The program performs a resmoothing (R) and a special splitting operation that eliminates plateaus in the data sequence (as the first S denotes; the second S indicates that the program will perform a second splitting).

5 RSSH

Uses a nonlinear smoothing method that calculates the median for a value and five points around it.  The program performs a resmoothing (R) and a special splitting operation that eliminates plateaus in the data sequence (as the S denotes; the second S indicates that the program will perform a second splitting).  The program also performs a Hanning (H), which is a running weighted average with weights at one-fourth, one-half, and one-fourth.

3 RSR

Uses a nonlinear smoothing method that calculates the median for a value and three points around it.  The program performs two resmoothings (as denoted by the R) and a special splitting operation to eliminate plateaus in the data sequence (as the R denotes).


Adjusted Data (Smoothing)

This option allows you to save the adjusted time-series data.


Smooth (Smoothing)

This option allows you to save the smoothed time-series data.


Target Variables (Smoothing)

These text boxes allow you to choose the names of the variables for which you want to save the values the program generated during this analysis.  You can enter new names for the variables or accept the defaults.


Math (Seasonal Decomposition)
Math

These options instruct the program to apply a mathematical transformation to the data.

None

No mathematical transformation is applied to the data.

Natural Log

A natural log transformation is applied to the data.

Base 10 Log

A base 10 log transformation is applied to the data.

Square Root

A square-root transformation is applied to the data.

Reciprocal

This reciprocal transformation is applied to the data:  (1/t).

Power

The program raises the data to a power.  Use the text box to enter the power.  For example, if you choose this option and enter 10 into the text box, the program raises each value to the power of 10.  Enter any numeric value except 0.

Box-Cox

The program scales the values by the geometric mean, which stabilizes the variance of the time-series data and makes the distribution closer to normal.

Use the Power text box to enter a value for the strength of the transformation.  Enter any numeric value except 0.  A power of 1 corresponds to the original data.

Use the Addend text box to enter a value the program will add to the original data before it raises the value to the power you choose.  For example, before taking the log, you might add (shift the data) one value so all the observations are positive.  Enter any numeric value.


Inflation (Seasonal Decomposition)
Inflation

These options allow you to specify how the program will adjust the data for a constant rate of inflation.

Apply at End of Period

Apply at Middle of Period

Rate


Data (Seasonal Decomposition)
Data

This option allows you to save the time-series data.


Adjusted Data (Seasonal Decomposition)
Adjusted Data

This option allows you to save the adjusted time-series data.


Type

These options allow you to choose the type of forecasting model you want to use.  Depending on the model you choose, the program either weights or smoothes past observations and fits a deterministic model or an ARIMA Model to obtain a forecast for future values.

Choose the type of smoothing, line or curve, or ARIMA Model you want drawn through the data and into the forecast periods.  In doing this, the program eliminates randomness from the data pattern into the future, and perhaps predicts more accurate future values.

None

Indicates that you do not want to apply a forecasting model.  Use this option if you want to compare less than five models.  For example, if you want to compare four models, choose Model E, then click the None option button.  The program will not forecast values for Model E.

Random Walk

Randomly forecasts the next observation, based on the current observation and the mean and standard deviation for the difference of the values.

Mean

Estimates the model by using the average.  The model is Z(t) = mean.

Linear Trend

Fits a straight line through the data and into the forecast periods.  The program bases the linear trend on the function:  Z(t) = a + bt, where t represents the time index.  It estimates the coefficients by least squares.  This method is useful when the actual values follow a straight line.

Quadratic Trend

Fits a quadratic curve (second-order polynomial) through the data and into the forecast periods.  The program bases the quadratic curve on the function:  Z(t) = a + bt + ct2, where t represents the time index.  The program estimates the coefficients by least squares.  This method is useful when the actual values follow a quadratic curve.

Exponential Trend

Fits an exponential curve through the data and into the forecast periods.  The program first takes the natural logarithm of the Z(t) function and then uses least squares estimates.  The exponential curve is based on the function:  Z(t) = exp(a + bt).  This method is useful for data that are increasing or decreasing at a nonconstant rate.

S-Curve

Fits an S-shaped curve through the data and into the forecast periods.  The program first takes the natural logarithm of the Z(t) function and the reciprocal of t, and then uses least squares estimates.  The exponential curve is based on the function:  Z(t) = exp(a + b/t).  This method is useful only if the actual values follow the S-shaped curve.

Moving Average

Uses the moving average to smooth the data and predict future values.  The program computes a new average for each period by adding the next observation to the calculation and dropping the oldest observation.  This ensures that the number of points in each average is always the same.

When you choose this option, you must complete the Order text box, which determines the number of observations in each average.

Simple Exponential Smoothing

Smoothes the data and predicts future values by exponentially weighting the past values.  In this method, the program gives recent values relatively more weight than older observations.

When you choose this option, you must complete the Alpha text box.

Brown’s Linear Exponential Smoothing

Smoothes the data and predicts future values by applying a double-smoothing formula to the data using one parameter, alpha.  In other words, the program smoothes the data twice using the alpha parameter.  This type of smoothing is useful for nonseasonal data.

When you choose this option, you must complete the Alpha text box.

Holt’s Linear Exponential Smoothing

Applies a double-smoothing formula to the data using two smoothing parameters, alpha and beta — alpha to smooth the estimate of the level, and beta to smooth the estimate of the trend.  This type of smoothing is useful for nonseasonal data, but provides more flexibility than Brown's Linear Exponential Smoothing.

When you choose this option, you must complete the Alpha and Beta text boxes.

Quadratic Exponential Smoothing

Assumes that the data follow a trend that is characterized as a second-order polynomial by using three levels of smoothing with one parameter, alpha, to remove the quadratic trend.  This method is also known as Brown's quadratic exponential smoothing.

When you choose this option, you must complete the Alpha text box.

Winter’s Exponential Smoothing

Applies three separate smoothing parameters (alpha, beta, and gamma) to estimate the level of the series (stationarity), linear trend, and seasonality.

This method is appropriate for seasonal data; however, it is sensitive to values for the three smoothing parameters and may give poor results for some values.  Experiment using different combinations of values until you are satisfied with the numerical results and the graph you produce shows reasonable performance tracking.  If the best results occur for values of alpha and beta that are larger than 0.5, this model may not be appropriate for the data.

When you choose this option, you must complete the Alpha, Beta, and Gamma text boxes.

ARIMA Model

Estimates and forecasts models using the methods prescribed by Box and Jenkins (1976).  The ARIMA (Auto Regressive Integrated Moving Average) analysis allows you to model a discrete time series as a function of a constant autoregressive term (AR), and a moving-average (MA) term.  You can apply one seasonal (SAR or SMA) and one nonseasonal (AR or MA) parameter of each type.

When you choose this option, you must complete the AR, SAR, MA, SMA, Nonseasonal Order, and Seasonal Order text boxes.


Math (Forecasting)
Math

These options instruct the program to apply a Mathematical transformation to the data.

None

No mathematical transformation is applied to the data.

Natural Log

A natural log transformation is applied to the data.

Base 10 Log

A base 10 log transformation is applied to the data.

Square Root

A square-root transformation is applied to the data.

Reciprocal

This reciprocal transformation is applied to the data:  (1/t).

Power

The program raises the data to a power.  Use the text box to enter the power.  For example, if you choose this option and enter 10 into the text box, the program raises each value to the power of 10.  Enter any numeric value except 0.

Box-Cox

The program scales the values by the geometric mean, which stabilizes the variance of the time-series data and makes the distribution closer to normal.

Use the Power text box to enter a value for the strength of the transformation.  Enter any numeric value except 0.  A power of 1 corresponds to the original data.

Use the Addend text box to enter a value the program will add to the original data before it raises the value to the power you choose.  For example, before taking the log, you might add (shift the data) one value so all the observations are positive.  Enter any numeric value.


Parameters and Terms

These text boxes allow you to choose the parameters and terms you want to use for the model.  The text boxes that are active depend on the type of model you choose.

Alpha

This text box allows you to choose the value you want to use as the first smoothing constant.  This parameter smoothes the estimates of the level of the time series.  Enter a number greater than 0 and less than 1.  The larger the value, the more weight the program gives to the most recent observations.  This text box is active when you choose Simple Exponential Smoothing, Brown's Linear Exponential Smoothing, Holt's Linear Exponential Smoothing, Quadratic Exponential Smoothing, or Winter's Exponential Smoothing.

Beta

This text box allows you to choose the value you want to use as the second smoothing constant.  This parameter smoothes the estimates of the linear trend.  Enter a number greater than 0 and less than 1.  The larger the value, the more weight the program gives to the most recent observations.  This text box is active when you choose Holt's Linear Exponential Smoothing or Winter's Exponential Smoothing.

Gamma

Use this text box to specify the value you want the system to use as the third smoothing constant.  This parameter smoothes the estimates of the seasonal index.  Enter a number greater than 0 and less than 1.  The larger the value, the more weight the system gives to the most recent observations.  This text box is active when you specify Winter's Exponential Smoothing.

Order

This text box allows you to choose the number of points the program will use for each average when it applies a moving average.  Enter an integer greater than 0;  the larger the number, the greater the smoothing effect.  This text box is active when you choose Moving Average.

AR

This text box allows you to choose the number of nonseasonal autoregressive parameters you want to estimate.  Enter an integer from 0 to 6.  This text box is active when you choose an ARIMA Model.

SAR

This text box allows you to choose the number of seasonal autoregressive parameters you want to estimate.  Enter an integer from 0 to 6.  This text box is active when you complete the Seasonality text box on the Forecast Analysis dialog box and choose an ARIMA Model.

MA

This text box allows you to choose the number of nonseasonal moving-average parameters you want to estimate.  Enter an integer from 0 to 6.  This text box is active when you choose an ARIMA Model.

SMA

This text box allows you to choose the number of seasonal moving-average parameters you want to estimate.  Enter an integer from 0 to 6. This text box is active when you complete the Seasonality text box on the Forecasting Analysis dialog box and choose an ARIMA Model.

Optimize

This check box allows the program to search for a value(s) that minimizes the mean square error.  The program uses the value(s) as a starting point and performs an iterative search to find the optimum value(s).  The check box is active when you choose Simple Exponential Smoothing, Brown's Linear Exponential Smoothing, Holt's Linear Exponential Smoothing, Quadratic Exponential Smoothing, or Winter's Exponential Smoothing.  Note:  The program may find a local optimum rather than a global optimum; you should try different starting values for the parameter(s) to obtain the best results.

Constant

This check box allows you to use a constant term in the model.  The check box is active when you choose an ARIMA Model.


Seasonal

These options allow you to choose the method the program will use to perform a seasonal adjustment on the data.  The option you choose determines how the program will combine the terms.

The options are available when you complete the Seasonality text box on the Forecasting Analysis dialog box and choose Random Walk, Mean, Linear Trend, Quadratic Trend, Exponential Trend, S-Curve, Moving Average, Simple Exponential Smoothing, Brown’s Linear Exponential Smoothing, Holt’s Exponential Smoothing, or Quadratic Exponential Smoothing.

None

No seasonal adjustment is made to the data.

Multiplicative

The program uses the multiplicative ratio-to-moving-average method to make the seasonal adjustment.  The program assumes that the components of the data (trend, seasonal, and random effects) cause proportional changes in the series, and therefore expresses the result as a product of the components.

Additive

The program uses the additive difference from the moving-average method to make the seasonal adjustment.  It simply adds or subtracts given amounts and expresses the result as a sum of the components.


Estimation...

This command displays the Estimation Options dialog box.  The dialog box allows you to limit and stop the model-estimation process.  The command is available when you choose one of these types of methods for forecasting:  Simple Exponential Smoothing, Brown’s Linear Exponential Smoothing, Holt’s Linear Exponential Smoothing, Quadratic Exponential Smoothing, Winter’s Exponential Smoothing, or the ARIMA Model.

See also

Estimation Options Dialog Box


Regression...

This command displays the Regression Variable(s) Dialog Box, which allows you to choose one or more independent variables for a regression analysis.  The command is available when you choose one of these types of models:  Mean, Linear Trend, Quadratic Trend, Exponential Trend, S-Curve, or ARIMA Model.

See also

Regression Variable(s) Dialog Box


Crosscorrelation Function Analysis Dialog Box

This dialog box allows you to choose or enter the variables the program will use in the analysis.

Second Time Series

Number of Lags


Second Time Series

This text box allows you to enter the variable that contains the second set of time-series data.


Number of Lags

This text box allows you to enter the maximum number of lags for which the program should calculate the crosscorrelations.  Enter any positive integer; the default is 24.


Plot (Vertical Line or Connected Scatterplot)

Determines how the periods will display on the plot.

Vertical Line

Displays the periods as vertical lines.

Connected Scatterplots

Displays the periods as connected points within each season.


Multiplicative

This option uses the multiplicative ratio-to-moving-average method.  The program assumes that the components of the data (trend, seasonal, and random effects) cause proportional changes in the series, and expresses the result as a product of the components.


Estimation

These options allow you to limit and stop the model-estimation process.

Stopping Criterion 1

Enter the number of iterations the program should use to stop the estimation process.  The program stops the process when the change in the residual sum of squares between the iterations reaches the minimal change you choose.  Enter a number greater than or equal to 0.

Stopping Criterion 2

Enter the number of iterations the program should use to stop the estimation process.  The program stops the process when the change in all the parameter estimates between the iterations reaches the minimal relative change you choose.  Enter a number greater than or equal to 0.

Maximum Iterations

Enter the maximum number of iterations the program should use to perform the estimation.  Enter an integer between 1 and 1000.

Backforecasting

Indicate if the program should backforecast to obtain starting values for the modeling errors.  After you choose a Forecasting method, the program applies it to the time series, starting at the last value and moving to the beginning of the data.


Type

These options allow you to choose a plot.

Time Sequence Plot

Produces a plot of the forecast residuals.  The plot is a connected line plot for the residuals against time.

Probability Plot (Horizontal)

Produces a horizontal probability plot of the residuals.  The program plots the residuals on the Y-axis from smallest to largest.  The X-axis is a normal probability scale (it “straightens out” the plot of a cumulative normal distribution).  If the residuals do not fall approximately along a straight line, they are not from a normal distribution, which suggests that you may not have used the best model for the data.

Probability Plot (Vertical)

Produces a vertical probability plot of the residuals.  The program plots the residuals on the X-axis from smallest to largest.  The Y-axis is a normal probability scale (it “straightens out” the plot of a cumulative normal distribution).  If the residuals do not fall approximately along a straight line, they are not from a normal distribution.  This suggests that you may not have used the best model for the data.


Points

Plots the observations as points; this option is one of the defaults.


Lines

The plot contains lines connecting the observations; this option is one of the defaults.


Plot

Determines how the periods will display on the plot.

Vertical Lines

Displays the periods as vertical lines.

Connected Scatterplots

Displays the periods as connected points within each season.


Create Design Options Dialog Box

This dialog box allows you to choose a design class; set the number of response variables and experimental factors (or components); set parameters specific to a given design class; and enter a descriptive comment that identifies the design.

Design Class

Number of Response Variables

Number of Experimental Factors (or Components)

Number of Control Factors (Inner/Outer Arrays)

Number of Noise Factors (Inner/Outer Arrays)

Comment


Design Class

Choose the type of design you want to create: Screening, Response Surface, Mixture, Multilevel Factorial, Inner/Outer Arrays, Single Factor Categorical, Multi-Factor Categorical, or Variance Components (Hierarchical).


Response Surface

Creates a Response Surface Design.  Response surface methodology is a process for locating an optimal value in a higher-order model.  The design helps determine if the experimental region contains the optimum, then builds a mathematical model to locate it.


Mixture

Creates a Mixture Design.  Mixture designs let you design and create experiments where two or more ingredients or components are used make a product.


Number of Response Variables

Enter the number of response variables that will be used in the experiment.  Enter an integer from 1 to 16; the default is 1.


Number of Experimental Factors
Number of Experimental Factors (Components)

Enter the number of experimental factors that will be used in the experiment.  Enter an integer.  The list below provides the range of factors available for each specific design class:

Screening Designs  (2-16 factors)

Response Surface Designs  (2-8 factors)

Mixture Designs  (2-12 components)

Multilevel Factorial Designs  (2-8 factors)

Inner/Outer Arrays Designs  (See Control/Noise Factor)

Single Factor Categorical Designs  (1 factor)

Multi-Factor Categorical Designs  (2-8 factors)

Variance Components Designs  (2-8 factors)


Comment

Enter a description of the experiment, which will display on tables.


Skip Define
Skip Define Command – no longer used

This command allows you to create an experimental design with default factor names and lows and highs in coded units; that is, it allows you to skip the dialog boxes you useto define factors and variables.  When you use this command, the program displays the appropriate Design Selection dialog box.


Factor Definition Options Dialog Box

This dialog box allows you define the factors for an experiment.

Available Options for Screening Designs and Response Surface Designs; Continuous is available only for Screening Designs:

Factor

Name

Low

High

Units

Continuous

Back

Available Options for Multilevel Factorial Designs:

Factor

Name

Low

High

Number of Levels

Units

Back

Available Options for Single Factor Categorical Designs Multi-Factor Categorical Design, and Variance Components (Hierarchical) Designs:

Factor

Name

Number of Levels

Units

Back

Labels...


Factor

Determines which factor is active on the dialog box. For example, if you click option button A, your entries in the Name, Low, High, and Units text boxes define the first factor.  Any changes you make to its corresponding Name, Low, High, or Units text boxes redefine the factor.

If you are using the Inner/Outer Arrays Design, the program assigns the control factors first followed by the noise factors.


Name

Enter the name of the active factor.  This name identifies the factor on worksheets, tables and graphs for the experiment.  Enter an alphanumeric string of up to 32 characters, including an underscore; the entry must begin with a letter.


Low

Enter the lowest value that will be used for the active factor.  If the factor is continuous, enter a number less than the highest value.  If the factor is categorical, enter an alphanumeric string of up to 12 characters. The default is -1.0.


High

Enter the highest value that will be used for the active factor.  If the factor is continuous, enter a number greater than the lowest value.  If the factor is categorical, enter an alphanumeric string of up to 12 characters.  The default is 1.0.


Units

Enter a label that will be used for each factor unit.  The label identifies estimates of the effects on tables and graphs.  Enter an alphanumeric string of up to 10 characters.


Continuous

Defines a factor as either continuous (quantitative) or categorical (qualitative).  You can enter a combination of continuous and categorical factors in an experiment.

Entering categorical factors restricts your ability to add centerpoints to the design.  If there is one categorical factor in an experiment, you can add face-centered points in pairs; you cannot add other types of centerpoints.  If there are two or more categorical factors, you cannot add centerpoints.


Back
Back… Command

Redisplays the previous dialog box.


Response Definition Options Dialog Box

This dialog box allows you to choose names and units for the response variables.

Response

Name

Units

Back Command


Response

Determines which response variable is active on the dialog box. For example, if you click option button 1, your entries in the Name and Units text boxes define the first response variable.  Any changes you make to its corresponding Name and Units text boxes redefine the response variable.


Name

Enter the name of the active response variable that will be used to identify the variable on worksheets, tables, and graphs for the experiment.  Enter an alphanumeric string of up to 32 characters, including an underscore; the entry must begin with a letter.


Units

Enter a label that will be used for the active response variable to identify estimates of the response on tables and graphs for the experiment.  Enter an alphanumeric string of up to 10 characters, including an underscore; the entry must begin with a letter.


Screening Design Selection Dialog Box

This dialog box allows you to choose an available Screening design.  To display a list of available designs, click the Down Arrow button to the right of the selection list.

Name

Runs

Resolution

Error d. f.

Block Size

Display Blocked Designs

Back


Name

Displays the name of each design.


Runs

Displays the total number of runs (experimental trials) necessary to complete the base design.


Resolution

Displays the resolution of the design (III, IV, V, or V+).  Design resolution is the degree of confounding in two-level fractional screening designs (that is, the degree to which factors are confused so you cannot separate their effects).

Designs of resolution III do not confound main effects with each other, but do confound main effects with two-factor interactions.  Designs of resolution IV do not confound main effects and two-factor interactions, but do confound two-factor interactions with other two-factor interactions.  Designs of resolution V do not confound main effects and three-factor interactions with each other, but do confound two-factor interactions with higher-order interactions.  Designs with resolutions higher than resolution V (including full factorial designs) are shown as V+.

Resolutions for some blocked designs are marked with an asterisk (*) to indicate that the design has that resolution only if you ignore the interactions between block effects.


Error d.f.

Displays the degrees of freedom available for the error if you run the base experiments with no centerpoints, and if you estimate all the main effects, two-factor interactions, and quadratic effects.

Error degrees of freedom are necessary for testing the significance of factor effects using confidence intervals, ANOVA, and the Standardized Pareto Chart.  You can increase the error degrees of freedom by adding centerpoints or by replicating experimental runs.


Block Size

Displays the number of runs per block in the design.  If the design is not blocked, the number of runs and the block size are identical.


Display Blocked Designs

Indicates if blocked designs will display in the selection list.  Displaying Blocked Designs is the default.


Screening Design Options Dialog Box

This dialog box allows you to choose options for the design.

Base Design

Runs

Error d. f.

Centerpoints

Placement

Replicate Design

Randomize

Generators... Command

Back Command


Blocked Screening Design Options Dialog Box

This dialog box allows you to choose options for the blocked design you are using.

Base Design

Runs

Error d. f.

Centerpoints

Replicate

Randomize

Back Command


Centerpoints

Determines if centerpoints will be used and where they will be placed in the design.  If you add centerpoints, the runs and degrees of freedom are updated.

In the Number text box, enter the number of centerpoints that will be added to each block.  Enter a positive integer or 0; the default is 0.  If you are creating a Response Surface design, the default is 1.  For a Box-Behnken design, the number of factors in the design determines the default.


Base Design

Displays the name of the design.


Error d. f.

Displays the degrees of freedom available for the error.


Number (of Centerpoints)
Number

This text box allows you to enter the number of centerpoints you want to add to each block.  Use centerpoints to check for curvature, to add degrees of freedom, or to test for lack-of-fit.  Enter an integer greater than or equal to 0.

If there is one categorical factor in the experiment, you can enter only even integers.  If you have more than one categorical factor in the experiment, you cannot add centerpoints.


Random (Placement of Centerpoints)
Random

Randomizes the centerpoints with the design points in the block.  When you choose this option, you must also choose the Randomize check box.


Spaced (Placement of Centerpoints)
Spaced

Spaces the centerpoints evenly within the block.  When there are two or more centerpoints in each block, the first and last run in the block are always centerpoints.  Allow an equal number of runs between each pair of centerpoints in the design.


First (Placement of Centerpoints)
First

Places the centerpoints at the beginning of each block.


Last (Placement of Centerpoints)
Last

Places the centerpoints at the end of each block.


Number (of Replicates)
Number

Enter the number of times the design will be repeated.  The program updates the number of runs and the degrees of freedom available for error.  It places each replicate design in its own block.  Enter an integer.


Randomize

Indicates if the runs will be created in random order.


Design Generators Dialog Box
Generators… Command

Displays the Design Generators dialog box.


Create/Augment Design (Screening) Tabular Options Dialog Box
Create/Augment Design Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the design when you are using the Create and Augment features.  The available options depend on the design you are using.

Design Summary

Worksheet

Alias Structure

Correlation Matrix


Design Summary

The Design Summary option displays a summary of the design you choose.  The summary information includes the design class, design name, and file name.  Other information about the base design depends on the analysis you are creating.

For example, if you are creating a Screening, Multilevel Factor, Single-Factor Categorical, or Multi-Factor Categorical design, the information includes the number of experimental factors, blocks, responses, runs, error degrees of freedom, and indicates if the factors were randomized.  A table shows the lowest and highest values for each of the factors, and indicates if the factors are continuous or randomized.  The name of the response variable is shown.


Worksheet

The Worksheet option displays a Worksheet that contains the experimental runs that will be performed, as well as the order in which you should run them.

Print the Worksheet to record the information, then write or type in the values for the responses into the blank spaces provided.  Restore the DataSheet and enter the values into the appropriate column(s) of the DataSheet, then analyze the design.

Use the Worksheet Options dialog box to choose options for the Worksheet.


Alias Structure

The Alias Structure option displays the alias pattern for the design, which shows the main effects, interactions, and any confounding that involves them.  If the main effects and interactions are clear of confounding, an appropriate message displays.  Confounded effects are joined by a plus sign; for example, A + BC indicates that the main effect, A, is confounded with the two-factor interaction, BC.

Use the Alias Structure Options dialog box to enter a value for the highest-order interaction.


Correlation Matrix

The Correlation Matrix option shows the extent of confounding among the effects.  A perfectly orthogonal design will show a diagonal matrix with 1’s on the diagonal and 0’s off the diagonal.  Any non-zero terms off the diagonal imply that the estimates of the effects that correspond to that row and column will be correlated.


Create/Augment Screening Design Graphical Options Dialog Box
Create/Augment Design Graphical Options Dialog Box

This dialog box allows you to choose graphical options for a design when you are using the Create and Augment features.

Power Curve


Power Curve

The Power Curve option displays a plot that determines whether or not an experiment can detect effects of the magnitude you expect.

Use the Power Curve Options dialog box to change the number of degrees of freedom for the error and to enter a number for the alpha risk.


Worksheet Options Dialog Box

This dialog box allows you to choose options for the Worksheet.

Line Spacing

Start Row

End Row

Responses to Include


Single Spacing
Single Spacing – not used

This option allows you to use single spaced lines on the worksheet.


Double Spacing
Double Spacing – not used

This option allows you to use double spaced lines on the worksheet.


Triple Spacing
Triple Spacing – not used

This option allows you to use triple spaced lines on the worksheet.


Responses to Include

Click the check boxes for the variables that will display in the Worksheet.


Alias Structure Options Dialog Box

This dialog box allows you to choose the maximum order interaction, which is the highest-order interaction shown.  Enter any positive integer, up to the number of factors in the design.


Maximum Order Interaction

Enter a value for the highest-order interaction; this will be the highest-order interactions shown.  Enter any positive integer, up to the number of factors in the design.


Correlation Matrix Options Dialog Box

This dialog box allows you to enter a value for the highest-order effects that will be estimated.  Enter a positive integer, up to the number of factors in the design; the default is 2.

Because hardware and software configurations differ, you may not have enough memory to estimate higher-order models.  If that is the case, you can enter the number of effects then use the Exclude Effects Options dialog box to selective remove individual terms from the model.


Maximum Order Effect

Enter a value for the highest-order effects that will be estimated.  Enter a positive integer, up to the number of factors in the design; the default is 2.

Because hardware and software configurations differ, you may not have enough memory to estimate higher-order models.  If that is the case, you can enter the number of effects then use the Exclude Effects Options dialog box to selectively remove individual terms from the model.


Power Curve Options Dialog Box

This dialog box allows you to enter values for the error degrees of freedom and alpha risk.

Error Degrees of Freedom

Alpha


Error Degrees of Freedom

Enter a value for the number of degrees of freedom for the error.  Increasing the degrees of freedom increases the statistical probability of detecting significant factor effects.

You can increase degrees of freedom by adding additional experimental runs.  The default is the number of degrees of freedom in the current design.


Alpha

Enter a value for the alpha risk for the power curve.  The alpha risk (the probability of a Type I error) determines the probability of declaring an effect significant when, in fact, it is not.  Enter a number greater than 0 and less than 100; typical values are 1, 5, or 10 percent.


Design Summary
Design Summary – use generic

The Design Summary displays a summary of the design you choose, including the design class, type, and name.  Notice that because you have not yet saved the design, the file name is shown as <<Untitled>>.  Other information includes the number of experimental factors, blocks, response variables, centerpoints per block, runs, and the error degrees of freedom.  Tables at the bottom of the summary display information about the factors and responses.


Worksheet

The Worksheet option displays a Worksheet that contains the experimental runs that will be performed, as well as the order in which you should run them.

Print the Worksheet to record the information, then record the values for the responses in the blank spaces provided.  Restore the DataSheet and enter the values into the appropriate columns of the DataSheet, then analyze the design.

Use the Worksheet Options dialog box to choose options for it.


Alias Structure

The Alias Structure option displays the alias pattern for the design, which shows the main effects, interactions, and any confounding that involves them.  If the main effects and interactions are clear of confounding, an appropriate message displays.  Confounded effects are joined by a plus sign; for example, A + BC indicates that the main effect, A, is confounded with the two-factor interaction, BC.

Use the Alias Structure Options dialog box to enter a value for the highest-order interaction.


Correlation Matrix

The Correlation Matrix option shows the extent of confounding among the effects.  A perfectly orthogonal design will show a diagonal matrix with 1’s on the diagonal and 0’s off the diagonal.  Any non-zero terms off the diagonal imply that the estimates of the effects that correspond to that row and column will be correlated.

Use the Correlation Matrix Options dialog box to enter a value for the highest-order effects that will be displayed.


Power Curve

The Power Curve option displays a plot that determines whether or not an experiment can detect effects of the magnitude you expect.

Use the Power Curve Options dialog box to choose options for the plot.


Response Surface Design Selection Dialog Box

This dialog box allows you to choose the Response Surface design that will be created.

Name

Runs

Error d. f.

Largest Block

Display Blocked Designs

Back Command


Largest Block

Displays the number of runs in the largest block in the design.  If you do not block the design, the number of runs and the block size are identical.


Three-Level Design Options Dialog Box

This dialog box allows you to choose options for a three-level design.

Base Design

Runs

Error d. f.

Centerpoints

Placement

Replicate Design

Randomize

Generators... Command

Back Command


Composite Design Options Dialog Box

This dialog box allows you to choose options for the design.

Base Design

Runs

Error d. f.

Design Characteristics

Centerpoints

Placement

Replicate Design

Axial Distance

Randomize

Generators... Command

Back Command


Rotatable Design

Creates a rotatable design that is used to determine the axial distance.  In a rotatable design, the variance of the predicted response is constant on a hyperspherical surface center at the design origin.


Orthogonal Design

Creates an orthogonal design that is used to determine the axial distance.  An orthogonal design is one in which the estimates of all the terms in the second-order model are uncorrelated.


Rotatable and Orthogonal

Creates a design that is both rotatable and orthogonal that is used to determine the axial distance.


Face Centered

Creates a face-centered design that determines axial distance.  The program sets the axial distance to 1, which places the star points (rather than the centerpoints) in the center of the faces of the factorial cube.

The resulting experimental design has only three levels rather than five.  In this case, the Low and High levels for each factor you set on the Factor Definition Options dialog box describes the boundaries of the design space.


Axial Distance

Displays the distance from the center of the design to each of the star points.  You change the axial distance in an orthogonal design by using a different number of centerpoints.


Blocked Composite Design Options Dialog Box

This dialog box allows you to choose options for the design.

Base Design

Runs

Error d. f.

Design Characteristics

Centerpoints

Placement

Replicate Design

Randomize

Axial Distance

Axial Distance for Rotatability

Generators... Command

Back Command


Design Characteristic
Design Characteristics

Displays the design as orthogonal blocks.


Axial Distance for Rotatability

Displays the axial distance necessary for the design to be rotatable.


Create/Augment Design (Response Surface) Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the design when you are using the Create and Augment features.

Design Summary

Worksheet

Correlation Matrix


Component Definition Options Dialog Box

This dialog box allows you define the components for an experiment.

Component

Name

Low

High

Mixture Total

Units

Back Command


Component

Determines which component is active on the dialog box. For example, if you click option button A, your entries in the Name, Low, High, and Units text boxes define the first component.  Any changes you make to its corresponding Name, Low, High, or Units text boxes redefine the component.


Name

Enter the name of the active component.  This name identifies the component on worksheets, tabular output, and analyses for the experiment.  Enter an alphanumeric string of up to 10 characters, including an underscore; the entry must begin with a letter.


Low

Enter a value for the lowest constraint you want to use for the active component.  Enter a number less than the value you enter into the High text box.


High

Enter a value for the highest constraint you want to use for the active component.  Enter a number greater than the value you enter into the Low text box.


Units

[Optional]  Enter a label that will be used for each component unit.  The label identifies estimates of the effects on tables and graphs.  Enter an alphanumeric string of up to 10 characters.


Mixture Total

Enter the sum of the components or blend total for each experimental run.  The default is 1.


Mixture Design Selection Dialog Box

This dialog box allows you to choose an available Mixture design.  To display a list of available designs, click the Down Arrow button to the right of the selection list.

Name

Linear, Quadratic, Special Cubic, Cubic

Back Command


Name

Displays the name of each design.


Linear, Quadratic, Special Cubic, Cubic

Displays the number of runs for each type of model.  The Cubic model is not available for a Simplex-Centroid design.


Mixture Design Options Dialog Box

This dialog box allows you to choose options for the design.

Base Design

Runs

Model Type

Number of Replicate Points

Augment Design

Randomize

Back Command


Linear Model Type
Linear

This option creates experimental runs for a Linear model.


Quadratic Model Type
Quadratic

This option creates experimental runs for a Quadratic model.  A Quadratic model is a linear model that includes binary blends; for example, AB, AC, and BC.


Special Cubic Model Type
Special Cubic

This option creates experimental runs for a Special Cubic model.  A Special Cubic model is a Quadratic model that includes tertiary blends; for example, ABC.


Cubic Model Type
Cubic

This option creates experimental runs for a Cubic model.  A Cubic model is a Special Cubic model with additional blends; for example, AB(A - B).  This model is not available with a Simplex-Centroid design.


Number of Replicate Points

Enter the number of experimental blends that will be replicated.  The replicate runs are used to perform a lack-of-fit test during the analysis.  It adds full blends first, binary blends second, and so on.   Enter an integer greater than 0; the default is 0.  The Runs area is updated based on the number you enter into this text box.


Augment Design

Indicates if you want to add additional blends to the design.  If you choose a Simplex-Centroid design, axial check blends are added.  If you choose a Simplex-Lattice design, the overall centroid and axial check blends are added.


Create/Augment Design (Mixture) Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the design when you are using the Create and Augment features.

Design Summary

Worksheet


Design Summary

The Design Summary for Mixture Designs displays a summary of the design you choose, including the design class, type, and name.  Notice that because you have not yet saved the design, the file name is shown as <<Untitled>>.  Other information includes the number of components, response variables, runs, and the mixture total.  Tables at the bottom of the summary display information about the components and responses.


Design Summary

The Design Summary displays a summary of the design you choose, including the design class, type, and name.  Notice that because you have not yet saved the design, the file name is shown as <<Untitled>>.  Other information includes the number of components, blocks, response variables, centerpoints per block, runs, and the error degrees of freedom.  Tables at the bottom of the summary display information about the factors and responses.


Open Experimental Files Dialog Box
Open Experiment Files Dialog Box

This dialog box allows you to choose the experiment file you want to open.

Look In

Allows you, if necessary, to choose the drive and folder in which the file you want to open resides.

File Name

Choose or enter the name of the file you want to open.

Files of Type

Choose or enter the name of the type of file you want to open.

Important Note: If you previously used a DOS version of STATGRAPHICS Plus, before you can use the designs and experiments you created in that application, you must rename the files.  Rename the files, using the file extension .sfx, then bring them into the Windows version.


Save Design File As Dialog Box

This dialog box allows you to choose or enter a name for the current experimental design file you want to save.

Save In

Allows you, if necessary, to choose a drive and folder in which you want to save the design file on your hard disk.

File Name

Choose or enter the name of the file you want to save.

Save as Type

Choose or enter the name of the type of file you want to save.


Analyze Design - Data Input Dialog Box
Analyze Design Dialog Box

This dialog box allows you to choose the name of the variable that contains the response data you want to analyze.  Only response variables are appropriate to use, not factor names or blocking variables.

You can also transform the data in any of the variables.

Data

Select

Sort


Data

Enter the name of the variable that contains the response data you want to analyze.  You can only choose response variables; the list of variables does not contain factor names or blocking variables.


Analyze Design Tabular Options Dialog Box
Analyze Design Tabular Options Dialog Box – use generic see CSV$ file

This dialog box allows you to choose tabular options for the design.

Analysis Summary

ANOVA Table

Regression Coefficients

Correlation Matrix

Predictions

Path of Steepest Ascent

Optimization


Analysis Summary

The Analysis Summary option displays each of the estimated effects and interactions as well as the standard error for each of the effects, which measures their sampling error.


ANOVA Table

The ANOVA Table option shows the results of partitioning the variability in the selected variable into separate items for each of the effects.  The program then tests the statistical significance of each effect by comparing the mean square with an estimate of the experimental error.

The ANOVA Table includes, for each main effect and interaction, the sum of squares, the degrees of freedom (df), the mean square, an F-ratio calculated by using the residual mean square (or the error term you specify), and the p-value for the F-ratio.  It also includes the R-Squared and Adjusted R-Squared statistics, the standard error for the estimate, the mean absolute error, and the Durbin-Watson statistic, which measures the correlation among the residuals.


Regression Coefficients

The Regression Coefficients option displays the regression equation, which was fit to the data.

The program uses the regression model to plot the responses in Response plots.  A regression model cannot be estimated if there are confounded effects.


Predictions

The Predictions option displays a table that contains information about the values that the variable generated using the fitted model.

The table includes the observed value, if any; the predicted value of the variable using the fitted model, and the confidence limits for the mean response.

Each item corresponds to the values of the experimental factors in a specific row in the data file.

To create forecasts for additional combinations of the factors, add additional rows to the bottom of the data file.  In each new row, enter values for the experimental factors, but leave the cell for the response empty.  When you return to the Predictions pane, the forecasts are added to the table for the new row(s), but the model remains unaffected.


Path of Steepest Ascent

The Path of Steepest Ascent option displays the path of steepest ascent (or descent).  This is the path from the center of the current experimental region along which the estimated response changes most quickly for the smallest change in the experimental factors.  The path indicates good locations to run additional experiments if your goal is to increase or decrease the variable you are using.

The program can also determine the amount all the other factors have to change to stay on the path of steepest ascent.  It also can compute the estimated variable at each of the points along the path.


Influential Points
Influential Points – No longer used with DOE

The Influential Points tabular option displays the number of observations that are flagged for large residual, leverage, or DFITS values.  The leverage and DFITS statistics estimate the influence of an individual observation on the fitted model.  In addition, the program reports the Mahalanobis distance, which also helps you identify unusual values.  You can reduce the influence by adding additional runs to the experiment or by adding replicate runs of the influential point.


Analyze Screening Design - Graphical Options Dialog Box
Screening Designs Graphical Options Dialog Box

This dialog box allows you to choose graphical options when you analyzing Screen.


Pareto Charts

The Pareto Charts option shows each of the estimated effects in decreasing order of magnitude.  The length of each bar is proportional to the standardized effect.  The standardized effect is the estimated effect divided by its standard error, which is equivalent to computing a t-statistic for each effect.

The vertical line on the plot judges the effects that are statistically significant.  Bars that extend beyond the line correspond to effects that are statistically significant at the 95 percent confidence level.


Main Effects Plots

The Main Effects Plots option shows the estimated variable as a function of each experimental factor.  In each plot the factor of interest varies from its lowest level to its highest level, while all the other factors remain constant at their central values.


Interaction Plots

The Interaction Plots option shows the estimated variable as a function of pairs of factors.  In each plot one factor varies from its lowest level to its highest level.

On one line, the second factor is held at its lowest level, while on the other line, the second factor is held at its highest level.  All other factors, except the two involved in the interaction, are held constant at their central values.


Normal Probability Plots of Effects

The Normal Probability Plots of Effects option displays a plot that distinguishes real effects from those that are simply noise.  One point appears on the plot for each effect in the model.

The plot is particularly useful when there are few or no degrees of freedom available to estimate the experimental factor. Its basic premise is effects that are not real and simply manifestations of noise behave as though they come from a normal distribution centered at zero.  The plot is scaled so these effects fall off the line.


Response Plots

The Response Plots option displays one of two Response plots, which show the contours for the chosen variable as a function of the selected factors.  Each contour line represents combinations of the factors that give a value for the variable.  The other factors are held constant.

Using the two Response Plots options together creates a plot you can use to compare two different response plots of the same data.


Diagnostic Plots

The Diagnostic Plots option displays the residuals versus the predicted values for the chosen variable.  Any nonrandom pattern could be an indication that the model you chose does not adequately describe the observed data.

The plot is particularly useful in showing heteroscedasticity; the variability of the residuals changes as the values of the dependent variable change.


Estimate Effects Options Dialog Box

This dialog box determines how the effects will be estimated.

Maximum Order Effect

Ignore Block Numbers

Estimate Sigma From

Display

Confounding Pattern

Exclude... Command


Ignore Block Numbers

Indicates if blocking variables should be excluded from the estimations.  The default is not excluding them.  If you replicate the base design and run the replicates with the base experiments (in the same block), you can exclude the blocking variable.


Estimate Sigma From Experimental Data
Experimental Data

Uses all the degrees of freedom that remain after the program estimates the standard errors for the effects.


Estimate Sigma From External Data
External Data

Allows you to choose the standard errors for the effects.  The program uses this value to test for significance of effects in results such as an ANOVA table and a standardized Pareto Chart.  Enter a number greater than 0.


Display Standard Errors
Standard Errors

Displays standard errors for the estimated effects.  The program bases standard errors on the total error with the associated degrees of freedom.


Display Confidence Intervals
Confidence Intervals

Displays confidence intervals for the estimated effects.  Use the text box to enter a number for the confidence level.  Enter a number between 1 and 100; common values are 90, 95, or 99 percent.


Confounding Pattern from Original Design
From Original Design

Uses the original base design to determine the confounding pattern.


Confounding Pattern from Data
From Data

Looks at all the current experimental runs to determine the confounding pattern.


Exclude Effects Options Dialog Box

This dialog box allows you to exclude effects.  After you choose Maximum Order Effect on the Estimate Effects Options dialog box and click Exclude, this dialog box displays with the interactions shown in the Include column.

To exclude factors, double-click those that are to be excluded to move them into the Exclude column.  When you click OK on both dialog boxes, the factors are excluded from the analysis.


Analysis of Variance Options Dialog Box

This dialog box determines if a lack-of-fit statistical test will be performed to test the adequacy of the model.  If the test is performed, the results display at the bottom of the ANOVA table.

If a model has significant lack of fit, as indicated by a p-value less than .05, you should not use it to predict the response.  The default is excluding the test.


Prediction Options Dialog Box
Predictions Options Dialog Box

This dialog box determines the statistics that will be displayed in the Predictions report.

Include

Predict

Confidence Level


Observed Y

Displays the observed values for the response variable.


Fitted Y

Includes the estimated values for the response variable.


Residuals

Includes the difference between the observed and the fitted response values.


Studentized Residuals

Includes residuals that are scaled by estimates of the variance with observations removed from the data.  A large studentized residual may indicate an influential observation.


Standard Errors for Forecasts

Includes the standard deviation for the distribution of the estimated values.


Confidence Limits for Individual Forecasts

Includes end points for the prediction interval of the individual estimated values.


Confidence Limits for Forecast Means

Includes end points for the confidence interval of the means for each estimated value.


Predict Experimental Runs
Experimental Runs

Displays predictions for all the experimental runs in the DataSheet.


Predict Added Runs Only
Added Runs Only

Displays predictions for experimental runs in the DataSheet that do not contain response values.


Confidence Level

Enter a value that will be used to calculate the confidence intervals.  Enter a number between 1 and 100; the default is 95 percent.  Other common values are 90 or 99 percent.


Path of Steepest Ascent Options Dialog Box

This dialog box allows you to choose the factor that will be stepped, the number by which the factor will be incremented, the number of steps that will be taken, and the resolution.

Factor to Step

Step By

Number of Steps

Resolution


Factor to Step

Determines the factors that will be stepped.


Step by

Enter a number that will be used to increment the factor you selected.  The factor is incremented by this value, and used to calculate the levels for the other factors in the model along the gradient at this point.  Enter a positive or negative number; the default is 1.


Number of Steps

Enter the number of steps that will be taken on the path of steepest ascent or descent.  Enter any positive integer; the default is 5.


Resolution

Enter the number of density values that will be calculated.  Enter a number between 1 and 100.


Pareto Chart Options Dialog Box

This dialog box determines if a standardized Pareto Chart will display and also allows you to choose the value that will be used to calculate the location of the vertical line.

Standardize

Alpha


Standardize

Indicates if a standardized Pareto Chart will display.  A standardized chart is similar to the regular Pareto Chart except that it shows each effect divided by its standard error.

The chart includes a vertical line you use to test the significance of the effects.  An effect that goes beyond the critical line is significant.  Displaying a standardized Pareto Chart is the default.


Alpha

Enter a percentage that will be used to calculate the location of the vertical line on the chart.  Enter a number between 0 and 100; the default is 5.  Other common values are 1, 5, or 10 percent.

This text box is active only when you choose a standardized Pareto Chart.


Main Effects Plot Options Dialog Box

This dialog box determines the factors that will appear on the plot.  For example, if Factors A, B, and C are listed on the dialog box and you choose Factors A and B, those are the factors that will be on the plot.


Factors

Displays the Response Plot Factors dialog box, which lets you choose the factors that will appear on the plot.


All
All… Command

Allows you to choose all the factors at one time.


Interaction Plot Options Dialog Box

This dialog box is used to choose the effects that will be included on the Interaction Plot.  The plot shows the difference in the responses due to the combination of two factors.  The All… command allows you to choose all the factors at one time.

Factors

Reverse Factors


Reverse Factors

Reverses the placement of the factors on the plot.


Effects Normal Probability Plot Options Dialog Box

This dialog box allows you to choose the type of Normal Probability Plot that will be created, to choose the direction of the plot, and to indicate if the plot will display the fitted line and labels for the effects.

Plot Type

Direction

Fitted Line


Normal Plot

This option allows you to display a Normal Plot.


Half-Normal
Half-Normal Plot

This option allows you to display a Half-Normal Plot, which identifies estimated effects that are large relative to noise.  Large effects appear on the right side of the plot.  This plot is useful for fractional factorial designs.  It is also known as a Daniel Plot.


Label Effects

Indicates if labels will be displayed for the effects on the plot.


Response Plot Options Dialog Box

This dialog box allows you to choose the type of Response Plot that will be displayed.

Type

Contours

Resolution

Surface

Contours Below

Show Points

Wire Frame

Solid

Contoured

Factors


Surface Plot

Displays a Surface Plot, which is a three-dimensional model of the relationship among the response variable and two or more factors.


Contour Plot

Displays a Contour Plot, which is a two-dimensional plot that traces the contours of responses for two factors.  You can predict the next value for the response within the experimental design by following the ridge of the contour.


Square Plot

Displays a Square plot of the estimated effects for two factors.  The program plots the values of the response variable for all combinations of the high and low values for each factor you choose.

Use the Factors... command to choose the factors and to specify the high and low values.


Cube Plot

Displays a Cube Plot of the estimated effects for three factors.  The program plots the values for the response variable for all combinations of the high and low values for each factor you choose.

Use the Factors... command to choose the factors and to specify the high and low values.


From

Enter a value for the first contour line.  Enter a number less than the To value.


To

Enter a value for the last contour line.  Enter a number greater than the From values.


By

Enter a value for the spaces between the contour lines.  The contour levels are calculated using this value plus the values in the From and To text boxes.


Lines

Displays the plot with lines that connect the points along each contour; it is the default.


Painted Regions

Displays the plot with the regions of the contours painted (filled in).


Horizontal Division

Enter the number of horizontal lines that will be plotted on the Surface Plot.  Enter a number from 5 to 100; the default is 10.


Vertical Division

Enter the number of vertical lines that will be plotted on the Surface Plot.  Enter a number from 5 to 100; the default is 10.


Contours Below

Determines if a Contour Plot will be displayed below the Surface Plot.


Show Points

Determines if response values will be displayed on the plot.  This option is available only if you choose the Wire Frame option for a Surface Plot.


Wire Frame

Displays horizontal and vertical lines on the plot; it is the default.


Solid Surface Plot
Solid

Displays a solid surface on the plot.


Contoured

Displays a topographical representation, with colors that correspond with the height of the surfaces.


Response Plot Factors Dialog Box

This dialog box allows you to choose the factors that will appear on the Response Plot.

Factors

Low

High

Hold


Factors

[Optional]  Indicates the factors that will be plotted on the Square, Cube, Contour, and Surface plots.  The Square, Contour, and Surface plots require two factors; the Cube plot requires three.  You can also enter values in the Hold text boxes for the factors you do not choose.


Low (Factor Value)
Low

Enter a value for the lowest level for the factor you want to use on the Response Plot.  Enter a number less than the value you enter into the High text box.


High (Factor Value)
High

Enter a value for the highest level for the factor you want to use on the Response Plot.  Enter a number greater than the value you enter into the Low text box.


Hold (Factor Value)
Hold

Enter a value at which the factors that are not chosen for the plot will be held.


Diagnostic Plot Options Dialog Box

This dialog box allows you to choose the type of diagnostic plot that will be created.  You can also enter the name of the factor that will be used on the Residuals vs. Factor Plot and determine the direction of the plot, if a fitted line will appear, and enter a value for alpha.

Plot

Plot versus:

Direction

Fitted Line

Alpha


Observed versus Predicted

The Observed versus Predicted option creates a plot of the observed values versus the predicted values. The plot includes a line with a slope equal to 1.  The closer the points lie to the diagonal line, the better the model (at predicting the observed data).

Look for various anomalies, such as increases in variability around the line, as the value of the variable increases.  This is known as heteroscedasticity.  Also look for individual points that lie far away from the line, which are known as outliers.

You can use the plot to detect cases in which the variance is not constant, which indicates you may need to transform the response variable.


Residuals versus Predicted

The Residuals versus Predicted option creates a plot of the residuals versus the predicted values.  A nonrandom pattern could indicate that the selected model does not adequately describe the response data.

The plot is especially helpful in detecting heteroscedasticity, in which the variability of the residuals changes as the values for the response variable change.  If the model is correct and if all the assumptions are satisfied, the residuals should be structureless.


Residuals versus Run Order

The Residuals versus Run Order option creates a plot of the residuals in the order that the observations appear in the response variable.

The plot helps you identify sequential correlations among the residuals.  In a plot of residuals versus run order, any pattern over time may indicate a time effect.


Residuals versus Factor

The Residuals versus Factor option creates a plot of the residuals versus a factor you choose.

In a plot of residuals versus specific factors, curvature with respect to the reference line may indicate the need for a transformation or a curvilinear model.

When you create this plot, use the Plot versus: option to choose the factors that will be plotted.


Normal Probability Plot of Residuals

The Normal Probability Plot of Residuals option creates a plot with the residuals on the X-axis, plotted from smallest to largest.  The Y-axis is a normal probability scale (it "straightens" the plot of a cumulative normal distribution).

In a Normal Probability Plot, if the residuals do not fall approximately along a straight line, they are not from a normal distribution.  This indicates that a basic assumption for the model may have been violated.


Power Curve

The Power Curve option creates a plot that determines whether or not an experiment can detect effects of the magnitude you expect.

Use the Power Curve Options dialog box to choose options for the plot.


Plot Versus Factor
Plot versus:

Choose the factor or component that will be used on the Residuals versus Factor Plot or Residuals versus Component Plot.


Screening Design Analysis Summary
Analysis Summary

The Analysis Summary displays the estimated effects for the response variable.  It displays the confounding pattern if the effects are confounded (the effects of the factors are combined or confused so it is difficult to determine which effects are attributed to which factors).  When an estimate of the error is available, the program displays the standard error for each effect.


ANOVA Table

The ANOVA Table tabular option displays a standard analysis of variance (ANOVA) table.  For each main effect and interaction, the table includes the sum of squares, the degrees of freedom (df), the mean square, an F-ratio calculated by using the residual mean square (or the error term you specify), and the p-value for the F-ratio.  The table also includes the R-squared and adjusted R-squared statistics, the standard error for the estimate, the mean absolute error, and the Durbin-Watson statistic, which measures the correlation among the residuals.


Regression Coefficients

The Regression Coefficients tabular option displays estimates of the coefficients for a regression model fitted to the data in their original units.  The program uses the regression model to plot the responses in the Response plots.  The program cannot estimate a regression model if there are confounded effects.


Correlation Matrix

The Correlation Matrix option displays a correlation matrix for all the effects, based on the actual design matrix.

Use the Correlation Matrix Options dialog box to enter a value for the highest-order effects that will be displayed.


Predictions

The Predictions tabular option displays the predictions for the response variable.  The results show the response variable's observed and predicted (fitted) values for each run.  The results also display the confidence intervals.  You can also generate predictions by adding additional runs to the spreadsheet.


Path of Steepest Ascent

The Path of Steepest Ascent tabular option displays factor levels and response predictions that follow the direction of steepest ascent or descent for an estimated response function.  The information is useful for determining the design origin when you search for optimal conditions.  The program allows you to "walk" along the path of steepest ascent or descent for the estimated response surface.  Because this gradient is a continuous function of the terms in the model, the effects in the model must be continuous; that is, you must remove all the categorical factors, and all the interactions that involve categorical factors, before you choose the Path of Steepest Ascent option.


Influential Points

The Influential Points tabular option displays the number of observations that were flagged for large residual, leverage, or DFITS values.  The leverage and DFITS statistics estimate the influence of an individual observation on the fitted model.  In addition, the program reports the Mahalanobis distance, which also helps you identify unusual values.  You can reduce the influence by adding additional runs to the experiment or by adding replicate runs of the influential point.


Pareto Charts

The Pareto Charts graphical option displays a frequency histogram where the length of each bar on the chart is proportional to the absolute value of its associated estimated effect or the standardized effect.  The program displays the bars in the order of the size of the effects, with the largest effects on top, which lets you visually identify the most important effects.


Main Effects Plots

The Main Effects Plots graphical option displays a plot of the primary factors in the experiment.  The plot shows one or more of the main effects with a line drawn between the low and high levels of the corresponding factors.


Interaction Plots

The Interaction Plots graphical option displays a plot of the differences in the response due to the combination of two factors.


Normal Probability Plots of Effects

The Normal Probability Plots of Effects graphical option displays a plot of the cumulative distribution of the effects.  A Normal Probability Plot can help you distinguish effects from noise, especially when the design is unreplicated.  In this type of plot, effects that correspond to noise should behave as a random sample from a normal distribution; that is, they fall approximately along a straight line.  Effects that correspond to real signals fall further from the line.  A line on the plot helps you identify the points that correspond to noise and those that correspond to real signals.


Response Plots

The second Response Plots graphical option displays a plot of the effects for two of the factors on the response.  The plots are helpful in determining the influence of factors on the response variable and in locating optimal regions. You can choose one of four types of plots: Surface, Contour, Square, or Cube.  If you click the check boxes for both Response Plots, you can compare two different response plots for the same data; for example, you can create both a Surface Plot and a Contour Plot.


Diagnostic Plots

The Diagnostic Plots graphical option displays a Residuals versus Predicted plot for the response variable.  The plot is one of five diagnostic plots you can choose on the Diagnostic Plot Options dialog box.  These plots help you determine whether the model, as estimated, adequately fits the data.


Response Surface Design Analysis Summary
Analysis Summary

The Analysis Summary displays the estimated effects for the response variable.  It shows the confounding pattern if the effects are confounded (the effects of the factors are combined or confused so it is difficult to determine which effects are attributed to which factors).  When an estimate of the error is available, the program displays the standard error for each effect.


Response Surface Design Analysis Summary
Analysis Summary

The Analysis Summary displays the estimated effects for the response variable.  It shows the confounding pattern if the effects are confounded (the effects of the factors are combined or confused so it is difficult to determine which effects are attributed to which factors).  When an estimate of the error is available, the program displays the standard error for each effect.


Augment Design Dialog Box

This dialog box allows you to choose the method that will be used to augment the design. The available actions depend on the type of design you are using.

Replicate Design

Add a Fraction

Collapse Design

Clear Main Effects

Clear a Factor

Add Star Points


Replicate Design

Replicates an entire design, including the centerpoints and block structure.  When you replicate a design, each replicate is placed in its own block.

Use the Replicate Design Options dialog box to enter a value for the number of times the design will be repeated.  Enter a positive integer or 0; the default is 0.


Foldover Design

This option allows you to remove confounding of main effects from second-order interactions in a resolution III design.  The program adds new runs to the design in a way that clears the main effects from confounding and produces a resolution IV design.  You can also foldover a resolution IV design, which produces a resolution V design.  If the design can be augmented to add a new factor, the program displays the Foldover Design dialog box when you click the OK button.


Collapse Design

Removes a single factor from a factorial design.  The design that results is less fractioned, and may be a replicate of the original design.


Clear Main Effects

Removes confounding of all main effects from second-order interactions in a resolution III design.  The difference between this method and a Foldover Design is that this action always produces a resolution IV design.

This method does not allow you to add a new factor.  If the original design was unblocked, the additional runs are added in a new block.  If the original design was a blocked design, the additional runs follow the same block structure.


Clear a Factor

Clears all confounding from a factor that has other effects; that is, all the interactions that include that factor.  When you clear a factor, the main effect and its iterations appear without confounding.  The program adds runs that contain reversed factor levels (for the factor you choose), and unchanged factor levels for all the other factors, which doubles the number of runs in the design.


Add Star Points

Adds star points to a Screening design to create a Central Composite design.  The program calculates the axial distance, based on the number of star points and the number of base points in the base design, and creates a design that is orthogonally blocked.


Replicate Design Dialog Box

This dialog box allows you to enter the number of times the program should replicate the design.  Enter a positive integer in the Number of Replicates text box.


Foldover Design Dialog Box

This dialog box allows you to choose a new factor to add to the design.

New Factor Name

Old Level

New Level

Units

Continuous


New Factor Name

This text box allows you to enter the name of the new factor you want to add to the design.  Enter a valid variable name.


Old Level

This text box allows you to enter the value for the level of the new factor you want to associate with the runs in the original design.  If the factor is continuous, enter any number.  If the factor is categorical, enter an alphanumeric string of up to 10 characters.


New Level

This text box allows you to enter the value for the level of the new factor you want to associate with the added runs in the new design.  Your entry in this text box must not equal your entry in the Old Level text box.  If the factor is continuous, enter any number.  If the factor is categorical, enter an alphanumeric string of up to 10 characters.


Collapse Design Dialog Box

This dialog box allows you to remove a single factor from a factorial design.  The design that results is less fractioned and may be a replicate of the original design.

To remove a factor, click the option button that corresponds to the factor that will be removed.


Clear a Factor Dialog Box

This dialog box allows you to clear a factor from an original design.

To clear a factor, click the option button that corresponds to the factor that will be cleared.


Analyze Design (Mixture) Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the design.

Analysis Summary

ANOVA Table

Model Results

Correlation Matrix

Predictions

Optimization


Analysis Summary

The Analysis Summary option displays a table of results for fitting different models to the data.

The mean model consists of only a constant; the linear model of first-order items for each of the components; the quadratic model adds cross-products between pairs of components; the special cubic model adds terms involving products of three components.

Each model is shown with a P-value that tests to determine if the model is statistically significant when compared with the mean square for the term.  Normally, you would choose the most complicated model that has a P-value less than 0.05, assuming you are using a 95 percent confidence level.

The table in the lower portion of the pane shows the standard error of the estimate and the R-Squared statistics tabulated for each of the models.  There are some analysts who prefer to choose a model that maximizes the Adjusted R-Squared statistic.


ANOVA Table

The ANOVA Table option displays an analysis of variance for the model you select.  The table tests the overall significance of the model and includes R-Squared and Adjusted R-Squared statistics, the standard error for the estimate, the mean absolute error, and the Durbin-Watson statistic that measures the correlation among the residuals.


Model Results

The Model Results option displays the equation for the fitted model.  The values for the components are specified in pseudo-components.

Additional values are shown at the bottom of the table to help determine the utility of the model: R-Squared, Adjusted R-Squared, standard error of the estimate, the mean absolute error, and the Durbin-Watson statistic.


Correlation Matrix

The Correlation Matrix option shows the extent of confounding among the effects.  A perfectly orthogonal design will show a diagonal matrix with 1’s on the diagonal and 0’s off the diagonal.  Any non-zero terms off the diagonal imply that the estimates of the effects that correspond to that row and column will be correlated.


Analyze Design (Mixture) Graphical Options Dialog Box

This dialog box allows you to choose graphical options for Mixture designs.

Response Plots

Trace Plot

Diagnostic Plots


Response Plots

The Response Plots option displays one of two Response plots, which show the contours for the chosen variable as a function of the selected factors.  Each contour line represents combinations of the factors that give a value for the variable.  The other factors are held constant.

Using the two Response Plots options together creates a plot you can use to compare two different response plots of the same data.

Type

Contours

Surface

Resolution

Components... Command


Trace Plot

The Trace Plot option creates a plot of the effect that takes place on the chosen variable if each component is increased or decreased from the chosen reference blend.  As the component changes, all the other components adjust proportionally.

You can determine the distance of the current reference blend from the global maximum or minimum reference blend.


Estimate Model Options Dialog Box

This dialog box allows you to choose and analyze a model that is different from the model you chose when you created the design.

Model to Fit

Exclude... Command


Linear

Fits a Linear model.


Quadratic

Fits a Quadratic model.  A Quadratic model is a Linear model that includes binary blends; for example, AB, AC, and BC.


Special Cubic

Fits a Special Cubic model.  A Special Cubic model is a Quadratic model that includes tertiary blends; for example, ABC.


Cubic

Fits a Cubic model.  A Cubic model is a Special Cubic model with additional blends; for example, AB(A - B).


Mixture Response Plot Options Dialog Box
Response Plot Options Dialog Box

This dialog box allows you to choose the Response Plot that will be created: Surface or Contour.  You can also choose attributes for the plot.

Type

Contours

Surface

Resolution

Factors... Command


Surface Plot
Surface

This option displays a Surface Plot, which is a three-dimensional model of the relationship between the response variable and three components.  If you choose this type of plot, you can also choose options such as a Solid or Wire Frame suface.


Contour Plot
Contour

This option displays a Contour Plot, which is a two-dimensional plot that traces the contours of responses for three components.  You can predict the next value for the response within the experimental design by following the ridge of the contour.  If you choose this type of plot, you can also choose options such as the number of contours.


Component Options Dialog Box
Response Plot Components Dialog Box

This dialog box allows you to choose the components that will be plotted on the Response Plot.  To access the dialog box, click the Components… command button.

Components

Low

High

Hold


Components

[Optional]  Determines the components that will be plotted on the Contour and Surface plots.  You can also enter values in the Hold text boxes for the components you do not choose.  You must choose three components.


Low (Component Value)
Low

Displays the lower constraints for the components.


High (Component Value)
High

Displays the higher constraints for the components.


Hold (Component Value)
Hold

Enter the value at which the components that are not chosen for the plot will be held.


Trace Plot Options Dialog Box

This dialog box allows you to display the names of the components and the low and high constraints.  You can also choose the Reference Blend for the mixture in the design.

Name

Low

High

Reference Blend


Diagnostic Plot Options Dialog Box Mixture
Diagnostic Plot Options Dialog Box

This dialog box allows you to choose the type of plot that will be displayed and the component that will be used on the Residuals versus Component Plot.

Plot

Plot versus:


Residuals versus Component

The Residuals versus Component option displays a plot of the residuals versus a component you choose.  In this type of plot, curvature with respect to the reference line, may indicate the need for a transformation or for a curvilinear model.

When you create this plot, you can choose the factors using the Plot Versus option.


Plot Versus Component
Plot versus:

Choose the component that will be used to create the Residuals versus Component Plot.


Mixture Design Analysis Summary
Analysis Summary

The Analysis Summary option creates statistics for the Linear, Quadratic, Special Cubic, and Cubic models when they are estimable.  The results include conditional sums of squares, associated degrees of freedom, mean squares, F-ratios, and p-values for each model.  Estimate and analyze the highest-order model with a significant p-value (for example, less than .05).  If the program suggests a model type different from the design model, you can choose a different model using the Estimate Model Options dialog box.

Also displayed are the results for the SE (square root of the mean square error), the R-Squared for the full Linear, Quadratic, Special Cubic, and Cubic models.  Better models typically have a small SE value, large R-Squared, and Adjusted R-Squared values.


ANOVA Table

The ANOVA Table option creates a standard analysis of variance (ANOVA) table for testing the overall significance of the model.  The table also includes the R-Squared and Adjusted R-Squared statistics, the standard error of the estimate, the mean absolute error, and the Durbin-Watson statistic, which measures the correlation among the residuals.


Model Results

The Model Results option creates the model coefficients, standard errors, t-values and, when appropriate, associated p-values (not for the main components).  If a term is statistically insignificant (for example, it has a p-value greater than .05), you can drop the term by using the Exclude Effects Options dialog box.

Additional values are shown at the bottom of the table to help you judge the utility of the model: R-Squared, R-Squared (adjusted for degrees of freedom), and standard error of the estimate.  The adjusted R-Squared value is the amount of the variance the model accounts for.  It adjusts for the number of terms in the model.  Unlike R-Squared, the Adjusted R-Squared value may decrease if you enter variables that do not add significantly to the model.  The standard error of estimate is the square root of the mean square error.  It measures the standard deviation of the residuals.


Correlation Matrix

The Correlation Matrix option creates a correlation matrix for all the effects in the current Mixture model.  The correlations are calculated from the actual design matrix.

Use the Correlation Matrix Options dialog box to enter a value for the highest-order effects that will be displayed.


Response Plots

The Response Plots option displays one of two Response plots, which show the contours for the chosen variable as a function of the selected factors.  Each contour line represents combinations of the factors that give a value for the variable.  The other factors are held constant.

Using the two Response Plots options together creates a plot you can use to compare two different response plots of the same data.

Type

Contours

Surface

Resolution

Components... Command


Trace Plot

The Trace Plot option creates a plot of the effect that takes place on the chosen variable if each component is increased or decreased from the chosen reference blend.  As the component changes, all the other components adjust proportionally.

You can determine the distance of the current reference blend from the global maximum or minimum reference blend.


Experimental Design Save Results Dialog Box
Save Results Options Dialog Box (Experimental Designs)

The Save Results Options dialog box allows you to choose the results you want to save.  Click on the checkboxes in the Save list to select the options you wish to save as column variables.  The options available depend on the design class chosen.

You use the Target Variables text boxes to select the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options Dialog box, click the Save Results Options button on the Analysis toolbar (the fourth button from the left).


Design Characteristics

Defines the characteristics that determine the axial distance.

Rotatable

Creates a rotatable design.  In a rotatable design, the variance of the predicted response is constant on a hyperspherical surface center at the design origin.  The axial distance is α = (nc)1/4, where nc is the number of points in the cube portion of the design, excluding the centerpoints.

Orthogonal

Creates an orthogonal design.  An orthogonal design is one in which the estimates of all the terms in the second-order model are uncorrelated.  To produce an orthogonal design, the axial distance is set to α = {[(nc + ns + no)1/2 nc]2  (nc/4)]1/2, where

nc =  the number of cube points

ns =  the number of star points

no =  the number of centerpoints

Because the axial distance depends on the number of centerpoints, it is updated when you change the number of centerpoints.

You can make a design both rotatable and approximately orthogonal if you set the axial distance to the value of the rotatable designs, then set the number of centerpoints to the integer closest to no, where

nc =  the number of cube points

k =  the number of factors

Rotatable and Orthogonal

Creates a design that is both rotatable and orthogonal.  The formula immediately above is used to determine the number of centerpoints; you cannot add or subtract additional points; however, you can use the Placement options to designate where you want to place the centerpoints.

Face Centered

Creates a face-centered design where the axial distance is set to 1, which places the star points (rather than the centerpoints) in the center of the faces of the factorial cube.  The resulting experimental design has only three levels rather than five.  In this case, the Low and High levels for each factor you set on the 	Factor Definition Options dialog box describe the boundaries of the design space.


Centerpoints

Determines if centerpoints will be used and where they will be placed in the design.  If you add centerpoints, the runs and degrees of freedom are updated.

In the Number text box, enter the number of centerpoints that will be added to each block.  Enter a positive integer or 0; the default is 0.  If you are creating a Response Surface design, the default is 1.  For a Box-Behnken design, the default is determined by the number of factors in the design.


Placement

Determines where the centerpoints will be placed in the design.

Random

Randomizes the centerpoints with the design points in the block.  To choose this option, you must select the Randomize check box.  This option is the default.

Spaced

Spaces the centerpoints evenly within the block.  When there are two or more centerpoints in each block, the first and last run in the block are always centerpoints.

Allow an equal number of runs between each pair of centerpoints in the design.  For example, if each block has eight runs, the number of centerpoints can be two, three, five, or nine.  Two centerpoints means that all eight runs in the design are between the centerpoints.  Three centerpoints means that four runs in the design are between each pair of centerpoints.  Five centerpoints means that two runs in each design are between each pair of centerpoints.  Nine centerpoints means that one run in the design is between each pair of centerpoints.

First

Places the centerpoints at the beginning of each block.

Last

Places the centerpoints at the end of each block.


Model Type

Determines the type of model that will be used to create the experimental runs.

Linear

Creates experimental runs for a Linear model.

Quadratic

Creates experimental runs for a Quadratic model.  A Quadratic model is a Linear model that includes binary blends; for example, AB, AC, and BC.

Special Cubic

Creates experimental runs for a Special Cubic model.  A Special Cubic model is a Quadratic model that includes tertiary blends; for example, ABC.

Cubic

Creates experimental runs for a Cubic model.  A Cubic model is a Special Cubic model with additional blends; for example, AB(A - B).  This model is not available with a Simplex-Centroid design.


Exclude... Command

Displays the Exclude Effects Options dialog box with the terms listed in the Include options.  Double-click on the terms you want to exclude; the program lists the terms under the Exclude options.

When you click OK on the Exclude Effects Options and Estimate Model Options dialog boxes, the terms are excluded from the analysis.

See also

 Exclude Effects Options Dialog Box


Estimate Sigma From

Determines how the standard errors for the effects will be estimated.

Experimental Data

Uses all the degrees of freedom that remain after the effects are estimated; this option is the default.

External Data

Uses a specified sigma value, which tests for significance of effects in reports and graphs such as an ANOVA table and a standardized Pareto Chart.  Enter a number greater than 0.


Display

Determines whether standard errors or confidence intervals will be displayed for the estimated effects.

Standard Errors

Displays standard errors for the estimated effects.  They are based on the total error with the associated degrees of freedom.

Confidence Intervals

Displays confidence intervals for the estimated effects.  Enter a number between 1 and 100 for the confidence level that will be used to calculate the intervals; the default is 95 percent.  Other common values are 90 or 99 percent.


Confounding Pattern

Determines how the confounding pattern will be calculated.

From Original Design

Uses the original base design; it is the default.

From Data

Looks at all the current experimental runs to determine the confounding pattern.


Include

Determines the statistics that will be included in the Predictions report.

Observed Y

Displays the observed values for the response variable.  This option is one of the defaults.

Fitted Y

Displays the estimated values for the response variable.  This option is one of the defaults.

Residuals

Displays the difference between the observed and fitted response values.

Studentized Residuals

Displays residuals that are scaled by estimates for the variance with observations removed from the data.  A large studentized residual may indicate an influential observation.

Standard Errors for Forecasts

Displays the standard deviation for the distribution of the estimated values.

Confidence Limits for Individual Forecasts

Displays the end points for the prediction interval of the individual estimated values.

Confidence Limits for Forecast Means

Displays the end points for the confidence interval of the means for each estimated value.  This option is one of the defaults.


Predict

Determines if predictions will be made for the experimental runs or only added runs.

Experimental Runs

Displays predictions for all the experimental runs in the DataSheet.

Added Runs Only

Displays predictions for the experimental runs in the DataSheet that do not contain response values.


Screening Designs Graphical Options
Screening Designs Graphical Options Dialog Box

This dialog box allows you to choose graphical options for Screening Designs.

Pareto Charts

Main Effects Plots

Interaction Plots

Normal Probability Plots of Effects

Response Plots

Response Plots

Diagnostic Plots


Direction

Indicates the direction of the Normal Probability Plot: horizontal or vertical.  Vertical is the default.


Plot Type

Determines the type of plot that will be created.

Normal

Creates a Normal Probability Plot; this option is the default.

Half-Normal

Creates a Half-Normal Plot, which identifies the estimated effects that are large, relative to noise.  Large effects appear on the right side of the plot.  This plot is useful for plotting fractional factorial designs.  It is sometimes also known as a Daniel Plot.


Type

Determines the type of plot that will be displayed.  If you are using a Surface or Mixture design the options are Surface or Contour.  If you are using a Response Surface design, the options are Surface, Contour, Square, or Cube.

Surface

Displays a Surface Plot.  If you are using a Screening or Response Surface design, the plot is a three-dimensional model of the relationship between the response variable and two factors, which is the default.  If you are using a Mixture design, the plot is a three-dimensional model of the relationship between the response variable and three components.

Contour

Displays a Contour Plot.  If you are using a Screening or Response Surface design, the plot is a two-dimensional plot that traces the contours of responses for two factors.  If you are using a Mixture design, the plot is a two-dimensional plot that traces the contours of responses for three components.  You can predict the next value for the response within the experimental design by following the ridge of the contour.

Square

Displays a Square Plot for the estimated effects of two factors.  The values for the response variable for all combinations of the high and low values for each factor are plotted.  Use the Factors... command to choose the factors and to enter the high and low values.

Cube

Displays a Cube Plot for the estimated effects for three factors.  The values for the response variable for all combinations of the high and low values for each factor are plotted.  Use the Factors… command to choose the factors and to enter the high and low values.


Contours

Determines the attributes for the contours on a Contour Plot or for contours that are placed below a Surface Plot.  The options and text boxes are available only when you choose a Contour Plot or a Surface Plot and choose the Contours Below option.

From

Enter a numeric value for the first contour line.  Enter a number less than that in the To text box.

To

Enter a numeric value for the last contour line.  Enter a number greater than that in the From text box.

By

Enter a positive numeric value for the spacing of the contour lines.  This value, along with the values from the From and To text boxes, determine the contour levels.

Lines

Indicates if lines should be used to connect the points along each contour.  Connecting lines is the default.

Painted Regions

Indicates if painted (filled in) regions should appear for the regions of the contours.


Surface

Determines the attributes for a Surface Plot.  These options are available only when you choose a Surface Plot.

Horizontal Division

Enter the number of horizontal lines that will be plotted on the Surface Plot.  Enter a positive integer between 5 and 100; the default is 10.

Vertical Division

Enter the number of vertical lines that will be plotted on the Surface Plot.  Enter a positive integer between 5 and 100; the default is 10.

Contours Below

Indicates if a Contour Plot should be displayed below the Surface Plot.

Wire Frame

Indicates if the horizontal and vertical lines only should appear on the Surface Plot.

Solid

Indicates if a solid Surface Plot with horizontal and vertical divisions should appear on the plot.


Factors... Command

This command displays the Response Plot Factors dialog box, which allows you to choose the factors that will appear on the Response Plot.

See also

Response Plot Factors Dialog Box


Plot

Determines the plot that will be displayed.

Observed versus Predicted

Displays a plot of the observed versus predicted values.  The plot includes a line 	with a slope equal to 1.  If all the predictions are perfect, all the points are on the 	line.  You can use the plot to detect cases in which the variance is not constant or in which you need to transform the response variable.

Residuals versus Predicted

Displays a plot of the residuals versus predicted values.  Any differences in scatter around the reference line indicate a nonconstant variance.  Transforming the response may help to make the variance more constant.

Residuals versus Run Order

Displays a plot of the residuals in the order that the observations appear in the response variable.  This plot helps identify sequential correlations.  In a plot of 	residuals versus run order, any pattern over time may indicate a time effect.

Residuals versus Component

Displays a plot of residuals versus a component you specify.

Normal Probability Plot of Residuals

Displays a Normal Probability Plot of Residuals.  The residuals are plotted on the X-axis from smallest to largest.  The Y-axis is a normal probability scale (it "straightens out" the plot of a cumulative normal distribution).  In a Normal 	Probability Plot, if the residuals do not fall approximately along a straight line, 	they do not come from a normal distribution.  This indicates that a basic assumption for the model may have been violated.


Predictions (Mixture)
Predictions

The Predictions option creates the observed and predicted (fitted) values for each run of the response variable.  It also displays the confidence intervals.  You can generate predictions by adding additional runs to the DataSheet.


Influential Points (Mixture)
Influential Points

The Influential Points option displays the number of observations that were flagged for large residual, leverage, or DFITS values.  The leverage and DFITS statistics estimate the influence of an individual observation on the fitted model.

The program also reports the Mahalanobis distance, which can help to identify unusual values.  Leverage values near 1 indicate design points that have significant influence on the model.  You can reduce the influence by adding additional runs to the experiment or by adding replicate runs of the influential point.


Mixture Response Plot Options Dialog Box

This dialog box allows you to choose the type of response plot that will be created, choose attributes for the contours and surface on the plot, and enter the density values.

Type

Contours

Surface

Resolution

Components... Command


Components... Command

Displays the Response Plot Components dialog box, which allows you to choose the components that will appear on the Response Plot.

See also

Response Plot Components Dialog Box


Diagnostic Plots (Mixture)
Diagnostic Plots

The Diagnostic Plots option creates a Residuals versus Predicted Plot for the response variable.  The plot is one of five diagnostic plots you can choose on the Diagnostic Plot Options dialog box.  The plots are helpful in determining if the model as it was estimated fits the data.


Plot

Determines the type of plot that will be created.

Observed vs. Predicted

Plots the observed values versus the predicted values.  The plot includes a line with a slope equal to 1.  If all the predictions are perfect, all the points are on the line.  You can use the plot to detect cases in which the variance is not constant or in which you need to transform the response variable.

Residuals vs. Predicted

Plots the residual values versus the predicted values.  In this type of plot, curvature with respect to the reference line may indicate a missing factor.  Any differences in scatter around the reference line indicate a nonconstant variance.  Transforming the response variable may help to make the variance more constant.  This option is the default.

Residuals vs. Run Order

Plots the residuals in the order that the observations appear in the response variable.  The plot helps in identifying sequential correlations among the residuals.  In a plot of this type, any pattern over time may indicate a time effect.

Residuals vs. Factor

Plots the residuals versus a factor you specify.  In this of plot, curvature with respect to the reference line may indicate the need for a transformation or a curvilinear model.  When you choose this plot, you can select the factors to plot against using the Plot versus option (see below).

Normal Probability Plot of Residuals

Plots the residuals on the X-axis from smallest to largest.  The Y-axis is a normal probability scale (it “straightens” the plot of a cumulative normal distribution).  In this type of plot if the residuals do not fall approximately along a straight line, they do not come from a normal distribution.  This indicates that a basic assumption for the model may have been violated.

Power Curve

Creates a plot that shows the power of the design to detect a real effect.  You use the plot to estimate if the experiment can detect effects of the magnitude you expect.


Plot versus:

Enter the name of the factor that will be used on the Residuals vs. Factor Plot or on the Power Curve.


Line Spacing

Determines the spacing between the runs on the Worksheet.

Single

Uses single-spaced lines.

Double

Uses double-spaced lines; this option is the default.

Triple

Uses triple-spaced lines.


Horizontal

This option allows you to display the plot horizontally.


Save In

If necessary, allows you to choose a different disk drive.

File Name

Enter the name of the file you want to save.

List Files of Type

Choose the type of file you want to save.


Fitted Line

Indicates if a fitted line will appear on the Normal Probability Plot.  Displaying the fitted line is the default.


Alpha

Enter a value for the alpha risk, which is the probability of a Type I error.  The alpha risk determines the probability of declaring an effect significant, when in fact, it is not.  Enter a number greater than 0 and less than 100.  The default is 5 percent; typical values are 1, 5, or 10 percent.


Axial Distance

Displays the distance from the center of the design to each of the star points.  You change the axial distance by using a different number of centerpoints.


Generators... Command

Displays the Design Generators dialog box that shows the design generators used to create the last column(s) of the design matrix.  You can change the plus and minus signs.  When you click OK, the Blocked Composite Design Options dialog box redisplays.

When you click OK on the Blocked Composite Design Options dialog box, the centerpoints and replicate options you chose are used.  The program then places the experimental runs in the DataSheet and displays the Design Summary in the Response Surface Design Attributes window.


Model to Fit

Determines the model that will be used to fit the data.

Linear

Fits a Linear model.

Quadratic

Fits a Quadratic model, which is a Linear model that includes binary blends; for example, AB, AC, and BC.

Special Cubic

Fits a Special Cubic model, which is a Quadratic model that includes tertiary blends; for example, ABC.

Cubic

Fits a Cubic model, which is a Special Cubic model with additional blends; for example, AB(A - B).


Type

Determines the type of plot that will be displayed.

Surface

Displays a Surface Plot, which is a three-dimensional model of the relationship between the response variable and three components.  If you choose this type of plot, you can also choose options such as a Solid or Wire Frame surface.

Contour

Displays a Contour Plot, which is a two-dimensional plot that traces the contours of responses for three components.  You can predict the next value for the response within the experimental design by following the ridge of the contour.  If you choose this type of plot, you can also choose options such as the location of the contours.


Name

[Optional]  Displays the names of the components on the Trace Plot.


Low

Displays the lower constraints for the components.


High

Displays the upper constraints for the components.


Reference Blend

Enter values for the starting point for the mixture blend from which the program increments the component value to estimate the response variable.  For Simplex designs, the default is the centroid.


Number of Levels

Enter the number of levels that will be used for the active factor.  Enter a positive integer; the default is 3.


Factor

Determines the active factor for the experiment.


Select

[Optional]  Select a subset of the response variable.  For example, to analyze the first 50 experimental runs, enter first (50) into this text box.


Add a Fraction

Adds a fraction to the design, which removes all confounding of main effects from second-order interactions in a resolution III design.  The new runs are added to the design in a way that clears the main effects from confounding and produces a resolution IV design.


Model Type

Determines the type of model that will be used to create the experimental runs.

Linear

Creates experimental runs for a Linear model.

Quadratic

Creates experimental runs for a Quadratic model.  A Quadratic model is a linear model that includes binary blends; for example, AB, AC, and BC.

Special Cubic

Creates experimental runs for a Special Cubic model.  A Special Cubic model is a Quadratic model that includes tertiary blends; for example, ABC.

Cubic

Creates experimental runs for a Cubic model.  A Cubic model is a Special Cubic model with additional blends; for example, AB(A - B).  This model is not available with a Simplex-Centroid design.


Alpha

Enter a value for the alpha level, in percentages, that will be used to perform the hypothesis test for the mean. Enter a number between 0 and 100; the default is 5.  Other common levels are 1 and 10.


Greater Than Alternative Hypothesis

Performs a one-tailed test to determine if the mean is greater than the hypothetical mean.


Less Than Alternative Hypothesis

Performs a one-tailed test to determine if the mean is less than the hypothetical mean.


Not Equal Alternative Hypothesis

Performs a two-tailed test.


ANOVA Table

The ANOVA Table option creates a standard analysis of variance table.  The table includes the residual sums of squares, the degrees of freedom (Df) for the residual, the residual mean square, an F-ratio that is calculated using the residual mean square (or the error term you choose), and the p-value for the F-ratio.

The table includes statistics for each main effect and interaction in the analysis.  Notes at the bottom of the table identify the error term that was used as the denominator to calculate each F-ratio.  Until you use the ANOVA Table Options dialog box to change the default, the table is initially calculated for Type III sums of squares.

Use the ANOVA Table Options dialog box to indicate which method will be used to calculate the sums of squares for each factor and to choose a factor for which you want to choose an Error term.  You can also indicate the type of mean square that will be used as the denominator to calculate the F-ratio, and to view the error term.


ANOVA Table

The ANOVA Table option creates a standard analysis of variance table.  The table includes the residual sums of squares, the degrees of freedom (Df) for the residual, the residual mean square, an F-ratio that is calculated using the residual mean square (or the error term you choose), and the p-value for the F-ratio.

The table includes statistics for each main effect and interaction in the analysis.  Notes at the bottom of the table identify the error term that was used as the denominator to calculate each F-ratio.  Until you use the ANOVA Table Options dialog box to change the default, the table is initially calculated for Type III sums of squares.

Use the ANOVA Table Options dialog box to indicate which method will be used to calculate the sums of squares for each factor and to choose a factor for which you want to choose an Error term.  You can also indicate the type of mean square that will be used as the denominator to calculate the F-ratio, and to view the error term.


ANOVA Table Options Dialog Box

This dialog box allows you to select the method that will be used to:

•	calculate the sums of squares for each factor

•	select the factor for which you want to select an error term

•	select the type of mean square that will be the denominator

•	view the error terms.

Sums of Squares

Factor

Error Term

Selections


Average (Summary Statistic)

Displays the value for the mean of the data.  Use the value to measure the central tendency of the data.  This option is one of the defaults.


Barchart (Tabulation Analysis)

The Barchart option creates a plot of the frequency data as a series of bars whose sizes are proportional to the number of occurrences of each value of the variable.

Barcharts make it easy to understand data that are divided into classes.  If the data contain more than 20 classes, an error message displays in the graphics pane.


Barchart (Crosstabulation Analysis)
Barchart

The Barchart option creates a plot of the frequency data, which displays as a series of bars.

Use the Barchart Options dialog box to select options for the chart.


Barchart Analysis Graphical Options Dialog Box

This dialog box allows you to select graphical options for the Barchart Analysis.

Barchart (Barchart)


Barchart Analysis Tabular Options Dialog Box

This dialog box allows you to select tabular options for the Barchart Analysis.

Analysis Summary (Barchart Analysis)


Barchart Analysis Dialog Box

The Barchart Analysis creates a graphical display of a frequency table, where each bar represents an individual row or cell in the table. The height of the bar corresponds to the frequency, or the number of times that a value appears in the data.

Barcharts are a familiar and easily understood way of displaying data that can be divided into classes (categorical data).  For example, you might use Barcharts to present the Republican affiliation of members of various religious categories:  31 percent of Protestants surveyed reported affiliation with the Republicans, roughly 17 percent of Catholics did, and so on.

Graphs can include stacked bars, clustered bars, or percentages.  The bars can appear horizontally or vertically.  If the data contain more than 20 classes, an error message displays.

Use a Barchart only to summarize a nominal or ordinal variable.  In other words, the distance between the bars on the graph should have no true meaning.  If the variable is measured on an interval or ratio scale, use a Histogram to represent the data.  If your data contain more than one set of counts, use the Crosstabulation analysis to display multiple bars on the chart.

Counts

Labels (for Barchart)

Standard Errors

Sort

See also

Using the Barchart Analysis

Barchart Options


Barchart Options Dialog Box

This dialog box allows you to:

•	select a format for the bars on the chart

•	select the type of data that will appear on the plot

•	select the direction in which the plot will display

•	instruct the program what it should use to plot the data

•	select the starting point for the bars on the chart.

When you use the Tabulation, Crosstabulation, or Contingency Tables analyses, it is not necessary to use error bars, therefore, that option is not available.

Chart Type

Scaling

Direction

Error Bars

Baseline


Baseline

Enter the starting point for the bars on the chart.  Enter any number; usually 0, however, you can also enter other numbers to emphasize differing relationships among the classes.

If you use a number larger than the largest class in the data, bars descend from the baseline (on a vertical Barchart) or extend to the left of the baseline (on a horizontal Barchart).


Bonferroni

Bonferroni Method

Determines the statistically significant differences among the means.  Select this method when the F-ratio is not significant, but you still want to make a small number of planned comparisons.


Bonferroni Interval
Bonferroni Intervals

Use Bonferroni Intevals when the F-ratio is not significant, but you still want to make a small number of planned comparisons.

If you are performing a Multifactor ANOVA, this interval calculates the two-factor interactions.


Box-and-Whisker Plot

The Box-and-Whisker Plot option calculates a Box-and-Whisker Plot of the data.  The data are divided into four areas of equal frequency (quartiles). A box encloses the middle 50 percent, where the median is drawn as a vertical line inside the box.

Horizontal lines, known as whiskers, extend from each end of the box.  The left (or lower) whisker is drawn from the lower quartile to the smallest point within 1.5 interquartile ranges from the lower quartile.  The other whisker is drawn from the upper quartile to the largest point within 1.5 interquartile ranges from the upper quartile.


Box-and-Whisker Plot (Two-Sample Comparison Describe Analysis)

The Box-and-Whisker Plot option creates a plot that shows important features about a sample of data.  The plot divides the data for each sample into four equal areas of frequency.

A box encloses the middle 50 percent of the data; the median is drawn as a vertical line inside the box.  Horizontal lines, known as whiskers, extend from each end of the box.  The left (or lower) whisker is drawn from the first quartile to the smallest point within 1.5 interquartile ranges from the lower quartile.  The other whisker is drawn from the upper quartile to the largest point within 1.5 interquartile ranges from the upper quartile.

Individual points are plotted as values that fall beyond the whiskers, but within 3 interquartile ranges (suspect outliers).


Box-and-Whisker Plot Graphical Options Dialog Box

This dialog box allows you to select graphical options for the analysis.

Box-and-Whisker Plot (Box-and-Whisker Plot Analysis)

See also

Box-and-Whisker Plot Options


Box-and-Whisker Plot Tabular Options Dialog Box

This dialog box allows you to select tabular options for the analysis.

Analysis Summary (Box-and-Whisker Plot Analysis)


Box-and-Whisker Plot Analysis Dialog Box

The Box-and-Whisker Plot Analysis summarizes a set of univariate observations.  It provides an exploratory data-analysis tool that is useful for studying symmetry, checking distributional assumptions, and detecting outliers.  A Box-and-Whisker plot is particularly useful for comparing parallel batches of data.

The data are divided into four areas of equal frequency.  A box encloses the middle 50 percent, where the median is represented as a vertical line inside the box.  The mean may be plotted as a point.

Horizontal lines, called whiskers, extend from each end of the box.  The lower (left) whisker is drawn from the lower quartile to the smallest point within 1.5 interquartile ranges from the lower quartile.  The other whisker is drawn from the upper quartile to the largest point within 1.5 interquartile ranges from the upper quartile.  Values that fall beyond the whiskers, but within 3 interquartile ranges (suspect outliers), are plotted as individual points.

Far outside points (outliers) are distinguished by a special character (a point with a + through it).  Outliers are points more than 3 interquartile ranges below the lower quartile or above the upper quartile.  You can display the bars either horizontally or vertically.

Data

Select

Sort

See also

Using the Box-and-Whisker Plot Analysis

Box-and-Whisker Plot Options


Box-and-Whisker Plot Options Dialog Box

This dialog box allows you to select the direction of the plot and the features that will appear on the plot.

Direction

Features


Analysis Summary (Box-and-Whisker Plot Analysis)

The Analysis Summary option creates a summary of the analysis that includes the name of the variable you selected, the number of values in the variable, and the range of the values.


Box-and-Whisker Plot (One-Variable Analysis)
Box-and-Whisker Plot

The Box-and-Whisker Plot option creates a Box-and-Whisker Plot of the data.  The data are divided into four equal areas of frequency (quartiles).  A box encloses the middle 50 percent, where the median is drawn as a vertical line inside the box.

Horizontal lines, known as whiskers, extend from each end of the box.  The left (or lower) whisker is drawn from the lower quartile to the smallest point within 1.5 interquartile ranges from the lower quartile.  The other whisker is drawn from the upper quartile.

Use the Box-and-Whisker Plot Options dialog box to select options for the plot.


Boxcar Method
Boxcar

Assigns a constant density to each small interval around each value, which smoothes the density function into a series of overlapping rectangles or boxcars, similar to a simple moving average.


Casement Plot for the X-Y-Z Plot Analysis
Casement Plot

The Casement Plot option creates a plot of the X and Y variables in groups determined by the Z variable.  The scatterplots contain only those points that fall within the regions covered by the Z variable.


Casement Plot (X-Y-Z Plot Analysis)

The Casement Plot option creates the X and Y variables in groups determined by the Z variable.

The scatterplots contain only those points that fall within the regions covered by the Z variable.


Chi-Square Test (Crosstabulation Analysis)

The Chi-Square Test option creates the results of a hypothesis test that determines if the assumption that the row and column classifications are independent.

If the Contingency Table is a two-by-two table with less than 100 observations, the statistics will also include the results from Fisher’s Exact test.


Chi-Square Test

The Chi-Square Test option creates a two-way table.  Use the chi-square statistic to test the hypothesis that the two variables are independent (null hypothesis).

A small chi-square statistic, as indicated by a p-value less than .05 for a 95 percent confidence level, suggests that you should reject the null hypothesis (the two variables are not independent).  It also suggests that the two variables have some relationship.  In other words, the two variables are dependent.


Clustered Chart Type
Clustered

Places multiple bars side by side.


Coefficients of Variance (Summary Statistic)

The Coefficients of Variance option compares the standard deviation with the mean, which is helpful when you need to determine the distribution of the data.


Column Variable

Enter the name of the variable that will appear in the columns of the table.  The names become the items in the legend on a Barchart and a Mosaic Plot.


Comparison of Alternate Methods
Comparison of Alternative Models

The Comparison of Alternative Models option creates correlation coefficients and R-Squared values for several transformed model types, which you can use to quickly compare the R-Squared values for each transformed model against the linear model.  The preferred model is the linear model, unless another type of model significantly increases the R-Squared value.


Comparison of Alternative Models (Simple Regression Analysis)

The Comparison of Alternative Models option creates a table of the results of fitting several curvilinear models for the data.  It displays the correlation coefficients and R-Squared values for several transformed model types.  Compare the R-Squared values for each transformed model with the values for the linear model.  The preferred model is linear, unless another type of model significantly increases the R-Squared value.


Comparison of Alternative Models (Simple Regression Analysis)

The Comparison of Alternative Models option creates correlation coefficients and R-Squared values for several transformed model types, which you can use to quickly compare the R-Squared values for each transformed model against the linear model.  The preferred model is the linear model, unless another type of model significantly increases the R-Squared value.


Comparison of Means (Two-Sample Comparison Analysis)

The Comparison of Means option creates a table that shows the values for the 95 percent confidence intervals for the mean of both variables, and for the difference between the means, assuming equal variances, and not assuming equal variances.  The results of the t-tests are also shown; they compare the means of the null hypothesis with the alternative hypotheses.

The program uses the assumption, variances of the two populations are identical, to calculate the first confidence interval.  The second confidence interval is calculated without the assumption of equal variances.  Usually you use the first interval unless there is evidence that there is a large difference between the two variances.

The values for the calculated test statistic (t-test) and the p-value appear in the lower portion of the text pane.  If the p-value is small (less than a desired alpha level, such as .05), then the hypothesized difference between the means should be rejected.

Use the Confidence Intervals Options dialog box, which will calculate the difference between the means, to change the value for the confidence intervals.


Comparison of Means

The Comparison of Means option creates table that shows the values for the 95 percent confidence intervals for the mean of both variables, and for the difference between the means, assuming equal variances, and not assuming equal variances.  The results of the t-tests are also shown; they compare the means of the null hypothesis with the alternative hypotheses.

When it calculates the first confidence interval, the program assumes that the variances for the two populations are identical.  It calculates the second confidence interval without the assumption of equal variances.  Usually you use the first interval unless there is evidence that there is a large difference between the two variances.

The values for the calculated test statistic (t-test) and the p-value appear in the lower portion of the text pane.  If the p-value is small (less than a desired alpha level, such as .05), reject the hypothesized difference between the means.


Comparison of Medians (Two-Sample Comparison Analysis)

The Comparison of Medians option creates a summary of tests that include the results of a Mann-Whitney (Wilcoxon) test (a Rank test).

The Rank Test combines the two samples, sorts the data from smallest to largest, and compares the average ranks for the two samples of combined data.  If the p-value is small (less than a desired alpha level, such as .05), there is a statistically significant difference between the means at the 95 percent confidence level.


Comparison of Medians (Two-Sample Comparison Analysis)

The Comparison of Medians option creates a summary of tests that include the results of a Mann-Whitney (Wilcoxon) test (a Rank test).

The Rank Test combines the two samples, sorts the data from smallest to largest, and compares the average ranks for the two samples of combined data.  If the p-value is small (less than a desired alpha level, such as .05), there is a statistically significant difference between the means at the 95 percent confidence level.


Comparison of Standard Deviations (Two-Sample Comparison Analysis)

The Comparison of Standard Deviations option creates a summary of the analysis that includes the results from an F-test.  The test compares the ratio of the variance of the first population with the variance of the second population.

The summary also includes the confidence intervals for the standard deviations between the two samples (using the default confidence level, 95 percent), a ratio of the two variances, and the results of the hypothesis tests:  The null hypothesis that the standard deviations for the two samples are equal; the alternative hypothesis that the two samples are not equal; the standard deviation for one sample is greater than the standard deviation for the other.  If the p-value for any of the hypotheses is less than .05 for a 95 percent confidence interval, reject the null hypothesis.

Use the Confidence Intervals Options dialog box to change the value for the confidence intervals, which will calculate the confidence intervals for the standard deviations and the ratio of the variances.


Comparison of Standard Deviations

The Comparison of Standard Deviations option creates a summary of the analysis that includes the results from an F-test.  The test compares the ratio of the variance of the first population with the variance of the second population.

The summary also includes the:

•	confidence intervals for the standard deviations between the two samples (using the default confidence level, 95 percent)

•	ratio of the two variances

•	results for the hypothesis tests:  (1) the standard deviations for the two samples are equal; and (2) the two samples are not equal; the standard deviation for one sample is greater than the standard deviation for the other.

If the p-value for any of the hypotheses is less than .05 for a 95 percent confidence interval, reject the null hypothesis.


Component Effects Plot (Multiple Regression Analysis)

The Component Effects Plot option creates a Component-plus-Residuals Plot of the residuals around a line that is defined by the term

Bj(Xij - Xij),

which multiplies the centered value of the independent variable Xj by the associated value of its regression coefficient Bj.

You can use this plot to judge the relative magnitude of the residuals with respect to the explanatory power of the variable.  You can plot a Component-plus-Residuals Plot for any of the independent variables.

Use the Component Effects Plot Options dialog box to select options for the plot.


Component Effects Plot (Multiple Regression Analysis)

The Component Effects Plot option creates plot that shows the residuals around a line that is defined by the term

Bj(Xij - Xij),

which multiplies the centered value of the independent variable Xj by the associated value of its regression coefficient Bj.  You can use this plot to judge the relative magnitude of the residuals with respect to the explanatory power of the variable.  You can plot a Component-plus-Residuals Plot for any of the independent variables.


Component Effects Plot Options Dialog Box

This dialog box allows you to select an independent variable for the Component-plus-Residuals Plot.

Plot versus:


Conditional Sums of Squares (Multiple Regression Analysis)

The Conditional Sums of Squares option calculates additional analysis of variance statistics.  The table includes the contribution each independent variable made to the total regression sums of squares when it entered the regression (also called Type I sums of squares).

If you select the All Variables option on the Multiple Regression Options dialog box, the results depend on the order of the variables as you enter them into the Analysis dialog box.  For a stepwise regression, the results reflect the order in which the program entered the variables in the final model.

The program calculates F-ratios by dividing the mean square terms by the mean square error from the primary analysis of variance table.  The total sum of squares for the variable is the model sum of squares in the primary analysis of variance table.


Conditional Sums of Squares (Multiple Regression Analysis)

The Conditional Sums of Squares option creates additional analysis of variance statistics.  The table includes the contribution to the total regression sums of squares attributed to each independent variable as it enters the regression (also called Type I sums of squares).


Confidence Intervals (One-Variable Analysis)

The Confidence Intervals tabular option calculates the 95 percent confidence intervals for the mean and standard deviation.


Confidence Interval (One Variable Analysis)

The Confidence Intervals option calculates the 95 percent confidence intervals for the mean and standard deviation.  This interval can be assumed to contain the true mean divided by the standard deviation with 95 percent confidence.

Use the Confidence Intervals Options dialog box toselect options for the table.


Confidence Intervals (Multiple-Variable Analysis)

The Confidence Intervals tabular option calculates and displays the confidence intervals for the means of each of the variables (95 percent confidence intervals).

Use the Confidence Intervals Options dialog box to select options for this table,


Confidence Intervals (Individual s)

Calculates the confidence intervals using the individual standard errors.  Use the associated standard error to calculate the confidence intervals for each sample.


Confidence Intervals (Pooled s)

Calculates the confidence intervals using the pooled standard deviation from the factor levels or samples.  To calculate the pooled standard errors, the sample variances are first pooled.  Unless the variances of the samples are significantly different, you generally use this technique instead of using individual standard deviations.


Confidence Intervals Options Dialog Box

This dialog box lets you enter a value for the confidence level that will be used to calculate the confidence intervals for the mean and standard deviation.  The default is 95 percent; other common percentages are 90 and 99.

The confidence intervals option also allows for one-sided bounds as well as for two-sided intervals.

Bootstrap intervals (or bounds) for the mean, standard deviation, and median are formed by by selecting k random subsamples of n observations each with replacement from the n data values, calculating each statistic, and displaying percentiles for the k values of the computed statistics. When standard assumptions are violated (such as normality of the data values), the resulting intervals may be better than those usually computed.


Confidence Limits for Forecast Means

Includes the end points for the confidence interval of the means for each estimated value in the report.


Confidence Limits for Individual Forecasts

Includes the end points for the prediction interval of the individual estimated values in the report.


Constant in Model

Treats the constant; that is includes the constant in the model.  Deselect the option if you want to force the intercept to 0 (regression through the origin).

In a nonconstant model, the R-Squared value may be artificially inflated.


Correlation Matrix (Multiple Regression Analysis)

The Correlation Matrix option creates the Pearson correlation coefficients for the estimated coefficients in the model.


Correlation Matrix (Multiple Regression Analysis)

The Correlation Matrix option creates and displays the Pearson correlation coefficients for the estimated coefficients in the model.


Correlations (Multiple-Variable Analysis)

The Correlations option creates a matrix of Pearson Product-Moment correlation coefficients for the observed values.  This analysis provides a preliminary view of the relationships among the selected variables.

Each row and column corresponds to a variable.  Three numbers appear in each cell of the matrix: The correlation coefficient for the two variables represented by the cell, the sample size (in parentheses), and the p-value for the correlation.

Correlations range from -1 to +1.  A positive correlation suggests that two variables vary in the same direction, while a negative correlation suggests that two variables vary in the opposite direction; p-values below .05 indicate a statistically significant correlation at the 95 percent confidence level.

Statistically independent variables have an expected correlation coefficient of zero.


Correlations

The Correlations option creates a matrix of correlation coefficients for the observed values.  This analysis provides a preliminary view of the relationships among the variables you selected.

Each row and column corresponds to a variable.  Three numbers appear in each cell of the matrix: The correlation coefficient for the two variables represented by the cell, the sample size (in parentheses), and the p-value for the correlation.  Correlations range from 1 to +1.  A positive correlation suggests that two variables vary in the same direction, while a negative correlation suggests that two variables vary in the opposite direction.  Statistically independent variables have an expected correlation of zero.


Cosine Method
Cosine

Smoothes the local densities into a series of overlapping, bell-shaped intervals similar to a weighted moving average.  The Cosine method gives a smoother density trace.


Counts

Enter the name of the variable that contains the frequency counts, which are the number of observations in each class.  You can enter a maximum of 20 classes.  When you create the variable, make sure that it is categorical.


Covariances (Multiple-Variable Analysis)

The Covariances option creates a matrix of the estimated covariance for each pair of variables.

Covariance measures the linear association between two variables.  If the variables tend to fall above or below their means at the same time, the covariance is positive.  If one variable is above its mean while the other is below, the covariance is negative.

The value of the covariance is sensitive to scaling because it retains the units of the original data.


Covariances

The Covariances option creates a matrix of covariance measures for a set of observed values.  Covariance measures the linear association between two variables.  If the variables tend to fall above or below their means at the same time, the covariance is positive.  If one variable is above its mean while the other is below, the covariance is negative.  The value of the covariance is sensitive to scaling because it retains the units of the original data.


Covariates

Enter the names of up to three independent metric variables.  If you do not want to include covariates in the analysis, leave this text box blank.


Critical Values (Distribution Fitting Analysis)

The Critical Values option creates a table of critical values, which are the smallest values for the area that falls under the distribution curve.  These values should be no less than the values you selected for the probability.


Critical Values

Enter the values that will be used to calculate the areas under the selected distribution curve.


Critical Values

The Critical Values option creates a table of critical values, which are the smallest values for the area that falls under the distribution curve.  These values are no less than the values you selected for the probability.


Critical Values Options Dialog Box

This dialog box allows you to enter the values that will be used for the calculations.

Tail Areas


Crosstabulation Analysis Graphical Options Dialog Box

This dialog box allows you to select graphical options for the Crosstabulation analysis.

Barchart (Crosstabulation Analysis)

Mosaic Plot (Crosstabulation Analysis)

Skychart (Crosstabulation Analysis)


Crosstabulation Analysis Tabular Options Dialog Box

This dialog box allows you to select tabular options for the Crosstabulation analysis.

Analysis Summary (Crosstabulation Analysis)

Frequency Table (Crosstabulation Analysis)

Chi-Square Test (Crosstabulation Analysis)

Summary Statistics (Crosstabulation Analysis)


Crosstabulation Analysis Dialog Box

The Crosstabulation Analysis summarizes the joint distribution of two discrete variables through a crosstabulation.  The crosstabulation counts the number of times each unique value occurs in the first variable, then in the second.

When you analyze observations, the observations must be counted before they can be displayed in tabular or graphical form.

If the data are frequency counts instead of actual values, use the Contingency Table Analysis.

Row Variable

Column Variable

Select

Sort

To select options for the analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Crosstabulation Analysis

Frequency Table Options

Barchart Options

Mosaic Plot Options

Skychart Options


Frequency Table (Crosstabulation Analysis)

The Frequency Table tabular option creates and displays a table that shows the frequency with which the values of the first variable appear with each of the values of the second variable.  The first number in the table is the count or frequency.  The second is the percentage of the entire table that is represented by that cell.

Use the Frequency Table Options dialog box to select options for the table.


Crosstabulation Frequency Table
Frequency Table

The Frequency Table option creates a table that shows how often the values of the first variable appear with each of the values of the second variable.  The first number in the table is the count or frequency.  The second is the percentage of the entire table that is represented by that cell.


Analysis Summary (Crosstabulation Analysis)

The Analysis Summary tabular option creates and displays the names of the variables, the number of observations, and the number of rows and columns.


Crosstabulation Procedure Summary
Analysis Summary

The Analysis Summary option creates a summary that includes the names of the variables you selected and the number of observations, rows, and columns.


Save Results Options Dialog Box (Crosstabulation Analysis)

The Save Results Options dialog box allows you to select the results you want to save.  There are three selections: Cell Frequencies, Row Labels, and Column Labels.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Summary Statistics (Crosstabulation Analysis)

The Summary Statistics option creates the results of various statistical tests where lambda measures the usefulness of the row (or column) factor in predicting the other factor.  The statistics calculated are the following.

Lambda Values

These statistics range from 0 (knowing that one variable tells you nothing about the other variable) to 1 (knowing that one variable allows you to predict the other variable).

Uncertainty Coefficients and Pearson’s R

These statistics show the degree of linear relationship between the two variables.

Somer’s D Statistics

These statistics are for symmetric and asymmetric cases; that is, with rows and columns dependent, which show a symmetric measurement of association for variables that are measured on an ordinal scale.

Eta

This statistic is an appropriate measure of association for two variables when you measure the dependent variable on an interval scale and the independent variable on a nominal or ordinal scale.  Eta is similar to the Pearson correlaton coefficient, however, it is asymmetric and does not assume a linear relationship between the variables.

Contingency Coefficient

This statistic measures the strength of dependence between two characteristics.

Cramer’s V and Conditional Gamma

These statistics are chi-squared-based measures of association.

Kendall’s Tau b and c

These statistics measure the relative degree of agreement or disagreement between two variables.


Crosstabulation Summary Statistics
Summary Statistics

The Summary Statistics option creates information on the center, spread, and shape of the data:  The number of values in the variable; the average, variance, standard deviation, minimum and maximum values; and the sum of all the values.  This information is helpful when you need to determine if other statistical analyses might be appropriate to use with the data, or when you need to determine if you should transform the data.


Cumulative Counts

Displays the cumulative frequency for each bar (that is, include the frequency for all the classes up to and including the current class).  Deselect this option if you do not want successive bars to include previous class frequencies.


Data

Enter the name of the variable that contains the data that will be analyzed.


Density Trace (Two-Sample Comparison Analysis)

The Density Trace option creates and displays a Density Trace for each sample.  The plot estimates the probability density function for a continuous variable.  The plot is a smoothed Histogram that shows the basic shape of the density function.

The density is estimated by counting (in a weighted manner) the number of observations in an interval of fixed length, which is moved through the data, and then dividing that count by the width of the interval.

Unlike a Histogram, the Density Traces Plot uses overlapping intervals and a weight function to smooth the densities, resulting in a continuous line rather than a group of rectangles as in a Histogram.

Use the Density Trace Options dialog box to select options for this plot,


Density Trace

The Density Trace option creates a plot that allows you to view the shape or distribution of the data, especially the variations in density over the range of the data.

Unlike a Histogram, the Density Trace uses overlapping intervals and a weight function to smooth the densities, which results in a continuous line rather than a group of rectangles as in a Histogram.


Density Trace Options Dialog Box (One-Variable Analysis)

Use this dialog box to choose the method that will be used to estimate the density function, to enter the interval width, and the value that will be used for X-axis resolution of the plot.

Method

Interval Width

X-Axis Resolution


Density Trace (One-Variable Analysis)

The Density Trace graphical option calculates and displays a plot that allows you to view the shape or distribution of the data, especially the variations in density over the range of the data.

Unlike a Histogram, the Density Trace plot uses overlapping

intervals and a weight function to smooth the densities, resulting in a continuous line rather than a group of rectangles as in a Histogram.

Use the Density Trace Options dialog box to select options for this plot.


Density Traces (Output)
Density Trace Plot

The Density Trace option creates a plot you can use to view the shape or distribution of the data, especially the variations in density over the range of the data.  Unlike a histogram, the Density Trace uses overlapping intervals and a weight function to smooth the densities, resulting in a continuous line rather than a group of rectangles as in a histogram.

Use the Density Trace Options dialog box to choose the method that will be used to estimate the density function, to enter a value for the degree of overlap that will be used to compute the density trace, and to enter the number of density values that will be calculated.


Dependent Variable

Enter the name of the variable that contains the observations for the response variable.  The variable must contain all the data in the combined groups.


Diameter

Determines the size of the piechart.  The default is 100.


Display All Steps
All Steps

This option, when you use the Forward Selection or Backward Selection options, instructs the program to display each step in the stepwise regression.


Display Final Model Only
Final Model Only

This option, when you use the Forward Selection or Backward Selection options, instructs the program to display only the final model results.


Distribution Fitting Data Input Dialog Box
Distribution Fitting Analysis Dialog Box

The Distribution Fitting Analysis provides a way to determine if data follow a normal or another type of distribution.  This analysis fits one of several distribution functions, such as a normal, extreme value, lognormal, or Weibull.  Use the analysis to compare the data to the theoretical distribution and to provide chi-square (comparison of observed and expected frequencies) and Kolmogorov-Smirnov (goodness-of-fit) tests.  Calculations include cumulative distribution functions and inverse cumulative distribution functions.

Data

(Select)

Sort


Distribution Fitting Options Dialog Box

This dialog box allows you to select the type of distribution you want to fit.

Exponential Distribution

Extreme Value Distribution

Lognormal Distribution

Normal Distribution

Weibull Distribution


Analysis Summary (Distribution Fitting  Analysis)

The Analysis Summary option creates a summary of the analysis that includes the name of the variable you selected, the number of values and their range, and the mean and standard deviation for the distribution.


Distribution Fitting Procedure Summary
Analysis Summary

The Analysis Summary option creates a summary of the analysis that includes the name of the variable you selected, the number of values and their range, and the mean and standard deviation for the distribution.


Distribution Functions 1 and 2 (Distribution Fitting Analysis)
Distribution Functions 1 and 2

The Distribution Functions (1 and 2) options allow you to display a Normal Distribution Plot.  A normal distribution is a continuous probability distribution used to characterize a wide variety of data.  It is a symmetric, bell-shaped distribution determined completely by its mean and standard deviation.  A normal distribution is particularly important in statistics because sample means tend to follow the normal distribution as a result of the Central Limit Theorem.  The plot allows you to visually compare a density and a cumulative density function.


Distribution Functions
Distribution Functions 1 and 2

The Distribution Functions (1 and 2) options allow you to display a Normal Distribution Plot.  A normal distribution is a continuous probability distribution used to characterize a wide variety of data.  It is a symmetric, bell-shaped distribution determined completely by its mean and standard deviation.

A normal distribution is particularly important in statistics because sample means tend to follow the normal distribution as a result of the Central Limit Theorem.  The plot allows you to visually compare a density and a cumulative density function.


Distribution Functions Options Dialog Box

This dialog box allows you to select the function you want to use to produce the Distribution Plot.

Density Function Plot

CDF Plot

Survivor Function

Log Survivor Function Plot

Hazard Function Plot

X-Axis Resolution


Double Reciprocal Model
Double Reciprocal

Fits the reciprocal of the dependent variable and the reciprocal of the independent variable.  It is defined by the equation: Y = 1/(a + bX).


Draftsman's Plot (X-Y-Z Plot Analysis)

The Draftsman’s Plot option creates a series of two-variable plots for all combinations of the three selected variables.

The plot shows the top, front, and side views of the data.  Use these plots to detect positive, negative, or zero correlations; outliers; and/or curvature.


Draftman's Plot

The Draftsman’s Plot option creates a series of two-variable plots for all combinations of the three variables you select.  The plot shows the top, front, and side views of the data.

Use the plots to detect positive, negative, or zero correlation; outliers; and curvature.


Duncan
Duncan Method

This method protects the results against Type I errors for a small number of comparisons.


Error Term

Choose the type of mean square that will be used as the denominator to calculate the F-ratio for the factor you select in the Factor list box.  Click the name of the factor to select it.

None

The F-ratio will not be calculated.

Residual

Uses the error (estimated) mean square as the denominator to calculate the F-ratio for the factor.  This option is the default.


Exclude

Allows you to list the interactions you want to exclude.


Exclude Interactions Options Dialog Box

Allows you to exclude or include interactions from a model.

Include

Exclude


Exponential Distribution

Fits time-series data, such as arrival times, where arrivals are expected at a constant rate.  This distribution is a special case of both the Gamma and the Weibull distributions.

The Exponential (b) density function is relatively simple:  (1/b)ex/b for x=0; it has mean = b, and variance = b2.  This is the only continuous distribution that has a “memoryless” property.  For more information, see Law and Kelton.


Exponential Model

Fits an exponential model, which is equivalent to taking the natural log of Y.  It is defined by the equation: Y = exp(a + bX).


Extreme Value Distribution

Fits the limiting distribution for the maximum number of samples collected from a process.  This distribution applies when extremes rather than means, are collected from samples from an unknown or complex underlying distribution.


F-to-Enter

Enter a value for the F-ratio at or above which variables will be entered into the model (you chose either the Forward Selection or Backward Selection options).  Enter a number greater than or equal to the number in the F-to-Remove text box; the default is 4.


F-to-Remove

Enter a value for the F-ratio below which variables will be removed from the model (you chose either the Forward Selection or Backward Selection options).  Enter a number greater than or equal to 0 and less than or equal to the number in the F-to-Enter text box; the default is 4.


Factor

Choose the factor for which you want to select an error term in the Error Term list box.  Click the name of the factor to select it.


Factors

Enter the names of the variables that contain the sample numbers or level codes.  Each factor must contain one code for each point in the response variable. The program uses the codes to divide the data into groups.


Fit All Variables
All Variables

Enters all the variables into the model at one time.


Fit Backward Selection
Backward Selection

Performs a backward stepwise regression, which begins with all the variables in the model and removes them one at a time.


Fit Forward Selection
Forward Selection

Performs a forward stepwise regression, which begins with no variables in the model and adds them one at a time.


Fitted Line

Indicates if a fitted line will appear on the plot; this option is the default.


Fitted Y

Includes the estimated value of the dependent variable (forecast) in the report.


Flag Outliers

Indicates if outliers will be placed on separate high or low stems.  The default is flagged outliers.


Forecast at X

Enter the values for X for which the program will predict a value for Y.


Forecasts (Simple Regression Analysis)

The Forecasts option creates a table of the predicted values for Y using the fitted model.  The table displays the values for the prediction limits and confidence limits.  The prediction and confidence intervals correspond to the Inner and Outer bounds on the plot of the fitted model.

Use the Forecasts Options dialog box to enter a percentage for the confidence level that will be used to calculate the confidence limits; and to enter values for X that will be used to calculate a value for Y.


Forecasts (Simple Regression Analysis)

The Forecasts option creates a table of the predicted values for Y using the fitted model.  The table displays the values for the prediction limits and confidence limits.

The prediction and confidence intervals correspond to the Inner and Outer bounds on the plot of the fitted model.


Forecasts Options Dialog Box

Use this dialog box to enter a percentage for the confidence level and values for X.

Confidence Level

Forecast at X


Frequency Histogram (Distribution Fitting Analysis)

The Frequency Histogram option creates a Frequency Histogram with an overlayed distribution curve.  The program divides the data into sets of nonoverlapping intervals and plots bars for each interval.  The height of each bar is proportional to the number of observations that fall within that interval.  Use the plot to determine if the data follow the distribution you selected.


Frequency Histogram

The Frequency Histogram option creates a plot that divides the data into sets of nonoverlapping intervals and plots bars for each interval.  The height of each bar is proportional to the number of observations that fall within that interval.  From the plot, you can determine the distribution of the data.

In the Distribution Fitting Analysis the distribution curve overlays the Frequency Histogram.


Frequency Histogram Graphical Options Dialog Box

This dialog box allows you to select graphical options for the Frequency Histogram Analysis.

Frequency Histogram (Frequency Histogram Analysis)


Frequency Histogram Tabular Options Dialog Box

This dialog box allows you to select tabular options for the Frequency Histogram Analysis.

Analysis Summary


Frequency Histogram Analysis Dialog Box

The Frequency Histogram Analysis provides a way to summarize data that are measured on a discrete or continuous interval scale.  It is used to illustrate the major features of the distribution of the data, such as the number of school-age children in each of n families (Weiss and Hassett, 1991).

The range of possible values is divided into classes or groups.  For each group, a rectangle is drawn with a base height equal to the frequency of the values in that specific group, and an area proportional to the number of observations that fall into that group.

Data

Select

Sort

See also

Using the Frequency Histogram Analysis

Frequency Plot Options


Analysis Summary (Frequency Histogram Analysis)

The Analysis Summary option creates a summary of the analysis that includes the name of the selected variable, the number of observations in the variable, and the range of the values.


Frequency Histogram Procedure Summary
Analysis Summary

The Analysis Summary option creates a summary of the analysis that includes the name of the variable you selected, the number of observations in the variable, and the range of the values.


Frequency Plot Options Dialog Box

Allows you to:

•	select the number of classes into which the data will be grouped

•	enter the Lower and Upper limits for the first and last class

•	indicate if you want to keep the current scaling.

Number of Classes

Lower Limit

Upper Limit

Counts

Hold

Plot Type


Frequency Table Options Dialog Box

This dialog box allows you to indicate how the percentages will be calculated for the cells in the table.

Table Percentages From


Frequency Tabulation (One-Variable Analysis)

The Frequency Tabulation tabular option groups the data into the default number of class intervals, and produces a table of frequencies and cumulative frequencies that summarizes the distribution of the data.

Use the Frequency Tabulation Options dialog box to select options for this table,


Frequency Tabulation

The Frequency Tabulation option creates a table in which the program groups the data into the default number of class intervals.  The program also produces a table of frequencies and cumulative frequencies that summarizes the distribution of the data.


Frequency Tabulation Options Dialog Box

Enter the number of class intervals into which the data will be grouped, to enter a value for the Lower limit for the first class, to enter a value for the Upper Limit, and to indicate if the current scaling should be retained.

Number of Classes

Lower Limit

Upper Limit

Hold


Geometric Mean (Summary Statistic)

Displays the value for the geometric mean of the data, which is the result of multiplying n values and taking the nth root.  Use the value to measure the central tendency of the data.


Goodness-of-Fit Tests

The Goodness-of-Fit Tests option creates a standardized chi-square statistic that compares observed frequencies with the expected frequencies predicted by the fitted distribution.  If the p-value is less than .05 (for a 95 percent confidence level), the data do not fit the distribution.

The Kolmogorov-Smirnov one-sample test is run for for goodness-of-fit.  This calculation is a nonparametric method used to test the overall goodness-of-fit between the distribution of the data and the distribution you select.  DPLUS is the maximum amount that the empirical cumulative distribution function exceeds the fitted cumulative distribution function.  DMINUS is the maximum amount that the empirical cumulative distribution function falls below the fitted cumulative distribution function.  DN is the maximum of DPLUS and DMINUS.  If the approximate p-value falls below .05, then the two distributions are significantly different at a 95 percent confidence level.


Goodness-of-Fit Tests

The Goodness-of-Fit Tests option creates a standardized chi-square statistic that compares observed frequencies with the expected frequencies predicted by the fitted distribution.  If the p-value is less than .05 (for a 95 percent confidence level), the data do not fit the distribution.

The Kolmogorov-Smirnov one-sample test is run for for goodness-of-fit.  This calculation is a nonparametric method used to test the overall goodness-of-fit between the distribution of the data and the distribution you select.  DPLUS is the maximum amount that the empirical cumulative distribution function exceeds the fitted cumulative distribution function.  DMINUS is the maximum amount that the empirical cumulative distribution function falls below the fitted cumulative distribution function.  DN is the maximum of DPLUS and DMINUS.  If the approximate p-value falls below .05, then the two distributions are significantly different at a 95 percent confidence level.


Distribution Fitting - Graphical Options Dialog Box
Distribution Fitting Graphical Options Dialog Box

This dialog box allows you to select graphical options for the Distribution Fitting Analysis.  The options are listed below.

Density Trace (Distribution Fitting)

Symmetry Plot (Distribution Fitting)

Normal Probability Plot (Distribution Fitting)

Weibull Plot (Distribution Fitting)

Frequency Histogram (Distribution Fitting)

Distribution Functions 1 and 2 (Distribution Fitting)


One-Variable Analysis Graphical Options Dialog Box

This dialog box allows you to select graphical options for the One-Variable analysis.

Scatterplot (One-Variable Analysis)

Box-and-Whisker Plot (One-Variable Analysis)

Frequency Histogram (One-Variable Analysis)

Quantile Plot (One-Variable Analysis)

Normal Probability Plot (One-Variable Analysis)

Density Trace (One-Variable Analysis)

Symmetry Plot (One Variable Analysis)


Histogram

Displays the data as a series of successive bars that represent classes.  The width of the bars is equal to the class interval; the height of the bars is equal to the number of observations in each class.


Histogram Options Dialog Box

Enter a value for the number of classes and for the Lower and Upper Limits, then enter numbers for the Y-axis, and indicate if you want to retain the current scaling.

Number of Classes (Histogram Options)

Lower Limit

Upper Limit

Counts

Hold


Hold

Indicates that the current scaling should be retained even if you enter different values on the Analysis dialog box.


Hypothesis Test Options Dialog Box
Hypothesis Tests Options Dialog Box

Enter a value for the mean and alpha level, and select the type of test that will be performed.

Mean

Alpha

Alternative Hypothesis


Hypothesis Tests (One-Variable Analysis)

The Hypothesis Tests option calculates and displays the results of three tests that concern the center of the population from which the sample comes:  A t-statistic, p-value, and a recommendation to either accept or not accept Ho (the null hypothesis).

The first test is a t-test of the null hypothesis that the mean of the variable equals 0 versus the alternative hypothesis that the mean of the variable is not equal to 0.

The second test is a sign test of the null hypothesis that the median of the variable equals 0 versus the alternative hypothesis that the median of the variable is not equal to 0.

The third test is a signed rank test of the null hypothesis that the median of the variable is not equal to 0.  It is calculated by comparing the average ranks of values above and below the hypothesized median.  The sign and signed rank tests are less sensitive to the presence of outliers, but are somewhat more effective than the t-test if the data all come from a single Normal distribution.

Use the Hypothesis Tests Options dialog box to modify the null hypothesis and test options,


Hypothesis Tests

The Hypothesis Tests option creates the t-statistic, its p-value, and the recommendation to either accept or reject H0 (the null hypothesis).  The program also performs two nonparametric tests for the median: The Sign test and the Signed Rank test.


Include

Determines the interactions that will be excluded from the model.  When you double-click the interactions you want to exclude; the program displays the interactions in the Exclude list box.


Include All Data
All Data

Includes all the cases and uses all the nonmissing values for each variable.


Include Complete Cases Only
Complete Cases Only

Includes cases only if there are values for all the variables.


Include Prediction Limits
Prediction Limits

Includes prediction limits on the plot.


Independent Variable

Enter the names of one or more independent variables that will be used to predict the values for the dependent variable.  Enter numeric variables.


Influential Points

The Influential Points option creates the row numbers for the observations that are flagged as high leverage or DFITS.  The average leverage value is 2 divided by the number of complete observations.


Influential Points

The Influential Points option creates the row numbers for the observations that are flagged as high leverage or DFITS.  The average leverage value is 2 divided by the number of complete observations.


Interaction

Determines the interaction that will be used in the analysis.  Click an interaction to select it.


Interaction Plot
Interaction Plot (Multifactor ANOVA)

The Interaction Plot option creates a plot that shows any two-factor interactions that were estimated in the analysis using the current model.

Use the Interaction Plot Options dialog box to indicate the interval, factor, and confidence level that will be used to calculate the intervals.


Interaction Plot
Interaction Plot (Multifactor ANOVA)

The Interaction Plot option creates a plot that shows any two-factor interactions that were estimated in the analysis using the current model.


Interaction Plot Options Dialog Box

This dialog box allows you to choose the model that will be used to determine the two-factor interactions.

Interval

Interaction

Confidence Level

Plot on Axis


Interquartile Range (Summary Statistic)

The Interquartile Range option displays the value for the upper quartile minus the lower quartile, which is the range in which the middle 50 percent of the data fall.  Use the value to measure the spread or dispersion of the data.


Interval Plots (Multiple Regression Analysis)

The Interval Plots option plots the dependent variable versus the predicted values, their row number, or any of the independent variables.

Use the Interval Plots Options dialog box to select options for the plot,


Interval Plots (Multiple Regression Analysis)

The Interval Plots option plots the dependent variable versus the predicted values, their row number, or any of the independent variables.


Interval Plots Options Dialog Box

This dialog box allows you to choose the type of confidence limits that will be used; to indicate how the data will be plotted; and enter the confidence level.

Plot Limits For

Confidence Level

Plot versus:


Interval Width

Enter a value for the percentage of the range of data (the degree of overlap) that will be used to compute the Density Trace.  Enter an integer between 10 and 90; the default is 60 percent.

Increasing the interval width makes the Density Trace smoother, but may obscure the original data.  Widths between 25 and 50 percent often give good results.


Key Glyph (Multiple-Variable Analysis)

The Key Glyph option creates a single glyph with individual rays labeled with the name of their corresponding variables.

A Key Glyph is helpful when you need to interpret the glyphs on smaller Sunray and Star Plots.

The first variable you enter into the dialog box is the first one plotted, starting at the 12:00 o’clock position and continuing clockwise.


Key Glyph

The Key Glyph option creates a single glyph with individual rays labeled with the name of their corresponding variables.

A Key Glyph is helpful when you need to interpret the glyphs on smaller Sunray and Star Plots.

The first variable you enter into the dialog box is the first one plotted, starting at the 12:00 o’clock position and continuing clockwise.


Kolmogorov-Smirnov Test (Two-Sample Comparison Analysis)

The Kolmogorov-Smirnov option tests the null hypothesis that the two samples can reasonably be assumed to come from the same distribution.

The summary displays the maximum vertical distance between the cumulative distribution functions for the two samples (DN).  If the distance is large enough, the p-value will be small.  If the p-value is small (less than a desired alpha level, such as .05), reject the hypothesis.


Kolmogorov-Smirnov Test

The Kolmogorov-Smirnov option tests the null hypothesis that the two samples can reasonably be assumed to come from the same distribution.

The summary displays the maximum vertical distance between the cumulative distribution functions for the two samples (DN).  If the distance is large enough, the p-value will be small.  If the p-value is small (less than a desired alpha level, such as .05), reject the hypothesis.


Kruskal-Wallis Test

The Kruskal-Wallis Test option calculates the results of the Kruskal-Wallis test.  The Kruskal-Wallis test is a nonparametric method that tests the assumption that the medians of the factor levels are equal.

The values in the entire set of observations are first ranked from the lowest to the highest, a rank is assigned to each observation, the mean of the ranks is calculated for each group, and the hypothesis is tested for the assumption that the medians are the same.  If the p-value is less than .05, reject the hypothesis.

In large sample sizes (more than five observations in each sample or more than three samples), the test statistic tends toward a chi-square distribution).  Check the results for small sample sizes with standard tables for the Kruskal-Wallis statistic.

The program corrects for ties, ranks them by their average, and adjusts the test statistic to reflect the extent of the ties.


Kruskal-Wallis Test (Multiple-Sample Comparison Analysis)
Kruskal-Wallis Test

The Kruskal-Wallis Test option calculates the results of the Kruskal-Wallis test.  The Kruskal-Wallis test is a nonparametric method that tests the assumption that the medians of the factor levels are equal.

The values in the entire set of observations are first ranked from the lowest to the highest, a rank is assigned to each observation, the mean of the ranks is calculated for each group, and the hypothesis is tested for the assumption that the medians are the same.  If the p-value is less than .05, reject the hypothesis.

In large sample sizes (more than five observations in each sample or more than three samples), the test statistic tends toward a chi-square distribution).  Check the results for small sample sizes with standard tables for the Kruskal-Wallis statistic.

The program corrects for ties, ranks them by their average, and adjusts the test statistic to reflect the extent of the ties.


Kurtosis (Summary Statistic)

Displays the value for the kurtosis coefficient.  Use the value to measure the flatness or steepness of the distribution of the data  with respect to a Gaussian or normal distribution.

For a normal distribution, the kurtosis coefficient is 0.  When the coefficient is less than 0, the curve is flat with short tails.  When the coefficient is greater than 0, the curve is either very steep at the center or has relatively long tails.


Label Variable

Enter the name of the character variable that contains the labels for the observations.  Leave the text box blank if you want to use row numbers as the labels.


Labels (for Barchart)

[Optional]  Enter the name of the variable that contains the labels for each bar.


Labels:  Counts
Counts

Uses the frequency of the counts as the label for the segment.


Labels:  Labels
Labels

Uses the values in the variable as the label for the segment.


Labels:  None
None

Displays the Piechart without labels for the segment.


Labels:  Percent
Percent

Uses the percentage of the sum of the counts as the label for the segment.


Lack-of-Fit Test (Simple Regression Analysis)

The Lack-of-Fit Test option determines if the current regression model is adequate to fit the data, or if you should select a more complicated model.

The test is performed by comparing the variability for the residuals of the current model with the variability between observations at replicate values of the independent variable, X.  The test assumes that the observations, Y, for a given X, are independent and normally distributed, and that the distributions of Y have the same variance.

Significant lack-of-fit shows that the specified model does not adequately fit the response.  The test requires replicated observations at one or more values of X.  A p-value less than .05 indicates that the model does not adequately fit the data at the 95 percent confidence level.


Lack-of-Fit Test (Simple Regression Analysis)

The Lack-of-Fit Test option determines if the regression model adequately fits the data.  The Lack-of-Fit Test assumes that the observation, Y, for a given X, are independent and normally distributed, and that the distributions of Y have the same variance.

Significant lack-of-fit shows that the specified model does not adequately fit the response.  The test requires replicated observations at one or more X values.


Legends:  Counts
Counts

Uses the frequency of the counts as the legend label.


Legends:  Labels
Labels

Uses the values in the variable as the legend label.


Legends:  None
None

Displays the Piechart without a legend.


Legends:  Percent
Percent

Uses the percentage of the sum of the counts as the legend label.


Level Indicators

Saves the indicator variables for each factor level.  If you use character data, the program converts the data into a numeric-coded variable.


Linear Model

Fits a simple linear regression equation for Y in terms of X.  The program fits the data to the linear model before you select a different model.

This model is preferred when you are performing a simple regression.  The model is defined by the equation:  Y = a + bX.


Lines

Determines if lines will appear from the labels to the segments on the chart.  The default is lines.


Log Probit Model
Log Probit

Fits a response of observed proportions or probabilities at each level of an independent variable.  The model is appropriate when the response variable tends to follow a cumulative normal distribution.

The response function is a nonlinear S-shaped curve with asymptotes at 0 and 1.  The dependent variable must have values greater than 0 and less than 1.  It is defined by the equation Y = normal(a + b(Log X)).


Logarithmic-X Model
Logarithmic-X

Fits a logarithmic-X model; it is defined by the equation: Y = a + b(Log X).


Logistic Model
Logistic

Fits a response of observed proportions or probabilities at each level of an independent variable.

The response function is a nonlinear S-shaped curve with asymptotes at 0 and 1.  The dependent variable must have values greater than 0 and less than 1.  It is defined by the equation Y = exp(a + bX)(1 + exp(a + bX)).


Lognormal Distribution

Takes on various shapes if the distribution is positively skewed.  Use it for processes in which the value is a random proportion of the previous value, such as personal incomes or particle sizes from breakage processes.  The log of data that follow the lognormal distribution are normally distributed.


Lower Limit

Enter a value for the Lower limit for the first class.  Enter any number lower than the Upper limit; the default depends on the data.


Lower Quartile (Summary Statistic)

Displays the value below which 25 percent of the data will fall.  Use the value to measure the spread or dispersion of the data.


LSD
LSD Method

Used when the F-ratio is significant, and you want to make planned comparisons.


LSD Interval
LSD Intervals

Used when the F-ratio is significant and you want to make planned comparisons.

If you are using Multifactor ANOVA, the program uses this interval to calculate the two-factor interactions.


Mahalanobis Distances

Saves statistics that help identify unusual values for the independent variables in the regression.


Maximum (Summary Statistic)

Displays the maximum value for the data.  Use the value to measure the spread or dispersion of the data.  This option is one of the defaults.


Maximum Order Interaction

Enter a number for the highest order interaction that will be estimated.  Enter an integer between 1 and 4; the default is 1.

The program omits all higher-order interactions from the analysis along with any options that relate to them.


Maximum Steps
Max. Steps

Enter the maximum number of steps that will be performed before the selection process stops when you choose the Forward Selection or Backward Selection options.

Enter an integer greater than 0; the default is 50.


Mean

Enter a value for the hypothetical mean of the paired differences.  Enter any real number; the default is 0.


Mean Marker Check Box
Mean Marker

Displays the location of the average on the plot.  This option is one of the defaults.

The marker is represented by a plus sign (+).


Means Plot

The Means Plot option creates a plot of the mean for each factor level and the intervals around each mean.  The intervals are constructed so that if two means are the same, their intervals will overlap a given percentage of the time.

Any pair of intervals that do not overlap, vertically correspond to a pair of means that have a statistically significant difference.

Use the Means Plot Options dialog box to indicate the interval, factor, and confidence level that will be used to calculate the intervals.


Means Plot

The Means Plot option creates a plot of the mean for each factor level and the intervals around each means.  The intervals are constructed so that if two means are the same, their intervals will overlap a given percentage of the time.

Any pair of intervals that do not overlap, vertically correspond to a pair of means that have a statistically significant difference.

Use the Means Plot Options dialog box to indicate the interval, factor, and confidence level that will be used to calculate the intervals.


Means Plot Options Dialog Box (Subset Analysis)

This dialog box allows you to choose the method that will be used to calculate the values for the Means Plot.

Type

Factor

Confidence Level


Means Table and Plot Options Dialog Box

Allows you to choose the method that will be used to calculate the values for the Table of Means, and to enter a value for the confidence level.

Intervals

Confidence Level


Median (Summary Statistic)

Displays the value for the median of the data.  Use the value to measure the central tendency of the data.


Median Notch

This option adds a notch to the box around the median.  The length of the notch represents an approximate 95 percent confidence interval for the median.


Minimum (Summary Statistic)

Displays the minimum value for the data.  Use the value to measure the spread or dispersion of the data.  This option is one of the defaults.


Mode (Summary Statistic)

Displays the value for the mode of the data (the value with the highest frequency).  Use the value to measure the central tendency of the data.  If a value unique to the highest frequency is not created, no value displays.


Mosaic Plot (Crosstabulation Analysis)
Mosaic Plot

The Mosaic Plot option creates a plot of the data.  Rectangles whose areas are proportional to the cell counts are constructed.  The width of the bars is proportional to the percentage distribution of the variable.

Use the Mosaic Plot Options dialog box to select options for the plot.


Mosaic Plot

The Mosaic Plot option creates a plot that represents the frequencies in the cells of the data.  The program constructs rectangles whose areas are proportional to the frequencies in the table.


Mosaic Plot Options Dialog Box

Indicates the direction in which the plot will display:  Horizontal or Vertically.  Horizontal is the default.


Multifactor ANOVA - Graphical Options Dialog Box
Multifactor ANOVA Graphical Options Dialog Box

This dialog box allows you to choose graphical options for a Multifactor ANOVA.

Scatterplot (Multifactor ANOVA)

Means Plot (Multifactor ANOVA)

Interaction Plot (Multifactor ANOVA)

Residuals versus Factor Levels Plot (Multifactor ANOVA)

Residuals versus Predicted Plot (Multifactor ANOVA)

Residuals versus Row Number Plot (Multifactor ANOVA)


Multifactor ANOVA - Tabular Options Dialog Box
Multifactor ANOVA Tabular Options Dialog Box

This dialog box allows you to choose tabular options for a  Multifactor ANOVA.

Analysis Summary (Multifactor ANOVA)

ANOVA Table (Multifactor ANOVA)

Table of Means (Multifactor ANOVA)

Multiple Range Tests


Multifactor ANOVA Data Input Dialog Box
Multifactor ANOVA Dialog Box

The Multifactor ANOVA examines the effects of two or more factors on one variable; you typically use data you collect for a designed experiment.  The design can be balanced or unbalanced and can also include covariates.

You can select the default values and perform a standard analysis, or you can customize the analysis in a variety of ways, such as using either Type I or Type III sum of squares or selecting the order of the interactions.

Multifactor ANOVA is useful in a range of disciplines when it is suspected that two or more factors affect a key variable.  For example, in marketing studies, you might test to see how product sales are affected by alternative pricing, advertising techniques, and different packaging options.  In medical studies, you might test to determine how disease is combated by using different combinations of drugs, varying dosages of drugs, or by using alternative treatment schedules.  In agricultural studies, you might measure how weight gain and the overall health of cattle are affected by brands of feed, amounts of medication, and type of breed.

You can analyze models that test hypotheses using terms other than the mean squared error in the denominator.  If the study has only one factor, use the One-Way ANOVA Analysis.

Dependent Variable

Factors

Covariates

(Select)

Sort

To select options for the analysis use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a txt or graphics pane, then click the left mouse button on either Pane Options or Analysis Options.

See also

Using Multifactor ANOVA

Multifactor ANOVA Options

ANOVA Table Options

Confidence Intervals Options

Multiple Range Tests Options

Scatterplot Options

Means Plot Options

Interaction Plot Options

Residual Plot Options


Multifactor ANOVA Options Dialog Box

Enter a number for the highest order interaction.  You can also choose the interactions you want to exclude from the analysis by clicking the Exclude… command on the dialog box.

Maximum Order Interaction

Exclude...


Multifactor ANOVA Save Results Options Dialog Box
Save Results Options Dialog Box (Multifactor ANOVA)

The Save Results Options dialog box allows you to choose the results you want to save.  There are five options: Level Counts, Level Means, Level Standard Errors, Least Squares Means, and Residuals.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results Options button on the Analysis toolbar (the fourth button from the left).


Multifactor ANOVA Table of Means
Table of Means (Multifactor ANOVA)

The Table of Means option creates a table that shows the mean of the variable for each level of the factors.  The table includes the number of observations (Count) at each level, the mean, the standard error, and the lower and upper limits for the confidence intervals.

In a balanced design, the least squares means are equal to the arithmetic average; in an unbalanced design, the least squares means differ.  Using the arithmetic average in an unbalanced design instead of least squares means is not statistically valid because assumptions are made that are not true.

Use the Confidence Intervals Options dialog box to enter a value for the confidence level that will be used to calculate the confidence intervals for the least squares means.


Multifactor ANOVA Table of Means
Table of Means

The Table of Means option creates a table that shows the mean of the variable for each level of the factors.  The table includes the number of observations (Count) at each level, the mean, the standard error, and the lower and upper limits for the confidence intervals.

In a balanced design, the least squares means are equal to the arithmetic average; in an unbalanced design, the least squares means differ.  Using the arithmetic average in an unbalanced design instead of least squares means is not statistically valid because assumptions are made that are not true.

Use the Confidence Intervals Options dialog box to enter a value for the confidence level that will be used to calculate the confidence intervals for the least squares means.


Multifactor ANOVA Procedure Summary
Analysis Summary (Multifactor ANOVA)

The Analysis Summary option creates a summary of the analysis that contains the name of the dependent variable and the factors. It also displays the number of complete cases in the analysis.


Multifactor ANOVA Procedure Summary
Analysis Summary (Multifactor ANOVA)

The Analysis Summary option creates a summary of the analysis that contains the name of the dependent variable and the factors. It also displays the number of complete cases in the analysis.

Use the Multifactor ANOVA Options dialog box to enter the number of highest-order interactions that will be estimated.


Multiple Range Tests Options Dialog Box

Allows you to select the method that will be used to determine the statistically significant differences among the means, and to enter a value for the confidence level.

If you are using Multifactor ANOVA, an additional item appears on the dialog box:  Factor.

Method

Factor

Confidence Level


Multiple Range Tests

The Multiple Range Tests option creates applies a multiple comparison analysis to the data to determine which means are significantly different.

The top portion of the table identifies homogenous groups with columns of Xs that, within each column, indicate the group means for which there are no statistically significant differences.

The bottom portion of the table shows the estimated difference between each pair of means.  An asterisk indicates a statistically significant difference at a given confidence level; this statistic will vary depending on the method you are using.

Use the Multiple Range Tests Options dialog box to choose the method and the confidence level that will be used to calculate the statistically significant differences among the means.


Multiple Range Tests (Multiple-Sample Comparison Analysis)
Multiple Range Tests

The Multiple Range Tests option creates applies a multiple comparison analysis to the data to determine which means are significantly different.

The top portion of the table identifies homogenous groups with columns of Xs that, within each column, indicate the group means for which there are no statistically significant differences.

The bottom portion of the table shows the estimated difference between each pair of means.  An asterisk indicates a statistically significant difference at a given confidence level; this statistic will vary depending on the method you are using.


Multiple Regression - Graphical Options Dialog Box
Multiple Regression Graphical Options Dialog Box

This dialog box allows you to select Graphical Options for the Multiple Regression Analysis.

Component Effects Plot (Multiple Regression)

Observed versus Predicted Plot (Multiple Regression)

Residuals versus X Plot (Multiple Regression)

Residuals versus Predicted (Multiple Regression Analysis)

Residual versus Row Number Plot (Multiple Regression)

Interval Plots (Multiple Regression)


Multiple Regression - Tabular Options Dialog Box
Multiple Regression Tabular Options Dialog Box

This dialog box allows you to select tabular options for the Multiple Regression Analysis.

Analysis Summary (Multiple Regression)

Conditional Sums of Squares (Multiple Regression)

Confidence Intervals (Multiple Regression Analysis)

Correlation Matrix (Multiple Regression)

Reports (Multiple Regression)

Unusual Residuals (Multiple Regression)

Influential Points (Multiple Regression)


Multiple Regression Analysis Dialog Box

The Multiple Regression Analysis allows you to calculate a regression model between one dependent variable and one or more independent variables.  Use the analysis when you want to use weights to force the intercept to 0 (regression through the origin), or to perform a stepwise regression.  Like the Simple Regression Analysis, multiple regression uses least squares to estimate the regression model.

When you use this analysis, the program calculates a variety of statistics, including an analysis of variance table, and various plots.  You can control the way the program enters and removes variables from the model for a stepwise regression.

Dependent Variable

Independent Variables

Select

Weights

Sort

Use the Options dialog boxes to select options for the analysis.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left mouse button on either Pane Options or Analysis Options.

See also

Using the Multiple Regression Analysis

Multiple Regression Options

Confidence Intervals Options

Reports Options

Component Effects Plot Options

Residual Plot Options

Interval Plots Options


Multiple Regression Options Dialog Box

This dialog box allows you to select the independent variables, and how you should enter them.

Fit

Constant in Model

F-to-Enter

F-to-Remove

Maximum Steps

Display

Box-Cox Transformation

Power

Autocorrelation

You also choose whether to optimize the model, the value of the addend in the Box-Cox Transformation, and whether to apply a Cochrane-Orcutt Transformation.


Analysis Summary (Multiple Regression Analysis)

The Analysis Summary option creates a summary of the analysis that includes the estimated coefficients, standard errors, t-values, and p-values.

The p-values correspond to tests of the hypotheses that the coefficients are equal to 0, which is equivalent to concluding that there is no linear relationship between the independent and dependent variables.  Small p-values (less than an alpha level such as .05), indicate statistically significant nonzero coefficients.

The R-Squared statistic measures the proportion of the variability in Y that the model accounts for.  The values range between 0 and 100 percent.

The Adjusted R-Squared statistic at the bottom of the ANOVA table adjusts the standard R-Squared value, based on the number of coefficients in the model.  This statistic is useful for comparing regression models that have different numbers of independent variables.

The standard error of estimation is the estimated standard deviation of the residuals around the fitted line.  The mean absolute error is the mean of the absolute values of the residuals.

The Durbin-Watson statistic tests for significant autocorrelation in the residuals.  Values below 1.3 to 1.4 usually indicate significant serial correlation in the residuals.

Use the Multiple Regression Options dialog box to select options for the analysis.


Analysis Summary (Multiple Regression Analysis)

The Analysis Summary option creates a summary of the analysis that shows the estimated coefficients, standard errors, t-values, and p-values.

The p-values correspond to tests of the hypotheses that the coefficients are equal to 0.  Small p-values (less than an alpha level such as .05), indicate statistically significant nonzero coefficients.

The R-Squared statistic measures the proportion of the variability in Y that the model accounts for.  The Adjusted R-Squared statistic adjusts the standard R-Squared value, based on the number of coefficients in the model.

The standard error of estimation is the estimated standard deviation for the residuals around the fitted line.  The Durbin-Watson statistic tests for significant autocorrelation in the residuals.  For more information on these statistics, see the Multiple Regression section in the User Manual.


Save Results Options Dialog Box (Multiple Regression Analysis)

The Save Results Options dialog box allows you to select the results you want to save.  There are 12 selections: Predicted Values, Standard Error of Predictions, Lower Limits for Predictions, Upper Limits for Predictions, Standard Errors of Means, Lower Limits for Forecast Means, Upper Limits for Forecast Means, Residuals, Studentized Residuals, Leverages, DFITS Statistics, and Mahalanobis Distances.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Multiple-Sample Comparison - Graphical Options Dialog Box
Multiple-Sample Comparison Graphical Options Dialog Box

Allows you to select graphical options for the Multiple-Sample Comparison Analysis.

Scatterplot (Multiple-Sample Comparison)

Means Plot (Multiple-Sample Comparison)

Box-and-Whisker Plot (Multiple-Sample Comparisons Analysis)

Residuals versus Samples Plot (Multiple-Sample Comparison)

Residuals versus Predicted (Multiple-Sample Comparison)

Residuals versus Observation (Multiple-Sample Comparison)


Multiple-Sample Comparison - Tabular Options Dialog Box
Multiple-Sample Comparison Tabular Options Dialog Box

This dialog box allows you to select tabular options for the Multiple-Sample Comparison Analysis.

Analysis Summary (Multiple-Sample Comparison)

Summary Statistics

ANOVA Table (Multiple-Sample Comparison)

Table of Means (Multiple-Sample Comparison)

Multiple Range Tests (Multiple-Sample Comparison)

Variance Check (Multiple-Sample Comparison)

Kruskal-Wallis Test (Multiple-Sample Comparison)


Multiple-Sample Comparison Data Input Dialog Box
Multiple-Sample Comparison Dialog Box

You use the Multiple-Sample Comparison Analysis to compare several sets of data.  The observations in the samples are assumed to be independent.  For example, to compare the length of automobiles manufactured in the United States, Europe, and Japan, you use three separate length variables.  The size of the variables does not have to be equal.

This analysis is similar to One-Way ANOVA except you do not need a factor variable and you enter the data in separate columns in the DataSheet.

Samples

Select

Sort

To select options for the analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left mouse button on either Pane Options or Analysis Options.

See also

Using the Multiple-Sample Comparisons Analysis

Summary Statistics Options

Means Table and Plot Options

Multiple Range Tests Options

Box-and-Whisker Plot Options


Analysis Summary (Multiple-Sample Comparison Analysis)

The Analysis Summary option creates a summary of the analysis that includes the names of the variables in each sample and the number and range of the values in each sample.


Multiple-Sample Comparison Procedure Summary
Analysis Summary

The Analysis Summary option creates a summary of the analysis that includes the names of the variables in each sample and the number and range of the values in each sample.


Save Results Options Dialog Box (Multiple-Sample Comparison Analysis)

The Save Results Options dialog box allows you to select the results you want to save.  There are six selections: Counts, Means, Standard Deviations, Standard Errors, Labels, and Residuals.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Multiple-Variable Analysis Graphical Options Dialog Box

Allows you to select graphical options for the Multiple-Variable Analysis.

Scatterplot Matrix (Multiple-Variable Analysis)

Star Plots

Sunray Plot (Multiple-Variable Analysis)

Key Glyph (Multiple-Variable Analysis)


Multiple-Variable Analysis Tabular Options Dialog Box

Allows you to select tabular options for the Multiple-Variable Analysis.

Analysis Summary (Multiple-Variable Analysis)

Summary Statistics (Multiple-Variable Analysis)

Confidence Intervals (Multiple-Variable Analysis)

Correlations

Rank Correlations (Multiple-Variable Analysis)

Covariances (Multiple-Variable Analysis)

Partial Correlations (Multiple Variable Analysis)


Multiple-Variable Analysis Dialog Box

The Multiple-Variable Analysis allows you to analyze the relationship among several numeric variables by performing various statistical and graphical analyses.  For example, options in this analysis allow you to calculate specific summary statistics, such as standard deviations and average, confidence intervals, correlations, and covariances.

You can plot the data in a Scatterplot Matrix, as a Star Plot or as a Sunray Plot, or produce a Key Glyph.

Data

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Multiple-Variable Analysis

Multiple-Variable Analysis Options

Summary Statistics Options

Confidence Intervals Options

Star Plot/Sunray Plot Options

Save Results Options


Multiple-Variable Analysis Options Dialog Box

Allows you to select the data you want to include in the analysis.

Include


Analysis Summary (Multiple-Variable Analysis)

The Analysis Summary option creates a summary of the analysis that includes the names of the selected variables and the number of complete cases.

Use the Multiple-Variable Options dialog box to select options for the summary,


Analysis Summary (Multiple-Variable Analysis)

The Analysis Summary option creates a summary of the analysis that includes the names of the variables, and the number of complete cases.


Multiple X-Y Plot Graphical Options Dialog Box

Allows you to select graphical options for the Multiple X-Y Plot analysis.

Scatterplot (Multiple X-Y Plot Analysis)


Multiple X-Y Plot Tabular Options Dialog Box

Allows you to select tabular options for the Multiple X-Y Plot analysis.

Analysis Summary (Multiple X-Y Plot Analysis)


Multiple X-Y Plot Analysis Dialog Box

The Multiple X-Y Plot analysis produces scatterplots with one variable on the X-axis and one or more variables on the Y-axis.

You can choose to plot Y-axis variables with the scale on the left or the right.  The size of the scales adjusts automatically to reflect the range of the values.

You can generate scatterplots with lines, points, or both.

Y (Left Axis)

Y (Right Axis)

X

Select

Sort


Analysis Summary (Multiple X-Y Plot Analysis)

The Analysis Summary option creates a summary of the analysis that includes the names of the selected variables and the total number of plotted points.


Analysis Summary (Multiple X-Y Plot Analysis)

The Analysis Summary option creates a summary of the analysis that includes the names of the selected variables and the total number of plotted points.


Multiple X-Y-Z Plot Graphical Options Dialog Box

Allows you to select graphical options for the Multiple X-Y-Z Plot analysis.

Scatterplot (Multiple X-Y-Z Analysis)


Multiple X-Y-Z Plot Tabular Options Dialog Box

Allows you to select tabular options for the Multiple X-Y-Z Plot analysis.

Analysis Summary (Multiple X-Y-Z Plot Analysis)


Multiple X-Y-Z Plot Analysis Dialog Box

The Multiple X-Y-Z Plot Analysis produces a scatterplot for three or more variables.

One variable each is plotted on the X- and Y-axes; one or more variables are plotted on the Z-axis.  You can choose to plot Z-axis variables with the scale on the left or the right.

The size of the scales is adjusted automatically to reflect the range of the values.

Z (Left Axis)

Z (Right Axis)

X

Y

Select

Sort


Analysis Summary (Multiple X-Y-Z Plot Analysis)

The Analysis Summary option displays the names of the selected variables, and the total number of grouped values.


Analysis Summary (Multiple X-Y-Z Plot Analysis)

The Analysis Summary option displays the names of the selected variables, and the total number of grouped values.


Scatterplot (Multiple X-Y-Z Plot Analysis)

The Scatterplot option creates and displays a three-dimensional scatterplot of the data with only the points plotted.


Scatterplot for the Multiple X-Y-Z Plot Analysis
Scatterplot

The Scatterplot option creates a three-dimensional scatterplot of the data with only the points plotted.


Multiplicative Model
Multiplicative

Fits a multiplicative model and is equivalent to taking the natural logs of Y and X.  It is defined by the equation: Y = aX^b.


Dependent Variable

Enter the name of the response variable that contains the data in the analysis.


ANOVA Table
ANOVA Table (Multifactor ANOVA)

The ANOVA Table option creates a standard analysis of variance table.  The table includes the residual sums of squares, the degrees of freedom (Df) for the residual, the residual mean square, an F-ratio that is calculated using the residual mean square (or the error term you choose), and the p-value for the F-ratio.

The table includes statistics for each main effect and interaction in the analysis.  Notes at the bottom of the table identify the error term that was used as the denominator to calculate each F-ratio.  Until you use the ANOVA Table Options dialog box to change the default, the table is initially calculated for Type III sums of squares.

Use the ANOVA Table Options dialog box to indicate which method will be used to calculate the sums of squares for each factor and to choose a factor for which you want to choose an Error term.  You can also indicate the type of mean square that will be used as the denominator to calculate the F-ratio, and to view the error term.


Multiple Range Tests

The Multiple Range Tests option applies a multiple comparison analysis to the data to determine which means are significantly different.

The top portion of the table identifies homogenous groups with columns of Xs that, within each column, indicate the group means for which there are no statistically significant differences.  The bottom portion of the table shows the estimated difference between each pair of means.  An asterisk indicates a statistically significant difference at a given confidence level; this statistic will vary depending on the method you are using.

Use the Multiple Range Tests Options dialog box to choose the method and the confidence level that will be used to calculate the statistically significant differences among the means.


Exclude...

Displays the Exclude Interactions Options dialog box.  Two list boxes appear on the dialog box: Include in the left section; Exclude in the right section.  Initially, all the interactions are listed in the Include list box.

Double-click the names of the terms you want to exclude from the analysis.  When you highlight the names, they move from one column to the other.  When you click the OK button on the Exclude Interactions Options and the Multifactor ANOVA Options dialog boxes the program excludes the terms in the Exclude column from the analysis.


Factor

Choose the factor for which you want to select an error term in the Error Term list box.  Click the name of the factor to select it.


Factor

Choose the factor that will be used in the analysis.  Click the name of the factor to select it.


Dependent Variable

Enter the name of the dependent variable whose values will be predicted by the estimated model.  Enter a numeric variable.


Confidence Intervals (Multiple Regression Analysis)

The Confidence Intervals tabular option calculates and displays the 95 percent confidence intervals for the coefficient estimates.  The estimates and the standard errors are identical to those shown in the initial table of model fitting results.


Means Plot (Multiple-Sample Comparison Analysis)

The Means Plot graphical option creates and displays a plot of the means for each sample and the intervals for the means.  Bars that do not overlap indicate a significant difference between the two means.  Bars that overlap indicate no significant difference between the means.

Use the Means Table and Plot Options dialog box to select options for this plot.


Summary Statistics (Multiple-Sample Comparison)

The Summary Statistics tabular option creates and displays statistical information about the center, spread, and shape of the data.  The number of values in each variable (Count); the average, variance, standard deviation, and total.

This information is helpful when you need to determine if other statistical analyses might be appropriate to use with the data, or when you need to determine if you need to transform the data.

Use the Summary Statistics Options dialog box to select options for this table.


Table of Means

The Table of Means tabular option creates and displays the number of observations (Count) in each sample, the means (average), the pooled standard errors, and the lower and upper limits for the means.

Use the Means Table and Plot Options dialog box to select options for this table.


Multiple Range Tests (One-Way ANOVA)
Multiple Range Tests

The Multiple Range Tests option applies a multiple comparison analysis to the data to determine which means are significantly different.

The top portion of the table identifies homogenous groups with columns of Xs that, within each column, indicate the group means for which there are no statistically significant differences.  The bottom portion of the table shows the estimated difference between each pair of means.  An asterisk indicates a statistically significant difference at a given confidence level; this statistic will vary depending on the method you are using.

Use the Multiple Range Tests Options dialog box to choose the method and the confidence level that will be used to calculate the statistically significant differences among the means.


Kruskal-Wallis Test

The Kruskal-Wallis Test tabular option creates and displays the results of the Kruskal-Wallis test, which is a nonparametric method that tests the assumption that the medians of the samples are equal.

The program first ranks the values in the entire set of observations from the lowest to the highest, assigns a rank to each observation, calculates the mean of the ranks for each sample, and tests the hypothesis for the assumption that the medians are the same.  If the p-value is less than .05, reject the hypothesis.

In large sample sizes (more than five observations in each sample or more than three samples), the test statistic tends toward a chi-square distribution (skewed distribution).  Check the results for small sample sizes with standard tables for the Kruskal-Wallis statistic.  The program corrects for ties, ranks them by their average, and adjusts the test statistic to reflect the extent of the ties.


Summary Statistics (One Variable Analysis)

The Summary Statistics tabular option creates and displays statistical information about the center, spread, and shape of the data:  The number of values in the variable; the average, variance, standard deviation, minimum and maximum values; the standardized skewness and standardized kurtosis; and the sum of all the values.

This information is helpful when you need to determine if other statistical analyses might be appropriate to use with the data, or when you need to determine if you should transform the data.

Use the Summary Statistics Options dialog box to select options for this table.


Frequency Histogram (One Variable Analysis)

The Frequency Histogram graphical option creates and displays a Frequency Histogram of the data.

The data are divided into sets of nonoverlapping intervals and plots bars for each interval.  The height of each bar is proportional to the number of observations that fall within that interval, which allows you to see the distribution of the data.

Use the Frequency Plot Options dialog box to select options for this plot.


Quantile Plot (One-Variable Analysis)

The Quantile Plot graphical option creates and displays the quantiles for the data.  The Y-axis represents the proportion of values that are below a particular value.


Normal Probability Plot (One-Variable Analysis)

The Normal Probability Plot graphical option constructs and displays a plot you use to determine if the data come from a normal distribution.

A Normal Probability Plot consists of an arithmetic (interval) horizontal axis scaled for the data and a vertical axis scaled so the cumulative distribution function of a normal distribution plots as a straight line.  The closer the data are to the reference line, the more likely they follow a normal distribution.

Use the Normal Probability Plot Options dialog box to select options for this plot.


Symmetry Plot (One-Variable Analysis)

The Symmetry Plot graphical option calculates and displays a plot that is helpful in determining the symmetry of the data.

Use this plot if you want to use analyses that are best applied to a symmetrical distribution.  A symmetrical dataset would closely follow the reference line.


Analysis Summary (Barchart Analysis)

The Analysis Summary tabular option creates and displays a summary of the analysis.  The summary includes the name of the selected variable, the number of values in the variable, and the sum of the values.


Barchart (Barchart Analysis)

The Barchart graphical option creates and displays a barchart from a column of numeric values.

Use the Barchart Options dialog box to select options for the plot,.


Frequency Histogram (Frequency Histogram Analysis)

The Frequency Histogram graphical option creates a histogram of the values in the variables.

Use the Frequency Plot Options dialog box to select options for the plot.


Box-and-Whisker Plot (Box-and-Whisker Plot Analysis)

The Box-and-Whisker Plot graphical option creates and displays a plot that is a graphical summary of the presence of outliers in the data.  The central box covers the middle 50 percent of the data; the sides of the box are the lower and upper quartiles, and the vertical line drawn through the box is the median.  The whiskers extend out to the lower and upper values of the data (the range).  The program plots the mean as a single point.

The data are divided into four areas of equal frequency, which allows you to visually examine the shape of the distribution to detect skewness.  You can show outliers as individual points beyond the whiskers, add notches to show confidence intervals for the medians, or add markers to show the means.

To select options for this plot, use the Box-and-Whisker Plot Options dialog box.


Fitted Line

Determines the method that will be used to fit a straight line.

None

Plots the Normal Probability Plot without the fitted line.

Using Quartiles

Plots the Normal Probability Plot with the fitted line drawn through the median at 0.5 with the slope determined by the quartiles.  This option is the default.

Using Least Squares

Plots the Normal Probability Plot with the line fitted using least squares regression.


Chart Type

Determines the format for the bars on the chart.

Clustered

Draws a separate bar for each level of the classification variable. This option is the default.

Stacked

Draws the bars for each level of the classification variable stacked one on top of the other.  The length of the bar indicates the number of observations in that row.


Scaling

Determines how the types of data will appear on the plot.

Frequencies

Draws bars whose length corresponds to the frequency count for each level of the classification factor.  This option is the default.

Percentages

Draws bars that correspond to the occurrence (in percentages) for each level of the classification factor.


Error Bars

These options instruct the program what it should use to plot the data.

I-Beams

Plots the bars as I-beams; it is the default.  Do not use this option if you are using stacked bars, no standard errors, or if the data are in percentages.

Lines

Plots the bars as lines.


Baseline

Enter a value that will determine where the bottom of the bars will be placed when you produce Clustered bars.  If the baseline is not zero, the bars can extend in both directions.  Enter any number; usually 0; however, you can also enter other numbers to emphasize differing relationships among the classes.  If you use a number larger than the largest class in the data, the bars descend from the baseline (on a vertical Barchart) or extend to the left of the baseline (on a horizontal Barchart).


Features

Determines the features that will be included on the plot.

Median Notch

Places a notch around the median to indicate an approximate confidence interval for the median.  The length of the notch represents an approximate 95 percent confidence interval for the median.  Notches that overlap indicate that there is no significant difference between the sample medians.

Outlier Symbols

Plots individual points that are beyond the whiskers as two different point symbols —Outside or Far Outside.  Outside points, which are shown as small squares, are points that lie more than 1.5 times the interquartile range above or below the box.  Far Outside points, which are shown as small squares with plus signs through them, are points that lie more than 3.0 times the interquartile range above or below the box.  This option is one of two defaults.

Mean Marker

Displays the location of the average on the plot. This option is one of two defaults.


Scatterplot (Multiple X-Y-Z Analysis)

The Scatterplot graphical option creates and displays a plot of three or more variables.

One variable each is plotted on the X- and Y-axes, one or more variables is plotted on the Z-axis.  You can plot Z-axis variables with the scale on the left or the right.

The size of the scales is automatically adjusted to reflect the range of the values.


Counts

Determines options for the Y-axis scale.

Relative

Displays the values for the Y-axis as proportions of the total count. If you want to display Counts, de-select this option.

Cumulative

Displays the cumulative frequency for each bar; that is, the frequency for all the classes up to and including the current class will be included. De-select this option if you do not want successive bars to include previous class frequencies.


Plot Type

Determines the data that will be displayed.

Histogram

Displays the data as a series of successive bars that represent classes.  The width of the bars is equal to the class interval; the height of the bars is equal to the number of observations in each class.  This option is the default.

Polygon

Displays the data as a line on a plot.  To form a Frequency Polygon plot the frequency and midpoint for each class, then connect the points with straight lines.


Standard Errors

Enter the name of the variable that contains the values for the length of the error bars that will be plotted.  You can also enter observations, counts, or the name of a variable that contains counts (must be 0).


Alternative Hypothesis

Determines the type of alternative hypothesis test that will be used.

Not Equal

Performs a two-tailed test; it is the default.  A two-tailed test is used to detect a difference in means between two populations regardless of the direction of the difference.

Less Than

Performs a one-tailed test, which determines if the population mean is less than a hypothesized value; that is, it is the same as a two-tailed test except that the value for the resulting probability is divided by 2, which adjusts for the fact that the alternative hypothesis is rejected only when the difference between the two means is sufficiently large and in the direction of interest.

Greater Than

Performs a one-tailed test, which determines if the population mean is greater than a hypothesized value.


Method

Determines the method that will be used to estimate the density function.

Boxcar

Assigns a constant density to each small interval around each value, which smoothes the density function into a series of overlapping rectangles or boxcars, similar to a simple moving average.

Cosine

Smoothes local densities into a series of overlapping, bell-shaped intervals, similar to a weighted moving average.  This method gives a smoother density trace; it is the default.


Include

Determines the type of data that will be included in the analysis.

Complete Cases Only

Includes only rows that contain a value for each variable that will be analyzed; it is the default.

All Data

Includes all the cases and uses all the nonmissing values for each variable.


Table Percentages From

Enter values that will determine how the percentages will be calculated and the percentages that will appear in each cell of the table.

Entire Table

Calculates the percentages using the sum of all the frequencies; it is the default.

Row Totals

Calculates the percentages using the row frequencies.

Column Totals

Calculates a percentage for each cell based on the frequency for that column.


Confidence Intervals (for Means) Options Dialog Box

Enter a value for the confidence level that will be used to calculate the confidence intervals for the difference between the means.  The default is 95 percent; other common levels are 90 and 99 percent.


Counts

Determines the type of data that will display in the bars of the Histogram.

Relative

Displays the percentage of the data in each class as the scale for the Y-axis.  If you do not choose this option, the number of observations in each class will display as the scale for the Y-axis.

Cumulative

Displays data for that class and all the classes lower than that class.  If you do not choose this option, the data for only that class will display.


Hold

Retains the current scaling even if you change the values in the dialog box.  When you click OK, the new graph displays using the scaling from the previous graph.  The default is not holding the scaling.


Intervals

Determines the method that will be used to calculate the values.

None

Does not calculate the confidence intervals.

Standard Errors (Pooled s)

Calculates the standard error value using the weighted averages for all the samples.  When the counts for each of the samples are equal, the pooled standard errors are all equal.

Standard Errors (Individual s)

Uses the value for the standard error to reflect the variation within each sample.

Confidence Intervals (Pooled s)

Calculates the confidence intervals using the pooled standard deviation from the samples.  To calculate the pooled standard errors, the sample variances are first pooled.  Unless the variances of the samples are significantly different, you generally use this technique instead of using individual standard deviations.

Confidence Intervals (Individual s)

Calculates the confidence intervals using the individual standard errors.  Use the associated standard error to calculate the confidence intervals for each sample.

LSD (Least Significant Differences) Intervals

Used when the F-ratio is significant, and you want to make planned comparisons.  This option is the default.

Tukey HSD (Honestly Significant Differences) Intervals

Used when you plan to make many comparisons.  This test is based on the studentized range distribution.  The Type I error is smaller than the LSD.

Scheffe Intervals

Used when the F-ratio is significant, and you want to make unplanned comparisons between pairs of means.  Scheffe is the most conservative method because the Type I error rate is the smallest.

Bonferroni Intervals

Used when the F-ratio is not significant, but you still want to make a small number of planned comparisons.


Method

Determines the method that will be used to determine statistically significant differences among the means.

LSD (Least Significant Differences)

Used when the F-ratio is significant and you want to make planned comparisons.  This method is the default.

Tukey HSD (Honestly Significant Differences)

Used when you plan to make many comparisons.  This test is based on the studentized range distribution.  The Type I error is smaller than LSD, Newman-Keuls, and Duncan.

Scheffe

Used when the F-ratio is significant and you want to make unplanned comparisons between pairs of means.  Scheffe is the most conservative method because the Type I error rate is the smallest.

Bonferroni

Used when the F-ratio is not significant, but you still want to make a small number of planned comparisons.

Newman-Keuls

Used if the R-ratio is significant and you want to test multiple hypotheses.  The Type I error rate is smaller with this method than with the Duncan method.

Duncan

Used if you want to protect the results against Type I errors for a small number of comparisons.


Sums of Squares

Determines the method that will be used to calculate the sums of squares for each factor.

Type I

Computes the sums of squares for each factor in the order you entered the factors into the Factors text box.  The effect of each factor is measured as it occurs.

Type III

Computes additional sums of squares for each factor as if that factor was the last one added to the model.


Type

Determines how the values for the Means Plot will be calculated.

Confidence Intervals

Calculates the confidence interval using the individual standard errors.  Use the associated standard error to calculate the confidence intervals for each sample.

LSD (Least Significant Differences) Intervals

Used when the F-ratio is significant and you want to make planned comparisons.  This option is the default.

Tukey HSD (Honestly Significant Differences Intervals)

Used when you plan to make many comparisons.  This test is based on the studentized range distribution.  The Type I error is smaller than the LSD.

Scheffe Intervals

Used when the F-ratio is significant, and you want to make unplanned comparisons between pairs of means.  Scheffe is the most conservative method because the Type I error rate is the smallest.

Bonferroni Intervals

Used when the F-ratio is not significant, but you still want to make a small number of planned comparisons.


Interval

Determines the model that will be used to determine the two-factor interactions shown on the plot.

None

Does not calculate two-factor interactions; it is the default.

Confidence Interval

Uses the confidence intervals to calculate the two-factor interactions.

LSD (Least Significant Differences) Interval

Uses the least significant differences interval to calculate the two-factor interactions.  Use this option when the F-ratio is significant and you want to make planned comparisons.

Tukey HSD (Honestly Significant Differences) Interval

Uses the Tukey HSD intervals to calculate the two-factor interactions.  Use this option when you plan to make many comparisons.  This test is based on the studentized range distribution.  The Type I error is smaller than LSD.

Scheffe Interval

Uses the Scheffe interval to calculate the two-factor interactions.  Use this option when the F-ratio is significant and you want to make unplanned comparisons between pairs of means.  Scheffe is the most conservative method because the Type I error rate is the smallest.

Bonferroni Interval

Uses the Bonferroni interval to calculate the two-factor interactions.  Use this option when the F-ratio is not significant, but you still want to make a small number of planned comparisons.


Plot on Axis

Determines the factor in the interaction that will be plotted against the response variable.

First Factor

Plots the response variable against the first factor in the interaction.  This option is the default.

Second Factor

Plots the response variable against the second factor in the interaction.


Fit

These options allow you to select the independent variables that will be fit in the model, as well as to indicate how they will be entered.

All Variables

Enters all the variables at one time.

Forward Selection

Performs a forward stepwise regression, which begins with no variables in the model and adds them one at a time.

Backward Selection

Performs a backward stepwise regression, which begins with all the variables in the model and removes them one at a time.


Display

These options allow you to select the method that will display the model for a stepwise regression when you choose the Forward or Backward Selection options.

Final Model Only

Displays only the final model results.

All Steps

Displays each step in the stepwise regression.  This option is the default.  To view all the step results, scroll down the Analysis Summary pane.


Plot Limits For

These options allow you to choose the type of confidence limits.

No Limits

Plots the confidence limits; it is the default.

Predicted Values

Plots the confidence limits for the predicted value.

Means

Plots the confidence limits for the means.

Forecasts

Plots the confidence limits only for the forecasts.

Forecast Means

Plots the confidence limits only for the forecast means.


Plot versus:

Allows you to choose how the data will be plotted: against predicted values, by their row number in the Data Editor, or by an independent variable.


Error Bars

Determines the type of bar that will appear on the chart.

I-Beams

Plots the bars as I-beams; it is the default.

Lines

Plots the bars as lines.


Confidence Level

Enter a value that will be used to calculate the confidence levels for the intervals.  Enter a numeric value greater than 0 and less than 100.  The default is 95; other common values are 90 and 100.


Standard Errors

[Optional]  Enter the name of the variable that contains the values for the length of the error bars.  You can enter observations, counts, or the name of a variable that contains counts (must be 0).


Confidence Level (Sample Size Describe)

Enter a number (in percentages) that will be used as the significance level for the proposed test.


Method (Two-Sample Comparison Analysis)

Determines the method that will be used to shape the window or “kernel,” that is passed over the data to estimate the density function.

Boxcar

Uses the Boxcar method.  A boxcar kernel is flat and smoothes the density function into a series of overlapping rectangles (boxcars), similar to a simple moving average.

Cosine

Uses the Cosine method.  A cosine kernel is curved and smoothes the data into a series of overlapping, bell-shaped intervals, similar to a weighted moving average.  This method, which is the default, gives a smoother result, but takes longer to calculate.


Data

Enter the name of the variable that contains the observations that will be analyzed.


Newman-Keuls
Newman-Keuls Method

Use this method if the F-ratio is significant and you want to test multiple hypotheses.  The Type I error rate is smaller with this method than with the Duncan Method.


None

Indicates that you do not want to calculate two-factor interactions.


None (No Intervals)
None

Indicates that you do not want to calculate confidence intervals.


Normal Distribution

Useful in instances when you plot a Frequency Histogram of the data, and the bars form a common, bell-shaped curve.


Normal Probability Plot (Distribution Fitting Analysis)

The Normal Probability Plot graphical option creates and displays a plot that consists of an arithmetic (interval) horizontal axis scaled for the data and a vertical axis scaled so the cumulative distribution function of a normal distribution plots as a straight line.

The closer the data are to the reference line, the more likely they follow a normal distribution.  From this plot you can determine if the data come from a normal distribution.


Normal Probability Plot

The Normal Probability Plot graphical option creates and displays a plot that consists of an arithmetic (interval) horizontal axis scaled for the data and a vertical axis scaled so the cumulative distribution function of a normal distribution plots as a straight line.

The closer the data are to the reference line, the more likely they follow a normal distribution.  From this plot you can determine if the data come from a normal distribution.


Normal Probability Plot Options Dialog Box

This dialog box determines the direction of the plot and the method that will be used to plot the fitted line.

Direction

Fitted Line


Number of Classes

Enter the number of classes into which the program will divide the data. Enter an integer between 1 and 1000; the default depends on the data.


Observed versus Predicted Plot

The Observed versus Predicted graphical option plots the observed values versus the predicted values for the dependent variable.

The plot includes a line with slope equal to 1.  If all the predictions are perfect, all the points are on the line.  You can use the plot to detect cases in which the variance is not constant or to determine if you need to transform the dependent variable.


Observed versus Predicted Plot

The Observed versus Predicted graphical option plots the observed values versus the predicted values for the dependent variable.  The plot includes a line with slope equal to 1.  If all the predictions are perfect, all the points should be on the line.

You can use the plot to detect cases in which the variance is not constant, which indicates you may need to transform the dependent variable.


Observed Y

Includes in the report, the values for the dependent variable.


Offset Slice #

Enter the number of the segment you want to offset from the circle.  For example, if an analysis contains four variables, the piechart contains four segments; entering 4 will offset segment 4.  Segments are counted in a clock-wise direction, starting at 12:00; the default is 0.


One-Variable Analysis Dialog Box

The One-Variable analysis allows you to analyze data in a numeric variable by performing various statistical and graphical analyses.  For example, options in this analysis allow you to calculate specific summary statistics, such as standard deviation and average; percentiles, stem-and-leaf displays, and confidence intervals.

You can plot the data in a Scatterplot, Histogram, Normal Probability Plot, or Symmetry Plot, among others.

Data

Select

Sort

Delete...

Transform...

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the One-Variable Analysis

Summary Statistics Options

Percentiles Options

Frequency Tabulation Options

Stem-and-Leaf Display Options

Confidence Intervals Options

Hypothesis Tests Options

Box-and-Whisker Plot Options

Frequency Plot Options

Normal Probability Plot Options

Density Trace Options

Save Results Options


Analysis Summary (One-Variable Analysis)

The Analysis Summary option creates a summary of the analysis.  The summary displays the name of the variable you selected, and the range of the values.


Save Results Options Dialog Box (One-Variable Analysis)

The Save Results Options dialog box for the One-Variable Analysis allows you to select the results you want to save.  There are six selections: Summary Statistics, Percentiles, Frequencies, Cumulative Frequencies, Relative Frequencies, and Cumulative Relative Frequencies.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names for the variables or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


One-Way ANOVA - Graphical Options Dialog Box
One-Way ANOVA Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Scatterplot (One-Way ANOVA)

Means Plot (One-Way ANOVA)

Box-and-Whisker Plot (One-Way ANOVA)

Residuals versus Factor Levels Plot (One-Way ANOVA)

Residuals versus Predicted Plot (One-Way ANOVA)

Residuals versus Row Number Plot (One-Way ANOVA)

Analysis of Means (ANOM) Plot (One Way ANOVA)


One-Way ANOVA - Tabular Options Dialog Box
One-Way ANOVA Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (One-Way ANOVA)

Summary Statistics (One-Way ANOVA)

ANOVA Table (One-Way ANOVA)

Table of Means (One-Way ANOVA)

Multiple Range Tests

Variance Check (One-Way ANOVA)

Kruskal-Wallis Test (One-Way ANOVA)


One-Way ANOVA Dialog Box

In One-Way ANOVA, you classify each observation into groups according to one factor.  For example, to examine how a particular fertilizer affects the growing rate of corn, you could group cornfields according to the type of fertilizer used on different fields.  Or, to determine how the cylinders in an automobile engine affect its mileage rate, you could classify automobiles according to the number of engine cylinders.

You use One-Way ANOVA to analyze the effect of one qualitative factor on one response variable.  The design can be balanced or unbalanced; in other words, the group sizes do not have to be equal.

If you are analyzing the effects of two or more variables, or if you need covariates in your analysis, use the Multifactor ANOVA Analysis.

If you entered your data in two separate columns, use the Multiple Samples Analysis.

Dependent Variable

Factor

(Select)

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using One-Way ANOVA

Summary Statistics Options

Means Table and Plot Options

Multiple Range Test Options

Box-and-Whisker Plot Options


Factor

Enter the name of the variable that contains the sample numbers or codes.  The variable must contain a code for each observation in the response variable.  The program uses the codes to divide the data into groups.


Analysis Summary (One-Way ANOVA)

The Analysis Summary option creates a summary of the analysis.  The summary displays the name of the dependent variable and the factor.  It also shows the number of observations and levels in the analysis.


Analysis Summary (One-Way ANOVA)

The Analysis Summary option creates a summary of the analysis.  The summary displays the name of the dependent variable and the factor.  It also shows the number of observations and levels in the analysis.


Save Results Options Dialog Box (One-Way ANOVA)

The Save Results Options dialog box allows you to select the results you want to save.  There are seven selections: Level Counts, Level Means, Level Sigmas, Level Standard Errors, Level Labels, Level Indicators, and Residuals.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names for the variables or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results Options button on the Analysis toolbar (the fourth button from the left).


Outlier Symbols

Plots individual points beyond the whiskers (outside points or the suspect outliers).  For far outliers — those points more than 3 interquartile ranges below the first quartile or above the third quartile —a special character (a point with a plus sign through it) is used so the outliers are easy to distinguish.


Partial Covariances
Partial Correlations

Indicates that you want to generate a matrix of estimated partial correlation coefficients for a set of observed values.

A partial correlation coefficient measures the relationship between two variables while controlling for possible effects of the other variables.  These effects are controlled by removing the linear relationship with the other variables before calculating the correlation coefficients between the two variables of interest.


Partial Covariances (Multiple Variable Analysis)
Partial Correlations (Multiple Variable Analysis)

The Partial Correlations option creates a matrix of estimated partial correlation coefficients for a set of observed values.

A partial correlation coefficient measures the relationship between two variables while controlling for possible effects of the other variables.  Removing the linear relationship with other variables controls the effects before the calculations are made between the two variables.

Partial correlation is useful for uncovering hidden relationships, identifying intervening variables, and detecting false relationships.


Partial Correlations (Multiple-Variable Analysis)

The Partial Correlations option creates a matrix of estimated partial correlation coefficients for a set of observed values.

A partial correlation coefficient measures the relationship between two variables while controlling for possible effects of the other variables.  Removing the linear relationship with other variables controls the effects before the calculations are made between the two variables.

Partial correlation is useful for uncovering hidden relationships, identifying intervening variables, and detecting false relationships.


Percentiles (One-Variable Analysis)

The Percentiles option creates the percentiles for the data.  The results show the percentage of the values that are equal to or less than a value you select.

To select options for this table, use the Percentiles Options dialog box.


Percentiles Options
Percentiles (One-Variable Analysis)

The Percentiles option creates the percentiles for the data.  The results show the percentage of the values that are equal to or less than a value you select.

To select options for this table, use the Percentiles Options dialog box.


Percentiles Options Dialog Box

Enter values for other percentages.  If you do not want to calculate a percentile, enter 0.


Piechart (Tabulation Analysis)

The Piechart option creates a plot of segments whose size is proportional to the number of occurrences of each value of the variable you selected.

You can offset a segment of the chart to display that portion more prominently.  Depending on the hardware you are using, you can use either color or fill patterns to differentiate the individual segments.  If the data contain more than 20 classes, an error message displays in the graphics pane.


Piechart

The Piechart option creates a plot of segments whose circumference represent the frequency that corresponds to one row in a frequency table.

Depending on the hardware you are using, you can use either color or fill patterns to differentiate the individual segments.  If the data contain more than 20 classes, an error message displays in the graphics pane.

To select options for the plot, use the Piechart Options dialog box.


Piechart Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the Piechart Analysis.

Piechart (Piechart)


Piechart Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the Piechart Analysis.

Analysis Summary (Piechart Analysis)


Piechart Analysis Dialog Box

The Piechart Analysis segments a circle into shaded and colored wedges according to the capabilities of your computer’s graphics hardware.  You can also offset one segment of the chart to display it more prominently.

A Piechart is useful for displaying breakdowns of percentages for up to 20 classification factors (the factors that contain the tabulated data).

Counts

Labels

Sort

Delete...

See also

Using the Piechart Analysis

Piechart Options


Piechart Options Dialog Box

Allows you to:

•	select labels for the legend

•	select labels for the individual segments of the graph

•	enter the size of the circle

•	enter the number of the segment that will be offset

•	indicate if you want lines to appear from the label to the segments on the graph.

Legends

Labels

Diameter

Offset Slice #

Lines


Analysis Summary (Piechart Analysis)

The Analysis Summary option creates a summary of the analysis.  The summary includes the name of the selected variable, the number of observations the variable represents, and the sum of the values.


Analysis Summary (Piechart Analysis)

The Analysis Summary option creates a summary of the analysis.  The summary includes the name of the selected variable, the number of observations the variable represents, and the sum of the values.


CDF Plot

The CDF Plot option creates a plot using a cumulative distribution function that shows the probability of observing a value less than or equal to a specified value.


Density Function Plot

The Density Function Plot option creates a plot using a function that gives the rate at which the cumulative probability increases at a given point.


Plot Frequencies
Frequencies

Plots frequencies.


Hazard Function Plot

The Hazard Function Plot option creates a plot using a function that shows the probability of failure during a small increment of time when no failure occurs before the specified time.

The Hazard Function is the Probability Density Function divided by the Survivor Function.


Forecasts (for Plot Limits)

Plots confidence limits for only the forecasts.


Forecast Means (for Plot Limits)

Plots confidence limits for only the forecast means.


Means (for Plot Limits)

Plots confidence limits for the means.


No Limits (for Plot Limits)

Produces the plot without confidence limits.


Predicted Values (for Plot Limits)

Plots confidence limits for the predicted values.


Plot Lines Check Box
Plot Lines

Plots lines on the Scatterplot.


Log Survivor Function Plot

The Log Survivor Function Plot option creates a plot using a function that shows the probability of observing a value greater than a specified value (in log units); that is, the log of the survivor function.


Plot of Fitted Model (Simple Regression Analysis)

The Plot of Fitted Model option creates a plot of the results of fitting a linear model that describes the relationship between the two variables you selected.

The equation of the Fitted Model is shown as a solid line.  The plot includes both confidence limits for the means (the middle lines) and the prediction limits (the outer lines).

Use the Plot of Fitted Model Options dialog box to indicate the type of limits that will be included; to enter a value for the confidence level, and to enter a number that will be used to change the resolution of the lines..


Plot of Fitted Model (Simple Regression Analysis)

The Plot of Fitted Model option creates a plot of the results of fitting a linear model that describes the relationship between the two variables you selected.

The equation of the Fitted Model is shown as a solid line.  The plot includes both confidence limits for the means (the middle lines) and the prediction limits (the outer lines).


Plot of Fitted Model Options Dialog Box

This dialog box allows you to indicate the tyupe of limits that will be included on the plot, to enter a value for the confidence level, and to enter a number that will be used to change the resolution of the lines.

Include

Confidence Level

X-Axis Resolution


Plot on Axis:  First Factor
First Factor

Plots the response variable against the first factor in the interaction.  This option is the default.


Plot on Axis:  Second Factor
Second Factor

Plots the response variable against the second factor in the interaction.


Plot Options Dialog Box

Determines how the data will appear on the plot.

Points

Plots points; this option is the default.

Lines

Plots lines.


Plot Percentages
Percentages

Plots percentages.


Plot Survivor Function
Survivor Function

The Survivor Function option creates a plot using a function that shows the probability of observing a value greater than a specified value.  The survivor function is 1-CDF.

For reliability data, the survivor function shows the probability of surviving to time x without failure.


Plot versus Predicted Values
Predicted Values

Plots residuals versus the fitted values, which can help identify sequential correlations among the residuals.


Plot versus Row Number
Row Number

Plots residuals versus their row number, which can help identify sequential correlations among the residuals.


Plot versus:  (Independent Variable)
Plot versus:

Allows you to select the independent variable that will be used for the Component-plus-Residuals plot.


Polygon

Creates a frequency polygon by plotting the frequency and midpoint for each class, then connects the points with straight lines.


Probability Plot Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the Probability Plot.

Normal Probability Plot


Probability Plot Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the Probability Plot.

Analysis Summary (Probability Plot Analysis)


Normal Probability Plot Analysis Dialog Box

The Normal Probability Plot Analysis is used to test a single sample to determine whether or not it is likely to be a sample taken from a normally distributed population.  The purpose of the test is to produce a graph and to determine if the shape of the plotted points form a linear pattern (that is, if the points roughly follow a straight line).

The plot also provides an easy way to identify outliers.  Outliers clearly highlight potential performance bottlenecks.  The points (effects are arranged in ascending order of their value.  The plot consists of an arithmetic (interval) horizontal axis and a vertical axis scaled so the cumulative distribution function (cdf) plots as a straight line.

Data

Select

Sort

See also

Using the Normal Probability Plot Analysis

Normal Probability Plot Options Dialog Box


Analysis Summary (Probability Plot Analysis)

The Analysis Summary option creates a summary of the analysis.  The summary includes the name of the selected variables, and the range of the values.


Quantile Plot (Two-Sample Comparison Analysis)

The Quantile Plot option creates a plot that shows the fraction of data that are below a particular value.

Use the plot to compare the cumulative distributions for the two samples, or to estimate percentiles.  The Y-axis represents the proportion of values that are below the value.


Quantile Plot

The Quantile Plot option creates a plot that shows the fraction of data that are below a particular value.

Use the plot to compare the cumulative distributions for the two samples, or to estimate percentiles.  The Y-axis represents the proportion of values that are below the value.


Quantile-Quantile Plot (Two-Sample Comparison Analysis)

The Quantile-Quantile Plot option creates a plot of the quantile values plotted as pairs.

The y = x line is drawn on the graph so you can compare the cumulative distributions of the two samples.  If the distributions are similar, the points fall along this line.


Quantile-Quantile Plot

The Quantile-Quantile Plot option creates a plot of the quantile values plotted as pairs.

The y = x line is drawn on the graph so you can compare the cumulative distributions for the two samples.  If the distributions are similar, the points fall along this line.


Range (Summary Statistic)

Displays the value for the range of the data.  Use the value to measure the spread or dispersion of the data.  This option is one of the defaults.


Rank Correlations (Multiple-Variable Analysis)

The Rank Correlations option creates a matrix of Spearman rank correlation coefficients that is similar to the correlation coefficients matrix described in the Correlations tabular option.

The difference is that the ranks of the values are used rather than the values themselves.

Select this option if you can rank order the data, but you cannot assign values on an interval scale.


Rank Correlations

The Rank Correlations option creates a matrix of Spearman rank correlation coefficients that is similar to the correlation coefficients.

The difference is that the ranks of the values are used rather than the values themselves.  Select this option if you can rank order the data, but you cannot assign values on an interval scale.


Reciprocal-X Model
Reciprocal-X

Fits a reciprocal-X model.  It is defined by the equation:  Y = a + b/X.


Reciprocal-Y Model
Reciprocal-Y

Fits a reciprocal-Y model.  It is defined by the equation:  Y = 1/(a + bX).


Relative Counts

Displays the percentage of data in each class as the scale for the Y-axis.  If you do not select this option, the number of observations in each class will display as the scale for the Y-axis.


Reports (Multiple Regression Analysis)

The Reports option creates values for the forecasts and confidence limits for cases when values are missing for the dependent variables but not for the independent variables.

To select options for the table, use the Reports Options dialog box.


Reports (Multiple Regression Analysis)

The Reports option creates values for the forecasts and confidence limits for cases when values are missing for the dependent variables but not for the independent variables.


Reports Options Dialog Box

This dialog box allows you to indicate the reports you want to include in the Reports table.

Include


Residual Plot Options Dialog Box

Determines the type of residuals that will appear on the plot.

Plot


Residual Plots Options Dialog Box
Residual Plot Options Dialog Box

Determines the factor that will be plotted against the residuals.  Click the factor to select it.


Residual versus Level Codes Plot


Residuals versus Predicted Plot (One-Way ANOVA)

The Residuals versus Predicted option creates a plot of the residuals versus the predicted values.

The plot is helpful when the variance is not constant and you need to transform the response variable.


Residuals

Plot the residuals, which is the difference between the observed and the fitted values.


Residuals versus Factor Levels Plot

The Residuals versus Factor Levels option creates a plot of the residuals versus the factor level.  The residuals are equal to the observed values minus the mean for the group from which they originate.  Check the plot to ensure that the variability within each level is approximately the same.

Use the Residuals Plot Options dialog box to choose the factor that will be plotted against the residuals.


Residuals versus Factor Levels Plot

The Residuals versus Factor Levels option creates a plot of the residuals versus the factor level.  The residuals are equal to the observed values minus the mean for the group from which they originate.  Check the plot to ensure that the variability within each level is approximately the same.

Use the Residuals Plot Options dialog box to choose the factor that will be plotted against the residuals.


Residuals versus Observation Plot (Multiple-Sample Comparison Analysis)

The Residuals versus Observations option creates a plot of the residuals versus the observations.

The plot is helpful when you need to identify sequential correlations among the residuals.


Residuals versus Observations Plot

The Residuals versus Observations option creates a plot of the residuals versus the observations.

The plot is helpful when you need to identify sequential correlations among the residuals.


Residuals versus Predicted Plot (Multifactor ANOVA)

The Residuals versus Predicted option creates a plot of the residuals versus the predicted values.

The plot is helpful when the variance is not constant and you need to transform the variables.

To select options for the plot, use the Residual Plot Options dialog box.


Residuals versus Predicted Plot (Multiple Regression Analysis)
Residuals versus Predicted Plot

The Residuals versus Predicted option creates a plot of the residuals versus the predicted values.

The plot is helpful when the variance is not constant and you need to transform the variables.


Residuals versus Row Number Plot (Multiple Regression Analysis)

The Residuals versus Row Number Plot option creates a plot of the residuals versus the row number.  The residuals appear on the plot in the order you entered the observations into the DataSheet.  Any pattern other than a random scatter, could indicate some serial correlation or time dependence in the data.

Use the Residual Plot Options dialog box to choose options for the plot.


Residuals versus Row Number Plot

The Residuals versus Row Number Plot option creates a plot of the residuals versus the row number.  The residuals appear on the plot in the order you entered the observations into the DataSheet.  Any pattern other than a random scatter, could indicate some serial correlation or time dependence in the data.


Residuals versus Samples Plot (Multiple-Sample Comparison Analysis)

The Residuals versus Samples option creates and displays a plot of the residuals versus the samples.

The plot is helpful when you need to determine if the variance is not constant across different samples.


Residuals versus Samples Plot (Multiple-Sample Comparison Analysis)

The Residuals versus Samples option creates a plot of the residuals versus the samples.

The plot is helpful when you need to determine if the variance is not constant across the different samples.


Residuals versus X Plot

The Residuals versus X option plots the residuals versus any independent variable.

You can use the plot to check the adequacy of the model with respect to the independent variable you selected.  You can also use the plot to determine if the variance of the residuals is constant in relation to the selected independent variable.

To select options for the plot, use the Residual Plot Options dialog box.


Residuals versus X Plot

The Residuals versus X option plots the residuals versus any independent variable.

You can use the plot to check the adequacy of the model with respect to the independent variable you selected.  You can also use the plot to determine if the variance of the residuals is constant in relation to the selected independent variable.


Residuals Predicted
Residuals versus Predicted Plot (Multifactor ANOVA)

The Residuals versus Predicted Plot option creates a plot of the residuals versus the predicted levels.  The plot is helpful for for detecting heteroscedasticity, in which the variance changes, together with the mean.  If the points form a general funnel-shaped pattern, there is an indication of a type of heteroscedasticity that can often be corrected by transforming the dependent variable.  Try using the Analysis dialog box to enter LOG(n), SQRT(n), or 1/n as the dependent variable.


Residuals Row Number
Residuals versus Row Number Plot (Multifactor ANOVA)

The Residuals versus Row Number Plot option creates a plot of the residuals versus the row number.  The residuals appear on the plot in the order you entered the observations into the DataSheet.  Any pattern other than a random scatter, could indicate some serial correlation or time dependence in the data.


Residuals versus Level Codes


Residuals versus Predicted Plot (Multiple-Sample Comparison Analysis)

The Residuals versus Predicted Plot option creates a plot of the residuals versus the predicted values.

The plot is helpful when the variance is not constant and you need to transform the variables.


Residuals versus Row Number

The Residuals versus Row Number Plot option creates a plot of the residuals versus the row number.  The residuals appear on the plot in the order you entered the observations into the DataSheet.  Any pattern other than a random scatter could indicate some serial correlation or time dependence in the data.


Residuals versus Samples

The Residuals versus Samples Plot option creates a plot of the residuals versus the sample number.  The residuals appear on the plot in the order you entered the samples into the DataSheet.  Any pattern other than a random scatter could indicate some serial correlation or time dependence in the data.


Residuals versus X

The Residuals versus X Plot option creates a plot of the residuals versus variable X.  The residuals appear on the plot in the order of the X observations into the DataSheet.  Any pattern other than a random scatter could indicate some serial correlation or time dependence in the data.


Row Number Label
Row Number

Uses row numbers to identify the glyphs.


Row Variable

Enter the name of the variable that will appear in the rows of the table.  The names are displayed on the Y-axis on a Barchart and a Mosaic Plot.


S-Curve Model
S-Curve

Takes the natural log of Y and the reciprocal of X.  The double reciprocal, multiplicative, and S-Curve models transform the independent variable, linearizing the nonlinear relationship between the independent and dependent variables.

This transformation of the dependent variable helps remedy error terms that are not normal and that do not have constant variance.  It is defined by the equation Y = exp(a + b/X).


Scaling by Frequencies
Frequencies

Plots frequencies.


Scaling by Percentages
Percentages

Plots percentages.


Scatterplot (Multiple-Sample Comparison Analysis)

The Scatterplot option calculates, plots, and displays the values for each variable along a single axis as point symbols with no connecting lines.


Sample 1
Sample 1 (Two Data Columns)

Enter the name of the variable that contains the first set of data that will be compared.  Enter a numeric variable.


Sample 2
Sample 2 (Two Data Columns)

Enter the name of the variable that contains the second set of data that will be compared.  Enter a numeric variable.


Samples

Enter the names of the variables that contain the data that will be compared.


Save Results Options Dialog Box (Multiple-Variable Analysis)

The Save Results Options dialog box allows you to select the results you want to save.  There are four selections: Correlations, Rank Correlations, Covariances, and Partial Correlations.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names for the variables or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Row Labels

Saves the class values for each row in a variable.


Summary Statistics (One-Variable Analysis)

The Summary Statistics option saves statistical information about the center, spread, and shape of the data:  the number of values in the variable; the average, variance, standard deviation, minimum and maximum values; and the sum of all the values.

This information is helpful when you need to determine if other statistical analyses might be appropriate to use with the data, or when you need to determine if you should transform the data.


Scatterplot

The Scatterplot option creates a plot of the values.


Scatterplot Matrix (Multiple-Variable Analysis)

The Scatterplot Matrix option creates a matrix plot of all two-variable scatterplots.

The Scatterplot Matrix visually presents the relationships among the pairs of variables and is helpful in identifying strongly correlated pairs..


Scatterplot Matrix (Multiple-Variable Analysis)

The Scatterplot Matrix option creates a matrix plot of the variables with points for the data.

The Scatterplot Matrix visually presents the relationships among the pairs of variables.


Scatterplot Options Dialog Box

Choose the factor that will be used in the analysis.


Scheffe
Scheffe Method

Uses the Scheffe Method when the F-ratio is significant and you want to make unplanned comparisons between pairs of means.

Scheffe is the most conservative method because the Type I error rate is smallest.


Scheffe Interval
Scheffe Intervals

Uses the Scheffe Intervals when the F-Ratio is significant, and you want to make unplanned comparisons between pairs of means.

Scheffe is the most conservative method because the Type I error rate is the smallest.

If you are using Multifactor ANOVA, this interval is used to calculate the two-factor interactions.


Select

[Optional]  Selects a subset of the observations.  For example, to analyze the first 50 values in each variable, enter first (50) into this text box.


Selections

Allows you to view the error term you selected.


Simple Regression - Graphical Options Dialog Box
Simple Regression Graphical Options Dialog Box

This dialog box allows you to select graphical options for the analysis.

Plot of Fitted Model (Simple Regression)

Observed versus Predicted Plot (Simple Regression)

Residuals versus X Plot (Simple Regression)

Residuals versus Predicted Plot (Simple Regression)

Residuals versus Row Number Plot (Simple Regression)


Simple Regression - Tabular Options Dialog Box
Simple Regression Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Simple Regression)

Lack-of-Fit Test (Simple Regression)

Forecasts (Simple Regression)

Comparison of Alternative Models (Simple Regression)

Unusual Residuals (Simple Regression)

Influential Points (Simple Regression)


Simple Regression Analysis Dialog Box

The Simple Regression Analysis estimates a linear or nonlinear regression between two variables.

The model relates one dependent variable to one independent variable by minimizing the sum of the squares of the residuals for the fitted line.  In addition to a straight line, you can also use the analysis to estimate a number of standard nonlinear models.  The analysis also calculates and compares the goodness of fit for each model.

The analysis can automatically fit any of 12 models.  The preferred model is the linear model unless another model type significantly increases the R-Squared value.  To select the best model, you must fit the data to all the models and compare the statistics.  You can also use the Comparison of Alternative Models tabular option to compare correlation coefficients and R-Squared values for several transformed model types.

You can plot the fitted line and the residuals for all the models.  STATGRAPHICS Plus also creates and plots predictions for given values of X.  You can also save the residuals and predictions for use in future analyses.

Y (Dependent Variable)

X (Independent Variable)

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Simple Regression Analysis

Simple Regression Options

Forecast Options

Plot of Fitted Model Options

Residual Plot Options


Simple Regression Options Dialog Box

This dialog box allows you to choose the type of model

Type of Model


Analysis Summary (Simple Regression Analysis)

The Analysis Summary option creates a summary of the analysis, which shows the results of fitting a linear model that describes the relationship btween the two variables.  The equation of the fitted linear model is: Y = a + b*X.  In the regression model, the estimate for the intercept is the value for “a”; the estimate for the slope is the value of “b”.

The summary includes:

•	The standard error, t-statistic, and p-value for each estimate.  The t-statistic tests to see if the true value of the coefficient is equal to 0, which is equivalent to concluding that there is no linear relationship between the independent and dependent variables.  Low probability levels (less than .05 for a 95 percent confidence level) for the intercept and slope suggest significant values.

•	An ANOVA table for the model where the F-ratio suggests the significance of the results; a high F-ratio suggests a significant model.

•	The correlation coefficient that measures the linear relationship between the independent and dependent variables.

•	The R-Squared value (the square of the correlation coefficient expressed as a percentage).

•	The standard error of estimation, which is the estimated standard deviation of the variable that is not explained by the estimated model.  The R-Squared value shows the percentage of variability in the Y values explained by the X variable.

•	The Adjusted R-Square, better suited for comparing models with different numbers of independent variables.

•	The Durbin-Watson, which tests for autocorrelation or serial correlation in the residuals in a least squares regression analysis.  As the auto-correlation increases, the Durbin-Watson decreases.  The larger the auto-correlation, the less reliable the results of the regression analysis.

•	The Lag-1 Residual Autocorrelation, which is the first-order autocorrelation.


Analysis Summary (Simple Regression Analysis)

The Analysis Summary tabular option creates and displays a summary of the analysis that shows the statistics for a fitted linear model:  Y = a + b*X.

In the regression model, the estimate for the intercept is the value for “a”; the estimate for the slope is the value of “b”.

The summary includes the following.

•	The standard error, t-statistic, and p-value for each estimate.  The t-statistic tests to see if the true value of the coefficient is equal to 0.  Low probability levels (less than .05 for a 95 percent confidence level) for the intercept and slope suggest significant values.

•	An ANOVA table for the model where the F-ratio suggests a significant model.

•	The correlation coefficient that measures the linear relationship between the independent and dependent variables.

•	The R-Squared value (the square of the correlation coefficient expressed as a percentage). The R-Squared value shows the percentage of variability in the Y values explained by the X variable.

•	The standard error of the residual mean square, which is the estimated standard deviation of the variable not explained by the estimated model.

•	The Adjusted R-Square, better suited for comparing models with different numbers of independent variables.

•	The Durbin-Watson, which tests for autocorrelation or serial correlation in the residuals in a least squares regression analysis.  As the auto-correlation increases, the Durbin-Watson decreases.  The larger the auto-correlation, the less reliable the results of the regression analysis.

•	The Lag-1 Residual Autocorrelation, which is the first-order autocorrelation.


Save Results Options Dialog Box (Simple Regression Analysis)

The Save Results Options dialog box allows you to  the results you want to save.  There are eight selections: Predicted Values, Lower Limits for Predictions, Upper Limits for Predictions, Lower Limits for Forecast Means, Upper Limits for Forecast Means, Residuals, Studentized Residuals, and Leverages.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or acccept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results Options button on the Analysis toolbar (the fourth button from the left).


Skewness (Summary Statistic)

Displays the value for the skewness of the data.  Use this value to measure the symmetry or shape of the data.  A skewness of 0 suggests that the data are symmetrically distributed.  Positive values of skewness indicate that the upper tail of the curve is longer than the lower tail; negative values indicate that the lower tail is longer.


Skychart (Crosstabulation Analysis)

The Skychart option creates a three-dimensional histogram, whose bar height is proportional to the number of observations in each cell.

The row variable is plotted along one axis, the column variable on another axis, and the frequency variable on the third axis.

This three-dimensional graph helps you to visualize the relationship between the two variables and to see the distribution of the data.

To select options for this plot, use the Skychart Options dialog box.


Skychart

The Skychart graphical option creates and displays a three-dimensional histogram, whose bar height is proportional to the number of observations in each cell.  The row variable is plotted along one axis, the column variable on another axis, and the frequency variable on the third axis.

This three-dimensional graph helps you to visualize the relationship between the two variables and to see the distribution of the data.


Skychart Options Dialog Box

Allows you to select the type of data that will appear on the plot:  Frequencies or Percentages.  The default is Frequencies.


Sort

Sorts the variable names alphabetically; sorted is the default.


Square Root-X Model
Square Root-X

Fits a square root-X model.  The reciprocal-X, logarithmic-X, and square root-X transformations linearize a nonlinear relationship between the dependent and independent variables.

The transformations are suitable when the error terms are normal and have constant variance.  It is defined by the equation Y = a + b sqrt(X).


Square Root-Y Model
Square Root-Y

Fits a square root-Y model.  The exponential, reciprocal-Y, and square root-Y transformations can help remedy error terms that are not normal and that do not have constant variance.  It is defined by the equation Y = (a + bX)^2.


Stacked Chart Type
Stacked

Stacks multiple bars one on top of the other.


Standard Deviation (Summary Statistic)

Displays the value for the standard deviation of the data.  Use the value to measure the spread or dispersion of the data (the standard deviation uses a divisor of n - 1).  This option is one of the defaults.


Standard Error (Summary Statistic)

Displays the value for the standard error of the mean.  Use the value to measure the spread or dispersion of the data.


Standard Errors for Forecasts

Includes in the report, the standard deviation of the distribution of estimated values.


Standard Error X

[Optional]  Enter the name of the variable that contains the standard error values that will be plotted on the X-axis.  If the variable contains means, you may want to plot standard error bars.  If you plot standard error bars, enter the name of the variable that contains the values for the standard errors for the X values.  This variable must be the same length as the variable for the Y-axis.


Standard Error Y

[Optional]  Enter the name of the variable that contains the standard error values that will be plotted on the Y-axis.  If the variable contains means, you may want to plot standard error bars.  If you plot standard error bars, enter the name of the variable that contains the values for the standard errors for the Y values.  This variable must be the same length as the variable for the X-axis.


Standard Error Z

[Optional]  Enter the name of the variable that contains the standard error values that will be plotted on the Z-axis.  If the variable contains means, you may want to plot standard error bars.  If you plot standard error bars, enter the name of the variable that contains the values for the standard errors of the Z values.  This variable must be the same length as the variable for the Z-axis.


Standard Errors (Individual s)

Uses the value for the standard error to reflect the variation within each factor level or sample.


Standard Errors (Pooled s)

Calculates the standard error value using the weighted averages for all the factor levels or samples.  When the counts for each of the factor levels or samples are equal, the pooled standard errors are all equal.


Standard Skewness Coefficient
Std. Skewness

Displays the value for the standard skewness coefficient, which you use to measure the symmetry or shape of the data.

When you use large samples, the standardized skewness coefficient is approximately standard normal.  When the values for the standardized skewness coefficient are outside the range -2.0 to +2.0, the data may depart significantly from a normal distribution.


Standardized Kurtosis (Summary Statistic)

Tests for significant deviations from the normal distribution.  When you use large samples, the standardized kurtosis coefficient is approximately standard normal.  When the values for the standardized kurtosis coefficient are outside the range -2.0 to +2.0, the data may depart significantly from a normal distribution.  This option is one of the defaults.


Standardized Skewness (Summary Statistic)

Displays the value for the standard skewness coefficient.  Use the value to measure the symmetry or shape of the data.  When you use large samples, the standardized skewness coefficient is approximately standard normal.  When the values for the standardized skewness coefficient are outside the range -2.0 to +2.0, the data may depart significantly from a normal distribution.  This option is one of the defaults.


Star Plot/Sunray Plot Options Dialog Box

Allows you to enter a character variable for the observations, to select labels to identify the type of glyph, and enter a number for the starting glyph.

Label Variable

Label

Starting Row Number

Sort


Star Plots (Multiple-Variable Analysis)

The Star Plots graphical option creates and displays a graph of multivariate data that allows you to visually compare different observations and see the relative values for all the variables at once.

Each star represents one observation in the data.  Each star is an n-polygon drawn so the distance of the vertices from the center point represents that observation’s values in relation to the other variables.

The first variable in the list is plotted starting at the 12 o’clock position, and then, moving in a clockwise direction, the remaining variables are plotted.

The shortest ray is used to plot the smallest value in each variable and the longest ray to plot the largest value.  You can plot 25 glyphs at a time.

To select options for this plot, use the Star Plot/Sunray Plot Options dialog box.


Star Plots

The Star Plots graphical option creates and displays a graph of multivariate data that allows you to visually compare different observations and see the relative values for all the variables at once.

Each star represents one observation in the data.  Each star is an n-polygon drawn so the distance of the vertices from the center point represents that observation’s values in relation to the other variables.

The first variable in the list of variables is plotted starting at the 12 o’clock position, and then, moving in a clockwise direction, the remaining variables are plotted.  The shortest ray is used to plot the smallest value in each variable and the longest ray to plot the largest value.  You can plot 25 glyphs at a time.


Starting Row Number

Enter the number of the starting glyph number when you have more than 25 observations.  The default is 1.


Stem-and-Leaf Display (One-Variable Analysis)

The Stem-and-Leaf Display tabular option shows the range and concentration of the values, the symmetry of the data, and indicates if there are gaps or outliers.

To select options for this display, use the Stem-and-Leaf Display Options dialog box.


Stem-and-Leaf Display

The Stem-and-Leaf Display tabular option creates and displays a table of the range of the values, the concentration of the values, the symmetry of the data, and whether there are gaps or outliers.


Stem-and-Leaf Display Options Dialog Box

Determines if outliers should be flagged; flagged outliers is the default.


Studentized Residuals

Include the studentized residuals in the report.  Studentized residuals are the residuals scaled by an estimate of the variance from the data with the observation removed.


Studentized Residuals

Plots the studentized residuals, which are the residuals scaled by an estimate of the variance from the data with the observation removed.

A large studentized residual value may indicate an outlier and an influential observation.


Sum (Summary Statistic)

Displays the simple sum of the observations in the variable.


Summary Statistics
Summary Statistics (One-Way ANOVA)

The Summary Statistics tabular option creates and displays statistical information about the center, spread, and shape of the data: the number of values (Count) in the variable; the average, variance, and standard deviation; and total.

This information is helpful when you need to determine if other statistical analyses might be appropriate to use with the data, or when you need to determine if you should transform the data.

To select options for this summary, use the Summary Statistics Options dialog box.


Summary Statistics (Two-Sample Comparison Analysis)
Summary Statistics

The Summary Statistics tabular option creates and displays statistical information about the center, spread, and shape of the data: the number of values (Count) in the variable; the average, variance, and standard deviation; and the minimum and maximum values.  It also displays the values for the standardized skewness and standardized kurtosis, and the sum of all the values.

This information is helpful when you need to determine if other statistical analyses might be appropriate to use with the data, or when you need to determine if you should transform the data.

To select options for this summary, use the Summary Statistics Options dialog box.


Summary Statistics Options Dialog Box

Allows you to select the summary statistics you want to calculate and display.

Average

Median

Mode

Geometric Mean

Variance

Standard Deviation

Standard Error

Minimum

Maximum

Range

Lower Quartile

Upper Quartile

Interquartile Range

Skewness

Standardized Skewness

Kurtosis

Standardized Kurtosis

Coefficient of Variation

Sum


Sunray Plot (Multiple-Variable Analysis)

The Sunray Plot graphical option creates and displays a plot that allows a visual comparison of the observations with the means for the variables.

A separate glyph is plotted for each observation in the data.  A glyph consists of a series of rays drawn from a center point and lines that connect the rays that (usually) form a polygon.  Each ray is scaled so the middle represents the sample means of the variable.

You can plot 25 glyphs at a time.

To select options for this plot, use the Star Plot/Sunray Plot Options dialog box.


Sunray Plots

The Sunray Plots graphical option creates and displays a Sunray Plot that allows for a visual comparison of observations with the means for the variables.

A separate glyph is plotted for each observation in the data.  A glyph consists of a series of rays drawn from a center point and lines that connect the rays that (usually) form a polygon.  Each ray is scaled so the middle represents the sample means of the variable.

You can plot 25 glyphs at a time.


Symmetry Plot (Distribution Fitting Analysis)

The Symmetry Plot graphical option creates and displays a plot, which helps you assess the symmetry of the data.  Use this plot to determine whether the data could be used in analyses that are best applied to a symmetrical distribution.

Symmetric data closely follow the line on the plot.


Symmetry Plot

The Symmetry Plot graphical option creates and displays a Symmetry Plot, which helps you assess the symmetry of the data.  Use this plot to determine whether the data could be used in analyses that are best applied to a symmetrical distribution.

Symmetric data closely follow the line on the plot.


Table of Means
Table of Means (One-Way ANOVA)

The Table of Means tabular option creates and displays a table that shows the number of observations (Count) at each level, the means (average), the pooled standard errors, and the lower and upper confidence intervals for the means.


Table of Means (Multiple-Sample Comparison Analysis)
Table of Means

The Table of Means displays the number of observations (Count) from each factor level or sample, the means (average), the pooled standard errors, and the lower and upper confidence intervals for the means.


Table Percentages from Column Totals
Column Totals

Calculates a percentage for each cell based on the frequency of that column.


Table Percentages from Entire Table
Entire Table

Calculates percentages using the sum of all the frequencies.


Table Percentages from Row Totals
Row Totals

Calculates percentages using the row frequencies.


Tabulation Analysis Graphical Options Dialog Box

Allows you to select graphical options for the Tabulation analysis.

Barchart (Tabulation Analysis)

Piechart (Tabulation Analysis)


Tabulation Analysis Tabular Options Dialog Box

Allows you to select tabular options for the Tabulation analysis.

Analysis Summary (Tabulation Analysis)

Frequency Table (Crosstabulation Analysis)


Tabulation Analysis Dialog Box

The Tabulation Analysis summarizes the distribution of a single categorical variable through a frequency tabulation.

The tabulation counts the number of times each value occurs, or the number of observations that fall within specified intervals, depending on the type of data you are tabulating.

The data you analyze can be in one of two forms:  (1) observations that must be counted before they are displayed in tabular or graphical form, and (2) counts that represent the results of a previous tabulation and that are ready for immediate display.

Data

(Select)

Sort


Distribution Fitting - Tabular Options Dialog Box
Distribution Fitting Tabular Options Dialog Box

Allows you to select tabular options for the Distribution Fitting analysis.

Analysis Summary (Distribution Fitting)

Tests for Normality

Goodness-of-Fit Tests (Distribution Fitting)

Tail Areas (Distribution Fitting)

Critical Areas (Distribution Fitting)


One-Variable Analysis Tabular Options Dialog Box

Allows you to select tabular options for the One-Variable analysis.

Analysis Summary (One-Variable Analysis)

Summary Statistics (One Variable Analysis)

Percentiles (One-Variable Analysis)

Frequency Tabulation (One-Variable Analysis)

Stem-and-Leaf Display (One-Variable Analysis)

Confidence Intervals (One-Variable Analysis)

Hypothesis Tests (One-Variable Analysis)


Frequency Table (Tabulation Analysis)

The Frequency Table tabular option creates and displays a table that shows the number of observations that fall within each class (frequency) and the relative, cumulative, and cumulative relative frequencies.


Tabulation Frequency Table
Frequency Table

The Frequency Table tabular option creates and displays a table that shows the number of observations that fall into each class (frequency) and the relative, cumulative, and cumulative relative frequencies.


Analysis Summary (Tabulation Analysis)

The Analysis Summary tabular option creates and displays a summary of the analysis that includes the name of the selected variable, and the number of observations and unique values in the variable.


Tabulation Procedure Summary
Analysis Summary

The Analysis Summary tabular option creates and displays a summary of the analysis that includes the name of the variable you selected, and the number of observations and unique values in the variable.


Save Results Options Dialog Box (Tabulation Analysis)

The Save Results Options dialog box allows you to select the results you want to save.  There are two selections: Class Frequencies and Class Labels.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Tail Areas (Distribution Fitting Analysis)

The Tail Areas tabular option creates and displays the area under the density curve at specified points using the cumulative distribution function.

This function calculates the probability that a random variable will fall below a given value.


Tail Areas

Enter the probabilities that will be used to calculate the corresponding critical values.


Tail Areas

The Tail Areas tabular option creates and displays the area under the density curve at specified points using the cumulative distribution function.

This function calculates the probability that a random variable will fall below a given value.


Tail Areas Options Dialog Box (Weibull Analysis)
Tail Areas Options Dialog Box

Allows you to enter the values that will be used to calculate the tail areas for five or fewer critical values.


Tests for Normality

The Tests for Normality tabular option creates and displays several statistics you use to test data to determine if they are normally distributed.

The table shows the chi-square goodness-of-fit statistic, the Shapiro-Wilk's W statistic, the z-score for skewness, and the z-score for kurtosis.  These values are significant if the p-value is less than .05 (95 percent confidence level test).  The Shapiro-Wilk’s test is the most powerful test for normality

See the User Manual for complete information on each of these statistics.


Tests for Normality

The Tests for Normality tabular option creates and displays several statistics you use to test data to determine if they are normally distributed.

The table shows the chi-square goodness-of-fit statistic, the Shapiro-Wilk's W statistic, the z-score for skewness, and the z-score for kurtosis.

These values are significant if the p-value is less than .05 (95 percent confidence level test).  The Shapiro-Wilk’s test is the most powerful test for normality

See the User Manual or Online Help for complete information on each of these statistics.


Tukey HSD
Tukey HSD Method

Uses the Tukey Honestly Significant Differences method when you plan to make many comparisons.

This test is based on the studentized range distribution.  The Type I error is smaller than LSD, Newman-Keuls, and Duncan methods.


Tukey HSD Interval
Tukey HSD Intervals

Uses the Tukey Honestly Significant Differences (HSD) intervals when you plan to make many comparisons.

The test is based on the studentized range distribution.  The Type I error is smaller than the LSD.

If you are using the Multifactor ANOVA, this interval is used to calculate the two-factor interactions.


Two-Sample Comparison Analysis Dialog Box

The titles of the first two text boxes on this dialog box differ, depending on how you want to enter the data (see Input Options on the dialog box).  If you decide to use data as Two Data Columns (the first option, and the default), the titles are: Sample 1 and Sample 2.  If you decide to use Data and Code Columns (the second option), the titles are: Data and Sample Code.

Sample 1 (Two Data Columns)

Sample 2 (Two Data Columns)

Sample Code (Data and Code Columns)

Select

Sort

Transform...

Data (Data and Code Columns)

Input

Delete...

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

Using the Two-Sample Comparison Analysis

Summary Statistics Options

Confidence Intervals Options

Histogram Options

Density Trace Options

Box-and-Whisker Plot Options


Analysis Summary (Two-Sample Comparison Analysis)

The Analysis Summary tabular option creates and displays a summary of the analysis, which displays the names of the variables in each sample, and the number and range of the values in each sample.


Analysis Summary (Two-Sample Comparison Analysis)

The Analysis Summary tabular option creates and displays a summary of the analysis, which displays the names of the variables in each sample, and the number and range of the values in each sample.


Frequency Histogram (Two-Sample Comparison Analysis)

The Frequency Histogram graphical option creates and displays two histograms, one for each sample, which is helpful when you need to visualize the shape of two distributions.

The data in each sample are divided into sets of nonoverlapping intervals, and plots bars for each interval.  The height of each bar is the number of observations that fall within that interval.

In a two-sample analysis, the plot is divided horizontally.  The histogram for Sample 1 appears in the upper half of the plot; the histogram for Sample 2 appears inverted in the lower half of the plot.

To select options for this plot, use the Histogram Options dialog box.


Two-Sample Frequency Histograms
Frequency Histogram

The Frequency Histogram graphical option shows two histograms, one for each sample, which is helpful when you need to visualize the shape of two distributions.

The data in each sample are divided into sets of nonoverlapping intervals, and bars are plotted for each interval.  The height of each bar is the number of observations that fall within that interval.

In a two-sample analysis, the plot is divided horizontally.  The histogram for Sample 1 appears in the upper half of the plot; the histogram for Sample 2 appears inverted in the lower half of the plot.


Type I Sums of Squares
Type I

Computes the sums of squares for each factor in the order in which it was entered into the Factors text box.  The effect of each factor is measured as it occurs.


Type III Sums of Squares
Type III

Computes additional sums of squares for each factor (as though that factor was the last one added to the model).  The effect of each factor is measured as it occurs.


Univariate Plot Analysis Graphical Options Dialog Box
Univariate Plot Graphical Options Dialog Box

Allows you to select graphical options for the Univariate Plot Analysis.

Scatterplot (Univariate Plot Analysis)

Time Sequence Plot (Univariate Plot Analysis)


Univariate Plot Analysis Tabular Options Dialog Box
Univariate Plot Tabular Options Dialog Box

Allows you to select tabular options for the Univariate Plot.

Analysis Summary (Univariate Plot Analysis)


Univariate Plot Analysis Dialog Box

The Univariate Plot Analysis lets you create a scatterplot for a single numeric variable.  The technique applies to a method of grouping data that involves one characteristic of the members of a population or sample, otherwise known as univariate data.

For example, you might examine the age of welfare recipients but not examine their gender or ethnicity.  You can enter point codes to show the levels of the classification factor.

Data

Point Codes

Select

Sort

To select options for the analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options… or Analysis Options…

See also

Using the Univariate Plot Analysis


Analysis Summary (Univariate Plot Analysis)

The Analysis Summary option creates the results of an analysis for a single column of data.  The summary includes the name of the selected variable, the number of values in the variable, and the range of the values.


Scatterplot (Univariate Plot Analysis)

The Scatterplot option creates a plot that is useful for identifying individual data values that represent regions of highest density, and for determining if outliers are present.  A horizontal axis covers the range of the data, while the vertical axis has no real meaning unless it is jittered.  The vertical jittering for this analysis is set, by default, to the maximum.

Use this plot when you want to investigate the distribution and range of observations in a variable.  Although you can easily identify the range of the data, it may be difficult to identify individual points if they overlap.  To reduce the amount of overlapping, you can jitter the points using the Jittering button on the Analysis toolbar.


Unusual Residuals (Simple Regression Analysis)
Unusual Residuals

The Unusual Residuals option creates a table of all the observations that have studentized residuals less than -2 or greater than 2.  The table also shows the corresponding row, observed independent and dependent values, and the residual.  Take a close look at any values greater than 3 to determine if they are outliers, which you should remove from the analysis.


Unusual Residuals

The Unusual Residuals tabular option creates and displays the observations that have studentized residuals less than -2 or greater than 2.  Thetable also shows the corresponding row, observed independent and dependent values, fitted value, and the residual.  Take a close look at any values greater than 3 to determine if they are outliers, which you should remove from the analysis.


Upper Limit

Enter a value for the Upper limit for the last class.  Enter any number greater than the Lower limit; the default depends on the data.


Upper Quartile (Summary Statistic)

Displays the value above which 25 percent of the data will lie.  Use the value to measure the spread or dispersion of the data.


Variable Label
Variable

Uses labels to identify a glyph.  The name of the label corresponds to the variable you enter into the Label Variable text box.


Variance (Summary Statistic)

Displays the value for the variance of the data.  Use the value to measure the spread or dispersion of the data (the variance uses a divisor of n - 1).  This option is one of the defaults.


Variance Check (One Way ANOVA)
Variance Check (One-Way ANOVA)

The Variance Check tabular option performs and displays the results of four statistical tests: Cochran’s C test, Bartlett’s test, Levene’s test, and Hartley’s test.

Use the tests to conffim the assumption that the variance of the factor levels is equal.  If the significance levels are greater than .05, do not reject the hypothesis; that is, the variances are not significantly different (are equal).

P-values for Cochran’s C test, Bartlett’s test, and Levene’s test are also displayed.  To judge the significance of Hartley’s test, refer to standard tables.


Variance Check

The Variance Check tabular option creates and displays the results of four tests: Cochran’s C test, Bartlett’s test, Levene’s test, and Hartley’s test.

The results confirm the assumption that the variance of the factor levels is equal.  If the significance levels are greater than .05, do not reject the hypothesis; that is, the variances are not significantly different (are equal).

P-values for Cochran’s C test, Bartlett’s test, and Levene’s test are also displayed.  To judge the significance of Hartley’s test, refer to standard tables.


Vertical Option
Vertical

Displays the plot vertically.


Weibull Distribution

Produces a distribution that is an appropriate model for product failures.  It is appropriate because its failure rate curves can take various shapes.

This distribution is a generalization of an exponential distribution.


Weibull Plot (Distribution Fitting Analysis)

The Weibull Plot graphical option creates and displays a Weibull Probability Plot.

A Weibull distribution is characterized by two parameters: Shape and Scale, and is used for random variables that are constrained to be greater than or equal to zero.

The distribution is one of the few distributions you can use to model negatively skewed data.


Weibull Plot

The Weibull Plot graphical option creates and displays a Weibull Probability Plot.

A Weibull distribution is characterized by two parameters: Shape and Scale, and is used for random variables that are constrained to be greater than or equal to zero.

The distribution is one of the few distributions you can use to model negatively skewed data.


Weights

Enter the weighting factor that will be applied to the residuals when the model coefficients are estimated.  Enter a numeric variable.  If you use this option, the result is a weighted least squares regression.


X

Enter the name of the variable that contains the data that will be plotted on the X-axis. The data for the variable can consist of any valid set of numbers.


X (Independent Variable)

Enter the name of the independent variable.  The variable must be numeric.


X-Axis Resolution

Enter a number that will be used to smooth the curve. Enter a number from 20 and 200; the default is 30.  The higher the number, the smoother the curve.


X-Y Plot - Graphical Options Dialog Box
X-Y Plot Graphical Options Dialog Box

Allows you to select graphical options for the X-Y Plot.

Scatterplot (X-Y Scatterplot Analysis)


X-Y Plot - Tabular Options Dialog Box
X-Y Plot Tabular Options Dialog Box

Allows you to select tabular options for the X-Y Plot Analysis.

Analysis Summary ( X-Y Plot Analysis)


X-Y Plot Analysis Dialog Box

The X-Y Plot Analysis creates a two-dimensional scatterplot for one variable versus another, which you use to examine their relationships. You can produce lineplots, scatterplots, connected scatterplots, coded scatterplots, and plots with standard error bars.

An X-Y lineplot displays connecting lines without points, while an X-Y scatterplot shows points only (no connecting lines).  A connected X-Y scatterplot connects lines with points; a coded X-Y scatterplot is more informative than the basic X-Y scatterplot because it uses coded points to show the levels of a classification factor.  You can designate the point codes.

When the points in a scatterplot represent means rather than individual values, you may find it useful to illustrate the uncertainty surrounding the points.  You can plot standard error bars for the X- or Y- variables, or both.  Standard error bars are lines that extend from the means, plus and minus one standard error.

Y

X

Select

Sort

To select options for the analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the X-Y Plot Analysis

X-Y Plot Options


X-Y Plot Options Dialog Box

This dialog box allows you to customize the scatterplot.  You can enter a code for the points, enter values for the standard error of X and Y; indicate if points or lines will appear on the plot, and indicate if you want to use sorted variables.

Point Codes

Standard Error X

Standard Error Y

Plot (Points or Lines)

Sort

Delete...

Transform...


Analysis Summary (X-Y Plot Analysis)

The Analysis Summary option creates a summary of the analysis, which includes the name of the selected variable and the total number of paired values.


Analysis Summary (X-Y Plot Analysis)

The Analysis Summary tabular option creates and displays the name of the selected variables, and the total number of paired values.


X-Y-Z Plot Graphical Options Dialog Box

Allows you to select graphical options for the X-Y-Z Plot analysis.

Scatterplot (X-Y-Z Plot Analysis)

Draftsman's Plot (X-Y-Z Plot Analysis)

Casement Plot (X-Y-Z Plot Analysis)


X-Y-Z Plot Tabular Options Dialog Box

Allows you to select tabular options for the X-Y-Z Plot analysis.

Analysis Summary (X-Y-Z Plot Analysis)


X-Y-Z Plot Analysis Dialog Box

The X-Y-Z Plot Analysis is similar to the X-Y Plot Analysis, except that it plots three variables rather than two.  The analysis produces three-dimensional graphs, with the X-axis plotted horizontally along the bottom of the screen, the Y-axis extending back into the screen, and the Z-axis aligned vertically.

The analysis is suitable for small sets of data because large numbers of points and lines make it difficult to read the plot.

An X-Y-Z Lineplot displays connecting lines without points.  An X-Y-Z Scatterplot shows points only (no connecting lines).  A Connected X-Y-Z Scatterplot connects points with lines.  A Coded X-Y-Z Scatterplot uses codes points to show the levels for a classification factor.

Z

X

Y

Select

Sort

Delete...

Transform...

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the X-Y-X Plot Analysis

X-Y-Z Scatterplot Options


X-Y-Z Plot Options Dialog Box

Allows you to:

•	enter the variable that contains the classification factors

•	enter the name of the variables that contain the values for Standard Error X, Y, and Z

•	indicate if you want to plot points or lines

•	indicate where the reference lines should be drawn.

Point Codes

Standard Error X

Standard Error Y

Standard Error Z

Plot (Points or Lines)

Reference Lines

Sort

Delete...

Transform...


Analysis Summary (X-Y-Z Plot Analysis)

The Analysis Summary tabular option creates and displays a summary of the analysis that includes the names of the selected variables, and the total number of plotted points.


Analysis Summary (X-Y-Z Plot Analysis)

The Analysis Summary tabular option creates and displays a summary of the analysis that includes the names of the selected variables, and the total number of plotted points.


Scatterplot (X-Y-Z Plot Analysis)

The X-Y-Z Scatterplot graphical option creates and displays a scatterplot for three or more variables.

One variable each is plotted on the X- and Y-axes; one or more variables are plotted on the Z-axis.  You can plot Z-axis variables with the scale on the left or the right.  The sizes of the scales are automatically adjusted to reflect the range of the values.

To select options for the plot, use the Plot Options dialog box.  You can also use the Smooth/Rotate button on the Analysis toolbar to change the angle from which you view this plot.


X-Y-Z Scatterplot (X-Y-Z Plot Analysis)

The X-Y-Z Scatterplot graphical option creates and displays a three-dimensional scatterplot of the data with only the points plotted.

The pattern of the points indicates the strength and direction of the correlation among the values.  The more the points tend to cluster around the line, the stronger the relationship (the higher the correlation).


Y

Enter the name of the variable that contains the data that will be plotted on the Y-axis. The data can consist of any valid set of numbers.


Y (Dependent Variable)

Enter the name of the dependent or response variable.  The variable must be numeric.


Y (Left Axis)

Enter the name of one or more variables that contain the data that will plot on the Y (Left Axis).  Enter one variable per line.  The data for the Y variable can consist of any valid set of numbers.


Y (Right Axis)

Enter the name of one or more variables that contain the data that will plot on the Y (Right Axis).  Enter one variable per line.  The data for the Y variable can consist of any valid set of numbers.  This text box is optional if you complete the Y (Left Axis) text box.


Z Text Box
Z

Enter the name of the variable that contains the data that will be plotted on the Z-axis.  The variable must be the same length as the variable for the other axes.  The data for the Z variable can consist of any valid set of numbers.


Z (Left Axis)

Enter the name of one or more variables that contain the data that will be plotted on the Z-axis.  Enter one variable per line.  The variables are plotted with the scale on the left axis.  The data for the variable can consist of any valid set of numbers.


Z (Right Axis)

Enter the name of one or more variables that contain the data that will be plotted on the Z-axis.  Enter one variable per line.  The variables are plotted with the scale on the right axis.  The data for the variable can consist of any valid set of numbers.  This text box is optional if you complete the Z (Left Axis) text box.


Options for Two Sample Comparison
Input

Determines how the data will be entered.

Two Data Columns

Enter the data in two columns: one column for each of the two samples.  This option is the default.

Data and Code Columns

Enter data in one column and level codes in the other column.


Box-and-Whisker Plot (One-Way ANOVA)
Box-and-Whisker Plot

The Box-and-Whisker Plot graphical option creates and displays a graphical summary of the presence of outliers in the data.

The data are divided into four areas of equal frequency (quartiles).  A box encloses the middle 50 percent, where the median is drawn as a vertical line inside the box.

Horizontal lines, known as whiskers, extend from each end of the box.  The left (or lower) whisker is drawn from the lower quartile to the smallest point within 1.5 interquartile ranges from the lower quartile.  The other whisker is drawn from the upper quartile to the largest point within 1.5 interquartile ranges from the upper quartile.

To select options for this plot, use the Box-and-Whisker Plot Options dialog box.


Data (Data and Code Columns)

Enter the name of the variable that contains the first set of data you want to compare.  Enter a numeric variable.


Sample Code (Data and Code Columns
Sample Code (Data and Code Columns)

Enter the name of the numeric or character variable that contains a code that corresponds to each item in the variable.  The code for the variable must have two unique values; enter one code for each value.


Residuals versus Observation Plot (Multiple-Sample Comparison Analysis)

The Residuals versus Observation graphical option creates and displays a plot of the residuals versus the observations.  The plot is helpful when you need to identify sequential correlations among the residuals.


Residuals

Includes the residuals in the report.  Residuals are the differences between the observed and fitted values.


Analysis Summary (X-Y-Z Plot Analysis)

The Analysis Summary tabular option creates and displays a summary of the analysis that includes the names of the selected variables, and the total number of grouped values.


Scatterplot (One-Variable Analysis)

The Scatterplot graphical option creates and displays a scatterplot of the values for the variable along a single axis as point symbols with no connecting lines.  The pattern of the points indicates the strength and direction of the correlation among the values.

The plot allows you to easily identify the range of the data, however, it may be difficult to identify individual points if they overlap.  To reduce the amount of overplotting, you can jitter the points, which is the default.


Scatterplot
Scatterplot (Multifactor ANOVA)

The Scatterplot option creates a plot of the values for the response variable at each of the factor levels.

The values are plotted as point symbols (with no connecting lines) along a single horizontal axis.

Use the Scatterplot Options dialog box to choose the factor that will be used in the analysis.


Plus versus:
Plot versus:

Select the independent variable you want to use for the Residuals versus X Plot.


Residual Plot Options Dialog Box

Allows you to select the type of residuals that will be included on the plot and the independent variable that will be used for the Residuals versus Predicted Plot.

Plot (Residuals or Studentized Residuals)

Plot versus:


Plot

Determines the type of residuals that will be included on the plot.

Residuals

Plots the difference between the observed and the fitted values.

Studentized Residuals

Plots the residuals scaled by an estimate of the variance from the data with the observation removed.  A large value for the studentized residual may indicate an outlier and an influential observation.  This option is the default.


Plot versus:

Select the independent variable that will be used for the Residuals versus Predicted Plot.


Residual Plot Options Dialog Box

Allows you to select the type of residuals that will be included and the independent variable that will be used for the Residuals versus Row Number Plot.


Plot versus:

Select the independent variable that will be used for the Residuals versus Row Number plot.


Unusual Residuals (Simple Regression Analysis)

The Unusual Residuals tabular option calculates and displays the observations with the studentized residuals that are less than -2 or greater than 2.

The table also shows the corresponding row, observed independent and dependent values, fitted value, and residual.


Influential Points (Simple Regression Analysis)

The Influential Points option creates a table that lists all the observations that have leverage values above three times that of an average point.  The average leverage value is 2 divided by the number of complete observations.

Leverage determines how influential each observation is in calculating the coefficients for the estimated model.  Look carefully at points more than five times the average leverage to determine how much the model would change if you removed them from the data.


Observed versus Predicted Plot (Simple Regression Analysis)

The Observed versus Predicted option creates a plot of the observed values versus the predicted values for the dependent variable (the fitted model).

The closer the points lie to the diagonal line, the better the model (at predicting the observed data).

Look for various anomalies, such as increases in variability around the line as the value of the variable (the observed data) increases.  This is known as heteroscedasticity.  Also look for individual points that lie far away from the line, which are known as outliers.

You can use the plot to detect cases in which the variance is not constant, which indicates you may need to transform the dependent variable.


Residuals versus X Plot (Simple Regression Analysis)

The Residuals versus X option creates a plot of the studentized residuals versus the values for the independent variable.

Nonrandom patterns could indicate that the model you selected does not adequately describe the observed data, and any values outside the range of -3 to +3 are be outliers.

Use the plot to determine the nonlinear relationship between Y and X.  You can also use the plot to determine if the variance of the residuals is constant.  If the model is correct, and if all the assumptions are satisfied, the residuals should appear structureless; that is, no pattern will be apparent.

Use the Residual Plot Options dialog box to indicate the type of residuals that will appear on the plot.


Residuals versus Predicted Plot (Simple Regression Analysis)

The Residuals versus Predicted Plot option creates a plot of the studentized residuals versus the predicted values of the variable you selected.

Nonrandom patterns indicate that the model you selected does not adequately describe the observed data.

This plot is especially helpful in showing heteroscedasticity, in which the variability of the residuals changes as the values of the dependent variables change.  If the model is correct, and if all the assumptions are satisfied, the residuals should be structureless.

Use the Residual Plot Options dialog box to indicate the type of residuals that will appear on the plot.


Residuals versus Row Number (Simple Regression Analysis)

The Residuals versus Row Number option creates a plot of the studentized residuals versus their row number.  If the row order corresponds to the order in which the data were collected, any nonrandom pattern could indicate serial correlation in the data.  Ideally, the points should appear structureless.

Use the Residual Plot Options dialog box to indicate the type of residuals that will appear on the plot.


Residuals versus Predicted Plot
Residuals versus Predicted Plot (Multifactor ANOVA)

The Residuals versus Predicted Plot option creates a plot of the residuals versus the predicted levels.  The plot is helpful for for detecting heteroscedasticity, in which the variance changes, together with the mean.  If the points form a general funnel-shaped pattern, there is an indication of a type of heteroscedasticity that can often be corrected by transforming the dependent variable.  Try using the Analysis dialog box to enter LOG(n), SQRT(n), or 1/n as the dependent variable.


Means Plot (One-Way ANOVA)

The Means Plot graphical option creates and displays a plot of the mean for each factor level and the intervals for the means.

Bars that do not overlap indicate a significant difference between the two means.  Bars that overlap indicate no significant difference between the means.


Variance Check (Multiple-Sample Comparison Analysis)

The Variance Check tabular option performs and displays the results of three tests: Cochran’s C test, Bartlett’s test, Levene’s test and Hartley’s test, which confirm the assumption that the variance of the samples are equal.

If the significance levels are greater than .05, do not reject the hypothesis; that is, the variances are not significantly different (are equal).

P-values for Cochran’s C test, Bartlett’s test, and Levene’s test are also displayed.  To judge the significance of Hartley’s test, refer to standard tables.


Summary Statistics (Two-Sample Comparison Analysis)

The Summary Statistics tabular option creates and displays statistical information about the center, spread, and shape of the data: the number of values in each variable (Count); and the average, variance, standard deviation, and the minimum and maximum values.

It also displays the values for the standardized skewness and standardized kurtosis, and the sum of all the values.

This information is helpful when you need to determine if other statistical analyses might be appropriate to use with the data, or when you need to determine if you should transform the data.


Summary Statistics (Multiple-Variable Analysis)

The Summary Statistics tabular option creates and displays statistical information about the center, spread, and shape of the data: the number of values in the variable; the average, variance, standard deviation, minimum and maximum values; the standardized skewness and standardized kurtosis; and the sum of all the values.

This information is helpful when you need to determine if other statistical analyses might be appropriate to use with the data, or when you need to determine if you should transform the data.

To select options for these statistics use the Summary Statistics Options dialog box.


Normal Probability Plot (Probability Plot Analysis)

The Normal Probability Plot graphical option creates and displays a Normal Probability plot.

The plot consists of an arithmetic (interval) horizontal axis scaled for the data and a vertical axis scaled so the cumulative distribution function of a normal distribution plots as a straight line.  The closer the data are to the reference line, the more likely they follow a normal distribution.

To select options for the plot, use the Normal Probability Plot Options dialog box.


Scatterplot (Multiple X-Y Plot Analysis)

The Scatterplot graphical option creates and displays a plot with one variable on the X-axis and one or more variables on the Y-axis.

The pattern of the points indicates the strength and direction of the correlation among the values.  The more the points tend to cluster around the straight line, the stronger the relationship (the higher the correlation).


Scatterplot (X-Y Scatterplot Analysis)

The Scatterplot option creates a scatterplot of one variable versus a second.  The pattern of the points indicates the strength and direction of the correlation between the two values.

The following guidelines are helpful when you interpret a two-dimensional scatterplot:

•	the more the points tend to cluster around a straight line, the stronger the linear relationship between two variables (the higher the correlation)

•	if the line around which the points tend to cluster runs from lower left to upper right, the relationship between the two variables is positive

•	if the line around which the points tend to cluster runs from upper left to lower right, the relationship between the two variables is negative

•	if there exists a random scatter of points, there is no relationship between the two variables (very low or zero correlation).

Use the X-Y Plot Options dialog box to customize the scatterplot.  You can enter a code for the points; enter values for the standard error of X and Y; indicate if points or lines will appear on the plot; and indicate if you want to use sorted variables.

To clearly see the pattern in the plot, choose a smoothing option from the Scatterplot Smoothing Options dialog box, which is accessed by clicking the Smooth/Rotate button on the Analysis toolbar.


Time Sequence Plot (Univariate Plot Analysis)

The Time Sequence Plot option creates a plot that is useful for detecting trends that occur over time, or for determining patterns in the data.  Use it only when the data are collected and stored in time order; the observations are plotted in the order in which they were entered into the DataSheet.

Use the Plot Options dialog box to indicate if points or lines will appear on the plot.  To clearly see the pattern in the plot, choose a smoothing option from the Scatterplot Smoothing Options dialog box, which is accessed by clicking the Smooth/Rotate button on the Analysis toolbar.


Reference Lines

Determines if reference lines will be drawn on the plot, and if so, where they will appear.  Reference lines provide perspective when you are locating points in three-dimensional space.

None

Creates the plot without reference lines; it is the default.

To Bottom

Draws vertical reference lines from the points to the bottom of the cube.

To Top

Draws vertical reference lines from the points to the top of the cube.

To Front

Draws horizontal reference lines from the points to the front of the cube.

To Back

Draws horizontal reference lines from the points to the back of the cube.

To Left

Draws horizontal reference lines from the points to the left of the cube.

To Right

Draws horizontal reference lines from the points to the right of the cube.


Legends

Determines the labels for each class on the chart.

Percent

Uses percentages, which is the percentage of the total count for the segments of the chart.

Counts

Uses counts, which show frequencies for the segments of the chart.

Labels

Uses labels from the Labels variable for the segments of the chart.

None

Displays the legend without labels.


Labels

Determines the labels for the segments of the chart.

Percent

Uses percentages, which is the percentage of the total count for the segments of the chart.  This option is the default.

Counts

Uses counts, which show frequencies for the segments of the chart.

Labels

Uses labels from the Labels variable for the segments of the chart; it is the default.

None

Displays the segments of the chart without legends.


Data (for One-Variable Analysis)

Enter the name of the numeric variable that contains the data that will be analyzed.


Label

Determines the label that will appear on the plot.

Row Number

Uses row numbers to identify the glyph; it is the default.

Variable

Uses labels to identify the glyph.  The name of the label should correspond to the variable you enter into the Label Variable text box.

Starting Row Number

Enter a number for the starting glyph when you have more than 25 observations. The default is 1.


Plot (Frequencies or Percentages)

Indicate the type of data that will appear on the chart.

Frequencies

Plots frequencies; it is the default.

Percentages

Plots percentages.


Number of Classes (Histogram Options)

Enter the number of classes into which the data will be divided.  Enter an integer between 1 and 1000; the default depends on the data.


Upper Limit

Enter a value for the Upper limit for the last class.  Enter any number greater than or equal to the Lower limit; the default depends on the data.


Residual Plot Options Dialog Box

Allows you to select the factor that will be plotted against the residuals.


Include

Determines what will be included on the plot.

Prediction Limits

Includes the prediction limits.  If you want to include both prediction and confidence limits on the plot, click both options.

Confidence Limits

Includes the confidence limits.  If you want to include both prediction and confidence limits on the plot, click both options.


X-Axis Resolution

Enter the number that will be used to change the resolution of the lines on the graph.  Enter an integer between 2 and 200; the default is 30.  Higher values give smoother lines.


Include

Indicate the values that will be included in the Report.

Observed Y

Includes the values for the dependent variable.

Fitted Y

Includes the estimated value for the dependent variable (forecast).  This option is one of the defaults.

Residuals

Includes the difference between the observed and fitted values.

Studentized Residuals

Includes the residuals scaled by an estimate of the variance from the data with the observation removed.  A large studentized residual value may indicate an outlier and an influential observation.  This statistic is also known as the R-student.

Standard Errors for Forecasts

Includes the standard deviation of the distribution for the estimated values.  This option is one of the defaults.

Confidence Limits for Individual Forecasts

Includes the end points of the prediction interval for individual estimated values.  This option is one of the defaults.


Type of Model

Determines the type of model the program will fit.

Linear

Fits a simple linear regression equation for Y in terms of X.  The program fits the data to the linear model before you choose a different model.  The model is defined by the equation:  X = a + bX.  This option is the default.

Exponential

Fits an exponential model.  This model is equivalent to taking the natural log of Y; it is defined by the equation: Y = exp(a + bX).

Reciprocal-Y

Fits a reciprocal-Y model; it is defined by the equation: Y = 1/(a + bX).

Reciprocal-X

Fits a reciprocal-X model; it is defined by the equation: Y = a + b/X.

Double Reciprocal

Fits the reciprocal of the dependent variable and the reciprocal of the independent variable; it is defined by the equation: Y = 1/(a + b/X).

Logarithmic-X

Fits a logarithmic-X model; it is defined by the equation: Y = a + b(Log X).

Multiplicative

Fits a multiplicative model and is equivalent to taking the natural logs of Y and X; it is defined by the equation: Y = aX^b.

Square Root-X

Fits a square root-X model; it is defined by the equation Y = a + b sqrt(X).  The reciprocal-X, logarithmic-X, and square root-X transformations linearize a nonlinear relationship between the dependent and independent variables.  The transformations are suitable when the error terms are normal and have constant variance.

Square Root-Y

Fits a square root-Y model; it is defined by the equation Y = (a + bX)^2.  The exponential, reciprocal-Y and square root-Y transformations can help remedy error terms that are not normal and that do not have constant variance.

S-Curve

Takes the natural log of Y and the reciprocal of X; it is defined by the equation Y = exp(a + b/X).  The double reciprocal, multiplicative, and S-curve models transform the independent variable, linearizing the nonlinear relationship between the independent and dependent variables.  This transformation of the dependent variable helps remedy error terms that are not normal and that do not have constant variance.

Logistic

Fits a response of observed proportions or probabilities at each level of an independent variable.  The response function is a nonlinear S-shaped curve with asymptotes at 0 and 1.  The dependent variable must have values greater than 0 and less than 1.  The model is defined by the equation: Y = exp(a + bX)(1 + exp(a + bX)).

Log Probit

Fits a response of observed proportions or probabilities at each level of an independent variable.  The model is appropriate when the response variable tends to follow a cumulative normal distribution.  The response function is a nonlinear S-shaped curve with asymptotes at 0 and 1.  The dependent variable must have values greater than 0 and less than 1.  It is defined by the equation: Y = normal(a + b(Log X)).


Point Codes

[Optional]  Enter the name of the variable that contains the classification levels for the coded scatterplot.  In this type of scatterplot, coded points appear on the plot.  You must provide a code for each data point.  If you use a numeric variable, it must contain only integers.  If you are not producing a coded scatterplot, leave this text box blank.


Delete...

Deletes highlighted text from an active text box.


Transform...

Displays the Generate Data dialog box, which lets you create values for the data.


Direction

Determines the direction of the plot.

Horizontal

Display the plot horizontally; this option is the default.

Vertical

Displays the plot vertically.


Two-Sample Comparison Analysis Tabular Options Dialog Box

Allows you to select tabular options for the Two-Sample Comparison analysis.

Analysis Summary (Two-Sample Comparison Analysis)

Summary Statistics (Two-Sample Comparison Analysis)

Comparison of Means (Two-Sample Comparison Analysis)

Comparison of Standard Deviations (Two-Sample Comparison Analysis)

Comparison of Medians (Two-Sample Comparison Analysis)

Kolmogorov-Smirnov Test (Two-Sample Comparison Analysis)


Two-Sample Comparison Analysis Graphical Options Dialog Box

Allows you to select graphical options for the Two-Sample Comparison analysis.

Frequency Histogram (Two-Sample Comparison Analysis)

Density Trace (Two-Sample Comparison Analysis)

Box-and Whisker Plot Two Sample Comparison Describe Analysis

Quantile Plot (Two-Sample Comparison Analysis)

Quantile-Quantile Plot (Two-Sample Comparison Analysis)


Point Codes

[Optional]  Enter the name of the variable that contains the classification levels for the coded scatterplot.  A different point type appears for each unique entry in the variable.  You can change the color and the type of the points by using the Point Options tab page.

If you are not producing a coded scatterplot, leave this text box blank.


Labels for Piechart Analysis

[Optional]  Enter the name of the variable that contains the labels for the classes.  Enter a different label for each class.  The first label corresponds to the first count in the DataSheet, the second label corresponds to the next, and so on.  If you use classification data and leave this text box blank, labels are generated from the level codes.  If you leave this text box blank, generic names are used for the classes.


X-Axis Resolution (Two-Sample Comparison Analysis)
X-Axis Resolution

Enter the number of locations at which the Density Traces will be calculated.  Selecting a larger value gives a more detailed curve, but takes longer to calculate.  Enter an integer between 20 and 200; the default is 30.  The higher the resolution, the smoother the line.


Select

[Optional]  Select a subset of the observations.  For example, to fit the first 50 values in each variable, enter first (50) into this text box.


Plot Options Dialog Box

Determines how the data will appear on the plot.

Points

Plots points; this option is the default.

Lines

Plots lines.


Colors... Command

Displays the Color dialog box, which you use to change the colors for the various attributes of a graph.

This is a standard Windows dialog box; see the Microsoft Windows documentation for more information.


Brushing Dialog Box

Allows you to select the variable that will be used to brush the points on a Scatterplot.  Brushing allows you to change the color of the points to indicate the value of an additional variable, and to display points that fall below the median in another color.  You can also change the range of the points that are plotted in the second color.  This option is the default.

When you brush points, the Label and Row text boxes on the Analysis toolbar are replaced by a Vertical scroll bar.  Use the scroll bar to indicate the value used to determine the point below which the data become a different color.  The values are displayed to the right of the Vertical scroll bar.

Brush With

Enter the numeric variable that will be used to brush the points.

Sort

Displays the Sort File Options dialog box you use to select sorting options.  You can sort in ascending or descending order, sort an entire file, sort only a selected portion of a file, or select variables for a first and second sort.


Change Link Dialog Box

Allows you to establish a DDE link between spreadsheet applications such as Excel, Lotus, or Quattro Pro and a DataSheet in STATGRAPHICS Plus.

When you use this technique, you will cut or copy an entire spreadsheet or a portion of it, store that data on the Clipboard, then paste (copy) it into the DataSheet.  Whenever the data changes in the application spreadsheet, it will also change in STATGRAPHICS Plus.

Change Link To

Enter the name of the selected link.

Automatic

Automatically updates the file whenever the source spreadsheet is changed.  Automatically updated is the default.


Character

Creates a character variable.  Character variables contain characters and/or numbers that are treated as characters.  You cannot run calculations on character variables.


Name (for a Column)

Enter a variable name for the column.  Each column (variable) can contain from one to 32 characters.

The name must begin with a letter (A-Z or a-z), an underscore (_), or a number sign (#).

The name can consist of letters (A-Z or a-z), digits (0-9), an underscore (_), a period (.), or a blank ( ) as well as any of the following symbols:  @, #, $, %, and &.

Embedded blanks are ignored in variable names; for example, Flow Rate and FlowRate are equivalent.


Combine Data File Dialog Box
Combine Data Files Dialog Box

Allows you to combine several files into a single file.  You can combine as many files as you like, but you must combine them two at a time.

File Name

Enter the name of the files to be combined.  You can enter a new name or select a name from the list of existing files.

List Files of Type

Select the type of files you want to combine.

Directories (Only for Windows 3.x versions)

Select the directory in which the file will reside.

Drives (Only for Windows 3.x versions)

Select the drive on which the file will reside.


Combine StatFolios Dialog Box

Allows you to combine several StatFolios into a single StatFolio.  You can combine as many StatFolios as you like, but you must combine them two at a time.

Note that the first StatFolio (the base StatFolio) should contain the variables you analyzed in the second StatFolio.  If you do not do this, when you try to open certain analyses in the newly combined StatFolio, a message displays:  "Input data no longer valid" (text) or "No output due to data error" (graphs).

File Name

Enter the name of the StatFolios to be combined.  You can enter a new name or select a name from the list of existing files.

List Files of Type

Select the type of files you want to combine.

Directories (Only for Windows 3.x versions)

Select the directory in which the StatFolio will reside.

Drives (Only for Windows 3.x versions)

Select the drive on which the StatFolio will reside.


Generate Data Dialog Box

Allows you to transform data using mathematical functions called operators.  Operators let you perform functions that range from basic math (for example, +, -, SQRT, and LOG) to complex types of calculations.

You use operators in formulas, known as expressions, you create in the Generate Data dialog box.  You can insert the expression into a dialog box or create a new variable in the file.

See Appendix B in the User Manual and the Online Help for more information about operators and their use.

Beginning with Version 3, the last expression you create is stored and redisplayed the next time you select the Transform… option.  This technique is helpful when you create similar, complicated expressions on a regular basis.

Expression

Enter a mathematical expression.  An expression can contain one or more phrases with one operator and a right argument (values or phrases that appear to the right of the operator).

When the dialog box initially displays, the text box contains the name of the selected variable or column.

Variables

This list box allows you to select the variable you want to include in an expression.  Double-click the name of the variable to display it in the Expression text box.

Operators

Select the operator or operators you want to include in the expression.  In addition to the operator name, each item in the list indicates the correct syntax.  For example, ABS(?) indicates that the ABS operator takes a single right argument.  Double-click the operator to display it in the Expression text box.


Date and Time

Adds the date and time to a header.  The date and time appear in the upper-left corner of the page, below the header, if there is one.


Hold

Indicates that you want to retain the current scaling even if you change the data on the Analysis dialog box.


Horizontal Angle

Specifies the horizontal viewpoint for a three-dimensional graph.  You can increase or decrease the setting from -90 to 90 degrees.


Horizontal (Graphics Scaling)

Changes the horizontal scaling of a plot.  Enter a number from 10 to 100.


Horizontal (Offset)

Sets the horizontal offset when you jitter points.  You can select from Less to More.


Links Dialog Box

Allows you to edit links you established between spreadsheets.  The dialog box lists the links currently established between the source application and the open file.

The dialog box displays the name of the document in the source application, the page or sheet number, and the row and column numbers you used to establish the link.


Log (Scaling)

Indicates that you want to change the axis scale for the tickmarks on the graph using the Log option.  The Log option uses logarithmic scaling to calculate the axis scale for the tickmarks.


Modify Column Dialog Box

Allows you to:

•	enter new or modify existing data in a DataSheet

•	enter a value for the width of the column

•	select the type of data you will be entering

•	use the Define… command to enter an expression that will be used for the

formula or the data transformation.

Note:  The Modify Column… command on the Edit pull-down menu is available only after you highlight a column on the DataSheet.

Name

Enter the name of the column (variable) you want to create or modify.  See Using Naming Conventions for information creating new variable names.

Comment

Enter a comment that describes the column or variable.

Width

Enter a number that will determine the width of the column.

Type

Select the type of variable you want to create or change.

Numeric

Contains only numbers; has a floating decimal place.

Character

Contains characters and/or numbers treated as characters.

Integer

Contains numbers without decimal places.

Date

Contains numbers in MM/DD/YY format.

Month

Contains numbers in MM/YY format.

Quarter

Contains data in Q1/YY, …, Q4/YY format.

Time (HH:MM)

Contains numbers in hour and minute format.

Time(HH:MM:SS)

Contains numbers in hr:min:sec format.

Fixed Decimal

Contains numbers with a fixed number of decimal places.

Formula

Contains data based on existing columns.

Define… Command

When you are using the Modify Column dialog box, displays the Generate Data dialog box that lets you enter an expression or transform data.


No Power

Indicate you want to change the axis scale for the tickmarks on the graph.  A power of 10 is used for the calculation.


One Pane/Page
1 Pane/Page

Prints one pane per page.


Open Data File Dialog Box

Allows you to select a file to open.

Look In

If necessary, allows you to select a different disk drive.

File Name

Enter the name of the file you want to open.

List Files of Type

Select the type of file you want to open.

Directories (Only for Windows 3.x versions)

Select the directory in which the file will reside.

Drives

Select the drive on which the file will reside


Open StatFolio Dialog Box

Allows you to select a StatFolio to open.

Look In

If necessary, allows you to select a different disk drive.

File Name

Enter the name of the StatFolio you want to open.

List Files of Type

Select the type of file you want to open.

Directories (Only for Windows 3.x versions)

Select the directory in which the StatFolio will reside.

Drives

Select the drive on which the StatFolio will reside


Outline Color
Outline

Changes the color of the outline for the fill pattern.


Page Setup Dialog Box

Allows you to change the default page settings by selecting different values for the attributes.

The changes you make remain in effect until you change the values for attributes again.  The settings are retained even after you start and end other STATGRAPHICS sessions.

Margins

Changes the margin settings for the top, bottom, left, and right margins.  The defaults are 0.5 inch for top and bottom and 0.1 inch for left and right.

Enter a number between 0 and 10 for each margin option you want to change.

Header

Adds the text that will appear as the header in the upper-left corner of each printed page.  If you do not want to use a header, leave this text box blank.

Text

Enter the wording for the header that will appear on the page, if any.

Date and Time

Adds the date and time to the header.  The data and time appear below the header in the upper-left corner of the page, if there is a header.

File Names

Adds the names of the StatFolio and the file to the header, if there is one.

Output

Select the number of panes you want printed per page.

1 Pane/Page

Prints one page per page; it is the default.

Multiple Panes/Page

Prints multiple panes per page.

Graphics Setting

Select the scaling for the graphics.

Horizontal

Changes the horizontal scaling.  Enter a number from 10 to 100 percent; the default is 100 percent.

Vertical

Changes the vertical scaling.  Enter a number from 10 to 100 percent; the default is 50 percent.

Black and White

Converts the graphics from a grey-scale, which represents the colors on your monitor, to a pure black and white image.

Print Background

Prints the background color when you are using a color printer.

Wide Lines

Doubles the line width.


Size (Scrollbar)
Point Size (Scrollbar)

Adjusts the size (smallest to largest) of the points.


Portrait

Prints in Portrait mode, which means the print appears vertically.


Primary Column

Select the variable that will be used for the first sort.


Print Analysis Dialog Box

Allows you to print the text and graphics that make up an analysis.

Print Range

Prints the selected range of pages.

All Panes

Prints all the panes in the analysis.  This option is the default.

Visible Panes

Prints only the panes that are currently visible.

All Text Panes

Prints all the text panes in the analysis.

All Graphics Panes

Prints all the graphics panes in the analysis.

Print Quality

Select the quality of the print (for printers with selectable levels of print quality).  A high print quality produces better looking text and graphics, but prints slower and uses more toner, ink, or print media.  A lower print quality prints faster, and uses less toner, ink, or print media.  You printer determines which settings you can select.  The print driver determines the default.

Print to File

Prints to a file instead of to a printer.

Copies

Enter the number of copies you want to print.  The default is 1.

Collate Copies

Collates the copies if you are printing more than one.  If you collate copies, one complete set is printed and collated at one time.  The printer you use will determine if you can collate copies.

Setup… Command

Displays the Print Setup dialog box, which you use to select a different printer, and to select the paper size and source.  See the section, “Using the [Print] Setup… Command for more information.


Print Comments Dialog Box

Allows you to print the comments for the current StatFolio.

Printer

Displays the name of the current printer.  To change printers, use the Setup… command.  See the section, “Using the [Print] Setup… Command” or Online Help for more information.

Print Range

Prints the selected range of pages.

All

Prints the entire contents of the window.  This option is the default.

Selection

Prints the highlighted sentence or paragraph.

Rows

This option is not available for this dialog box.

Print Quality

Select the quality of the print (for printers with selectable levels of print quality).  A high print quality produces better looking text and graphics, but prints slower and uses more toner, ink, or print media.  A lower print quality prints faster, and uses less toner, ink, or print media.  You printer determines which settings you can select.  The print driver determines the default.

Print to File

Prints to a file instead of to a printer.

Copies

Enter the number of copies you want to print.  The default is 1.

Collate Copies

Collates the copies if you are printing more than one.  If you collate copies, one complete set is printed and collated at one time.  The printer you use will determine if you can collate copies.

Setup… Command

Displays the Print Setup dialog box, which you use to select a different printer, and to select the paper size and source.  See the section, “Using the [Print] Setup… Command for more information.


Print From/To Row
From/To

Select the number of the rows you want to print.  Enter the starting row number in the From text box; enter the ending row number in the To text box.

These text boxes are available when you select to print only the rows on a selected DataSheet.


Print Setup Dialog Box

Allows you to select a different printer, select the paper size and source, and select the print mode.

Default Printer

Sends the file to the default printer.

Specific Printer

Selects a printer other than the default and view other information about the default printer such as its status and type.

Orientation

Prints in Portrait mode, which means the print appears vertically.


Print Spreadsheet Dialog Box

Allows you to print a spreadsheet (DataSheet) window.

Print Range

Select the portions of the DataSheet you want to print.

All Rows

Prints the entire contents of the window; it is the default.

Selection

Prints the range of rows and columns you select.

Rows

Prints the rows you select.  Enter the starting row number in the From text box; enter the ending row number in the To text box.

Print Quality

Selects the quality of the print (for printers with selectable levels of print quality).  A higher print quality produces better looking text and graphics, but prints slower and uses more toner, ink, or print media.  A lower print quality prints faster, and uses less toner, ink, or print media.  Your printer determines which settings you can select.  The default is set by the printer driver.

Copies

Enter the number of copies you want to print.  The default is 1.

Print to File

Prints to a file instead of to a printer.

Collate Copies

Collates the printed copies, if you are printing more than one copy.  If collate the copies, one complete set is printed and collated at one time.  The printer you use  determines if you can collate copies.

Setup… Command

Displays the Print Setup dialog box you use to select a different printer, choose a paper size and source.


Print To File

This check box allows you to indicate if you want to print to a file instead of to a printer.  When the dialog box displays, this option is not selected.


Print Visible Panes

This option prints only the panes that are currently visible on your computer screen.


Reset

This option allows you to reset the settings as System or User-defined settings.


Save

This option saves new graphics settings.  The option is available only when you select the User-defined option on the Graphics Defaults dialog box.


Save Data File As Dialog Box

This dialog box allows you to do two things:  (1) indicate where you want to save the document on the hard disk, and (2) indicate the name of the file.  If you use Windows 95, the names of the items on the dialog box will be slightly different.

File Name

Enter the name of the file you want to save.  You can enter a new name or select a name from the list of existing files.

Save File As Type

Select the type of file in which you want to save this file.

Directories

Select the directory in which you want the file to reside.

Drives

Select the drive on which you want the file to reside.


Save Graph Dialog Box

This dialog box allows you to save a graph as a metafile.  This is helpful when you want to save graphs you have created an in analysis so you can re-create them using other software programs.  A metafile allows you to do this.

File Name

Enter the name of the graph you want to save.  You can enter a new name or select a name from the list of existing files.  The program automatically adds the .wmf extension.

Save File As Type

Select the file format in which you want to save the graph.  Currently, you can only save a graph in metafile format (.wmf).

Directories

Select the directory in which you want the graph to reside.

Drives

Select the drive on which you want the graph to reside.


Save StatFolio As Dialog Box

This dialog box allows you to enter a name for the StatFolio you are currently saving.

File Name

Enter the name you want to use to save the StatFolio.  You can enter a new name or select a name from the list of StatFolios.

Save File As Type

Enter the format in which you want to save the StatFolio.

Directories (Only for Windows 3.x versions)

Select the directory in which you want the StatFolio to reside.

Drives (Only for Windows 3.x versions)

Select the drive on which you want the StatFolio to reside.


Scaling By
By

This text box allows you to enter the value the program will use to calculate the distance between each numeric tickmark for the axis scale you want to change.  Enter any positive numeric value.


Scaling From
From

This text box allows you to enter the minimum value the program will use for the axis you want to change.


Scaling To
To

This text box allows you to enter a value the program will use for the maximum distance on the axis you want to change.


Secondary Column

This text box allows you to select the variable you want to use as the second sort.  Click the down Arrow to the right of the list box to list the variables in the current file.


Sort File Options Dialog Box

Allows you to sort one column, two or more adjacent columns, or an entire spreadsheet into ascending or descending order.  You can also rearrange the values you select according to the contents of a primary or secondary column.

Ascending Order

Sorts the file in ascending order.

Descending Order

Sorts the file in descending order.

Apply to Entire File

Sorts the entire file.

Apply to Selected Range Only

Sorts only the portion of the file that is highlighted.

Primary Column

Allows you to select the variable that will be used for the first sort.

Secondary Column

Allows you to select the variable that will be used for the second sort.


Text Options Dialog Box

Allows you to make changes to the titles and labels on a graph.  Text appears on a graph as a title or as labels.  Title refers to text that displays at the top of a graph.  Labels refer to text that identifies the axes on graphs.

Text

Enter the text for the title or label that will be changed, replaced, repositioned, or deleted.

Note:  The number between the braces, for example, {1}, is an internal reference to variable names entered in the text box(s) on Plot or Analysis dialog boxes.  For example, suppose you create a Univariate Plot and use mpg as the variable name, then create a Scatterplot.  When you access the Text Options dialog box from the Scatterplot, the Text text box contains:  Scatterplot for {1}.  The {1} refers to the variable name in the Univariate Plot.

Direction

Select the display direction of the text and/or label:  horzonital or vertical.

Fonts…

Displays the Font dialog box, which allows you to chaange the attributes for the font.  This is a standard Windows text box.


Tickmarks

These options allows you to select the type of tickmarks you want to appear on the graph.  There are three options:  No Tickmarks, Tickmarks Inside the Frame, or Tickmarks Outside the Frame.  These options are available only when you choose one of the three axes:  X, Y, or Z.


Print Range

These options allow you to select what you want to print.

All Rows

Prints the entire contents of the window; it is the default.

Selection

Prints the range of rows and columns you select in the spreadsheet.

Rows

Prints the rows you select in the Print Spreadsheet dialog box.  Enter the starting row number in the From text box; enter the ending row number in the To text box.


Fill Options Dialog Box

This dialog box allows you to change the styles and colors of fill patterns to distinguish the bars, boxes, wedges, and other fill areas on a graph.  If you view and print the graph in color, you can coordinate the color of each outline and areas of the graph.  If you view and print the graph in black and white, you can use different patterns to achieve the same effect.


Line Options Dialog Box

Use this dialog box to change the thickness or type of the the line that appears on the graph.  Line thickness is changed by moving the slidebar between the thinnest and thickest markers.


Point Options Dialog Box

Use this dialog box to change all of the attributes for a point: its shape, size, and color.


Layout Options Dialog Box

This dialog box allows you to change the appearance of a graph by customizing its axes and grids.  Use the buttons and radio buttons to modify the tickmarks and colors.


Grid Options Dialog Box

Use the buttons and radio buttons on this dialog box to set the direction of the grid and the type that will be displayed.


Combine Counts Less Than
Counts Less Than

Combines classes that have less than the number of defects you choose.  Use the text box to enter the count.  The program combines all the classes below the count into one class.  Enter an integer greater than 1.


Combine Percentages Less Than
Percentages Less Than

Combines classes that have less than the percentages you choose.  Use the text box to enter the percentages.  The program combines all the classes below the percentage into one class.  Enter a numeric value greater than 0.


Combine Smallest Classes
Smallest Classes

Combines the smallest classes.  Use the text box to enter the number of classes.  The program combines the smallest classes into one class.  Enter an integer greater than 1.


Cumulative Pareto Chart (Pareto Analysis)

The Cumulative Pareto Chart option produces a Pareto Chart in cumulative format.  The base of the bar for each defect-type class is plotted at the top of the previous bar; the height of the bar is equal to the weighted score for the class.

The Cumulative Pareto Chart graphical option displays a Pareto Chart in cumulative format.


Cumulative Pareto Chart (Pareto Analysis)

The Cumulative Pareto Chart graphical option displays a Pareto Chart in cumulative format.

The program plots the base of the bar for each defect class at the top of the previous bar.  The height of each bar is equal to the count for the class, times the weight for that class.


Display None
None

This option displays the total line without class labels.


Display Percentages
Percentages

This option displays the class percentages of the total score.


Display Scores
Scores

This option displays the class scores.


Labels

Labels

[Optional]  Enter the name of the variable that contains the labels that will be used for each defect class.  Enter one label for each class in row order if Tabulated, alphabetic order if untabulated.  If you use untabulated observations, the length of the variable should equal the number of values; in other words, you should have a label for each observation.  If you use tabulated counts, the length of the variable should equal the number of distinct classes.  The first label is assigned to the defect that occurs first, the second label to the defect that occurs second, and so on.   The labels identify the classes on reports.  If you leave this text box blank, default labels are created.


None (Do Not Combine Classes)
None

Indicate that you do not want to combine classes.


Pareto Analysis Data Input Dialog Box
Pareto Analysis Dialog Box

The Pareto analysis produces a Pareto Chart, which is a histogram for categorical data.  Manufacturers often use this tool, together with attributes control charts, to identify and rank order the most important causes of a problem within a process.  Pareto Charts also can track the progress of changes to a process.  The Pareto analysis also plots the frequency of each defect type.  Using this analysis, you can identify the most frequently occurring types of defects.

Vertical bars, with heights proportional to the number of times each defect occurs, are shown as well as a line that is drawn above the bars to plot the cumulative percentages or scores.

The analysis does not identify the most important defects, or the defects that are most cost effective to improve — it simply reveals the most frequent defects.

Data

Labels

Weights

Select

Sort

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Pareto Analysis

Pareto Analysis Options

Pareto Chart Options


Frequency Table (Pareto Analysis)

The Frequency Table option creates a table that shows either the number of occurrences of any unique values in the data (untabulated data) or the counts.  The table contains the rank, count, weight, weighted score, cumulative score, percent, and cumulative percent for each of the defect types.

The program sorts the data into classes according to the weighted score, with the highest weighted score listed first.  The Percentage column shows the percentage of the sum of the weighted scores represented by each class.


Frequency Table (Pareto Analysis)

The Frequency Table option creates a table that shows either the number of occurrences of any unique values in the data (untabulated data) or the counts.  The table contains the rank, count, weight, weighted score, cumulative score, percent, and cumulative percent for each of the defect types.  The program sorts the data into classes according to the weighted score, with the highest weighted score listed first.  The Percentage column shows the percentage of the sum of the weighted scores represented by each class.


Analysis Summary (Pareto Analysis)

The Analysis Summary option creates a summary that shows the name of the variable, the total count, and the number of classes in the analysis.

Use the Pareto Analysis Options dialog box to indicate if small classes should be combined into a style “other” class, and if so, the method that will be used to combine them: Counts Less than n, Percentages Less than n, or by Smallest Classes.


Analysis Summary (Pareto Analysis)

The Analysis Summary option creates a summary that shows the name of the variable, the total count, and the number of classes in the analysis.

Use the Pareto Analysis Options dialog box to indicate if small classes should be combined into a style “other” class, and if so, the method that will be used to combine them: Counts Less than n, Percentages Less than n, or by Smallest Classes.


Pareto Analysis Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Pareto Chart (Pareto Analysis)

Cumulative Pareto Chart (Pareto Analysis)


Pareto Analysis Options Dialog Box

This dialog box allows you to indicate if small classes should be combined into a style, and if so, the method that will be used to do so.

Combine Classes


Pareto Analysis Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Pareto Analysis)

Frequency Table (Pareto Analysis)


Pareto Chart (Pareto Analysis)

The Pareto Chart option creates a frequency distribution or histogram of the tabulated data arranged by category.  The total weighted score of each defect type or class is plotted against the various defect types to illustrate the defects that occur most frequently.  The chart contains a bar for each category of defect; the height of the bar represents the defect frequency or weighted score.  You can plot a maximum of 20 classes.

Use the Pareto Chart Options dialog box to indicate what the labels will display above each bar: Percentages, Scores, or None.


Pareto Chart (Pareto Analysis)

The Pareto Chart option creates a frequency distribution or histogram of the tabulated data arranged by category.  The total weighted score of each defect type or class is plotted against the various defect types to illustrate the defects that occur most frequently.  The chart contains a bar for each category of defect; the height of the bar represents the defect frequency or weighted score.  You can plot a maximum of 20 classes.

Use the Pareto Chart Options dialog box to indicate what the labels will display above each bar: Percentages, Scores, or None 1-6.


Pareto Chart Options Dialog Box

This dialog box allows you to indicate how the values for each class will display.

Display


Rotate X-Axis Labels

Indicate that the X-axis labels should be rotated.


Tabulated Counts

Enter frequency data, which represents the number of occurrences of a specific defect.  Use the text box to enter the counts. The numbers you enter become the heights of each bar on the Pareto Chart.

The program uses the counts without attempting to tabulate the data.


Untabulated Observations

Enter data that consist of individual observations.  Use the text box to enter the name of the variable that contains the observations.  The program tabulates (counts) the codes to determine the number for each type of defect that occurs.


Weights

[Optional]  Enter the name of the variable that contains the weighting factor the program will apply to each class.  If you use untabulated observations, the length of the variable should equal the number of data values.  If you use tabulated counts, the length of the variable should equal the number of distinct classes.  The variable must contain at least one positive value for each defect class.

If you use tabulated counts, the length of the variable should equal the number of distinct classes.


Process Capability Analysis Dialog Box

Process capability studies in STATGRAPHICS Plus estimate process capability for processes that generate data from one of eight distributions:  Normal, Exponential, Extreme Value, Gamma, Laplace, Logistic, Lognormal, and Weibull.

You can run the analysis with specifications that are one-sided, two-sided, or asymmetric.  Normal and distribution-free tolerance limits, and nonnormal capability indices are available as options.

The Process Capability Analysis evaluates a process to see if it is capable of producing products within specifications.  The analysis determines the closeness of the observed results to the nominal, or target value, and ensures that the results are within the specified Upper and Lower limits.

Data

USL

Nominal

LSL

Select

Sort

To choose options for the analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click th left on either Pane Options or Analysis Options.

See also

Using the Process Capability Analysis

Process Capability Analysis Options

Capability Indices

Capability Indices Options

Tests for Normality

Goodness-of-Fit Tests

Normal Tolerance Limits

Normal Tolerance Limits Options

Non-Normal Capability Indices

Distribution-Free Limits

Distribution-Free Tolerance Limits Options

Capability Plot

Capability Plot Options

Probability Plot

Probability Plot Options


USL

Enter a value for the Upper Specification Limit (USL).  Enter one numeric value or a variable that contains one numeric value.  The value you enter must be greater than the values you enter into the Lower Specification Limit (LSL) and Nominal text boxes.


Nominal

Enter a value for the target value of the process.  Enter one numeric value or a variable that contains one numeric value.  The value you enter must be greater than the value in the Lower Specification Limit (LSL) text box and less than the value in the USL text box.

Note:  For one-sided specifications, you must complete the Nominal text box and either the USL or the LSL text box.  For two-sided specifications, you must complete the USL, Nominal, and LSL text boxes.


LSL

Enter a value or a variable that contains one numeric value for the LSL.  The value you enter must be less than the values you enter into the USL and Nominal text boxes.


Process Capability Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Process Capability Analysis)

Capability Indices (Process Capability Analysis)

Tests for Normality (Process Capability Analysis)

Goodness-of-Fit Tests (Process Capability Analysis)

Normal Tolerance Limits (Process Capability Analysis)

Non-Normal Capability Indices (Process Capability Analysis)

Distribution-Free Limits (Process Capability Analysis)


Analysis Summary (Process Capability Analysis)

The Analysis Summary option displays the results of the analysis.   The goal of the analysis is to compare a set of data with a set of specifications to estimate the proportion of data that fall outside the specification limits.  The summary includes the name of the data variable; the type of distribution; the values for the sample size; and the parameters for the fitted distribution.  The table shows the percent of observations beyond the specification limits, the z-scores, and the percent of estimated observations beyond the specification limits calculated from the fitted distribution.  The values for the USL, Nominal, and LSL specifications are also shown.

By default, a 6.0 sigma limit is used to calculate the indices, which means that the sigma spread for the process is from -3.0 standard deviations (sigmas) to +3.0 standard deviations from the estimated process mean.  While you can use other sigma limits, 6.0 sigma limits is used most often because more than 99 percent of the measurements from a normally distributed process fall within the 6.0 sigma bounds.

For a normal distribution, the z-score indicates the number of standard deviations each limit is away from the sample mean.  For other distributions, the z-scores are computed from the corresponding percentiles of the selected distribution.  Capable processes have USL and LSL z-scores greater than +3 and less than 3, respectively.

The Observed Beyond Specifications and Estimated Beyond Specifications columns represent the total percentage of the area under the fitted normal curve that fall above and below the specification limits for the distribution.  If you select another distribution, the program calculates the tail areas for that distribution.

Use the Process Capability Analysis Options dialog box to choose another distribution, to enter values for the two parameters of the distribution, and to enter a value for the sigma limits that will be used in the calculations.


Capability Indices (Process Capability Analysis)

The Capability Indices option computes capability indices for the variable you choose to summarize the comparison between the data and the specifications.  The program uses either 6-sigma limits or sigma limits you choose to calculate the indices.  In the example shown here, 6 sigma limits were used.  The report also displays confidence intervals for Cp and Cpk (Pp and Ppk). See the StatAdvisor for information about each type of distribution.

Use the Capability Indices Options dialog box to choose the indices you want computed, and to indicate if you want to use 6 sigma limits or user-specified limits in the calculations.  You can also enter a value for the confidence level and indicate how the indices will be labeled.


Normal Tolerance Limits (Process Capability Analysis)

The Normal Tolerance Limits option displays the values for the sample size; sample mean; and sample standard deviation; the USL, Nominal, and LSL limits for the specifications; and the resulting values for the tolerance interval.

The interval is calculated by taking the mean of the data, times a multiple of the standard deviation.  The results are helpful in choosing reasonable specifications for the process if they are currently not being met.  The interval is reliable only if the data come from a normal distribution.

Use the Normal Tolerance Limits Options dialog box to enter values for the sample size, confidence level, and population proportion you want the tolerance interval to cover.


Non-Normal Capability Indices (Process Capability Analysis)

The Non-Normal Capability Indices option produces estimates of the usual capability indices without assuming that the data come from a normal distribution.  The program first computes the sample skewness, then the kurtosis of the variable.  Then, based on the estimated skewness and kurtosis, it chooses a distribution from the general class of Pearson curves, and calculates estimated percentiles from the fitted curve.   It uses these percentiles instead of the mean plus or minus 3.0 to calculate the capability indices.


Distribution-Free Limits (Process Capability Analysis)

The Distribution-Free Limits option calculates tolerance limits without assuming that the variable comes from a normal distribution.  The interval is calculated using the smallest and largest values in the data, or the second smallest, or the third smallest, and so on.

Use the Distribution-Free Tolerance Limits Options dialog box to enter values for the confidence level, or the population proportion and interval depth.


Process Capability Analysis Options Dialog Box

This dialog box allows you to choose another distribution, enter values for the two parameters of the distribution, and enter a value for the sigma limits that will be used in the calculations.

Distribution

Distribution Parameters

Sigma Limits


Distribution Parameters:  Standard Deviation
Standard Deviation

Enter a value for the standard deviation that will determine the calculations.

This text box is available when you choose the Exponential, Normal, and Lognormal distributions.


Distribution Parameters:  Mode
Mode

Enter a value that will determine the calculations.  This text box is available when you choose the Extreme Value distribution.  Enter a positive value.


Distribution Parameters:  Scale
Scale

Enter a value that will determine the scale of the horizontal axis on the plot.  This text box is available when you choose the Extreme Value and Weibull distributions.  Enter a positive value.


Distribution Parameters:  Shape
Shape

Enter a value that will determine the shape of the distribution. This text box is available when you choose the Weibull distribution.

Values greater than 1, produce probability density functions (pdf) with a single peak.

Values less than 1, produce pdfs that are a reverse “J”.

A value of 1 produces a pdf that is equivalent to the pdf produced by an Exponential distribution.


Sigma Limits

Enter a value that will be used for the width of the sigma limits when the calculations are performed.  Enter a number greater than 0 and less than 21.


Capability Indices Options Dialog Box

This dialog box allows you to choose the indices that will be calculated, and to indicate if 6 sigma limits or user-specified limits should be used in the calculations.  You can also enter a value for the confidence level and indicate how the indices will be labeled.

Indices

Based On

Confidence Level

Label As


Cp

Displays the value for the inherent capability of the process.  In general, if the mean of the data is located close to the midpoint of the tolerances, then a Cp less than 1.00 indicates that the process is not capable.

A Cp above 1.33 indicates that the process is capable.  A Cp between 1.00 and 1.33 indicates that the process is capable, but should be monitored as Cp approaches 1.00.


Cpk

Displays a value for the capability in relation to the mean.  Cpk is a worse case index of the process.

It is the ratio of the smaller of the distance from the Upper control limit to the mean or the Lower control limit to the mean, whichever is smaller, to half the sigma range.

Cpk is useful even if the mean of the data is not close to the midpoint of the tolerances.  A Cpk larger than 1.00 indicates that both sigma limits fall within the specification limits and the process is capable of performing to specification.

A Cpk of less than 1.00 means that at least one of the sigma limits is outside of a specification limit and the process may not be capable of performing to specification.


Cpk (upper)

Displays the distance from the Upper specification limit to the mean, divided by half the sigma range.


Cpk (lower)

Displays the distance from the Lower specification limit to the mean, divided by half the sigma range.


Cr

Displays the capability ratio of the process.  It is the reciprocal of the Cp index.

If the mean of the data is located close to the midpoint of the tolerances, then a Cr greater than 1.00 indicates that the process is not capable.

A Cr less than 0.75 indicates that the process is capable.

A Cr between 0.75 and 1.00 indicates that the process is capable, but should be monitored as Cr approaches 0.75.


Cpm

Displays the modified Cp index, which is calculated using the nominal value instead of the calculated mean.  It is a more conservative index than Cp and you interpret it in the same manner.

For small sample sizes, Cpm is a better measure than Cp.


K

Displays the comparison ratio of the process mean to the nominal specification.  K is a measure of the closeness of the center of the process from the nominal or target of the process.

If K is 0, the mean and the nominal value are identical.  If K is positive, the mean is above the nominal value.  If K is negative, the mean is below the nominal value.

When the absolute value of K is small, the process mean is close to the nominal specification.  A small value of K can occur even if the process is not capable.


Based On

Determines if 6 sigma limits or user-specified limits will be used to calculate the capability indices.  You can use the User-Specified Limits only when you choose the Normal distribution.

6.0 Sigma Limits

Uses 6.0 sigma limits to calculate the capability indices; this option is the default.

User-Specified Limits

Uses the value you enter as the sigma limits used to calculate the capability indices.  For example, if you enter 8 sigma limits, the program calculates Cp by dividing by 8 standard deviations rather than by 6 standard deviations.


Based on User-Specified Limits

Uses the sigma limits you choose in the Process Capability Options dialog box to calculate the capability indices.


Capability Indices Confidence Level
Confidence Level

Enter a value for the confidence level that will be used to calculate the Cp, Cpk, and Cpm intervals.  Enter a numeric value greater than 0 and less than 100.


Normal Tolerance Limits Options Dialog Box

This dialog box allows you to enter values for the sample size, confidence level, and population proportion you want the tolerance interval to cover.

Sample Size

Confidence Level

Population Proportion


Sample Size

Enter a value for the hypothetical sample size.  Enter an integer greater than 5 and less than 1,000,000.

When you enter a new value, the Upper and Lower interval limits are adjusted.  A larger sample size improves the precision of the parameter estimates and produces a narrower tolerance interval.


Population Proportion

Enter a value for the proportion of the population the tolerance interval will contain.  Enter a number greater than 0 and less than 100, specified as a percentage.  Larger values produce wider tolerance intervals.


Distribution-Free Tolerance Limits Options Dialog Box

This dialog box allows you to enter values for the confidence level, or the population proportion and interval depth.

Input

Interval Depth


Interval Depth

Enter a value that represents the depth that will be used to calculate the tolerance interval limits.  Enter an integer greater than 0 and less than half the sample size.

Enter 1 if the first and last points of the sorted data will be used; enter 2 if the second and next-to-last points will be used; and so on.


Process Capability Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Capability Plot (Capability Process Analysis)

Probability Plot (Process Capability Analysis)


Capability Plot (Capability Process Analysis)

The Capability Plot option displays a histogram of the variable and a fitted curve of the distribution you are using.  The three taller vertical lines identify the nominal value and the specification limits.  The two shorter vertical lines show the sample mean plus and minus 3.0 standard deviations for a normal distribution or equivalent percentiles for a nonnormal distribution.  Because the shorter lines are not inside the taller lines, the process would be incapable of meeting the specifications.

Use the Capability Plot Options dialog box to enter values for the number of classes,


Probability Plot (Process Capability Analysis)

The Probability Plot option displays a quantile-quantile plot.  To create the plot, the program sorts the values from smallest to largest, then plots the sorted values against the equivalent quantiles of the fitted distribution.  The points should fall approximately along a straight line.  A reference line superimposed on the plot helps determine the closeness of the points to the line.  If the points show significant curvature, it may indicate that you need to choose a different distribution.

Use the Probability Plot Options dialog box to indicate if the plot will display horizontally or vertically and if the fitted line should display on the plot.


Capability Plot Options Dialog Box

This dialog box allows you to enter values for the Capability Plot.

Histogram

Hold

Display Indices

X-Axis Resolution

Decimal Places for Indices


Display Indices

Indicate if indices should be displayed on the plot.


Probability Plot Options Dialog Box

This dialog box allows you to choose the direction of the plot and the method that will be used to fit the straight line.

Direction

Fitted Line


Analysis Summary (Process Capability Analysis)

The Analysis Summary option displays the results of the analysis.   The goal of the analysis is to compare a set of data with a set of specifications to estimate the proportion of data that fall outside the specification limits.  The summary includes the name of the data variable; the type of distribution; the values for the sample size; and the parameters for the fitted distribution.  The table shows the percent of observations beyond the specification limits, the z-scores, and the percent of estimated observations beyond the specification limits calculated from the fitted distribution.  The values for the USL, Nominal, and LSL specifications are also shown.

By default, a 6.0 sigma limit is used to calculate the indices, which means that the sigma spread for the process is from -3.0 standard deviations (sigmas) to +3.0 standard deviations from the estimated process mean.  While you can use other sigma limits, 6.0 sigma limits is used most often because more than 99 percent of the measurements from a normally distributed process fall within the 6.0 sigma bounds.

For a normal distribution, the z-score indicates the number of standard deviations each limit is away from the sample mean.  For other distributions, the z-scores are computed from the corresponding percentiles of the chosen distribution.  Capable processes have USL and LSL z-scores greater than +3 and less than 3, respectively.

The Observed Beyond Specifications and Estimated Beyond Specifications columns represent the total percentage of the area under the fitted normal curve that fall above and below the specification limits for the distribution.  If you choose another distribution, the program calculates the tail areas for that distribution.

Use the Process Capability Analysis Options dialog box to choose another distribution, to enter values for the two parameters of the distribution, and to enter a value for the sigma limits that will be used in the calculations.


Capability Indices (Process Capability Analysis)

The Capability Indices option computes capability indices for the variable you choose to summarize the comparison between the data and the specifications.  The program uses either 6-sigma limits or sigma limits you choose to calculate the indices.  In the example shown here, 6 sigma limits were used.  The report also displays confidence intervals for Cp and Cpk (Pp and Ppk). See the StatAdvisor for information about each type of distribution.

Use the Capability Indices Options dialog box to choose the indices you want computed, and to indicate if you want to use 6 sigma limits or user-specified limits in the calculations.  You can also enter a value for the confidence level and indicate how the indices will be labeled.


Normal Tolerance Limits (Process Capability Analysis)

The Normal Tolerance Limits option displays the values for the sample size; sample mean; and sample standard deviation; the USL, Nominal, and LSL limits for the specifications; and the resulting values for the tolerance interval.

The interval is calculated by taking the mean of the data, times a multiple of the standard deviation.  The results are helpful in choosing reasonable specifications for the process if they are currently not being met.  The interval is reliable only if the data come from a normal distribution.

Use the Normal Tolerance Limits Options dialog box to enter values for the sample size, confidence level, and population proportion you want the tolerance interval to cover.


Non-Normal Capability Indices (Process Capability Analysis)

The Non-Normal Capability Indices option produces estimates of the usual capability indices without assuming that the data come from a normal distribution.  The program first computes the sample skewness, then the kurtosis of the variable.  Then, based on the estimated skewness and kurtosis, it chooses a distribution from the general class of Pearson curves, and calculates estimated percentiles from the fitted curve.   It uses these percentiles instead of the mean plus or minus 3.0 to calculate the capability indices.


Distribution-Free Limits (Process Capability Analysis)

The Distribution-Free Limits option calculates tolerance limits without assuming that the variable comes from a normal distribution.  The interval is calculated using the smallest and largest values in the data, or the second smallest, or the third smallest, and so on.

Use the Distribution-Free Tolerance Limits Options dialog box to enter values for the confidence level, or the population proportion and interval depth.


Capability Plot (Process Capability Analysis)

The Capability Plot graphical option displays a plot of the capability indices and a histogram of the data, with a density function curve for the distribution.

The plot identifies the LSL, Nominal, USL, and the tolerance limits.  When the sigma limits are inside the Upper and Lower specification limits, the process is capable of meeting the specifications.  When the 6.0 sigma limits are outside the Upper and Lower specification limits, the process is not capable of meeting the specifications.


Probability Plot (Process Capability Analysis)

The Probability Plot graphical option displays a plot of the distribution of the data.  The closer the data are to the reference line, the more likely they follow the specified distribution.


 X-bar and R Charts Analysis Dialog Box

The X-bar and R charts are the most commonly used pair of variables charts.   X-bar is the average of the values in small subgroups — a measure of location, while R is the range of values within each subgroup (highest minus lowest) — a measure of spread.

Data

Subgroup Numbers or Size

Subgroups Labels

Select

Sort

Delete...

Transform...

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis options.

See also

Using the X-bar and R Charts Analysis

X-bar and R Charts Options

Subgroup Reports Options

Runs Tests Options

Process Capability Indices Options

Control Chart Options - Initial Study

Control Chart Options - Control to Standard

Tolerance Chart Options


Observations

Enter individual observations.  Use the text box to enter or choose the name of the variable that contains the observations.


Subgroup Statistics

Enter the subgroup statistics.

Means

Enter or choose the name of the variable that contains the means of the subgroups you want to analyze.

Ranges

Enter or choose the name of the variable that contains the ranges you want to analyze.  The values you enter must correspond to the values you enter in the Means text box.


Subgroup Numbers or Size

Enter a number for the size of the subgroups.  If all the subgroups are the same size, enter a single number.  If you are using Observations, and the subgroups are of different sizes, enter a numeric variable that identifies the subgroup to which each observation belongs.  The observations are organized into subgroups automatically.  If you are using Subgroup Statistics, enter one subgroup size for each subgroup statistic.  Enter values between 2 and 25.


Subgroup Labels

 [Optional]  Enter the name of the variable that contains the labels that will be used for the subgroups.  The labels are used to identify the subgroups on reports.   Enter one label for each subgroup; include labels for subgroups that you plan to remove from the analysis.  The first label is assigned to the first subgroup; the second label to the second subgroup; and so on.  If you leave this text box blank, the program creates default names for the subgroup labels.


X-bar and R Charts Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the X-bar and R Charts Analysis.

Analysis Summary (X-bar and R Charts Analysis)

Subgroup Reports (X-bar and R Charts Analysis)

Runs Tests (X-bar and R Charts Analysis)

Capability Indices ( X-bar and R Charts Analysis)


Analysis Summary (X-bar and R Charts Analysis)

The Analysis Summary option displays a summary of the analysis.  The analysis is designed to determine if the data are from a process that is in statistical control.  The control charts are produced with the assumption that the data are from a normal distribution with the mean and standard deviation parameters.

The summary also shows the type of study (Initial or Control to Standard), the variable name, the number of subgroups, the subgroup size, and the number of subgroups excluded from the study.

Values for the UCL, Centerline, and LCL and the number of subgroups beyond the limits are shown along with the estimates for the process mean and sigma, and mean range.

Use the X-bar and R Charts Options dialog box to choose options for the analysis.

Use the Exclude... command on the dialog box to choose the subgroups you want to exclude from the analysis.  When you click the button, the Exclude/Include Options dialog box displays.


Subgroup Reports (X-bar and R Charts Analysis)

The Subgroup Reports option creates a table that displays the values that will be plotted on the control chart.  Points that are beyond the limits are noted with an asterisk; points that are excluded, are noted by an X.

Use the Subgroup Reports Options dialog box to choose the type of reports that will be included: All Subgroups, Subgroups Beyond Limits, X-bars Beyond Limits, Ranges Beyond Limits, or Excluded Subgroups.


Runs Tests

The Runs Tests option searches for and identifies any unusual patterns in the data.  The tests are helpful in detecting processes that are slowly drifting away from the target (even though no points may fall outside the control limits).  A nonrandom pattern indicates that a process is out of control.   The report displays the subgroup at which the unusual pattern was detected as well as the rule that was violated.

Use the Runs Tests Options dialog box to indicate the guidelines for the tests and the violation rules.


Capability Indices ( X-bar and R Charts Analysis)
Capability Indices

The Capability Indices option calculates the capability indices you choose that are based on the estimated process mean and standard deviation.   Sigma limits of 6.0 are used to calculate the indices.  The values help to determine the capability of a process to produce products that meet a standard.

Use the Process Capability Indices Options dialog box to choose the indices you want calculated, and to enter values for the USL, Nominal, and LSL specifications.


X-bar and R Charts Options Dialog Box

This dialog box allows you to choose options for the analysis.

Type of Study

Normalize

Average Subgroup Size

Recalculate At

Control Limits

Range Control Limits

Control to Standard

Exclude... Command


Normalize

Indicates if the data should be normalized to z-scores.  If you deselect this option, the program uses the original units.


Average Subgroup Size

Indicates if the average subgroup size should be used to calculate the control limits. This option does not affect the analysis if the subgroup sizes are equal.


 Control Limits

Determines the values for the location of the control limits on the Chart.  If you enter a value of 0 in either option, the corresponding control limit is removed from the analysis.

Upper Sigma

Enter a value for the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10.  The default is 3.0.

Lower Sigma

Enter a value for the multiple of sigma that will be used to calculate the LCL.  Enter a numeric value greater than or equal to -10 and less than or equal to 0.  The default is -3.0.


Range Control Limits

Determines the values for the UCL and LCL on the Range Chart.

Upper Sigma

Enter a value for the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10.  The default is 3.0.

Lower Sigma

Enter a value for the multiple of sigma that will be used to calculate the LCL.  Enter a numeric value greater than or equal to -10 and less than or equal to 0.  The default is -3.0.


Specify Parameters

Determines the values for the control limits.

Mean

Enter a value for the process mean; enter any numeric value.

Sigma

Enter a value for the process sigma; enter any positive numeric value.


Specify Control Limits

This option allows you to choose values for the control limits for the X-bar and Range Charts.  You must choose the Centerline and Upper limits, the Centerline and Lower limits, or all three.

For an X-bar Chart and a Range Chart, use the Upper text box to enter the UCL.

Enter a numeric value that is greater than the values in the Centerline and Lower text boxes.  Use the Centerline text box to enter the Centerline.  Enter a numeric value that is less than the value in the Upper text box and greater than the value in the Lower text box.  Use the Lower text box to enter the LCL.  Enter a numeric value that is less than the values in the Upper and Centerline text boxes.


Exclude/Include Options Dialog Box

Exclude

Determines the subgroups that will be excluded or included in the analysis and the method that will be used to do it.

Manual

Choose the subgroups you want to exclude from the analysis.

Automatic

Indicates that the out-of-control subgroups should be automatically excluded until all the remaining subgroups are within the control limits.

Reset

Indicates you want to include all the subgroups in the analysis; it is useful only after you exclude subgroups.

Exclude Subgroup

Enter the number of the subgroup that will be excluded from the analysis.  This text box is available only when you choose Manual from the Exclude Method options.

Include Subgroup

Enter the number of a subgroup you previously excluded and want to re-enter.


Method

Choose the method that will be used to exclude or include subgroups.

Automatic

Automatically excludes out-of-control subgroups until all the remaining subgroups are within the control limits.

Reset

Includes all the subgroups.  This option is useful only after you exclude subgroups.

Exclude

This text box allows you to enter the number of the subgroup you want to exclude from the analysis.  This text box is available only when you choose Manual from the Exclude Method options.

Include

Enter the number of a subgroup you previously excluded and want to re-include.  The program re-enters the subgroup into the analysis.


Automatic

Automatically excludes out-of-control subgroups until all the remaining subgroups are within the control limits.


Reset

This option allows you to include all the subgroups.  This option is useful only after you exclude subgroups.


Exclude Subgroup

This text box allows you to enter the number of the subgroup you want to exclude from the analysis.  This text box is available only when you choose Manual from the Exclude Method options.


Include Subgroup

This text box allows you to enter the number of a subgroup you previously excluded and want to re-include.  The program re-enters the subgroup into the analysis.


Subgroup Reports Options Dialog Box
Subgroup Reports Options

Choose the subgroups you want to include in the Subgroup Reports.

Display


All Subgroups

Includes all the subgroups in the report.


Subgroups beyond Limits

Lists the subgroups that are beyond the control limits.


X-bars beyond Limits

Lists the subgroups that have s beyond the control limits.


Ranges beyond Limits

This option lists the subgroups that have ranges beyond the control limits.


Excluded Subgroups

This option lists the excluded subgroups.


Runs Tests Options Dialog Box

This dialog box allows you to choose the sequence of items that will be used in the Runs Tests.

Runs Above/Below Centerline of Length n or Greater

Runs Up/Down of Length n or Greater

Sets of n Subgroups with at Least n beyond n Sigma

Sets of n Subgroups with at Least n beyond n Sigma

Sets of at Least n Subgroups at or Within n Sigma

Sets of at Least n Subgroups Outside n Sigma


Runs Above/Below Centerline of Length n or Greater

Searches for all consecutive subgroups that fall above or below the Centerline.  Enter a number for the length of the set; enter a positive integer.  The default is 8.


Runs Up/Down of Length n or Greater

Searches for increasing or decreasing consecutive runs.  For example, if the program finds eight consecutive subgroups in ascending order (4, 5, 6, 7, 10, 12, 15, 16), it reports the last subgroup in the run.  Enter the length of the set; enter a positive integer; the default is 8.


Sets of n Subgroups with at Least n beyond n Sigma

Searches for subgroup sets that have subgroups beyond a sigma level you choose.  Enter a number for the size of the subgroup sets, the number of subgroups beyond the specified sigma, and the sigma level.  Enter positive integers for the number of subgroups; enter a positive numeric value less than or equal to 10 for the sigma limit.  The defaults are 5, 4, and 1.0, respectively.


Sets of n Subgroups with at Least n beyond n Sigma

Searches for subgroup sets that have subgroups beyond a sigma level you choose.  Enter the size of the subgroup sets, the number of subgroups beyond the specified sigma, and the sigma level.  Enter positive integers for the number of subgroups; enter a positive numeric value less than or equal to 10 for the sigma limit.  The defaults are 3, 2, and 2.0, respectively.


Sets of at Least n Subgroups at or Within n Sigma

Searches for subgroup sets that are within a sigma level you choose.  Enter a positive integer for the number of subgroups in a set and the sigma levl.  Enter a positive integer for the number of subgroups; enter a positive numeric value less than or equal to 10 for the sigma level.  The defaults are 15 and 1.0, respectively.


Sets of at Least n Subgroups Outside n Sigma

Searches for subgroup sets that are outside a sigma level you choose.  Enter the size of the subgroup, the number of subgroups beyond the specified sigma, and the sigma level.  Enter a positive integer for the number of subgroups; enter a positive numeric value less than or equal to 10 for the sigma level.  The defaults are 8 and 2.0, respectively.


Process Capability Indices Options Dialog Box

This dialog box allows you to choose capability indices and to enter values for the specifications.

Indices

Specifications


X-bar and R Charts Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the X-bar and R Charts Analysis.

X-bar Chart (X-bar and R Charts Analysis)

Range Chart (X-bar and R Charts Analysis)

Tolerance Chart (X-bar and R Charts Analysis)

OC Curve

ARL Curve


X-bar Chart (X-bar and R Charts Analysis)

The X-bar Chart option creates a plot of the means for each of the subgroups.  A process is considered out of control if points are shown outside the control limits, or if points are shown within the control limits, but arranged in a nonrandom sequence.

Use the Control Chart Options dialog box to choose options for the X-bar Chart.


Range Chart

The Range Chart option displays a plot of control limits based on the ranges of the subgroups.  The process is out of control if the points are shown outside the control limits, or points are shown within the control limits but arranged in a nonrandom sequence.


Tolerance Chart (X-bar and R Charts Analysis)

The Tolerance Chart graphical option displays a plot of the observations by subgroup.  The horizontal line shows the grand mean of the observations.  The vertical line shows the subgroup ranges.  You can include specification limits on the chart.

Because you use the Tolerance Chart to examine individual observations, this chart is available only when you choose Observations on the dialog box.


OC Curve

The OC (Operating Characteristic) Curve option creates a plot that shows the probability that the next point that is plotted on the control chart will remain inside the control limits as a function of the true process mean.

It is useful for judging the effectiveness of a control chart in detecting when a process drifts away from the target. The X-axis shows the shift in the average; the Y-axis the probability of not detecting the shift.


Control Chart Options Dialog Box (Initial Study)

This dialog box allows you to choose the warning limits that will display on the Control Chart.  You can also choose a moving average and exponentially weighted moving average for the plot.

Outer Warning Limits

Inner Warning Limits

Moving Average

Exponentially Weighted Moving Average

Decimal Places for Limits

Mark Runs Rules Violations


Outer Warning Limits

Plots outer warning limits on the chart.

Sigma

Enter the number of sigmas from the centerline you want to plot the outer warning limits.  Enter a number greater than 0 and less than or equal to 10.  The default is 2.


Inner Warning Limits

Plots inner warning limits on the chart.

Sigma

Enter the number of sigmas from the centerline you want to plot the inner warning limits.  Enter a number greater than 0 and less than or equal to 10.  The default is 1.


Moving Average

Superimposes a simple moving average of the subgroup statistics on the chart.

Order

Enter the number of points that will be included in the moving average.  Enter a positive integer; the default is 3.


Exponentially Weighted Moving Average

Superimposes an exponentially weighted moving average of the subgroup statistics on the chart.

Lambda

Enter the number that will be used as a weight for the preceding term in the moving average.  A small number results in a very smooth estimate.  A lambda of 1 produces a smoothed curve identical to the data.  Enter a numeric value greater than 0 and less than or equal to 1; the default is 0.1.


Control Chart Options Dialog Box (Control to Standard)
Control Chart Options Dialog Box

Choose the warning limits you want to display on the Control Chart.  You can also choose a moving average and exponentially weighted moving average for the plot.

Outer Warning Limits

Inner Warning Limits

Moving Average

Exponentially Weighted Moving Average

Decimal Places for Limits

Mark Runs Rules Violations


Outer Warning Limits (Control to Standard)
Outer Warning Limits

Plots the outer warning limits.

Upper

Enter a value for the Upper outer warning limit  Enter any numeric value greater than the Lower limit.

Lower

Enter a value for the Lower outer warning limit.  Enter any numeric value less than the Upper limit.


Inner Warning Limits (Control to Standard)
Inner Warning Limits

Plots the inner warning limits.

Upper

Enter a value for the Upper inner warning limit.  Enter any numeric value greater than the Lower limit.

Lower

Enter a value for the Lower inner warning limit.  Enter any numeric value less than the Upper limit.


Tolerance Chart Options Dialog Box

This dialog box allows you to set specification limits for the Tolerance Chart.

Specifications

Decimal Places for Limits

Plot (Points or Nominal Specification Line)


Upper Specification
Upper

Enter a value for the Upper specification.  Enter one numeric value.  The value you enter must be greater than the values in the Lower and Nominal text boxes.


Nominal Specification
Nominal

Enter the target value for the process.  Enter one numeric value.  The value you enter must be greater than the value in the Lower text box and less than the value in the Upper text box.


Lower Specification
Lower

Enter a value for the Lower specification.  The value you enter must be less than the values in the Upper and Nominal text boxes.


Save Results Options Dialog Box ( and R Chart Analysis)
Save Results Options Dialog Box (X-bar and R Chart Analysis)

The Save Results Options dialog box allows you to choose the results you want to save.  There are six choices: Means, Ranges, Sizes, Labels, Process Means, and Process Sigma.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (X-bar and R Charts Analysis)

The Analysis Summary option displays a summary of the analysis.  The analysis is designed to determine if the data are from a process that is in statistical control.  The control charts are produced with the assumption that the data are from a normal distribution with the mean and standard deviation parameters.

The summary also shows the type of study (Initial or Control to Standard), the variable name, the number of subgroups, the subgroup size, and the number of subgroups excluded from the study.

Values for the UCL, Centerline, and LCL and the number of subgroups beyond the limits are shown for the X-bar and S charts.  Estimates are shown for the process mean and sigma, and the mean sigma.

Use the X-bar and R Charts Options dialog box to choose options for the analysis.

Use the Exclude... command on the dialog box to choose the subgroups you want to exclude from the analysis.  When you click the button, the Exclude/Include Options dialog box displays.


Subgroup Reports

The Subgroup Reports tabular option displays the X-bar and Range values for each subgroup.


Runs Tests (X-bar and R Charts Analysis)

The Runs Tests option performs a battery of tests that help determine if a sequence of observations is in a nonrandom pattern, which indicate that a process is out of control.


Capability Indices

The Capability Indices option calculates several process capability indices based on the estimated process mean and standard deviation.  These indices help determine the capability of a process to produce products that must meet a quality standard.  The capability indices will not be calculated until you enter values for the USL, Nominal, and LSL values on the Process Capability Indices Options dialog box.

Use the Process Capability Indices Options dialog box to choose the indices you want to include, and to enter values for the upper and lower specification limits and the target for the nominal.


X-bar Chart (X-bar and R Charts Analysis)
X-bar Chart

The X-bar Chart graphical option displays a chart with control limits that are based on the mean of the observations.  The process is out of control if points are shown outside the control limits, or points are shown within the control limits but arranged in a nonrandom sequence.


Range Chart (X-bar and R Charts Analysis)

The Range Chart option creates a plot that shows the ranges for each of the subgroups.  It indicates if any points are beyond the control limits.  A process is out of control if points are shown outside the control limits, or if points are within the control limits, but arranged in a nonrandom sequence.

Use the Control Chart Options dialog box to choose options for the Range Chart.


Tolerance Chart (X-bar and R Charts Analysis)

The Tolerance Chart option creates a plot of the individual values for the variable, arranged by subgroup.  A horizontal line shows the grand mean of the observations; a vertical line shows the subgroup ranges.  You can include specification limits on the chart.

Use the Tolerance Chart Options dialog box to enter values for the Upper, Nominal, and Lower specifications, to enter the number of decimal places that should be used for displaying the limits, and to indicate if points or the nominal specification line will display on the plot.


OC Curve

The OC Curve graphical option displays a plot that illustrates the probability of not detecting a shift in the true process parameter on the subgroup immediately after a shift occurs.  The X-axis shows the shift in the average.  The Y-axis shows the probability of not detecting the shift.

The OC Curve is not available if you perform a Control to Standard study and choose the control limits on the X-bar and R Charts Options dialog box.


X-bar and S Charts Analysis Dialog Box

X-bar and S charts were developed for the times when it is desirable to estimate the process standard deviation directly instead of using the range.  For example, the S Chart is generally more appropriate than the R Chart when the subgroup size is eight or more.  The process standard deviation, S, is more difficult to calculate, and usually is less sensitive in detecting special causes of variation when only a single value in a subgroup is unusual.  These charts are also always used as a pair.

Data

Subgroup Numbers or Size

Subgroup Labels

Select

Sort

Delete...

Transform...

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the X-bar and S Charts Analysis

X-bar and S Charts Options

Subgroup Reports Options

Runs Tests Options

Process Capability Indices Options

Control Chart Options - Initial Study

Control Chart Options - Control to Standard

Tolerance Chart Options


Subgroup Reports

The Subgroup Reports option creates a table that displays the values that will be plotted on the control chart.  Points that are beyond the limits are noted with an asterisk; points that are excluded are noted with an X.

Use the Subgroup Reports Options dialog box to choose the type of reports that will be included.


X-bar and S Charts Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the X-bar and S Charts analysis.

Analysis Summary (X-bar and S Charts Analysis)

Subgroup Reports

Runs Tests (X-bar and S Charts Analysis)

Capability Indices (X-bar and S Charts Analysis)


Analysis Summary (X-bar and S Charts Analysis)

The Analysis Summary option displays a summary of the analysis.  The analysis is designed to determine if the data are from a process that is in statistical control.  The control charts are produced with the assumption that the data are from a normal distribution with the mean and standard deviation parameters.

The summary also shows the type of study (Initial or Control to Standard), the variable name, the number of subgroups, the subgroup size, and the number of subgroups excluded from the study.

Values for the UCL, Centerline, and LCL and the number of subgroups beyond the limits are shown for the X-bar and S charts.  Estimates are shown for the process mean and sigma, and the mean sigma.

Use the X-bar and R Charts Options dialog box to choose options for the analysis.

Use the Exclude... command on the dialog box to choose the subgroups you want to exclude from the analysis.  When you click the button, the Exclude/Include Options dialog box displays.


Subgroup Reports Options Dialog Box

This dialog box allows you to choose the contents of the report.

Display

Determines what will display in the Subgroup Report

All Subgroups

Includes all the subgroups.

Subgroups Beyond Limits

Includes a list of the subgroups that are beyond the control limits.

s Beyond Limits

Includes a list of the subgroups that have s beyond the control limits.

Sigmas Beyond Limits

Includes a list of the subgroups that have standard deviations beyond the control limits.

Excluded Subgroups

Includes a list of the excluded subgroups.


X-bar and S Charts Options Dialog Box

This dialog box allows you to indicate if you want to perform an Initial study or a Control to Standard; to indicate if the subgroup data should be normalized to z-scores; and to indicate if the average subgroup size should be used to calculate the control limits.  You can also recalculate control limits for specified sets of subgroups.  You can enter values for the Upper and Lower Sigma for the Control Limits and the Sigma Control Limits.

For a Control-to-Standard study, you can choose to either specify parameters (mean and sigma) or to specify control limits for the two charts: X-bar Chart and S Chart.  For each of these you can enter values for the Upper, Centerline, and Lower limits.

Use the Exclude... command on the dialog box to choose the subgroups you want to exclude from the analysis.  When you click the button, the Exclude/Include Options dialog box displays.

Type of Study

Normalize

Average Subgroup Size

Recalculate At

Control Limits

Sigma Control Limits

Control to Standard

Exclude... Command


Sigma Control Limits

Determines the values for the location of the control limits on the S Chart.

Upper Sigma

Enter a value for the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10; the default is 3.0.

Lower Sigma

Enter a value for the multiple of sigma that will be used to calculate the LCL.  Enter a numeric value less than or equal to 0 and greater than or equal to -10; the default is -3.0.


Specify Control Limits

Enter values for the control limits.  You must choose the Centerline and Upper limits, the Centerline and Lower limits, or all three.

For an X-bar Chart

Enter a value for the UCL.  Enter a numeric value that is greater than the values in the Centerline or Lower text boxes.

Use the Centerline text box to enter the value for the Centerline.  Enter a numeric value that is less than the value in the Upper text box and greater than the value in the Lower text box.

Use the Lower text box to enter the value for the LCL.  Enter a numeric value that is less than the values in the Upper and Centerline text boxes.

For an S Chart

Enter a value for the UCL.  Enter a numeric value that is greater than the value in the Centerline and Lower text boxes.

Use the Centerline text box to enter a value for the Centerline.  Enter a numeric value that is less than the value in the Upper text box and greater than the value in the Lower text box.

Use the Lower text box to enter a value for the LCL.  Enter a numeric value that is greater than or equal to zero and less than the values in the Upper and Centerline text boxes.


Subgroup Reports Options Dialog Box

Display

Determines what will display in the Subgroup report.

All Subgroups

The report includes all the subgroups.

Subgroups Beyond Limits

The report includes a list of the subgroups that are beyond the control limits.

X-bars Beyond Limits

The report includes a list of the subgroups that have s beyond the control limits.

Ranges Beyond Limits

The report includes a list of the subgroups that have ranges beyond the control limits.

Excluded Subgroups

The report includes a list of the excluded subgroups.


Sigmas beyond Limits

Lists the subgroups that have standard deviations beyond the control limits.


X-bar and S Charts Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the X-bar and S Charts Analysis.

X-bar Chart (X-bar and S Charts Analysis)

S Chart (X-bar and S Charts Analysis)

Tolerance Chart (X-bar and S Chart Analysis)

OC Curve

ARL Curve


S Chart

The S Chart option creates a plot of the standard deviations for each of the subgroups and shows the points that are beyond the control limits.

A process is out of control if points are shown outside the control limits, or if the points are shown within the control limits but arranged in a nonrandom sequence.


Save Results Options Dialog Box ( and S Chart Analysis)
Save Results Options Dialog Box (X-bar and S Chart Analysis)

The Save Results Options dialog box allows you to choose the results you want to save.  There are six options: Means, Sigmas, Sizes, Labels, Process Mean, and Process Sigma.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (X-bar and S Charts Analysis)

The Analysis Summary option displays a summary of the analysis.  The analysis is designed to determine if the data are from a process that is in statistical control.  The control charts are produced with the assumption that the data are from a normal distribution with the mean and standard deviation parameters.

The summary also shows the type of study (Initial or Control to Standard), the variable name, the number of subgroups, the subgroup size, and the number of subgroups excluded from the study.

Values for the UCL, Centerline, and LCL and the number of subgroups beyond the limits are shown for the X-bar and S charts.  Estimates are shown for the process mean and sigma, and the mean sigma.

Use the X-bar and S Charts Options dialog box to choose options for the analysis.

Use the Exclude... command on the dialog box to choose the subgroups you want to exclude from the analysis.  When you click the button, the Exclude/Include Options dialog box displays.


Subgroup Reports

The Subgroup Reports tabular option displays the X-bar and standard deviation values for each subgroup.


S Chart ( and S Charts Analysis)
S Chart (X-bar and S Charts Analysis)

The S Chart option creates a plot that shows the standard deviations for each of the subgroups.  It indicates if any points are beyond the control limits.  A process is out of control if points are shown outside the control limits, or if points are within the control limits, but arranged in a nonrandom sequence.

Use the Control Chart Options dialog box to choose options for the S Chart.


X-bar and S-Squared Charts Analysis Dialog Box

Montgomery (1997) notes that most quality engineers prefer to use either an R Chart or an S Chart to monitor process variability, using the S Chart with moderate to large sample sizes.  Others recommend using a control chart that uses limits based on the sample variances — the S-Squared Chart.

Data

Subgroup Numbers or Size

Subgroup Labels

Select

Sort

Delete...

Transform...

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the X-bar and S-Squared Charts Analysis

X-bar and S-Squared Charts Options

Subgroup Reports Options

Runs Tests Options

Process Capability Indices Options

Control Chart Options - Initial Study

Control Chart Options - Control to Standard

Tolerance Chart Options


Subgroup Statistics

This option allows you to enter subgroup statistics.  Use the Means text box to enter the s (means) of the subgroups you want to analyze.  Use the Variances text box to enter the variances you want to analyze.  These values must correspond with the values you enter in the Means text box.


X-bar and S-Squared Charts Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the X-bar and S-Squared Charts Analysis.

Analysis Summary (X-bar and S-Squared Charts Analysis)

Subgroup Reports (X-bar and S-Squared Analysis)

Runs Tests (X-bar and S-Squared Charts Analysis)

Capability Indices (X-bar and S-Squared Charts Analysis)


Analysis Summary (X-bar and S-Squared Charts Analysis)

The Analysis Summary option displays a summary of the analysis.  The analysis is designed to determine if the data are from a process that is in statistical control.  The control charts are produced with the assumption that the data are from a normal distribution with the mean and standard deviation parameters.

The summary also shows the type of study (Initial or Control to Standard), the variable name, the number of subgroups, the subgroup size, and the number of subgroups excluded from the study.

Values for the UCL, Centerline, and LCL and the number of subgroups beyond the limits are shown for the X-bar and S-Squared charts.  Estimates are shown for the process mean and sigma, and the pooled variance.

Use the X-bar and S-Squared Charts Options dialog box to choose options for the analysis.

Use the Exclude... command on the dialog box to choose the subgroups you want to exclude from the analysis.  When you click the button, the Exclude/Include Options dialog box displays.


Subgroup Reports (X-bar and S-Squared Charts Analysis)

The Subgroup Reports option creates a table that displays the values that will be plotted on the control chart.  Points that are beyond the limits are noted with an asterisk; points that are excluded are noted by with X.

Use the Subgroup Reports Options dialog box to choose the type of reports that will be included.


 X-bar and S-Squared Charts Options Dialog Box

This dialog box allows you to choose options for the analysis.

Type of Study

Average Subgroup Size

Recalculate At

Control Limits

S-Squared Control Limits

Control to Standard

Specify Parameters

Specify Control Limits

Exclude... Command


S-Squared Control Limits

Determines the location of the control limits on the S-Squared Chart.

Upper Sigma

Enter a value for the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10.  The default is 3.0.

Lower Sigma

Enter a value for the multiple of sigma that will be used to calculate the LCL.  Enter a numeric value less than or equal to 0 and greater than or equal to

-10.  The default is -3.0.


Specify Control Limits

Determines the control limits for the X-bar and S-Squared charts.

Upper (Chart)

Enter a numeric value for the UCL.  The number must be greater than the values you enter into the Centerline and LCL text boxes.

Centerline (Chart)

Enter a numeric value for the Centerline.  The number must be less than the value you enter for the UCL, and greater than the value you enter for the LCL.

Lower (Chart)

Enter a numeric value for the LCL.  The number must be less than the values you enter for the UCL and Centerline.

Upper (S-Squared Chart)

Enter a positive numeric value for the UCL.  Enter a value that is greater than the value in the Centerline and LCL text boxes.

Centerline (S-Squared Chart)

Enter a numeric value for the Centerline.  The number must be greater than or equal to zero and less than the value for the UCL, and greater than the value for the LCL.

Lower (S-Squared Chart)

Enter a numeric value for the LCL.  The number must be greater than or equal to zero and less than the values for the UCL and Centerline.


Subgroup Reports Options Dialog Box

This dialog box allows you to choose the contents of the report.

Display


Variances beyond Limits

This option lists the subgroups that have variances beyond the control limits.


X-bar and S-Squared Charts Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the X-bar and S-Squared Charts Analysis.

X-bar Chart (X-bar and S-Squared Charts Analysis)

S-Squared Chart (X-bar and S-Squared Charts Analysis)

Tolerance Chart (X-bar and S-Squared Charts Analysis)

OC Curve (X-bar and S-Squared Charts Analysis)

ARL Curve (X-bar and S-Squared Analysis)


S-Squared Chart ( and S-Squared Charts Analysis
S-Squared Chart (X-bar and S-Squared Charts Analysis

The S-Squared Chart graphical option displays an S-Squared Chart with control limits based on the variances of the subgroups.

The process is out of control if points are shown outside the control limits, or points are shown within the control limits but arranged in a nonrandom sequence.


Save Results Options Dialog Box ( and S-Squared Chart Analysis)
Save Results Options Dialog Box (X-bar and S-Squared Chart Analysis)

The Save Results Options dialog box allows you to choose the results you want to save. There are six options: Means, Variances, Sizes, Labels, Process Mean, and Process Sigma.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (S-Squared Charts Analysis)

The Analysis Summary option displays a summary of the analysis.  The analysis is designed to determine if the data are from a process that is in statistical control.  The control charts are produced with the assumption that the data are from a normal distribution with the mean and standard deviation parameters.

The summary also shows the type of study (Initial or Control to Standard), the variable name, the number of subgroups, the subgroup size, and the number of subgroups excluded from the study.

Values for the UCL, Centerline, and LCL and the number of subgroups beyond the limits are shown for the X-bar and S charts.  Estimates are shown for the process mean and sigma, and the mean sigma.

Use the X-bar and S Charts Options dialog box to choose options for the analysis.

Use the Exclude... command on the dialog box to choose the subgroups you want to exclude from the analysis.  When you click the button, the Exclude/Include Options dialog box displays.  See Figure 3-4 for an example of this dialog box.


Subgroup Reports

Display

Determines what will display in the Subgroup Report.

All Subgroups

Includes all the subgroups.

Subgroups Beyond Limits

Includes a list of the subgroups that are beyond the control limits.

s Beyond Limits

Includes a list of the subgroups that have s beyond the control limits.

Variances Beyond Limits

Includes a list of the subgroups that have variances beyond the control limits.

Excluded Subgroups

Includes a list of the excluded subgroups.


S-Squared Chart ( and X-Squared Charts Analysis)
S-Squared Chart (X-bar and S-Squared Charts Analysis)

The S-Squared Chart graphical option displays an S-Squared Chart with control limits based on the variances of the subgroups.

The process is out of control if points are shown outside the control limits, or points are shown within the control limits but arranged in a nonrandom sequence.


Individuals Charts Analysis Dialog Box

There are instances when it is necessary for process control to be based on individual readings, instead of subgroups.  This usually happens when the sample is made up on a single unit.  Montgomery (1997) provides some examples; for example, when:

•	automated inspection and measurement technology is used and every unit that is manufactured is analyzed

•	the production rate is very slow and it is inconvenient to let sample sizes of n > 1 accumulate before they are analyzed

•	repeat measurements on a process differ only because of laboratory or analysis error (chemical processes).

The control process uses the moving range of two successive observations to estimate the variability.

Observations

Labels

Select

Sort

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Individuals Charts Analysis

Individuals Charts Options

Individuals Charts Report Options

Runs Tests Options

Process Capability Indices Options

Control Chart Options - Initial Study

Control Chart Options - Control to Standard


Labels

[Optional]  Enter the labels that will be used for the observations.  The labels identify the observations on reports.  You must enter one label for each observation in the data; include labels for observations you plan to remove from the analysis.

The first label is assigned to the first observation in the data, the second label to the second observation, and so on.  If you leave this text box blank, default labels are created.


Individuals Charts Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the Individuals Charts Analysis.

Analysis Summary (Individuals Chart Analysis)

Individuals Chart Reports (Individuals Charts Analysis)

Runs Tests (Individuals Charts Analysis)

Capability Indices (Individuals Charts Analysis)


Analysis Summary (Individuals Chart Analysis)

The Analysis Summary option displays a summary of the analysis.  The analysis is designed to determine if the data are from a process that is in statistical control.  The control charts are produced with the assumption that the data are from a normal distribution with the mean and standard deviation parameters.

The summary also shows the type of study (Initial or Control to Standard), the variable name, the number of observations and the number of observations excluded from the study.  Values for the UCL, Centerline, and LCL and the number of observations beyond the limits are shown for the X and MR(2) charts.  Estimates are shown for the process mean and sigma, and the mean MR(2).

Use the Individuals Charts Options dialog box to choose options for the analysis.

Use the Exclude... command on the dialog box to choose the observations you want to exclude from the analysis.  When you click the button, the Exclude/Include Options dialog box displays.


Individuals Charts Report (Individuals Charts Analysis)

The Individuals Chart Reports option creates a table that displays the values that will be plotted on the control chart.  Points that are beyond the limits are noted with an asterisk; excluded points are noted with an X.

Use the Individuals Chart Report Options dialog box to choose the type of reports that will be included.


Individuals Charts Options Dialog Box

This dialog box allows you to choose options for the analysis.

Type of Study

Normalize

Recalculate At

X Control Limits

MR(2) Control Limits

Control to Standard

Specify Parameters

Specify Control Limits

Exclude... Command


X Control Limits

Enter values for the location of the control limits on the X Chart.    The options are available when you choose an Initial Study or when you choose a Control to Standard study and the Specify Parameters option.  For example, a value or 0 in either option removes the corresponding control limit from the analysis.

Upper Sigma

Enter a value for the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10; the default is 3.0.

Lower Sigma

Enter a value for the multiple of sigma that will be used to calculate the LCL.  Enter a numeric value less than or equal to 0 and greater than or equal to -10; the default is -3.0.


MR(2) Control Limits

Determines the location of the control limits on the MR(2) Chart.

Upper Sigma

Enter a value for the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10; the default is 3.0.

Lower Sigma

Enter a value for the multiple of sigma that will be used to calculate the LCL.  Enter a numeric value less than or equal to 0 and greater than or equal to -10; the default is -3.0.


Specify Control Limits

Determines the control limits for the X and MR(2) charts.

Upper (X Chart)

Enter a numeric value for the UCL.  The number must be greater than the values you enter into the Centerline and LCL text boxes.

Centerline (X Chart)

Enter a numeric value for the Centerline.  The number must be less than the value you enter for the UCL, and greater than the value you enter for the LCL.

Lower (X Chart)

Enter a numeric value for the LCL.  The number must be less than the values you enter for the UCL and Centerline.

Upper (MR(2) Chart)

Enter a positive numeric value for the UCL.  Enter a value that is greater than the value in the Centerline and LCL text boxes.

Centerline (MR(2) Chart)

Enter a numeric value for the Centerline.  The number must be greater than or equal to zero and less than the value for the UCL, and greater than the value for the LCL.

Lower (MR(2) Chart)

Enter a numeric value for the LCL.  The number must be greater than or equal to zero and less than the values for the UCL and Centerline.

Choose the control limits for the X and MR(2) charts.  You must enter the Centerline and Upper limits, the Centerline and Lower limits, or all three.


Individuals Charts Report Options Dialog Box
Individuals Chart Report Options Dialog Box

Display

Determines what will display in the Individuals Charts report.

All Observations

Includes all the observations.

Observations Beyond Limits

Includes a list of the observations that are beyond the control limits.

X Beyond Limits

Includes a list of the observations that are beyond the X-Chart control limits.

MR(2) Beyond Limits

Includes a list of the observations that have moving ranges beyond the control limits.

Excluded Observations

Includes a list of the excluded observations.


All Observations

Includes all the observations in the report.


Observations beyond Limits

Lists the observations beyond the control limits for the X Chart or MR(2) Chart.


X beyond Limits

Lists the observations beyond the control limits.


MR(2) beyond Limits

Lists the observations that have moving ranges beyond the control limits.


Excluded Observations

This option lists the excluded observations.


Individuals Charts Analysis Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the Individuals Charts Analysis.

X-Chart (Individuals Charts Analysis)

MR(2) Chart (Individuals Charts Analysis)

OC Curve (Individuals Charts Analysis)

ARL Curve (Individuals Charts Analysis)


X Chart (Individuals Charts Analysis)

The X Chart graphical option displays a plot of the individual points on an X Chart.

A process is out of control if points are shown outside the control limits, or within the control limits, but arranged in a nonrandom sequence.


MR(2) Chart (Individuals Charts Analysis)

The MR(2) Chart graphical option displays a chart of the moving ranges for successive observations.  A process is out of control if points are shown outside the control limits, or within the control limits but arranged in a nonrandom sequence.

For options, use the Control Chart Options dialog box for either an Initial Study or a Control to Standard.


Save Results Options Dialog Box (Individuals Chart Analysis)

The Save Results Options dialog box allows you to choose the results you want to save.  There are five options: Observations, Moving Ranges, Labels, Process Mean, and Process Sigma.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (Individuals Charts Analysis)

The Analysis Summary option displays a summary of the analysis.  The analysis is designed to determine if the data are from a process that is in statistical control.  The control charts are produced with the assumption that the data are from a normal distribution with the mean and standard deviation parameters.

The summary also shows the type of study (Initial or Control to Standard), the variable name, the number of observations and the number of observations excluded from the study.  Values for the UCL, Centerline, and LCL and the number of observations beyond the limits are shown for the X and MR(2) charts.  Estimates are shown for the process mean and sigma, and the mean MR(2).

Use the Individuals Charts Options dialog box to choose options for the analysis.

Use the Exclude... command on the dialog box to choose the observations you want to exclude from the analysis.  When you click the button, the Exclude/Include Options dialog box displays.


Individuals Charts Report

The Individuals Charts Report tabular option displays a report of the X and MR(2) values for each observation.


X Chart

The X Chart graphical option displays a plot of the individual points on the X Chart.

A process is out of control if points are shown outside the control limits, or within the control limits, but arranged in a nonrandom sequence.


MR(2) Chart

The MR(2) Chart graphical option displays a chart of the moving ranges for successive observations.

A process is out of control if points are shown outside the control limits, or within the control limits, but arranged in a nonrandom sequence.


Chart
 X-bar Chart – don’t use this topic

The X-bar Chart area of the Analysis Summary displays the values for the Upper control limit (UCL), Centerline, and Lower control limit (LCL) that the program uses in the analysis.  Sigma values are used to calculate the UCL and the LCL for the chart.  The summary also lists the number of subgroups that are beyond the control limits.

As in the Range Chart, a process is in control if all the values fall within the control limits.  If you choose a one-sided control chart; that is, you do not choose a UCL or a LCL, the corresponding line for the control limit is blank.  If the subgroup sizes differ, the program uses the average subgroup size to calculate the control limits.


Subgroup Information
Subgroup Information – don’t use this topic

This area of the Analysis Summary displays the number of subgroups the program uses for the analysis; the size of the subgroups, or the average size if the subgroups have different sizes; and the number of subgroups you want to exclude from the analysis.


Estimated
Estimated  - don’t use this topic

This area of the Analysis Summary displays the estimated values for the process mean, process sigma, and mean range.  When the subgroup sizes are unequal, the average subgroup size is used to calculate those values.


Standard
Standard – don’t use this topic

This area of the Analysis Summary displays the values for the process mean and sigma you enter on the X-bar and R Charts Options dialog box when you perform a Control to Standard study.  It also displays the standard mean range.


Chart ( and S Charts Analysis)
X-bar Chart

The X-bar Chart option creates a plot of the means for each of the subgroups.  A process is considered out of control if points are shown outside the control limits, or if points are shown within the control limits, but arranged in a nonrandom sequence.

Use the Control Chart Options dialog box to choose options for the X-bar Chart.


S Chart
S Chart- don’t use this topic

The S Chart area of the Analysis Summary displays the controls for the variation in the standard deviation of samples.

The summary shows the value for the Centerline, which represents the average value for the quality characteristics when a process is in control.  It also displays the values for the UCL, the LCL, and for the number of values that fall beyond those limits.

If you choose a one-sided control chart, that is, you choose either a UCL or a LCL, the corresponding line for the control limit is blank.  If the sizes of the subgroup differ, the average subgroup size is used as the default when the control limits are calculated.


Subgroup Information
Subgroup Information  - don’t use this topic

This area of the Analysis Summary displays the number of subgroups the program used for the analysis, the size of the subgroups or the average size if the sizes of the subgroups differ, and the number of subgroups you want to exclude from the study.


Estimated
Estimated – don’t use this topic

This portion of the Analysis Summary displays the estimated process mean, process sigma, and mean sigma.  When the sizes of the subgroup are not equal, the program uses the average subgroup size when it calculates those values.


Standard
Standard  - don’t use this topic

This area of the Analysis Summary displays the values for the process mean and process sigma you enter on the X-bar and S Charts Options dialog box when you perform a Control to Standard study.  It also displays the value for the standard mean sigma.


Runs Tests ( and S Charts Analysis)
Runs Tests (X-bar and S Charts Analysis)

The Runs Tests option searches for and identifies any unusual patterns in the data.  The tests are helpful in detecting processes that are slowly drifting away from the target (even though no points may fall outside the control limits).  A nonrandom pattern indicates that a process is out of control.  The report displays the subgroup at which the unusual pattern was detected as well as the rule that was violated.

Use the Runs Tests Options dialog box to indicate the guidelines for the tests and the violation rules.


Capability Indices ( and S Charts Analysis)
Capability Indices (X-bar and S Charts Analysis)

The Capability Indices option calculates several process capability indices based on the estimated process mean and standard deviation.  These indices help determine the capability of a process to produce products that must meet a quality standard.

Use the Process Capability Indices Options dialog box to choose the indices you want calculated, and to enter values for the USL, Nominal, and LSL specifications.


Chart ( and S Charts Analysis)
X-bar Chart (X-bar and S Charts Analysis)

The X-bar Chart graphical option displays a plot of the points on an X-bar Chart.  The control limits are based on the mean and standard deviation of the subgroups.

A process is out of control if the points are shown outside the control limits, or if the points are within the control limits but arranged in a nonrandom sequence.


Tolerance Chart ( and S Charts Analysis)
Tolerance Chart (X-bar and S Charts Analysis)

The Tolerance Chart option creates a plot of the individual values for the variable, arranged by subgroup.  A horizontal line shows the grand mean of the observations; a vertical line shows the subgroup ranges.  You can include specification limits on the chart.

Use the Tolerance Chart Options dialog box to choose options for the Tolerance Chart.


OC Curve ( and S Charts Analysis)
OC Curve (X-bar and S Charts Analysis)

The OC Curve graphical option produces a plot that shows the probability of not detecting a shift in the true process parameter that occurs in the subgroup immediately after a shift.

The X-axis shows the average shift.  The Y-axis shows the probability of not detecting the shift.


Chart
X Chart

This portion of the Analysis Summary shows the values for the UCL, Centerline, and LCL that the program uses in the analysis.  The program uses the sigma values to calculate the UCL and LCL for the chart.

It also lists the number of subgroups that are beyond the control limits.  As in the S-Squared Chart, a process is in control if all the values fall within the control limits.  If you choose a one-sided control chart, that is, you do not choose a UCL or an LCL, the corresponding line for the control limit is blank.  If the size of the subgroups differ, the program uses the average size to calculate the control limit.


S-Squared Chart

The S-Squared Chart option creates a plot that shows the variances for each of the subgroups.  It indicates if any points are beyond the control limits.  A process is out of control if points are shown outside the control limits, or if points are within the control limits, but arranged in a nonrandom sequence.

Use the Control Chart Options dialog box to choose options for the S-Squared Chart.


Subgroup Information

This area of the Analysis Summary displays the number of subgroups the program used for the analysis, the size of the subgroups, or the average size if the sizes of the subgroups are different, and the number of subgroups you want to exclude from the study.


Estimated
Estimated – don’t use this topic

This area of the Analysis Summary displays the estimated values for the process mean, process sigma, and pooled variance.  If the sizes of the subgroups are not equal, the program uses the average size to calculate these values.


Standard
Standard – don’t use this topic

This area of the Analysis Summary displays the values for the process mean and sigma you entered on the X-bar and S-Squared Charts Options dialog box.  It also displays the value for the standard variance.


Runs Tests

The Runs Tests option searches for and identifies any unusual patterns in the data.  The tests are helpful in detecting processes that are slowly drifting away from the target (even though no points may fall outside the control limits).  A nonrandom pattern indicates that a process is out of control.  The report displays the subgroup at which the unusual pattern was detected as well as the rule that was violated.

Use the Runs Tests Options dialog box to indicate the guidelines for the tests and the violation rules.


Capability Indices ( and S-Squared Charts Analysis)
Capability Indices (X-bar and S-Squared Charts Analysis)

The Capability Indices tabular option displays the values for the capability indices.  The program uses 6.0 sigma limits to calculate the indices.

Unlike the Process Capability Analysis, this option uses these values to calculate the estimated process sigma and displays the results in the Analysis Summary.  The values help determine the capability of a process to produce products that meet a standard.

The capability indices are not calculated until you enter values for the USL, Nominal, and LSL text boxes on the Process Capability Indices Options dialog box.

To choose options for this report, use the Process Capability Indices Options dialog box.


Chart ( and S-Squared Charts Analysis)
X Chart (X-bar and S-Squared Charts Analysis)

The X-bar Chart option creates a plot of the means for each of the subgroups.  A process is considered out of control if points are shown outside the control limits, or if points are shown within the control limits, but arranged in a nonrandom sequence.

Use the Control Chart Options dialog box to choose options for the X-bar Chart.


Tolerance Chart ( and S-Squared Charts Analysis)
Tolerance Chart (X-bar and S-Squared Charts Analysis)

The Tolerance Chart option creates a plot of the individual values for the variable, arranged by subgroup.  A horizontal line shows the grand mean of the observations; a vertical line shows the subgroup ranges.  You can include specification limits on the chart.

Use the Tolerance Chart Options dialog box to choose options for the chart.


OC Curve ( and S-Squared Charts Analysis)
OC Curve (X-bar and S-Squared Charts Analysis)

The OC (Operating Characteristic) Curve option creates a plot that shows the probability that the next point that is plotted on the control chart will remain inside the control limits as a function of the true process mean.  It is useful for judging the effectiveness of a control chart in detecting when a process drifts away from the target. The X-axis shows the shift in the average; the Y-axis the probability of not detecting the shift.


X-Chart
X Chart

The X Chart option creates a plot of the individual measurements.  A process is considered out of control if points are shown outside the control limits, or if points are shown within the control limits, but arranged in a nonrandom sequence.

Use the Control Chart Options dialog box to choose options for the analysis.


MR(2) Chart

The MR(2) Chart option creates a plot of the moving ranges for each of the measurements.  It indicates if any points are beyond the control limits.  A process is out of control if points are shown outside the control limits, or if points are within the control limits, but arranged in a nonrandom sequence.

Use the Control Chart Options dialog box to choose options for the analysis.


Observation Information
Observation Information – don’t use this topic

This portion of the Analysis Summary displays the number of observations in the analysis and the number of observations that were excluded.


Estimated
Estimated – don’t use this topic

This portion of the Analysis Summary displays the values for the estimated process mean, process sigma, and the mean MR(2).


Standard
Standard  - don’t use this topic

This portion of the Analysis Summary displays the values for the estimated process mean and sigma, and the value for the standard mean MR(2).


Runs Tests (Individuals Charts Analysis)

The Runs Tests option searches for and identifies any unusual patterns in the data.  The tests are helpful in detecting processes that are slowly drifting away from the target (even though no points may fall outside the control limits).  A nonrandom pattern indicates that a process is out of control.   The report displays the subgroup at which the unusual pattern was detected as well as the rule that was violated.

Use the Runs Tests Options dialog box to indicate the guidelines for the tests and the violation rules.


Capability Indices (Individuals Charts Analysis)

The Capability Indices option creates capability indices you choose that are based on the estimated process mean and standard deviation.   Sigma limits of 6.0 are used to calculate the indices.  The values help to determine the capability of a process to produce products that meet a standard.

Use the Process Capability Indices Options dialog box to choose the indices you want calculated, and to enter values for the USL, Nominal, and LSL specifications.


OC Curve (Individuals Charts Analysis)
OC Curve

The OC Curve graphical option produces an OC curve that shows the probability of not detecting a shift in the true process parameter on the observation immediately after a shift occurs.

The X-axis shows the shift in the average.  The Y-axis shows the probability of not detecting the shift.


Runs Tests

The Runs Tests tabular option performs a battery of tests that help to detect small changes or patterns in a process that may not be evident on a control chart.  The program lists the last subgroup in each violated Runs test.  By default, the program includes all the options in the Runs tests.

Use the Runs Tests Options dialog box to choose options for this report.


Runs Tests (c Chart Analysis)

The Runs Tests tabular option performs a battery of tests that help to detect small changes or patterns in a process that may not be evident on a control chart.  The last observation is listed in each violated Runs test.  By default, all the options in the Runs tests are included.

To choose options for the test, use the Runs Tests Options dialog box.


Goodness-of-Fit Tests

The Goodness-of-Fit Tests option displays a table of the results for tests run to determine if the variable can be adequately modeled by the distribution you are using, which can be either normal or nonnormal distributions.  The tests are: Chi-Square and Kolmogorov-Smirnov.

The Chi-Square test divides the range of values in the variable into nonoverlapping intervals and compares the number of observations in each class with the number of expected observations, based on the distribution you are using.  If the p value is less than .05 (for a 95 percent confidence level), the data are not adequately modeled by the distribution.

The Kolmogorov-Smirnov test computes the maximum distance between the cumulative distribution of the data variable and the CDF of the distribution you are using.  If the approximate p value falls below .05, the data do not adequately fit the distribution you are using.


Range Chart

The Range Chart graphical option displays a plot of the data.

To choose options for the plot, use the Control Chart Options dialog box for either an Initial Study or a Control to Standard.


Tolerance Chart (Moving Average Chart Analysis)

The Tolerance Chart graphical option displays a plot that shows the observations by subgroup.  The horizontal line shows the grand mean of the observations.  The vertical line shows the subgroup ranges.  You can include specification limits on the chart.

Because you use the Tolerance Chart to examine individual observations, it is available only when you choose Observations from the Data options on the Moving Average Chart Analysis dialog box.

To choose options for the plot, use the Tolerance Chart Options dialog box.


OC Curve (Moving Average Chart Analysis)

The OC Curve graphical option displays a plot that shows the probability of not detecting a shift in the true process parameter on the subgroup immediately after a shift occurs.

The X-axis shows the shift in the average.  The Y-axis shows the probability of not detecting the shift.


Capability Indices

The Capability Indices tabular option displays the values for the capability indices, which the program calculates using the 6.0 sigma limits.  Unlike the Process Capability Analysis, this analysis uses the estimated values for the process sigma.  These values help to determine the capability of a process to produce products that meet a standard.  The program does not calculate the capability indices until you choose or enter the USL, Nominal, and LSL values on the Process Capability Indices Options dialog box.

To choose options for this report, use the Process Capability Indices Options dialog box.


Range Chart (EWMA Chart Analysis)

The Range Chart graphical option displays a plot of the data with control limits based on the ranges of the subgroups.

To choose options for the plot, use the Control Chart Options dialog box for either an Initial Study or a Control to Standard.


Tolerance Chart (EWMA Chart Analysis)

The Tolerance Chart graphical option displays a plot that shows the observations by subgroup.  A horizontal line shows the grand mean of the observations; a vertical line shows the subgroup ranges.  You can include specification limits on the chart.

Because you use the Tolerance Chart to examine individual observations, it is available only when you choose Observations from the Data options on the EWMA Chart Analysis dialog box.

To choose options for the plot, use the Tolerance Chart Options dialog box.


OC Curve (EWMA Chart Analysis)

The OC Curve graphical option produces aplot that shows the probability of not detecting a shift in the rue process parameter on the subgroup immediately after a shift occurs.

The X-axis shows the shift in the average; the Y-axis shows the probability of not detecting the shift.


Range Chart (CuSum Chart Analysis)

The Range Chart graphical option displays a plot of the data.

To choose options for plot, use the Control Chart Options dialog box for either an Initial Study or a Control to Standard.


Capability Indices

The Capability Indices tabular option displays the values for the capability indices, which the program calculates using the 6.0 sigma limits.  Unlike the Process Capability Analysis, this analysis uses the values for the estimated process sigma for the calculations.  These values help to determine the capability of the process to produce products that meet a standard.  The program does not calculate the capability indices until you enter the values for the USL, Nominal, and LSL on the Process Capability Indices Options dialog box.

To choose options for the report, use the Process Capability Indices Options dialog box.


MR(2) Chart

The MR(2) Chart graphical option displays an MR(2) Chart of the data.


OC Curve (MA Individuals Chart Analysis)

The OC Curve graphical option produces a plot that shows the probability of not detecting a shift in the true process parameter on the observation immediately after a shift occurs.

The X-axis shows the shift in the average.  The Y-axis shows the probability of not detecting the shift.


MR(2) Chart

The MR(2) Chart graphical option displays an MR(2) Chart of the data.


OC Curve (EWMA Individuals Chart Analysis)

The OC Curve graphical option produces an OC Curve, which shows the probability of not detecting a shift in the true process parameter on the observation immediately after a shift occurs.

The X-axis shows the shift in the average.  The Y-axis shows the probability of not detecting the shift.


Display

Determines the type of values that will display for each class.

Percentages

Displays class percentages of the total score.  This option is the default.

Scores

Displays class scores.

None

Displays the total line without class labels.


Distribution

These options allow you to choose the type of distribution the program will fit.  The default is Normal.


Plot (Points or Nominal Specification Line)

These options allow you to indicate if the program will plot points or the nominal specification line.

Points

Plots points.

Nominal

Plots the nominal specification line.


Data

Choose or enter the unique codes (numeric or character) that will be tabulated.

Untabulated Observations

Enter the data that consists of individual observations.  Use the text box to enter the observations.  The program tabulates (counts) the codes to determine the number of each type of defect that occurs.

Tabulated Counts

Enter frequency data, which represents the number of occurrences of a specific defect.  Use the text box to enter the counts. The numbers you enter become the height for each bar on the Pareto 	Chart.


Combine Classes

Determines if classes will appear on the Pareto Chart, and if so, how they will appear.

None

Indicates you do not want to combine classes.

Counts Less Than n

Combines into a single class, all the original classes that have frequencies less than the number of defects you enter into the text box.  Enter an integer greater than 1; the default is 2.

Percentages Less Than n

Combines into a single class, all the original classes that have percentages less than the percentage you enter into the text box.  Enter a numeric value greater than 0; the default is 5.0.

Smallest Classes

Combines the smallest classes into one class.  Use the text box to enter the number of classes.  Enter an integer between 2 and 14; the default is 3.


Distribution

Determines the type of distribution that will be fit.  The default is Normal.

Normal

Fits a distribution that is useful in instances when the bars of a Frequency Histogam form a common, bell-shaped curve.  This option is the default.

Exponential

Fits time-series data, such as arrival times, where arrivals are expected at a constant rate; useful for random variables that are constrained to be greater than 0.  This distribution is a special case of both the Gamma and the Weibull distributions.

Extreme Value

Fits a distribution that applies when extremes, rather than means, are collected from samples from an unknown or complex underlying distribution.

Gamma

Fits a distribution that is characterized by two parameters: Shape and Scale.  This distribution is often used to model data that are positively skewed, such as the time required to complete a task.

Laplace

Fits a distribution that is more peaked than a normal distribution. This distribution is characterized by two parameters: Mean and Scale.  This distribution is sometimes called the “double exponential” distribution because it looks like an exponential distribution with a mirror image.

Logistic

Fits a distribution that is useful for random variables that are not constrained to be greater than or equal to 0; characterized by two parameters: Mean and Standard Deviation.

Lognormal

Fits a distribution that is useful for processes in which the value is a random proportion of the previous value.  Data fit to this distribution should be values greater than 0; it is characterized by two parameters: Mean and Standard Deviation.  The distribution is positively skewed and can take on various shapes.  The log of data that follow the lognormal distribution are normally distributed.

Weibull

Fits a distribution that is useful for random variables that are constrained to be greater than 0; it is characterized by two parameters: Shape and Scale.  It is an appropriate model for product failures.  It is appropriate because its failure rate curves can take various shapes.  This distribution is a generalization of the exponential distribution.


Distribution Parameters

Determines the estimates for the distribution parameters (the sufficient statistics) that will be used for the calculations.  The estimates depend on the data, however, you can override the system-defined estimates.  The estimates are shown for each of the distribution options.

Parameters for a Normal Distribution

Mean

The estimate is 16.322.

Standard Deviation

The estimate is 0.443489.

Parameter for an Exponential Distribution

Mean

The estimate is 16.322.

Parameters for an Extreme Value Distribution

Mode

The estimate is 16.5216.

Scale

The estimate is 0.345787.

Parameters for a Gamma Distribution

Shape

The estimate is 1357.56.

Scale

The estimate is 83.1735.

Parameters for a Laplace Distribution

Mean

The estimate is 16.2.

Scale

The estimate is 2.9940.

Parameters for a Logistic Distribution

Mean

The estimate is 16.3196.

Standard Deviation

The estimate is 0.443078.

Parameters for a Lognormal Distribution

Mean

The estimate is 16.3221.

Standard Deviation

The estimate is 0.446338.

Parameters for a Weibull Distribution

Shape

The estimate is 40.6584.

Scale

The estimate is 16.532.


Indices

Determines the indices that will apear on the Capability Indices report and the Capability Plot.  If you use a one-sided specification, you cannot calculate capability indices for Cp, Cr, Cpm, or K.  If you use an asymmetric, two-sided specification, interpret the Cp, Cr, and Cpm indices with caution because they are based on symmetric limits.

Cp

Displays the inherent capability of the process.  In general, if the mean of the data is located close to the midpoint of the tolerances, then a Cp less than 1.00 indicates the process is not capable; a Cp above 1.33 indicates that the process is capable; a Cp between 1.00 and 1.33 indicates that the process is capable but should be monitored as Cp approaches 1.00.

Cpk

Displays a value for the capability in relation to the mean. Cpk is a worst-case index of the process.  It is the ratio of the distance from the UCL to the mean or the LCL to the mean, whichever is smaller, to half the sigma range.  Cpk is useful even if the mean of the data is not close to the midpoint of the tolerances.  A Cpk larger than 1.33 indicates that both sigma limits fall within the specification limits and the process is capable of performing to specification.  A Cpk of less than 1.00 means that at least one of the sigma limits is outside of a specification limit and the process may not be capable of performing to specification.

Cpk (upper)

Displays a value for the distance from the USL to the mean, divided by half the sigma range.

Cpk (lower)

Displays the distance from the LSL to the mean, divided by half the sigma range.

Cr

Displays a value for the capability ratio of the process.  It is the reciprocal of the Cp index.  If the mean of the data is located close to the midpoint of the tolerances, then a Cr greater than 1.00 indicates that the process is not capable.  A Cr less than 0.75 indicates that the process is capable.  A Cr between 0.75 and 1.00 indicates that the process is capable, but should be monitored as Cr approaches 1.00.

Cpm

Displays a value for the modified Cp index.  The program calculates Cpm using the nominal value instead of the calculated mean.  It is a more conservative index than Cp; you can interpret it in the same manner.  For small sample sizes, Cpm is a better measure than Cp.


K

Displays a value for the comparison ratio of the process mean to the nominal specification.  K is a measure of how far the center of the process is from the nominal or target of the process.  If K is 0, the mean and the nominal value are identical.  If K is positive, the mean is above the nominal value.  If K is negative, the mean is below the nominal value.  When the absolute value of K is small, the process mean is close to the nominal specification.  A small value of K can occur even if the process is not capable.


Based On

Choose the sigma limits that will be used to calculate the capability indices.  These options are available only when you choose a Normal distribution.

6.0 Sigma Limits

Uses 6.0 sigma limits in the calculations.

User-Specified Limits

Enter a value for the sigma limits.  For example, if you enter 8, the indices are calculated by dividing eight standard deviations.


Histogram

Determines options for the histogram.

Number of Classes

Enter a number that will represent the number of classes into which the data will be grouped.  Enter an integer between 1 and 300; the default is based on the data you use.

Lower Limit

Enter a value that will be used for the lower limit for the first class.  Enter any number; the default is based on the data you use.

Upper Limit

Enter a value that will be used for the upper limit for the last class.  Enter any number greater than or equal to the LSL; the default is based on the data you use.


Data

Determines the type of data that will be analyzed.

Observations

Choose this option if you are entering individual observations.  In the text box, enter the name of the variable that contains the individual observations; that is, if the data contain individual measurements, enter the variable name that contains that data.

Subgroup Statistics

Choose this option if you will be entering subgroup statistics.

Means

Enter the means of the subgroups that will be included in the analysis.

Ranges

Enter the ranges that will be included in the analysis.  The values you enter 	into this text box must correspond to the values you enter into the Means text box.


Type of Study

Determines the type of study; either Initial Study or Control to Standard.  The default is Initial Study.

Initial Study

Computes the control limits based on the data.

Control to Standard

Computes the control limits based on limits or the mean and sigma you enter.  In this type of study data do not influence the control limits.


Control to Standard

Determines the parameters or control limits.  Note:  You must enter values for either the Mean and Sigma parameters or for the control limits.  These options are available only when you choose Control to Standard from the Type of Study options.

Specify Parameters

Enter the values that will be used to calculate the control limits.

Mean

Enter a value for the process mean.  Enter any numeric value.

Sigma

Enter a value for the process sigma.  Enter any positive numeric value.

Enter values for the parameters or the control limits. These options are available only when you choose the Control to Standard.option.

Specify Control Limits

Determines the control limits for the X-bar and Range charts.

Upper (X-bar Chart)

Enter a numeric value for the UCL.  The number must be greater than the values you enter into the Centerline and LCL text boxes.

Centerline (X-bar Chart)

Enter a numeric value for the Centerline.  The number must be less than the value you enter for the UCL, and greater than the value you enter for the LCL.

Lower (X-bar Chart)

Enter a numeric value for the LCL.  The number must be less than the values you enter for the UCL and Centerline.

Upper (Range Chart)

Enter a positive numeric value for the UCL.  Enter a value that is greater than the values in the Centerline and LCL text boxes.

Centerline (Range Chart)

Enter a numeric value for the Centerline.  The number must be greater than or equal to zero and less than the value for the UCL, and greater than the value for the LCL.

Lower (Range Chart)

Enter a numeric value for the LCL.  The number must be greater than or equal to zero and less than the values for the UCL and Centerline.


Exclude... Command

Displays the Exclude/Include dialog box that determines the subgroups that will be excluded or included in the analysis and the method that will be used to do it.

Exclude Method

Determines the subgroups that will be excluded or included in the analysis and the method that will be used to do it.

Manual

Choose the subgroups you want to exclude from the analysis.

Automatic

Indicates that the out-of-control subgroups should be automatically excluded until all the remaining subgroups are within the control limits.

Reset

Indicates you want to include all the subgroups in the analysis; it is useful only after you exclude subgroups.

Exclude Subgroup

Enter the number of the subgroup that will be excluded from the analysis.  This text box is available only when you choose Manual from the Exclude Method options.

Include Subgroup

Enter the number of a subgroup you previously excluded and want to re-enter.


Display

Choose the subgroups that should be included in the Subgroup Reports. The default is All Subgroups.

All Subgroups

Includes all the subgroups in the reports.

Subgroups beyond Limits

Lists the subgroups that are beyond the control limits for the  or Range charts.

X-bars beyond Limits

Lists the subgroups that have s beyond the control limits.

Ranges beyond Limits

Lists the subgroups that have ranges beyond the control limits.

Excluded Subgroups

Lists the subgroups that have been excluded from the analysis.


Specifications

Determines the settings for the specification limits. Some settings may not be available.

USL

Enter a value for the USL.  Enter one numeric value.  The value you enter must be greater than the values you enter into the LSL and Nominal text boxes.

Nominal

Enter a value for the target of the process.  Enter one numeric value.  The value you enter must be greater than the value in the LSL and less than the USL.

LSL

Enter a value for the LSL.  Enter one numeric value.  The value you enter must be less than the values in the USL and Nominal text boxes.


Data

Determines the type type of data that will be analyzed.

Observations

Choose this option if you are entering individual observations.  In the text box, enter the name of the variable that contains the individual observations; that is, if the data contain individual measurements, enter the variable name that contains that data.

Subgroup Statistics

Choose this option if you will be entering subgroup statistics.

Means

Enter the means of the subgroups that will be included in the analysis.

Standard Deviations

Enter the standard deviations that will be included in the analysis.  The values you enter into this text box must correspond to the values you enter into the Means text box.


Control to Standard

Determines the parameters or control limits.  Note:  You must enter values for either the Mean and Sigma parameters or for the control limits. These options are available only when you choose the Control to Standard.option.

Specify Parameters

Determines the values for the control limits.

Mean

Enter a value for the process mean.  Enter any numeric value.

Sigma

Enter a value for the process sigma.  Enter any positive numeric value.

Specify Control Limits

Determines the control limits for the X-bar and S charts.

Upper (X-bar Chart)

Enter a numeric value for the UCL.  The number must be greater than the values you enter into the Centerline and LCL text boxes.

Centerline (X-bar Chart)

Enter a numeric value for the Centerline.  The number must be less than the value you enter for the UCL, and greater than the value you enter for the LCL.

Lower (X-bar Chart)

Enter a numeric value for the LCL.  The number must be less than the values you enter for the UCL and Centerline.

Upper (S Chart)

Enter a positive numeric value for the UCL.  Enter a value that is greater than the value in the Centerline and LCL text boxes.

Centerline (S Chart)

Enter a numeric value for the Centerline.  The number must be greater than or equal to zero and less than the value for the UCL, and greater than the value for the LCL.

Lower (S Chart)

Enter a numeric value for the LCL.  The number must be greater than or equal to zero and less than the values for the UCL and Centerline.


Data

Determines the type of data that will be analyzed.

Observations

Choose this option if you are entering individual observations.  In the text box, enter the name of the variable that contains the individual observations; that is, if the data contain individual measurements, enter the variable name that contains that data.

Subgroup Statistics

Choose this option if you will be entering subgroup statistics.

Means

Enter the means of the subgroups that will be included in the analysis.

Variances

Enter the variances that will be included in the analysis.  The values you enter into this text box must correspond to the values you enter into the Means text box.


Control to Standard

Determines the parameters or control limits.  Note:  You must enter values for either the Mean and Sigma parameters or for the control limits.  These options are available only when you choose Control to Standard from the Type of Study options.


Control to Standard

Determines the parameters or control limits.  Note:  You must enter values for either the Mean and Sigma parameters or for the control limits.  These options are available only when you choose Control to Standard from the Type of Study options.


Display

Choose the subgroups that will be included in the Individuals Charts report.

All Observations

Includes all the observations in the report.

Observations beyond Limits

Lists the observations that are beyond the control limits for the X-bar or MR(2) charts.

X-bars beyond Limits

Lists the observations that have observations beyond the control limits.

MR(2) beyond Limits

Lists the observations that have moving ranges beyond the control limits.

Excluded Observations

Lists the observations that have been excluded from the analysis.


Display

Determines what will display in the Subgroup Report.  The default is All Subgroups.

All Subgroups

Includes all the subgroups.

Subgroups beyond Limits

Lists the out-of-control subgroups that are beyond the control limits for the X-bar or Range charts.

X-bars beyond Limits

Lists the subgroups that have s beyond the control limits.

Ranges beyond Limits

Lists the subgroups that have ranges beyond the control limits.

Excluded Subgroups

Lists the excluded subgroups.


Tests for Normality (Process Capability Analysis)

The Tests for Normality option displays the results of several tests that determine if the data in the variable is adequately modeled by the normal distribution.  The tests are the Chi-Square goodness of fit, Shapiro-Wilks W, z-score for skewness, and z-score for kurtosis.

The Chi-Square test divides the range of values in the variable into equally probable classes, then compares the number of observations in each class with the number of expected observations.  This is an updated version of the standard chi-square goodness-of-fit statistic (see Madansky, 1988).

The Shapiro-Wilks W test compares the quantiles of the fitted normal distribution with the quantiles of the data (see Madansky, 1988).

The Standardized Skewness Test looks for a lack of symmetry in the data.  The z-score for skewness looks for symmetry in the data, while the z-score for kurtosis looks for a distribution shape that is either flatter or more peaked than the normal distribution.


Population Proportion

Enter a value for the proportion of the population that the tolerance interval will contain.  Enter a percentage greater than 0 and less than 100.  Larger values produce wider tolerance intervals.  The default is 99.73.


Input

Determines if confidence levels or population proportions will be used to calculate the tolerance interval.

Confidence Level

Indicates that a confidence level should be used to calculate the interval.  Use the text box to enter a percentage that is greater than 0 and less than 100.  The default is 95 percent.

Population Proportion

Indicates that a population proportion should be used to calculate the tolerance interval.  Enter a percentage greater than 0 and less than 100.  Larger values produce wider tolerance intervals.  The default is 95.


X-Axis Resolution

Enter the number of density values that should be used to calculate the fitted distribution curve.  Enter an integer between 10 and 300; 100 is the default.  The higher the resolution, the smoother the line.


Plot (Points or Nominal Specification Line)

Indicates if points or the nominal specification line will appear on the plot.  Both options are defaults.


Recalculate At

Enter up to four subgroup numbers to indicate the locations where control limits should be recalculated.  Each location must result in subgroup sets of two or more.  For example, Subgroup 3 is the first possible location and Subgroup 5 is the closest possible location after Subgroup 3.


Decimal Places for Limits

Enter a positive integer to indicate the number of decimal places that will be displayed for the control limits.


Mark Runs Rules Violations

Flags any runs that violate the out-of-control rules.  Specifically, a process is out of control if:

(1)	one point plots outside the 3-sigma control limits;

(2)	two out of three consecutive points plot beyond the 2-sigma warning limits

(3)	four out of five consecutive points plot at a distance of 1-sigma or beyond from the centerline;

(4)	eight consecutive points plot on one side of the centerline (Western Electric Handbook, 1956 in Montgomery, 1997).


Data

Enter the name of the variable that contains the data that will be analyzed.  The data must contain at least six nonmissing observations.


p Chart Analysis Dialog Box

A p Chart measures the proportion of defective or nonconforming items in a group of items being inspected.  The items could refer to a sample of 25 pieces, taken three times a day; some percentage of production grouped on an hourly or daily basis; or the proportion of on-time deliveries.

A fraction rejected p is defined as the ratio of the number of defective (nonconforming) items found in any inspection to the total number of items actually inspected.  A fraction rejected is almost always expressed as a decimal fraction.

This chart is the most versatile and widely used attributes control chart.  It can be applied to quality characteristics that are considered to be attributes, even though they might also have been measured as variables.  If the classification of an individual article is accepted or rejected as the result of an inspection, a p chart can be applied to one or more quality characteristics.

Proportions

Subgroup Sizes

Subgroup Labels

Select

Sort

See also

Using the p Chart Analysis

p Chart Options

Subgroup Reports Options

Runs Tests Options

Control Chart Options - Initial Study

Control Chart Options - Control to Standard


Proportions

Enter the name of the variable that contains the proportional data from the items in the samples. Enter numeric values between 0 and 1.


Subgroup Sizes

Enter a number for the size of the subgroups. If all the subgroups are the same size, enter a single number.  Enter integers greater than 1.


p Chart Tabular Options Dialog Box

Allows you to choose tabular options for the p Chart analysis.

Analysis Summary (p Chart Analysis)

Subgroup Reports (p Chart Analysis)

Runs Tests (p Chart Analysis)


Analysis Summary (p Chart Analysis)

The Analysis Summary contains information about the p Chart, subgroups, and estimated statistics.    For a Control to Standard study, the summary statistics are also included.

p Chart

The p Chart is based on the proportion of defective items.  This portion of the Analysis Summary shows the values for the Centerline, which represents the average proportion of defects when a process is in control, and the values for the Upper Control Limit (UCL), and the Lower Control Limit (LCL).  It also displays the number of values that fall beyond those limits.  If you choose a one-sided control chart, that is, you choose either an UCL or an LCL, the corresponding line for the control limit is blank.  If the sizes of the subgroup differ the average subgroup size is used as the default when the control limit is calculated.

Subgroup Information

Displays the number of subgroups used for the analysis, the size of the subgroups or the average size if the subgroups have different sizes, and the number of subgroups you want to exclude from the study.

Estimated

Displays the values for the estimated mean p value, and process sigma.  When the sizes of the subgroup are not equal, the average subgroup size is used to calculate these values.

Standard

Displays the mean p value you enter on the p Chart Options dialog box when you perform a Control to Standard study.  It also displays the value for the standard sigma.

To choose options for the p Chart Analysis, use the p Chart Options dialog box.


Subgroup Reports (p Chart Analysis)

The Subgroup Reports tabular option displays a report of the proportions for each subgroup.

To choose options for the report, use the Subgroup Reports Options dialog box.


p Chart Options Dialog Box

This dialog box allows you to choose options for the analysis.

Type of Study

Normalize

Average Subgroup Size

Recalculate At

p Chart Control Limits

Control to Standard

Exclude... Command


p Chart Control Limits

Determines the values for the location of the control limits on the p Chart.

Upper Sigma

Enter a value for the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10; the default is 3.0.

Lower Sigma

Enter a value for the multiple of sigma that will be used to calculate the LCL.  Enter a numeric value greater than or equal to –10 and less than or equal to 0.  The default is –3.0.


Specify Parameter

Enter the value that will be used to calculate the control limits.  Use the p text box to enter the process proportion.  Enter any numeric value greater than 0 and less than 1.


Specify Control Limits

Determines the control limits.

Upper

Enter a numeric value for the UCL.  The number must be greatr than the values you enter into the Centerline and LCL text boxes.

Centerline

Enter a numeric value for the Centerline.  The number must be less than the value you enter for the UCL, and greater than the value you enter for the LCL.

Lower

Enter a numeric value for the LCL.  The number must be less than the values you enter for the UCL and Centerline.


Subgroup Reports Options Dialog Box

This dialog box allows you to choose the subgroups that will be included in the Subgroup Reports.

Display


p Chart Graphical Options Dialog Box

Allows you to choose graphical options for the p Chart analysis.

p Chart (p Chart Analysis)

OC Curve (p Chart Analysis)

ARL Curve (p Chart Analysis)


p Chart (p Chart Analysis)

The p Chart graphical option displays a p Chart with control limits based on the proportions and the estimate of sigma.


Save Results Options Dialog Box (p Chart)

The Save Results Options dialog box allows you to choose the results you want to save.  There are five choices:  Proportions, Sizes Labels, Mean p, and Sigma.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (p Chart Analysis)

The Analysis Summary contains information about the p Chart, subgroups, and estimated statistics.    For a Control to Standard study, the summary statistics are also displayed.

p Chart

The p Chart is based on the proportion of defective items.  This portion of the Analysis Summary shows the values for the Centerline, which represents the average proportion of defects when a process is in control, and the values for the Upper Control Limit (UCL), and the Lower Control Limit (LCL).  It also displays the number of values that fall beyond those limits.  If you choose a one-sided control chart, that is, you choose either an UCL or an LCL, the corresponding line for the control limit is blank.  If the sizes of the subgroup differ the average subgroup size is used as the default when the control limit is calculated.

Subgroup Information

Displays the number of subgroups used for the analysis, the size of the subgroups or the average size if the subgroups have different sizes, and the number of subgroups you want to exclude from the study.

Estimated

Displays the values for the estimated mean p value, and process sigma.  When the sizes of the subgroup are not equal, the average subgroup size is used to calculate these values.

Standard

Displays the mean p value you enter on the p Chart Options dialog box when you perform a Control to Standard study.  It also displays the value for the standard sigma..

To choose options for the p Chart Analysis, use the p Chart Options dialog box.


Subgroup Reports (p Charts Analysis)

The Subgroup Reports tabular option displays the proportions for each subgroup.


p Chart (p Chart Analysis)

The p Chart graphical option displays a p Chart with control limits based on the proportions and the estimate of sigma.


np Chart Analysis Dialog Box

An np Chart is appropriate for use whenever the subgroup size varies and the control chart must show the actual number of rejected items rather than the fraction or proportion rejected.  If the actual numbers of rejects were to be plotted, the central line on the chart as well as the control limits would have to be changed each time there was a change in the size of the subgroup.  If the subgroup size remains constant, a chart for actual numbers can be used.

Counts

Subgroup Sizes

Subgroup Labels

Select

Sort

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the np Chart Analysis

np Chart Options

Subgroup Reports Options

Runs Tests Options

Control Chart Options - Initial Study

Control Chart Options - Control to Standard


Counts

Enter the name of the variable that contains the counts data from the fixed-size samples.  Enter integers greater than or equal to 0.


np Chart Tabular Options Dialog Box

Allows you to choose tabular options for the np Chart analysis.

Analysis Summary (np Chart Analysis)

Subgroup Reports (np Chart Analysis)

Runs Tests (np Chart Analysis)


Analysis Summary (np Chart Analysis)

The Analysis Summary contains information about the np Chart, subgroups, and estimated statistics.  For a Control to Standard study, the summary statistics are also displayed.

np Chart

This portion of the Analysis Summary is based on the number of defective items.  It shows the values for the Centerline, which represent the average number of defects when a process is in control; the values for the UCL and the LCL.  It also displays the number of values that fall beyond those limits.

If you choose a one-sided control chart, that is, you choose either an UCL or an LCL, the corresponding line for the control limit is blank.  If the sizes of the subgroups differ, the average size is used as the default when the control limit is calculated.

Subgroup Information

Displays the number of subgroups in the analysis, the size of the subgroups or the average size if the sizes of the subgroups differ, and the number of subgroups excluded from the analysis.

Estimated

Displays the values for estimated mean np and process sigma.  When the subgroup sizes are not equal the program uses the average size when it calculates the values.

Standard

Displays the value for the mean np you entered on the np Chart Options dialog box for a Control to Standard study.  It also displays the value for the standard sigma.

To choose options for the analysis, use the np Chart Options dialog box.


Subgroup Reports (np Chart Analysis)

The Subgroup Reports tabular option displays a report of the number of defective items for each subgroup.

To choose options for the report, use the Subgroup Reports Options dialog box.


np Chart Options Dialog Box

This dialog box allows you to choose options for the analysis.

Type of Study

Normalize

Average Subgroup Size

Recalculate At

np Chart Control Limits

Control to Standard

Specify Control Limits


np Chart Control Limits

Determines the values for the location of the control limits on the np Chart.

Upper Sigma

Enter a value for the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10; the default is 3.0.

Lower Sigma

Enter a value for the multiple of sigma that will be used to calculate the LCL.  Enter a numeric value greater than or equal to -10 and less than or equal to 0.  The default is -3.0.


Specify Parameter

Enter a value that will be used to calculate the control limits.  Use the np text box to enter the process standard for the number of defects.  Enter any positive numeric value.


np Chart Graphical Options Dialog Box

Allows you to choose graphical options for the np Chart analysis.

np Chart (np Chart Analysis)

OC Curve (np Chart Analysis)

ARL Curve (np Chart Analysis)


np Chart (np Chart Analysis)

The np chart graphical option displays an np Chart with control limits based on the number of defective items and the estimate of sigma.

To choose options for the chart, use the Control Chart Options dialog box for either an Initial Study or for a Control to Standard.


Save Results Options Dialog Box (np Chart Analysis)

The Save Results Options dialog box allows you to choose the results you want to save.  There five options:  nps, Sizes, Labels, Mean np, and Sigma.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (np Chart Analysis)

The Analysis Summary contains information about the np Chart, subgroups, and estimated statistics.  For a Control to Standard study, the summary statistics are also displayed.


Subgroup Reports (np Chart Analysis)

The Subgroup Reports tabular option displays the number of defective items for each subgroup.


np Chart (np Chart Analysis)

The np Chart graphical option displays an np Chart with control limits based on the number of defective items and the estimate of sigma.


u Chart Analysis Dialog Box

You use the u Chart analysis when the number of defects per unit is expressed as a rate, rather than as an absolute value.  This analysis is more appropriate than the c Chart analysis when the sample or subgroup sizes are not constant.

When you use this analysis you first perform an Initial Study to estimate the control limits, which sets a standard you use to measure the process.  You then perform a Control to Standard study and enter the control limits or parameters to determine if the process meets the standard.

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

Defects per Unit

Subgroup Sizes

Subgroup Labels

Select

Sort

See also

Using the u Chart Analysis

u Chart Options

Subgroup Reports Options

Runs Tests Options

Control Chart Options - Initial Study

Control Chart Options - Control to Standard


Defects per Unit

Choose or enter the name of the variable that contains the data you want to analyze.  Enter numeric values greater than or equal to 0.


u Chart Tabular Options Dialog Box

Alows you to choose tabular options for the u Chart analysis.

Analysis Summary (u Chart Analysis)

Subgroup Reports (u Chart Analysis)

Runs Tests (u Chart Analysis)


Analysis Summary (u Chart Analysis)

The Analysis Summary contains information about the u Chart, subgroups, and estimated statistics.  For a Control to Standard study, the summary statistics are also displayed.

u Chart

Displays values based on the rate of defects per unit.  It shows the value for the Centerline, which represents the average rate of defects when a process is in control, the values for the UCL and the LCL.  It also displays the number of values that fall beyond those limits.

If you choose a one-sided control chart, that is, you choose either an UCL or a LCL, the corresponding line for the control limit is blank.  If the sizes of the subgroup differ, the average size is used as the default when the control limits are calculated.

Subgroup Information

Displays the number of subgroups used for the analysis, the size of the subgroups or the average size if the sizes differ, and the number of subgroups you want to exclude from the study.

Estimated

Displays the estimated mean u value and process sigma.  When the sizes of the subgroups are not equal, the average size is used to calculate the values.

Standard

Displays the mean u value you enter on the u Chart Options dialog box when you perform a Control to Standard study.  It also displays the standard sigma.

To choose options for the analysis, use the u Chart Options dialog box.


Subgroup Reports (u Chart Analysis)

The Subgroup Reports tabular option displays a report of the defects per unit for each subgroup.

To choose options for the report, use the Subgroup Reports Options dialog box.


u Chart Options Dialog Box

Allows you to:

•	choose the type of study you want to perform

•	indicate if you want to normalize the data

•	indicate that you want to use the average subgroup size to calculate the control limits

•	choose the location of the control limits on the u Chart

•	choose the parameter or control limits

•	choose the subgroups you want to exclude from the analysis.

Type of Study

Normalize

Average Subgroup Size

Recalculate At

u Chart Control Limits

Control to Standard

Exclude... Command


u Chart Control Limits

Enter values for the location of the control limits on the u Chart.  The options are available when you choose an Initial Study or a Control to Standard study and the Parameter option.  For example, a value of 0 in either option removes the corresponding control limit from the analysis.

Upper Sigma

Enter the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10; the default is 3.0.

Lower Sigma

Enter the multiple of sigma that will be used to calculate the LCL.  Enter a numeric value less than or equal to 0 and greater than or equal to -10; the default is -3.0.


Specify Parameter

Enter the value that will be used to calculate the control limits.  Use the u text box to enter the process standard for the defect rate..  Enter any numeric value greater than 0 and less than 1.


u Chart Graphical Options Dialog Box

Allows you to choose graphical options for the u Chart analysis.

u Chart (u Chart Analysis)

OC Curve (u Chart Analysis)

ARL Curve (u Chart Analysis)


u Chart (u Chart Analysis)

The u Chart option creates a plot of the nonconformities for each of the observations.  A process is considered out of control if points are shown outside the control limits, or if points are shown within the control limits, but arranged in a nonrandom sequence.

Use the Control Chart Options dialog box to choose options for the u Chart.


Save Results Options Dialog Box (u Chart)

The Save Results Options dialog box allows you to choose the results you want to save.  There are five options: us, Sizes, Labels, Mean u, and Sigma.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or choose the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (u Chart Analysis)

The Analysis Summary contains information about the u Chart, subgroups, and estimated statistics.  For a Control to Standard study, the summary statistics are also displayed.

u Chart

Displays values based on the rate of defects per unit.  It shows the value for the Centerline, which represents the average rate of defects when a process is in control, the values for the UCL and the LCL.  It also displays the number of values that fall beyond those limits.

If you choose a one-sided control chart, that is, you choose either an UCL or a LCL, the corresponding line for the control limit is blank.  If the sizes of the subgroup differ, the average size is used as the default when the control limits are calculated.

Subgroup Information

Displays the number of subgroups that will be used for the analysis, the size of the subgroups or the average size if the sizes differ, and the number of subgroups you want to exclude from the study.

Estimated

Displays the estimated mean u value and process sigma.  When the sizes of the subgroups are not equal, the average size is used to calculate the values.

Standard

Displays the mean u value you enter on the u Chart Options dialog box when you perform a Control to Standard study.  It also displays the standard sigma.

To choose options for the analysis, use the u Chart Options dialog box.


Subgroup Reports (u Chart Analysis)

The Subgroup Reports tabular option displays the defects per unit for each subgroup.


u Chart (u Chart Analysis)

The u Chart graphical option displays a u Chart with control limits based on defects per unit and the estimate of sigma.


c Chart Analysis Dialog Box

The c Chart analysis allows you to construct control limits based on an attribute that is related to a frequency, such as the number of defects per item, rather than the number of defects per sample.

The Poisson distribution is used as the model for the control limits.  This chart is useful when the item you produce may have more than one defect, and you need to count the defects rather than simply classifying the item as defective.

When you use this analysis you first perform an Initial Study to estimate the control limits, which sets a standard you use to measure the process.  You then perform a Control to Standard study and enter the control limits and parameters to determine if the process meets the standard.

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

Counts

Labels

Select

Sort

See also

Using the c Chart Analysis

c Chart Options

c Chart Report Options

Runs Tests Options

Control Chart Options - Initial Study

Control Chart Options - Control to Standard


c Chart Tabular Options Dialog Box

Allows you to choose tabular options for the c Chart analysis.

Analysis Summary (c Chart Analysis)

c Chart Report (c chart Analysis)

Runs Tests (c Chart Analysis)


Analysis Summary
Analysis Summary (c Chart)

The Analysis Summary contains information about the c Chart, subgroups, and estimated statistics.  For a Control to Standard study, the summary statistics are also displayed.

c Chart

Displays values based on the number of defects per item.  Values are shown for the Centerline, which represents the average number of defects per item when a process is in control, and the values for the UCL and the LCL.  It also displays the number of values that fall beyond those limits.

If you choose a one-sided control chart, that is, you choose either an UCL or a LCL, the corresponding line for the control limit is blank.

Observation Information

Displays the number of observations used for the analysis.

Estimated

Displays the estimated mean c value and process sigma.

Standard

Displays the mean c value you enter on the c Chart Options dialog box when you perform a Control to Standard study.  It also displays the standard sigma.

To choose options for the analysis, use the c Chart Options dialog box.


c Chart Report (c Chart Analysis)

The c Chart Report tabular option displays a report of the number of defects per item.


c Chart Options Dialog Box

Allows you to:

•	choose the type of study you want to perform

•	indicate if you want to normalize the data

•	choose the location of the control limits on the c Chart

•	choose the parameter or control limits

•	choose the observations you want to exclude from the analysis.

Type of Study

Normalize

Recalculate At

c Chart Control Limits

Control to Standard (c Chart)

Exclude... Command


c Chart Control Limits

Enter values for the control limits on the c Chart.  The options are available when you choose an Initial Study or a Control to Standard study and the Specify Parameter option.  For example, a value of 0 in either option removes the corresponding control limit from the analysis.

Upper Sigma

Enter the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10; the default is 3.0.

Lower Sigma

Enter the multiple of sigma that will be used to calculate the LCL.  Enter a numeric value less than or equal to 0 and greater than or equal to -10; the default is -3.0.


Specify Parameter

Enter the value that will be used to calculate the control limits.  Use the c text box to enter the process standard for the number of defects.  Enter any numeric value greater than 0 and less than 1.


c Chart Report Options Dialog Box

Allows you to choose the observations you want to include in the c Chart Report.

Display


c Chart Graphical Options Dialog Box

Allows you to choose graphical options for the c Chart analysis.

c Chart

OC Curve (c Chart Analysis)

ARL Curve (c Chart Analysis)


c Chart (c Chart Analysis)

The c Chart graphical option displays a plot with control limits based on the average number of defects per item and the estimate of sigma.

To choose options for the plot, use the Control Chart Options dialog box for either an Initial Study or a Control to Standard.


Save Results Options Dialog Box (c Chart)

The Save Results Options dialog box allows you to choose the results you want to save. There are four options:  Save Counts, Save Labels, Save Mean c, Save Sigma.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (c Chart Analysis)

The Analysis Summary contains information about the c Chart, subgroups, and estimated statistics.  For a Control to Standard study, the summary statistics are also displayed.

c Chart

Displays values based on the number of defects per item.  Values are shown for the Centerline, which represents the average number of defects per item when a process is in control, and the values for the UCL and the LCL.  It also displays the number of values that fall beyond those limits.

If you choose a one-sided control chart, that is, you choose either an UCL or a LCL, the corresponding line for the control limit is blank.

Observation Information

Displays the number of observations used for the analysis.

Estimated

Displays the estimated mean c value and process sigma.

Standard

Displays the mean c value you enter on the c Chart Options dialog box when you perform a Control to Standard study.  It also displays the standard sigma.

To choose options for the analysis, use the c Chart Options dialog box.


c Chart Report (c Chart Analysis)

The c Chart Report tabular option displays a report of the number of defects per item.

To choose options for the report, use the c Chart Report Options dialog box.


c Chart (c Chart Analysis)

The c Chart graphical option displays a c Chart with control limits based on the average number of defects per item and the estimate of sigma.


Moving Average Chart Analysis Dialog Box

A moving average is a way to smooth a curve that represents the data.  The individual observations are replaced by the mean of each observation and the observations on either side of it.  For example, if a variable has 10 observations, the program averages the first five observations.  A second subgroup is created by dropping the first observation and adding the sixth, then calculating the average.  The second observation drops the third subgroup, adds the seventh, and calculates the average; and so on.

You use the Moving Average Chart analysis to control current processes.  However, a Moving Average Chart incorporates the past history of the process into the charted points.  The chart is particularly useful in production lines that take some time to produce a single item.  By adding each new item to the subgroup as the item is produced, you always have an up-to-date picture of the process.

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

Data

Subgroup Numbers or Size

Subgroups Labels

Select

Sort

See also

Using the Moving Average Chart Analysis

Moving Average Chart Options

MA Chart Report Options

Process Capability Indices Options

Moving Average Control Chart Options

Control Chart Options

Tolerance Chart Options


Moving Average Chart Tabular Options Dialog Box

Allows you to choose tabular options for the Moving Average Chart analysis.

Analysis Summary (Moving Average Chart)

MA Chart Report (Moving Average Chart Analysis)

Capability Indices (Moving Average Chart)


Analysis Summary (Moving Average Chart)

The Analysis Summary contains five areas of information:  The Moving Average Chart, Range Chart, subgroups, and estimated statistics.  For a Control to Standard study, the program also displays the standard statistics.

Moving Average Chart

Displays the value for the Centerline, which represents the average value for the quality characteristic when a process is in control, and the values for the Upper Control Limit (UCL) and the Lower Control Limit (LCL).  The summary also displays the number of values that fall beyond those limits.  A process is in control if all the values fall within the control limits.

Range Chart

Displays the values for the UCL, Centerline, and LCL.  The sigma values are used to calculate the UCL and LCL.  The summary also lists the number of subgroups that are beyond the control limits.  A process is in control if all the values fall within the control limits.

Subgroup Information

Displays the number of subgroups used for the analysis, the size of the subgroups or the average size if the subgroups have different sizes, and the number of subgroups you want to exclude from the study.

Estimated

Displays the values for the estimated process mean, process sigma, and mean range.  When the sizes of the subgroup are not equal, the average size is used to calculate these values.

Standard

Displays the process mean and process sigma you enter on the Moving Average Chart Options dialog box when you perform a Control to Standard study.  It also displays the value for the standard mean range.

To choose options for the analysis, use the Moving Average Chart Options dialog box.


MA Chart Report (Moving Average Chart Analysis)

The MA Chart Report tabular option displays a report of the subgroups and their corresponding statistics for the Moving Average and Range Charts.

To choose options for the report, use the MA Chart Report Options dialog box.


Moving Average Chart Options Dialog Box

Allows you to:

•	choose the type of study you want to perform

•	enter the number of observations that will be used to calculate each point on the chart

•	choose the location of the control limits on the MA chart

•	choose the location of the control limits on the Range Chart

•	choose the standard process parameters

•	choose the subgroup you want to exclude from the analysis.

Type of Study

Order

MA Control Limits

Range Control Limits

Control to Standard

Exclude... Command


Order

Enter the number of observations that will be used to calculate each point on the Moving Average Chart.  Enter an integer greater than 1 and less than the number of subgroups; the default is 5.


MA Control Limits

Allows you to choose the location of the control limits on the Moving Average Chart.

Upper Sigma

Enter a value for the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10; the default is 3.0.

Lower Sigma

Enter a value for the multiple of sigma that will be used to calculate the LCL.  Enter a numeric value greater than or equal to -10 and less than or equal to 0; the default is -3.0.


MA Chart Report Options Dialog Box

Allows you to choose the subgroups you want to include in the MA Chart Report.

Display


Moving Average Chart Graphical Options Dialog Box

Allows you to choose graphical options for the Moving Average Chart analysis.

Moving Average Chart (Moving Average Chart Analysis)

Range Chart (Moving Average Chart Analysis

Tolerance Chart (Moving Average Chart Analysis)

OC Curve

ARL Curve (Moving Average Chart Analysis)


Moving Average Chart (Moving Average Chart Analysis)

The Moving Average Chart graphical option displays a plot of the moving averages for the observations.

A process is out of control if points are shown outside the control limits, or if points shown within the control limits are arranged in a nonrandom sequence.

To choose options for the plot, use the Moving Average Control Chart Options dialog box.


Moving Average Control Chart Options Dialog Box

Allows you to indicate the type of data that will appear on the plot and to indicate if you want the X-axis labels rotated.

Plot Original Data

Decimal Places for Limits


Plot Original Data

Indicate if subgroup data should appear on the plot.


Save Results Options Dialog Box (Moving Average Chart)

The Save Results Options dialog box allows you to choose the results you want to save.  There are six options: Moving Averages, Ranges, Sizes, Labels, Process Mean, and Process Sigma.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (Moving Average Chart Analysis)

The Analysis Summary contains five areas of information: the Moving Average Chart, Range Chart, subgroups, and estimated statistics.  For a Control to Standard study, the standard statistics also display.

Moving Average Chart

Displays the value for the Centerline, which represents the average value for the quality characteristic when a process is in control, and the values for the Upper Control Limit (UCL) and the Lower Control Limit (LCL).  The summary also displays the number of values that fall beyond those limits.  A process is in control if all the values fall within the control limits.

Range Chart

Displays the values for the UCL, Centerline, and LCL.  The sigma values are used to calculate the UCL and LCL.  The summary also lists the number of subgroups that are beyond the control limits.  A process is in control if all the values fall within the control limits.

Subgroup Information

Displays the number of subgroups used for the analysis, the size of the subgroups or the average size if the subgroups have different sizes, and the number of subgroups you want to exclude from the study.

Estimated

Displays the values for the estimated process mean, process sigma, and mean range.  When the sizes of the subgroup are not equal, the average size is used to calculate these values.

Standard

Displays the process mean and process sigma you enter on the Moving Average Chart Options dialog box when you perform a Control to Standard study.  It also displays the value for the standard mean range.

To choose options for the analysis, use the Moving Average Chart Options dialog box.


MA Chart Report (Moving Average Chart Analysis)

The MA Chart Report tabular option displays a report of the subgroups and their corresponding statistics for the Moving Average and Range Charts.


Moving Average Chart (Moving Average Chart Analysis)

The Moving Average Chart graphical option displays a plot of the moving averages of the observations.


Exponentially Weighted Moving Average (EWMA) Chart Analysis Dialog Box

The Exponentially Weighted Moving Average (EWMA) Chart analysis plots exponentially weighted moving averages that are the weighted average of the current observation and the estimate of the previous observation.

To calculate the weighted average, the current observation is multiplied by lambda and the estimate of the previous observation is multiplied by 1 — lambda.

The EWMA Chart is a tool useful for detecting small, persistent drifts in the process average; it provides a forecast that shows where the process average may fall the next sampling time.  The EWMA Chart is not sensitive to data that are non-normal.

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

Observations

Subgroup Statistics

Subgroup Numbers or Size

Subgroups Labels

Select

Sort

See also

Using the EWMA Chart Analysis

EWMA Chart Options

EWMA Chart Report Options

Process Capability Indices Options

EWMA Control Chart Options

Tolerance Chart Options


EWMA Chart Tabular Options Dialog Box

Allows you to choose tabular options for the EWMA Chart analysis.

Analysis Summary (EWMA Chart Analysis)

EWMA Chart Report (EWMA Chart Analysis)

Capability Indices (EWMA Chart Analysis)


Analysis Summary (EWMA Chart Analysis)

The Analysis Summary contains five areas of information about the EWMA Chart, Range Chart, subgroups, and estimated statistics.  For Control to Standard study, the Summary Statistics are also displayed.

EWMA Chart Report

Displays the value for the Centerline, which represents the average value for the quality characteristic when a process is in control.  It also shows the values for the Upper Control Limit (UCL) and the Lower Control Limit (LCL), and the number of values that fall beyond these values.  A process is in control if all the values fall within the control limits.

Range Chart

Displays the values for the UCL, Centerline, and the LCL that the program uses in the analysis.  The sigma values are used to calculate the UCL and the LCL.  The summary also lists the number of subgroups that are beyond the control limits.

A process is in control if all the values fall within the control limits.

If you choose a one-sided control chart, that is, you do not choose a UCL or an LCL, the corresponding line for the control limit is blank.  If the size of the subgroups differs, the average size is used to calculate the control limit.

Subgroup Information

Displays the number of subgroups used for the analysis, the size of the subgroups or the average size if the size of the subgroups differ, and the number of subgroups you want to exclude from the study.

Estimated

Displays the estimated values for the process mean, process sigma, and mean range.  When the size of the subgroups are not equal, the average subgroup size is used to calculate these values.

Standard

Displays the values for the process mean and sigma you enter on the EWMA Chart Options dialog box when you perform a Control to Standard study.  It also displays the values for the standard mean range.

To choose options for the analysis, use the EWMA Chart Options dialog box.


EWMA Chart Report (EWMA Chart Analysis)

The EWMA Chart Report tabular option displays a report of the EWMA and Range values for each subgroup.

To choose options for the report, use the EWMA Chart Report Options dialog box.


EWMA Chart Options Dialog Box

Allows you to choose the subgroups that will be included in the analysis.

Type of Study

Lambda

EWMA Control Limits

Range Control Limits

Control to Standard

Exclude... Command


Lambda

Enter a value for the weighting factor that will be applied to each new observation in the moving average calculation.  A larger value of lambda gives more weight to more recent subgroups.  Enter a value greater than or equal to .001 and less than or equal to 1; the default is 0.1


EWMA Control Limits

Enter values for the location of the control limits on the EWMA Chart.

Upper Sigma

Enter a value for the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10; the default is 3.0.

Lower Sigma

Enter a value for the multiple of sigma that will be used to calculate the LCL.  Enter a numeric value greater than or equal to -10 and less than or equal to 0; the default is -3.0.


EWMA Chart Report Options Dialog Box

Allows you to:

•	choose the type of study you want to perform

•	enter the weighting factor

•	choose the location of the control limits on the EWMA Chart

•	choose the location for the control limits on the Range Chart

•	choose the parameters for the study

•	choose the subgroups you want to exclude from the analysis.

Display


EWMA Chart Graphical Options Dialog Box

Allows you to choose graphical options for the EWMA Chart analysis.

EWMA Chart (EWMA Chart Analyis)

Range Chart (EWMA Chart Analysis)

Tolerance Chart (EWMA Chart Analysis)

OC Curve

ARL Curve


EWMA Chart (EWMA Chart Analyis)

The EWMA Chart graphical option displays a plot of the data.  The process is out of control if points are shown outside the control limits, or if points shown within the control limits are arranged in a nonrandom sequence.

To choose options for the plot, use the EWMA Control Chart Options dialog box.


EWMA Control Chart Options Dialog Box

Allows you to choose the type of data that will appear on the plot, and indicate if you want to rotate the X-axis labels.

Plot Original Data

Decimal Places for Limits


Save Results Options Dialog Box (EWMA Chart Analysis)

The Save Results Options dialog box allows you to choose the results you want to save.  There are six options: EWMAs, Ranges, Sizes, Labels, Process Mean, and Process Sigma.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (EWMA Chart Analysis)

The Analysis Summary contains five areas of information about the EWMA Chart, Range Chart, subgroups, and estimated statistics.  For Control to Standard study, the Summary Statistics are also displayed.

EWMA Chart Report

Displays the value for the Centerline, which represents the average value for the quality characteristic when a process is in control.  The report also shows the values for the Upper Control Limit (UCL) and the Lower Control Limit (LCL), and the number of values that fall beyond these values.  A process is in control if all the values fall within the control limits.

Range Chart

Displays the values for the UCL, Centerline, and the LCL that are used in the analysis.  The sigma values are used to calculate the UCL and the LCL.  The summary also lists the number of subgroups that are beyond the control limits.

A process is in control if all the values fall within the control limits.

If you choose a one-sided control chart, that is, you do not choose a UCL or an LCL, the corresponding line for the control limit is blank.  If the size of the subgroups differs, the average size is used to calculate the control limit.

Subgroup Information

Displays the number of subgroups used for the analysis, the size of the subgroups or the average size if the size of the subgroups differ, and the number of subgroups you want to exclude from the study.

Estimated

Displays the estimated values for the process mean, process sigma, and mean range.  When the size of the subgroups are not equal, the average subgroup size is used to calculate these values.

Standard

Displays the values for the process mean and sigma you enter on the EWMA Chart Options dialog box when you perform a Control to Standard study.  It also displays the values for the standard mean range.

To choose options for the analysis, use the EWMA Chart Options dialog box.


EWMA Chart Report (EWMA Chart Analysis)

The EWMA Chart Report tabular option displays a report of the EWMA and Range values for each subgroup.


EWMA Chart (EWMA Chart Analysis)

The EWMA Chart graphical option displays a plot of the data.

To choose options for the chart, use the EWMA Control Chart Options dialog box.


Cumulative Sum (CuSum) Chart Analysis Dialog Box

The Cumulative Sum (CuSum) Chart analysis produces a time-weighted chart based on all the data instead of only the last few samples.  This analysis plots the cumulative sums of the deviations for the sample values from the target value.

You use the CuSum Chart analysis to maintain current control of a process.  An upward or downward trend in the data indicates that the process mean has shifted and the process is out of control.  The chart allows you to detect sudden and persistent changes in the process average more rapidly than variables control charts do.  By detecting the change in the process sooner, you can adjust the process before large variations occur.

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

Observations

Subgroup Statistics

Subgroup Numbers or Size

Subgroups Labels

Select

See also

Using the Cumulative Sum (CuSum) Chart Analysis

CuSum Chart Options

CuSum Chart Report Options

CuSum Chart Options


CuSum Chart Analysis Tabular Options Dialog Box

Allows you to choose tabular options for the CuSum Chart analysis.

Analysis Summary (CuSum Chart Analysis)

CuSum Chart Report (CuSum Chart Analysis)


Analysis Summary (CuSum Chart Analysis)

The Analysis Summary contains five areas of information about the CuSum Chart, Range Chart, subgroups, and estimated statistics.  For a Control to Standard study, the Summary Statistics are also displayed.

CuSum Chart

Displays the number of standard deviations from the control mean at which a shift in the process is detected.  The summary also displays the alpha and beta values that represent the risk of having a Type I or a Type II error, and shows the sample number at which the program places the V-mask on the CuSum Chart.

Range Chart

Displays the value for the Centerline, which represents the average value for the quality characteristic when a process is in control, and the values for the Upper Control Limit (UCL), and the Lower Control Limit (LCL).  It also displays the number of values that fall beyond these limits.  A process is in control if all the values fall within the control limits.

Subgroup Information

Displays the number of subgroups used for the analysis and the size of the subgroups or the average size if the size of the subgroups differ.

Estimated

Displays the values for the estimated process mean, process sigma, and the mean range.  When the sizes of the subgroups are not equal, the average size is used to calculate the values.

Standard

Displays the values for the process mean and sigma you enter on the CuSum Chart Options dialog box when you perform a Control to Standard study.  It also displays the values for the standard mean range.

To choose options for the analysis, use the CuSum Chart Options dialog box.


CuSum Chart Report (CuSum Chart Analysis)

The CuSum Chart Report tabular option displays a report of the CuSum and range values for each subgroup.

To choose options for the report, use the CuSum Chart Report Options dialog box.


CuSum Chart Options Dialog Box

Allows you to:

•	choose the type of study you want to perform

•	choose the number of standard deviations from the control mean

•	choose the subgroup number at which you want to place the V-mask

•	choose the location of the control limits on the Range Chart

•	choose the standard process parameters

•	choose the subgroups you want to exclude from the analysis.

Type of Study

Detect n Sigma Shift

Place Mask at

CuSum Chart

Range Control Limits

Control to Standard

Exclude... Command


Detect n Sigma Shift

Choose the number of standard deviations from the control mean at which a shift can be detected.  The Alpha and Beta text boxes determine the confidence and power for the CuSum Chart.  Enter any numeric value greater than 0 and less than or equal to 10.


Place Mask At

Choose the subgroup number at which the V-mask will be placed on the chart.


CuSum Chart

Enter the values that will be used for the V-mask on the CuSum Chart.

Alpha

Enter a value for the Type I error that will be used for the alpha risk.  The alpha risk determines the probability of declaring a proces out of control when in fact it is not.  Enter a numeric percentage greater than 0 and less than or equal to 50; the default is 5 percent.

Beta

Enter a value for the Type II error that will be used for the beta risk.  The beta risk determines the probability of declaring a process in control when in fact it is not.  Enter a numeric percentage greater than 0 and less than or equal to 50; the default is 5 percent.


CuSum Chart Report Options Dialog Box

Allows you to choose the subgroups that will be included in the CuSum Chart Report.

Display


CuSum beyond Limits

Lists the subgroups or observations that are outside the V-mask.  The first subgroup that falls outside the V-mask indicates a shift in the process.


CuSum Chart Analysis Graphical Options Dialog Box

Allows you to choose graphical options for the CuSum Chart analysis.

Cumulative Sum Chart (CuSum Chart Analysis)

Range Chart (CuSum Chart Analysis)

ARL Curve (CuSum Chart Analysis)


Cumulative Sum Chart (CuSum Chart Analysis)

The Cumulative Sum Chart graphical option displays a plot of the data.

A V-mask is placed at the first point that a process is detected to be out of control — where the CuSum line crosses the arm of the V-mask.  This indicates you should search for an assignable cause.


Save Results Options Dialog Box (CuSum Chart Analysis)

The Save Results Options dialog box allows you to choose the results you want to save.  There are six options: Cumulative Sum, Ranges, Sizes, Labels, Process Mean, and Process Sigma.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (CuSum Chart Analysis)

The Analysis Summary contains five areas of information about the CuSum Chart, Range Chart, subgroups, and estimated statistics.  For a Control to Standard study, the Summary Statistics are also displayed.

CuSum Chart

Displays the number of standard deviations from the control mean at which a shift in the process is detected.  The summary also displays the alpha and beta values that represent the risk of having a Type I or a Type II error, and shows the sample number at which the V-mask is placed on the CuSum Chart.

Range Chart

Displays the value for the Centerline, which represents the average value for the quality characteristic when a process is in control, and the values for the Upper Control Limit (UCL), and the Lower Control Limit (LCL).  It also displays the number of values that fall beyond these limits.  A process is in control if all the values fall within the control limits.

Subgroup Information

Displays the number of subgroups used for the analysis and the size of the subgroups or the average size if the size of the subgroups differ.

Estimated

Displays the values for the estimated process mean, process sigma, and the mean range.  When the sizes of the subgroups are not equal, the average size is used to calculate the values.

Standard

Displays the values for the process mean and sigma you enter on the CuSum Chart Options dialog box when you perform a Control to Standard study.  It also displays the values for the standard mean range.

To choose options for the analysis, use the CuSum Chart Options dialog box.


CuSum Chart Report (CuSum Chart Analysis)

The CuSum Chart Report tabular option displays a report of the CuSum and range values for each subgroup.

To choose options for the report, use the CuSum Chart Report Options dialog box.


CuSum Chart (CuSum Chart Analysis)

The Cumulative Sum Chart graphical option displays a Cumulative Sum Chart. A V-mask is placed at the first point that it is detected that a process is out of control — where the CuSum line crosses the arm of the V-mask.  This indicates you should search for an assignable cause.


Moving Average Individuals Chart Analysis Dialog Box

The Moving Average (MA) Individuals Chart analysis creates a time-weighted chart that allows you to analyze the moving averages of individual observations.  An MR(2) Chart of moving ranges is also created for two successive observations at one time.

When you use this analysis you first perform an Initial Study to estimate the control limits, which sets a standard you use to measure the process.  You then perform a Control to Standard study and enter the control limits or parameters to determine if the process meets the standard.

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

Observations

Labels

Select

Sort

See also

Using the Moving Average Individuals Chart Analysis

MA Individuals Chart Options

MA Individuals Chart Report Options

Process Capability Indices Options

Moving Average Control Chart Options

Control Chart Options


MA Individuals Chart Analysis Tabular Options Dialog Box

Allows you to choose tabular options for the MA Individuals Chart analysis.

To choose options for the analysis, use the MA Individuals Chart Options dialog box.

Analysis Summary (MA Individuals Chart Analysis)

MA Individuals Chart Report (MA Individuals Chart Analysis)

Capability Indices (MA Individuals Chart Analysis)


Analysis Summary (MA Individuals Chart Analysis)

The Analysis Summary contains five areas of information: the Moving Average Chart, MR(2) Chart, observations, and estimated statistics.  For a Control to Standard study, the Summary Statistics are also displayed.

Moving Average Chart

Displays the value for the Centerline, which represents the average value for the quality characteristic when a process is in control.  It also displays the values for the Upper Control Limit (UCL), the Lower Control Limit (LCL), and the number of values that fall beyond these limits.  A process is in control if all the values fall within the control limits.

MR(2) Chart

Displays the values for the UCL, Centerline, and LCL that are used in the analysis.  The report also displays the sigma values used to calculate the UCL and the LCL, and lists the number of observations that are beyond the control limits.  A process is in control if all the values fall within the control limits.

Observation Information

Displays the number of observations used in the analysis.

Estimated

Displays the values for the estimated process mean, process sigma, and mean MR(2).

Standard

Displays the values for the process mean and sigma you entered on the MA Individuals Chart Options dialog box.  It also displays the value for the standard mean MR(2).

To choose options for the analysis, use the MA Individuals Chart Options dialog box.


MA Individuals Chart Report (MA Individuals Chart Analysis)

The MA Individuals Chart Report tabular option displays a report of the observation numbers and their corresponding statistics for the Moving Average Chart and the MR(2) Chart.

To choose options for the report, use the MA Individuals Chart Report Options dialog box.


MA Individuals Chart Options Dialog Box

Allows you to:

•	choose the type of study you want to perform

•	enter the number of observations that will be used

•	choose the location of the control limits on the Moving Average Chart

•	choose the location of the control limits on the MR(2) Chart

•	choose the standard process parameters

•	choose the observations you want to exclude from the analysis.

Type of Study

Order

MA Control Limits

MR(2) Control Limits

Control to Standard

Exclude... Command


MA Individuals Chart Report Options

Allows you to choose the observations that will be included in the MA Individuals Chart Report.

Display


MA Individuals Chart Analysis Graphical Options Dialog Box

Allows you to choose graphical options for the MA Individuals Chart analysis.

Moving Average Chart (MA Individuals Chart Analysis)

MR(2) Chart (MA Individuals Charts Analysis)

OC Curve

ARL Curve


Save Results Options Dialog Box (MA Individuals Chart Analysis)

The Save Results Options dialog box allows you to choose the results you want to save.  There are six options: Moving Averages, Moving Ranges, Labels, Process Mean, Included Observations, and Process Sigma.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (MA Individuals Chart Analysis)

The Analysis Summary contains five areas of information: the Moving Average Chart, MR(2) Chart, observations, and estimated statistics.  For a Control to Standard study, the Summary Statistics are also displayed.

Moving Average Chart

Displays the value for the Centerline, which represents the average value for the quality characteristic when a process is in control.  It also displays the values for the Upper Control Limit (UCL), the Lower Control Limit (LCL), and the number of values that fall beyond these limits.  A process is in control if all the values fall within the control limits.

MR(2) Chart

Displays the values for the UCL, Centerline, and LCL that are used in the analysis.  It also displays the sigma values that were used to calculate the UCL and the LCL, and lists the number of observations that are beyond the control limits.  A process is in control if all the values fall within the control limits.

Observation Information

Displays the number of observations used in the analysis.

Estimated

Displays the values for the estimated process mean, process sigma, and mean MR(2).

Standard

Displays the values for the process mean and sigma you entered on the MA Individuals Chart Options dialog box.  It also displays the value for the standard mean MR(2).

To choose options for the analysis, use the MA Individuals Chart Options dialog box.


MA Individuals Chart Report (MA Individuals Chart Analysis)

The MA Individuals Chart Report tabular option displays a report of the observation numbers and their corresponding statistics for the Moving Average Chart and the MR(2) Chart.

To choose options for the report, use the MA Individuals Chart Report Options dialog box.


EWMA Individuals Chart Analysis Dialog Box

The EWMA Individuals Chart analysis creates a time-weighted chart that allows you to analyze the exponentially weighted moving averages of individual observations.

The analysis is insensitive to data that are not normally distributed, making this an ideal tool for analyzing individual data (subgroup size = 1).

When you use this analysis you first perform an Initial Study to estimate the control limits, which sets a standard you use to measure the process.  You then perform a Control to Standard Study and enter the control limits and parameters to determine if the process meets the standard.

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis options.

Observations

Labels

Select

Sort

See also

Using the EWMA Individuals Chart Analysis

EWMA Individuals Chart Options

EWMA Individuals Chart Report Options

Process Capability Indices Options

EWMA Control Chart Options

Control Chart Options


EWMA Individuals Chart Analysis Tabular Options Dialog Box

Allows you to choose tabular options for the EWMA Individuals Chart analysis.

To choose options for the analysis, use the EWMA Individuals Chart Options dialog box.

Analysis Summary (EWMA Individuals Chart)

EWMA Individuals Chart Report (EWMA Individuals Chart Analysis)

Capability Indices (EWMA Individuals Chart Analysis)


Analysis Summary (EWMA Individuals Chart Analysis)

The Analysis Summary contains five areas of information about the EWMA Chart, MR(2) Chart, observations, and estimated statistics.  For a Control to Standard study, the Summary Statistics are also displayed.

EWMA Chart

Displays the value for the Centerline, which represents the average value for the quality characteristic when a process is in control.  It also displays the values for the Upper Control Limit (UCL), the Lower Control Limit (LCL), and the number of values that fall within these control limits.

MR(2) Chart

Displays the values for the UCL, Centerline, and LCL that are used in the analysis.  The sigma values are used to calculate the UCL and LCL.  The summary also lists the number of observations that are beyond the control limits.  Like the EWMA Chart, a process is in control if all the values fall within the control limits.

Observation Information

Displays the number of observations used in the analysis.

Estimated

Displays the values for the estimated process mean, process sigma, and the mean MR(2).

Standard

Displays the values for the process mean and sigma you enter on the EWMA Individuals Chart Options dialog box.  It also displays the value for the standard mean MR(2).

To choose options for the analysis, use the EWMA Individuals Chart Options dialog box.


EWMA Individuals Chart Report (EWMA Individuals Chart Analysis)

The EWMA Individuals Chart Report tabular option displays a report of the EWMA and MR(2) values.

To choose options for the report, use the EWMA Individuals Chart Options dialog box.


EWMA Individuals Chart Options Dialog Box

Allows you to:

•	choose the type of study that will be performed

•	enter the weighting factor

•	choose the location of the control limits on the EWMA Chart

•	choose the location of the control limits on the MR(2) Chart

•	choose the standard process parameters

•	choose the observations that will be excluded from the analysis.

Type of Study

Lambda

EWMA Control Limits

MR(2) Control Limits

Control to Standard

Exclude... Command


EWMA Individuals Chart Report Options
EWMA Individuals Chart Report Options Dialog Box

Allows you to choose the observations the program will include in the EWMA Individuals Chart Report.

Display


EWMA Individuals Chart Analysis Graphical Options Dialog Box

Allows you to choose graphical options for the EWMA Individuals Chart analysis.

EWMA Chart (EWMA Individuals Chart Analysis)

MR(2) Chart (EWMA Individuals Chart Analysis)

OC Curve)

ARL Curve


Save Results Options Dialog Box (EWMA Individuals Chart Analysis)

The Save Results Options dialog box allows you to choose the results you want to save.  There are five options: EWMAs, Moving Ranges, Labels, Process Mean, Included Observations, and Process Sigma.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (EWMA Individuals Chart Analysis)

The Analysis Summary contains five areas of information about the EWMA Chart, MR(2) Chart, observations, and estimated statistics.  For a Control to Standard study, the Summary Statistics are also displayed.

EWMA Chart

Displays the value for the Centerline, which represents the average value for the quality characteristic when a process is in control.  It also displays the values for the Upper Control Limit (UCL), the Lower Control Limit (LCL), and the number of values that fall within these control limits.

MR(2) Chart

Displays the values for the UCL, Centerline, and LCL that are used in the analysis.  The sigma values are used to calculate the UCL and LCL.  The summary also lists the number of observations that are beyond the control limits.  Like the EWMA Chart, a process is in control if all the values fall within the control limits.

Observation Information

Displays the number of observations used for the analysis.

Estimated

Displays the values for the estimated process mean, process sigma, and the mean MR(2).

Standard

Displays the values for the process mean and sigma you enter on the EWMA Individuals Chart Options dialog box.  It also displays the value for the standard mean MR(2).

To choose options for the analysis, use the EWMA Individuals Chart Options dialog box.


EWMA Individuals Chart Report (EWMA Individuals Chart Analysis)

The EWMA Individuals Chart Report graphical option displays a report of the EWMA and MR(2) values.


CuSum Individuals Chart Analysis Dialog Box

The Cumulative Sum (CuSum) Individuals Chart analysis produces a time-weighted chart based on all the data, not just the last few samples.

This analysis plots the cumulative sums of the deviations of the sample values from the target value.  You use the analysis to maintain current control of a process.  An upward or downward trend in the data indicates that the process mean has shifted and the process is out of control.

You can detect sudden or persistent changes in the process average more rapidly than you can by using variables control charts.  By detecting the change in the process sooner, you can adjust the process before large variations occur.

Because you use the analysis when the subgroup size is 1, this quality-control tool is particularly useful in chemical and process industries where individual items may be difficult to form into subgroups.

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

Observations

Labels

Select

Sort

See also

Using the Cumulative Sum Individuals Chart Analysis

CuSum Individuals Chart Options

CuSum Individuals Chart Report Options

Control Chart Options


CuSum Individuals Chart Analysis Tabular Options Dialog Box

Allows you to choose tabular options for the CuSum Individuals Chart analysis.

Analysis Summary (CuSum Individuals Chart Analysis)

CuSum Individuals Chart Report (CuSum Individuals Chart Analysis)


Analysis Summary (CuSum Individuals Chart Analysis)

The Analysis Summary contains five areas of information about the CuSum Chart, MR(2) Chart, observations, and estimated statistics.  For a Control to Standard study, the Summary Statistics are also displayed.

CuSum Chart

Displays the number of standard deviations from the control mean at which a shift is detected in a process.  The summary displays the values for alpha and beta that represent the risk of a Type I or a Type II error occurring.  It also displays the sample number at which the V-mask is placed on the chart.

MR(2) Chart

Displays the values for the UCL, Centerline, and LCL that are used in the analysis.  The sigma values are used to calculate the UCL and LCL.  The summary also lists the number of observations that are beyond the control limits.  Unlike the CuSum Chart, a process is in control if all the values fall within the control limits.

Observation Information

Displays the number of observations used in the analysis.

Estimated

Displays the values for the estimated process mean, process sigma, and the mean MR(2).

Standard

Displays the values for the process mean and sigma you enter on the CuSum Individuals Chart Options dialog box.  The report also displays the values for the standard mean MR(2) and the mean deviation.

To choose options for the analysis, use the CuSum Individuals Chart Options dialog box.


CuSum Individuals Chart Report (CuSum Individuals Chart Analysis)

The CuSum Individuals Chart Report tabular option displays a report of the observation numbers and their corresponding statistics for the CuSum Chart and the MR(2) Chart.

To choose options for the report, use the CuSum Individuals Chart Report Options dialog box.


CuSum Individuals Chart Options Dialog Box

Allows you to:

•	choose the type of study that will be performed

•	choose the number of standard deviations from the control mean

•	choose the sample number at which the V-mask will be placed

•	enter the values that will be used for the V-mask on the CuSum Chart

•	choose the location of the control limits on the MR(2) Report

•	choose the standard process parameters

•	choose the observations that will be excluded from the analysis.

Type of Study

Detect n Sigma Shift

Place Mask at

CuSum Chart

MR(2) Control Limits

Control to Standard

Exclude... Command


CuSum Individuals Chart Report Options

Allows you to choose the observations that will be included in the CuSum Chart Report.

Display


CuSum Individuals Chart Analysis Graphical Options Dialog Box

Allows you to choose the graphical options for the CuSum Individuals Chart analysis.

Cumulative Sum Chart (CuSum Individuals Chart Analysis)

MR(2) Chart (CuSum Individuals Chart Analysis)

ARL Curve (CuSum Individuals Chart Analysis)


Save Results Options Dialog Box (CuSum Individuals Chart)

The Save Results Options dialog box allows you to choose the results you want to save.  There are five options: Cumulative Sum, Moving Ranges, Labels, Process Mean, and Process Sigma.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (CuSum Individuals Chart Analysis)

The Analysis Summary contains five areas of information about the CuSum Chart, MR(2) Chart, observations, and estimated statistics.  For a Control to Standard study, the Summary Statistics are also displayed.

CuSum Chart

Displays the number of standard deviations from the control mean at which the program detects a shift in a process.  The summary displays the values for alpha and beta that represent the risk of a Type I or a Type II error occurring.  It also displays the sample number at which the V-mask is placed on the chart.

MR(2) Chart

Displays the values for the UCL, Centerline, and LCL that are used in the analysis.  The sigma values are used to calculate the UCL and LCL.  The summary also lists the number of observations that are beyond the control limits.  Unlike the CuSum Chart, a process is in control if all the values fall within the control limits.

Observation Information

Displays the number of observations used in the analysis.

Estimated

Displays the values for the estimated process mean, process sigma, and the mean MR(2).

Standard

Displays the values for the process mean and sigma you enter on the CuSum Individuals Chart Options dialog box.  It also displays the values for the standard mean MR(2) and the mean deviation.

To choose options for the analysis, use the CuSum Individuals Chart Options dialog box.


CuSum Individuals Chart Report (CuSum Individuals Chart Analysis)

The CuSum Individuals Chart Report tabular option for the CuSum Individuals Chart Analysis displays a report of the CuSum and MR(2) values.


Gage R&R Data Setup Dialog Box

The Gage R&R Data Setup feature lets you build a data file to use with one of the three Gage R&R methods: Average and Range, ANOVA, or Range.

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

Number of Operators

Number of Parts

Number of Trials

Randomize Trials

Default Operator Names

See also

Using the Gage R&R Analysis

Average and Range Method

Gage Report

Average and Range Method Options

Operator and Part Plot Options

Box-and-Whisker Plot Options

ANOVA Method

ANOVA Method Options

Interaction Options

Range Method

Range Method Options


Number of Operators

Enter the number of operators who will collect data for the analysis.  Enter an integer between 2 and 18.


Number of Parts

Enter the number of parts each operator will measure.  Enter an integer greater than 1.


Number of Trials

Enter the number of times each operator will measure each part.  Enter an integer greater than 1.


Randomize Trials

Indicate if the trials should be randomized for each operator.  The default is nonrandomized.


Default Operator Names

Indicate that the default names should be used for the operators.  Alternatively, it allows you to enter names.  The default is using the names already created.

If you want to enter names for the operators, dechoose the option; the Operator Names Options dialog box displays when you click OK.


Gage R&R Data Setup Tabular Options Dialog Box

Allows you to choose tabular options for the Gage R&R Data Setup portion of the analysis.

Analysis Summary (Data Setup)


Analysis Summary (Data Setup)

The Analysis Summary displays the number of operators, parts, and trials.  It shows if the test runs were generaated in a random or nonrandom order, and if you used default names or names you supplied for the operators.

The report also shows the setup for the operators, parts, and trials.  Use this setup to create variables for the analysis.


Operator Names Options Dialog Box

Allows you to enter labels in the text boxes for the names of the operators.  If you do not enter names, the program enters letters for the operator names.

To access this dialog box, deselect the Default Operator Names option on the Gage R&R Analysis Data Setup dialog box.


Save Results Options Dialog Box (Data Setup)

The Save Results Options dialog box allows you to choose the results you want to save.  There are four choices: Operators, Parts, Trials, and Measurements.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (Data Setup)

The Analysis Summary displays the number of operators, parts, and trials.  It shows if the test runs were generated in a random or nonrandom order, and if default names or names you supplied were used for the operators.

The report also shows the setup for the operators, parts, and trials.


Average and Range Method Dialog Box

The Average and Range Method creates a full gage repeatability and reproducibility analysis involving multiple operators, parts, and replications.  This method allows you estimate both repeatability and reproducibility.

To use this method, you must set up variables that contain operator names, part numbers, trial numbers, and measurements.  The design must be balanced; that is, each operator must measure each part the same number of times.

To choose options for this method, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

Operators

Parts

Trials

Measurements

Select

Sort

See also

Using the Average and Range Method

Using Gage R&R Data Setup


Operators

Enter the operator codes that will be used for each observation (measurement).

The number of values should be the same as the number of values in the Parts, Trials, and Measurements text boxes.  You can enter numbers or characters.


Parts

Enter the part numbers that will be used for each observation (measurement).

The number of values should be the same as the number of values in the Operators, Trials, and Measurements text boxes.


Trials

Enter the numeric values that indicate the trial numbers for each measurement.

The number of values should be the same as the number of values in the Operators, Parts, and Measurements text boxes.


Measurements

Enter the numeric measurements that will be used for each combination of operator, part, and trial.

The number of values should be the same as the number of variables in the Operators, Parts, and Trials text boxes.


Average and Range Method Tabular Options Dialog Box

Allows you to choose tabular options for the Average and Range Method.

Analysis Summary (Average and Range Method)

Gage Report (Average and Range Method)


Analysis Summary (Average and Range Method)

The Analysis Summary displays a summary of the analysis.  The summary includes the following information.

Variables

Displays the names of the variables that contain the values for the operators, parts, and trials, as well as the name of the variable that contains the measurements for each combination of values for the operators, parts, and trials.

Operators - The number of operators in the study.

Parts - The number of parts in the study.

Trials - The number of trials in the study

Average Range

Contains the values for the average range for all the trials the same operator repeats on the same part.

Range of X-Bars

Contains the values for the maximum difference between the averages of the operators.

Estimated Sigma

Displays values for the standard deviation of the measures of repeatability and reproducibility as well as the combined values for repeatability and reproducibility.

Estimated Variance

Displays values for the measures of repeatability and reproducibility as well as the combined values for repeatability and reproducibility.

Percent of Total

Displays values for the amount of the total estimated variance that can be attributed to repeatability and reproducibility.

To choose options for the analysis, use the Average and Range Method Options dialog box.


Gage Report (Average and Range Method)

The Gage Report tabular option displays a report that contains the values for the Measurement Unit Analysis and Study Variation statistics.

If you choose the Tolerance option, a Tolerance analysis is also performed.  If you choose the Process Sigma option, the results for a Process Sigma analysis appears in the report.

Percent of Tolerance values below 10 percent indicate that the gage system is capable.  Values above 30 percent indicate that the measurement system needs considerable improvement.  Values between 10 percent and 30 percent suggest that you should monitor the measurement system.

To choose options for the report, use the Average and Range Method Options dialog box.


Average and Range Method Options Dialog Box

Allows you to enter values for the tolerance width, sigma intervals, process sigma, and confidence level that will be used for the calculations.

Tolerance

Sigma Intervals

Process Sigma

Confidence Level


Tolerance

[Optional]  Enter a value for the total tolerance width of the part specifications (the upper specification minus the lower specification).

An estimate is made for the percentage of the tolerance taken up by each variance component.  Enter a numeric value greater than 0.  If you leave this text box blank, the Percent of Tolerance and Tolerance statistics will not appear in the Gage Report.


Sigma Intervals

Enter a value for the number of standard deviations that will be included in the Gage Report.  Enter a numeric value greater than 0.


Process Sigma

[Optional]  Enter a value for the process standard deviation that will be used in the Gage Report.  An estimate is made for the percentage of the process sigma taken up by each of the variance components.


Gage Report Confidence Level
Confidence Level

Enter a value for the confidence level that will be used to calculate the confidence intervals for the measurement units in the Gage Report.


Average and Range Method Graphical Options Dialog Box

Allows you to choose graphical options for the Average and Range Method.

Operator and Part Plot (Average and Range Method)

Range Chart by Operator (Average and Range Method)

Range Chart by Part (Average and Range Method)

Box-and-Whisker Plot (Average and Range Method)

R&R Plot (Average and Range Method)


Operator and Part Plot (Average and Range Method)

The Operator and Part Plot graphical option displays a multiple-line plot of the average measurement of each part by each operator.  The plot helps you determine if there is interaction between parts and operators.

Lines that cross, suggest an interaction and indicates that you should use the ANOVA Method to analyze the data.

To choose options for the plot, use the Operator and Part Plot Options dialog box.


Range Chart by Operator (Average and Range Method)

The Range Chart by Operator graphical option displays a range chart with an upper control limit at 3.0 sigma above the average range.  The ranges are grouped and plotted for each part that each operator measures.

This chart is useful for detecting differences in operator variation and out-of-control ranges that affect the analysis.


Range Chart by Part (Average and Range Method)

The Range Chart by Part graphical option displays a plot of the ranges for each part that each operator measures; the ranges are grouped by part.

This chart helps you detect unusual range values and differences in appraiser variation by part.


R&R Plot (Average and Range Method)

The R&R Plot graphical option displays a plot of repeatability and reproducibility with one box for each operator.  A point indicates the deviation of each trial from the average measurement of each part.

A vertical line connects the minimum and maximum deviations for each part; a horizontal line represents the average deviation for that operator.


Operator and Part Plot Options Dialog Box

Allows you to indicate if points or lines should appear on the plot and if the labels on the X-axis should be rotated.


Range Chart Options Dialog Box

Use this dialog box to specify the decimal places to be used for the limits.

Decimal Places for Limits


Analysis Summary (Average and Range Method)

The Analysis Summary displays a summary of the analysis.  The summary includes the following information.

Variables

Displays the names of the variables that contain the values for the operators, parts, and trials, as well as the name of the variable that contains the measurements for each combination of values for the operators, parts, and trials.

Operators - The number of operators in the study.

Parts - The number of parts in the study.

Trials - The number of trials in the study

Average Range

Contains the values for the average range for all the trials the same operator repeats on the same part.

Range of X-Bars

Contains the values for the maximum difference between the averages of the operators.

Estimated Sigma

Displays values for the standard deviation of the measures of repeatability and reproducibility as well as the combined values for repeatability and reproducibility.

Estimated Variance

Displays values for the measures of repeatability and reproducibility as well as the combined values for repeatability and reproducibility.

Percent of Total

Displays values for the amount of the total estimated variance that can be attributed to repeatability and reproducibility.

To choose options for the analysis, use the Average and Range Method Options dialog box.


Gage Report (Average and Range Method)

The Gage Report tabular option displays the Measurement Unit Analysis and Study Variation statistics.  If you specify the tolerance, a Tolerance analysis is also performed.

Percent of Tolerance values below 10 percent for R&R indicate that the gage system is capable.  Values above 30 percent indicate that the measurement system needs considerable improvement.  Values between 10 percent and 30 percent suggest that you should monitor the measurement system.

The Process Sigma analysis also displays when you choose an estimated process sigma.


Operator and Part Plot (Average and Range Method)

The Operator and Part Plot graphical option displays a multiple-line plot of the average measurement of each part by each operator.

The plot helps determine if there is any interaction between parts and operators.  Lines that cross, suggest interaction and indicate that you should use the ANOVA Method to analyze the data.


Range Chart by Operator (Average and Range Method)

The Range Chart by Operator graphical option displays a range chart with an upper control limit at 3.0 sigma above the average range.  The ranges are plotted for each part that each operator measures, and groups the ranges by operators.

This chart is useful for detecting differences in operator variation and out-of-control ranges that affect the analysis.


Range Chart by Part (Average and Range Method)

The Range Chart by Part graphical option displays a plot that shows the ranges for each part that each operator measures and the ranges by parts.

This chart helps you detect unusual range values and differences in appraiser variation by part.


R&R Plot (Average and Range Method)

The R&R Plot graphical option displays a plot of repeatability and reproducibility with one box for each operator.  A point indicates the deviation of each trial from the average measurement of each part.

The plot also uses a vertical line to connect the minimum and maximum deviations for each part.  The horizontal line represents the average deviation for that operator.


ANOVA Method Dialog Box

The ANOVA Method is similar to the Average and Range Method in that it is a full Gage R&R Analysis that involves multiple operators, parts, and replications.

The calculations in this method are more accurate than in the other Gage R&R methods; an estimate is made of the interaction between operators and parts is also made.  The ANOVA Method tests to determine if that interaction is significant.  If the interaction is not significant, you can remove the interaction from the study.

To use this method, you must set up variables that contain operator names, part numbers, trial numbers, and measurements.  The design must be balanced; that is, each operator must measure each part the same number of times.

To choose options for this method, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

Operators

Parts

Trials

Measurements

Choose

Sort

Delete...

Transform...

See also

Using the Gage R&R Analysis

Using Gage R&R Data Setup

Using the Average and Range Method


ANOVA Method Tabular Options Dialog Box

The Tabular Options dialog box allows you to choose tabular options for the ANOVA Method.

Analysis Summary (ANOVA Method)

ANOVA Table (ANOVA Method)

Gage Report (ANOVA Method)


Analysis Summary (ANOVA Method)

The Analysis Summary displays a summary of the analysis.  The summary includes the following information.

Variables

Displays the names of the variables that contain the values for the operators, parts, and trials, as well as the name of the variable that contains the measurements for each combination of values for the operators, parts, and trials.

Operators - The number of operators in the study.

Parts - The number of parts in the study.

Trials - The number of trials in the study.

Estimated Sigma

Contains the values for the standard deviation of the measures for repeatability, operator and part interaction, and the combined repeatability and reproducibility.

Estimated Variance

Displays values for the measures of repeatability and reproducibility as well as the combined values for repeatability and reproducibility.

Percent of Total

Displays the values for the amount of the total estimated variance that can be attributed to repeatability, reproducibility, and operator and part interaction.


ANOVA Table (ANOVA Method)

The ANOVA Table tabular option displays a standard analysis of variance (ANOVA) table, which presents sum of squares values that measure the amount of variation.  The sum of squares statistic measures the variability for operators, parts, and their interaction.

Each mean square is the sum of squares for the source of variation divided by the degrees of freedom (df) for the source.  The F-Ratio displays interactions between parts and operators.

The p-value determines if the F-Ratio is significant.  Small significance levels (less than 0.05 for most practical applications) indicate that the interaction between parts and operators is significant; therefore, the interaction should remain in the analysis.

To choose options for the table, use the Interaction Options dialog box.


Interaction Options Dialog Box

Allows you to include the operator-part interaction in the study.

When you choose the Include Interaction check box, an estimate is made for the interaction between operators and parts.  If the interaction is not significant, you can remove it from the study.

Include Interaction


Include Interaction

Indicates if an estimate should be made of the interaction between operators and parts.  If an interaction is not significant, you can remove it from the study.

If you deselect the option the estimate of the interaction is removed from the Analysis Summary, ANOVA Table, and Gage Report.


ANOVA Method Options Dialog Box

Allows you to choose the tolerance width, sigma intervals, process sigma, and confidence level that will be used for the calculations.

Tolerance

Sigma Intervals

Process Sigma

Confidence Level


ANOVA Method Graphical Options Dialog Box

Allows you to choose graphical options for the ANOVA Method.

Operator and Part Plot (ANOVA Method)

Box-and-Whisker Plot (ANOVA Method)

R&R Plot  (ANOVA Method)


Analysis Summary (ANOVA Method)

The Analysis Summary displays a summary of the analysis.  The summary includes the following information.

Variables

Displays the names of the variables that contain the values for the operators, parts, and trials, as well as the name of the variable that contains the measurements for each combination of values for the operators, parts, and trials.

Operators - The number of operators in the study.

Parts - The number of parts in the study.

Trials - The number of trials in the study.

Estimated Sigma

Contains the values for the standard deviation of the measures for repeatability, operator and part interaction, and the combined repeatability and reproducibility.

Estimated Variance

Displays values for the measures of repeatability and reproducibility as well as the combined values for repeatability and reproducibility.

Percent of Total

Displays the values for the amount of the total estimated variance that can be attributed to repeatability, reproducibility, and operator and part interaction.


ANOVA Table (ANOVA Method)

The ANOVA Table tabular option displays a standard analysis of variance (ANOVA) table that presents sum of squares values that measure the amount of variation.  The sum of squares statistics measure the variability for operators, parts, and their interaction.

Each mean square is the sum of squares for the source of variation divided by the degrees of freedom (df) for the source.  The F-Ratio displays interactions between parts and operators.  The p-value measures whether the F-Ratio is significantly large.  Small significance levels (less than 0.05 for most practical applications) indicate that the interaction between parts and operators is significant; as a result, the interaction should remain in the analysis.


Operator and Part Plot (ANOVA Method)

The Operator and Part Plot graphical option displays a multiple-line plot for the average measurement of each part by each operator.  The plot helps you determine whether there is any interaction between parts and operators.

Lines that cross suggest interaction.


Range Method Dialog Box

The Range Method involves only two operators who each make one measurement on two or more parts.  In this analysis, you cannot separate repeatability and reproducibility.

To choose options for this method, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

Operator A

Operator B

Select

Sort

See also

Using the ANOVA Method

Using the Average and Range Method

Using Gage R&R Data Setup


Operator A

Enter the name of the variable that contains the measurements taken by the first operator on a set of parts.


Operator B

Enter the name of the variable that contains the measurements taken by the second operator on the same set of parts.


Range Method Tabular Options Dialog Box

Allows you to choose tabular options for the Range Method.

Analysis Summary (Range Method)


Analysis Summary (Range Method)

The Analysis Summary displays the names of the variables, the number of parts, and the Gage R&R statistics.

The first portion of the report displays the variable names for the two operators you choose.  It also contains the number of parts in the study, the values for the average range for all the trials, the values for the estimated R&R in standard deviations, and variances.

If you enter a value for the tolerance (the Upper specification minus the Lower specification) on the Range Method Options dialog box, the Analysis Summary includes these additional values.

Gage R&R

Displays the product of the number of standard deviations (sigma intervals) and the estimated sigma.  The default is 5.15.

Percent of Tolerance

Displays the results of dividing the values in the R&R measurements by the tolerance value and then multiplying by 100.

Sigma Intervals

Displays the number used to obtain the percent of tolerance.

Tolerance

Displays the total tolerance width from the part specification.  This value is used as the denominator when the percent of tolerance is calculated for the combined Gage R&R.

To choose options for this report, use the Range Method Options dialog box.


Range Method Graphical Options Dialog Box

Allows you to choose graphical options for the Range Method.

Operator and Part Plot (Range Method)

Range Chart by Part (Range Method)

Box-and-Whisker Plot (Range Method)


Analysis Summary (Range Method)

The Analysis Summary displays the names of the variables, the number of parts, and the Gage R&R statistics.

The first portion of the report displays the variable names for the two operators you choose.  It also contains the number of parts in the study, the values for the average range for all the trials, the values for the estimated R&R in standard deviations, and variances.

If you enter a value for the tolerance (the Upper specification minus the Lower specification) on the Range Method Options dialog box, the Analysis Summary includes these additional values.

Gage R&R

Displays the product of the number of standard deviations (sigma intervals) and the estimated sigma.  The default is 5.15.

Percent of Tolerance

Displays the results of dividing the values in the R&R measurements by the tolerance value and then multiplying by 100.

Sigma Intervals

Displays the number used to obtain the percent of tolerance.

Tolerance

Displays the total tolerance width from the part specification.  This value is used as the denominator when the percent of tolerance is calculated for the combined Gage R&R.

To choose options for this report, use the Range Method Options dialog box.


Custom Chart Analysis Dialog Box

The Custom Chart Analysis allows you to create customized control charts.  You can use graphics options to modify the appearance of the chart to make them visually appealing and more useful.

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left mouse button on either Pane Options or Analysis Options.

Top Title

X-Axis Title

Y-Axis Title

X-Axis Scaling

Y-Axis Scaling


Top Title
Top

This text box allows you to enter the title you want to display above the chart.  Leave the text box blank if you do not want to use a title.


X-axis Title
X-Axis

This text box allows you to enter the title the program will display on the horizontal axis.  Leave the text box blank if you do not want to use an X-axis title.


Y-axis Title
Y-Axis

This text box allows you to enter the title the program will display on the vertical axis.  Leave the text box blank if you do not want to use a Y-axis title.


X-Axis Scaling

These options allow you to enter the scaling for the tickmarks on the X-axis.  Use the From text box to enter the minimum numeric value for the X-axis.  Use the To text box to enter the maximum numeric value for the X-axis.  Use the By text box to enter the distance between each numeric tickmark for the X-axis.  Enter any positive numeric value.


Y-Axis Scaling

These options allow you to enter the scaling for the tickmarks on the Y-axis.  Use the From text box to enter the minimum numeric value for the Y-axis.  Use the To text box to enter the maximum numeric value for the Y-axis.  Use the By text box to enter the distance between each numeric tickmark for the Y-axis.  Enter any positive numeric value.


Custom Chart Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the Custom Chart Analysis.

Analysis Summary


Analysis Summary (Custom Chart)

The Analysis Summary displays instructions for customizing the chart.

To choose options for the chart, use the Custom Chart Options dialog box.


Custom Chart Graphical Options Dialog Box

Allows you to choose graphical options for the Custom Chart analysis.

Custom Chart (Custom Chart Analysis)


Custom Chart (Custom Chart Analysis)

The Custom Chart graphical option displays a Custom Chart with the titles and axis scaling you chooseed on the Custom Chart Analysis dialog box.

To choose options for the chart, use the Custom Chart Options dialog box.


Custom Chart Options Dialog Box

Allows you to choose the position and direction of up to eight lines on a Custom Chart.

Lines


Position

These text boxes allow you to enter the values for the X- and Y-axis intercepts on a Custom Chart.  Enter any numeric value.  If you enter a value that does not fit within the axis scaling, the line will not appear on the chart.


Analysis Summary (Custom Chart)

The Analysis Summary displays instructions for customizing the chart.

To choose options for the chart, use the Custom Chart Options dialog box.


Custom Chart

The Custom Chart graphical option displays a Custom Chart with the titles and axis scaling you chooseed on the Custom Chart Analysis dialog box.


Multivariate Control Chart Analysis Dialog Box

You use the Multivariate Control Chart Analysis to construct control charts for samples that have more than one variable in which you can correlate different measurements.  This analysis is based on Hotelling's T-squared statistic and assumes that the data come from a multivariate normal distribution.

The analysis transforms the original correlated variables into new variables that are independent; it then constructs a single statistic based on the new variables.  The program plots the multivariate observations on a single control chart that has an upper limit.

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left mouse button on either Pane Options or Analysis Options.

Data

Standard Means

Standard Covariances

Select

Sort

See also

Using the Multivariate Control Chart Analysis

Multivariate Chart Options

Multivariate Chart Report Options

Multivariate Control Chart Options


Standard Means

This optional text box allows you to enter the values for the process standard averages for each variable.  You must include one value for each variable you enter in the Data text box.  If you leave this text box blank, the program calculates and uses the sample averages.  You can enter standard means without entering standard covariances.  If you do that, the program uses the sample covariances.


Standard Covariances

This optional text box allows you to enter the values for the covariances that will hold the process to a standard.  Enter the standard covariances from sample covariances you previously saved in a Multivariate Control Chart Analysis.  If you leave this text box blank, the program calculates and uses the sample covariances.


Multivariate Control Chart Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the Multivariate Control Chart Analysis.

Analysis Summary

Multivariate Chart Report


Analysis Summary

The Analysis Summary displays names of the variables you choose on the Multivariate Chart Options dialog box, the number of complete cases, the number of cases you exclude, the upper control limit for the alpha you choose, and the number of cases beyond the control limit.


Multivariate Chart Report

The Multivariate Chart Report tabular option displays a table of the observation numbers, the Hotelling T-squared statistic for each observation, and the value for each variable in each observation.  The program also displays the upper control limit and alpha value.  If a multivariate observation is beyond the control limit, the program displays an asterisk with that observation.

To choose options for the report, use the Multivariate Chart Report Options dialog box.


Multivariate Chart Options Dialog Box

This dialog box allows you to enter a value to change the alpha level for the control limit, and to choose the observations you want to exclude or include in the analysis.

Alpha

Exclude... Command


Alpha

This text box allows you to enter a value for the alpha risk.  The alpha risk (the probability of a Type I error) determines the probability of declaring a process out-of-control when, in fact, it is not.  Enter a number greater than 0 and less than 50.

Note:  Changes you make to this text box changes the upper control limit on the Multivariate Control Chart.


Multivariate Chart Report Options Dialog Box

This dialog box allows you to indicate the type of data the program will display in the report.

Display Data


Display Data

This check box allows you to indicate if you want the program to display individual values in the report.  If you dechoose the check box, the Observation and T-squared columns appear in the report.


Multivariate Control Chart Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the Multivariate Control Chart Analysis.

Multivariate Control Chart

Key Glyph

Control Ellipse (Multivariate Control Chart Analysis)


Multivariate Control Chart

The Multivariate Control Chart graphical option displays a chart with one point for each multivariate observation.  The closer the Hotelling T-squared statistic is to 0, the closer the observation is to the multivariate mean of the data.  If you provide standard means, the observation is closer to the corresponding standard mean.

To choose options for the graph, use the Multivariate Control Chart Options dialog box.


Multivariate Control Chart Options Dialog Box

Indicate if you want to plot points or multivariate glyphs.  The default is points.

Decimal Places for Limits


Plot Glyphs
Glyphs

This option plots multivariate glyphs.


Save Results Options Dialog Box (Multivariate Control Chart)

The Save Results Options dialog box allows you to choose the results you want to save.  There are four options: T-Squared, Means, Covariances, and Labels.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or choose the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (Multivariate Control Chart)

The Analysis Summary displays names of the variables you choose on the Multivariate Chart Options dialog box, the number of complete cases, the number of cases you exclude, the upper control limit for the alpha you choose, and the number of cases beyond the control limit.

To choose options for the analysis, use the Multivariate Chart Options dialog box.


Multivariate Chart Report

The Multivariate Chart Report tabular option for the Multivariate Control Chart Analysis displays a table of the observation numbers, the Hotelling T-squared statistic for each observation, and the value for each variable in each observation.  The program also displays the upper control limit and alpha value.  If a multivariate observation is beyond the control limit, the program displays an asterisk with that observation.


Multivariate Control Chart

The Multivariate Control Chart graphical displays a chart with one point for each multivariate observation.  The closer the Hotelling T-squared statistic is to 0, the closer the observation is to the multivariate mean of the data.  If you provide standard means, the observation is closer to the corresponding standard mean.


Range Method Options Dialog Box

This dialog box allows you to choose the width of the tolerance and the number of standard deviations.

Tolerance

Sigma Intervals


Read ASCII File Dialog Box

This dialog box allows you to import a file in ASCII format.  The program creates variables and converts the data to the proper format based on information you provide.

File Type:  Tab Delimited

File Type:  Blank Delimited

File Type:  Comma Delimited

File Type:  Formatted

Column Widths (Formatted Only)

Variable Names:  From First Row

Variable Names:  Generate Defaults

Missing Value


File Type:  Tab Delimited
Tab Delimited

This option allows you to choose an ASCII file as an unformatted text file that contains a list of values separated by tabs.


File Type:  Blank Delimited
Blank Delimited

This option allows you to choose an ASCII file as an unformatted text file that contains a linear list of values separated by spaces.


File Type:  Comma Delimited
Comma Delimited

This option allows you to choose an ASCII file as an unformatted text file that contains a linear list of values separated by commas.


File Type:  Formatted
Formatted

This option allows you to choose an ASCII file as one that contains columns of data in fixed column widths.


Column Widths (Formatted Only)

This text box allows you to choose the width of the variables in a formatted ASCII file.  The width of each variable is the number of characters or spaces from the first character in the column up to, but not including the first character in the next column.  Separate each number in the list with a space or comma.


Variable Names:  From First Row
From First Row

This option imports the entries in the first row of the ASCII file as variable names.


Variable Names:  Generate Defaults
Generate Defaults

This option generates default variable names.


Missing Value

This text box allows you to choose the code the program will use in the imported file for missing values (entries for which there is no data).


Read dBase File Dialog Box

This dialog box allows you to import a file from a dBase format.

Missing ValueCSMissing_Value


Read DIF File Dialog Box

This dialog box allows you to import a file in DIF format.  The program creates variables and converts the data to the proper format using information you provide.

Variable Names:  From First Row

Variable Names:  Generate Defaults

Missing Value


Read Lotus File Dialog Box

This dialog box allows you to import a file in Lotus format.  The program creates variables and converts the data to the proper format using information you provide.

Variable Names:  From First Row

Variable Names:  Generate Defaults

Missing Value


p Chart

The p Chart is based on the proportion of defective items.  This portion of the Analysis Summary shows the values for the Centerline, which represents the average proportion of defects when a process is in control, and the values for the Upper Control Limit (UCL), and the Lower Control Limit (LCL).  It also displays the number of values that fall beyond those limits.  If you choose a one-sided control chart, that is, you choose either an UCL or an LCL, the corresponding line for the control limit is blank.  If the sizes of the subgroup differ the program uses the average subgroup size as the default when it calculates the control limit.


Subgroup Information

This option displays the number of subgroups the program uses for the analysis, the size of the subgroups or the average size if the subgroups have different sizes, and the number of subgroups you want to exclude from the study.


Estimated

This portion of the Analysis Summary displays the values for the estimated mean p value, and process sigma.  When the sizes of the subgroup are not equal, the program uses the average subgroup size to calculate these values.


Standard

This portion of the Analysis Summary displays the mean p value you enter on the p Chart Options dialog box when you perform a Control to Standard study.  It also displays the value for the standard sigma..


OC Curve (p Chart Analysis)

The OC Curve graphical option produces a plot that shows the probability that a shift will not be detected in the true process parameter immediately after one occurs.

The X-axis shows the shift in the proportion; the Y-axis shows the probability of not detecting the shift.


np Chart

This portion of the Analysis Summary is based on the number of defective items.  It shows the values for the Centerline, which represents the average number of defects when a process is in control; the values for the UCL and the LCL.  It also displays the number of values that fall beyond those limits.

If you choose a one-sided control chart, that is, you choose either an UCL or an LCL, the corresponding line for the control limit is blank.  If the sizes of the subgroups differ, the program uses the average size as the default when it calculates the control limit.


Subgroup Information

This portion of the Analysis Summary displays the number of subgroups in the analysis, the size of the subgroups or the average size if the sizes of the subgroups differ, and the number of subgroups excluded from the analysis.


Estimated

This portion of the Analysis Summary displays the values for estimated mean np and process sigma.  When the subgroup sizes are not equal the program uses the average size when it calculates the values.


Standard

This portion of the Analysis Summary displays the value for the mean np you entered on the np Chart Options dialog box for a Control to Standard study.  It also displays the value for the standard sigma.


Runs Tests

The Runs Tests tabular option performs a battery of tests that help to detect small changes or patterns in a process that may not be evident on a control chart.  The program lists the last subgroup in each violated runs test.


c Chart

This portion of the Analysis Summary displays the values based on the number of defects per item.  Values are shown for the Centerline, which represents the average number of defects per item when a process is in control, and the values for the UCL and the LCL.  It also displays the number of values that fall beyond those limits.

If you choose a one-sided control chart, that is, you choose either an UCL or a LCL, the corresponding line for the control limit is blank.


Observation Information

This portion of the Analysis Summary displays the number of observations the program uses for the analysis.


Estimated

This portion of the Analysis Summary displays the estimated mean c value and process sigma.


Standard

This portion of the Analysis Summary displays the mean c value you enter on the c Chart Options dialog box when you perform a Control to Standard study.  It also displays the standard sigma.


OC Curve (c Chart Analysis)

The OC Curve graphical option produces a plot that shows the probability of not detecting a shift in the true process parameter on the subgroup immediately after a shift occurs.  The X-axis shows the shift in the number of defects per item; the Y-axis shows the probability of not detecting the shift.


u Chart

The u Chart portion of the Analysis Summary displays values based on the rate of defects per unit.  It shows the value for the Centerline, which represents the average rate of defects when a process is in control, the values for the UCL and the LCL.  It also displays the number of values that fall beyond those limits.

If you choose a one-sided control chart, that is, you choose either an UCL or a LCL, the corresponding line for the control limit is blank.  If the sizes of the subgroup differ, the program uses the average size as the default when it calculates the control limits.


Subgroup Information

This portion of the Analysis Summary displays the number of subgroups the program uses for the analysis, the size of the subgroups or the average size if the sizes differ, and the number of subgroups you want to exclude from the study.


Estimated

This portion of the Analysis Summary displays the estimated mean u value and process sigma.  When the sizes of the subgroups are not equal, the program uses the average size to calculate the values.


Standard

This portion of the Analysis Summary displays the mean u value you enter on the u Chart Options dialog box when you perform a Control to Standard study.  It also displays the standard sigma.


Runs Tests (u Chart Analysis)

The Runs Tests tabular option performs a battery of tests that help to detect small changes or patterns in a process that may not be evident on a control chart.  The program lists the last subgroup in each violated runs test.

Use the Runs Tests Options dialog box to choose options for the tests.


OC Curve

The OC Curve graphical option produces a plot that shows the probability of not detecting a shift in the true process parameter on the subgroup immediately after a shift occurs.  The X-axis shows the shift in the number of defects per unit; the Y-axis shows the probability of not detecting the shift.


Moving Average Chart

This portion of the Analysis Summary shows the value for the Centerline, which represents the average value for the quality characteristic when a process is in control, and the values for the Upper Control Limit (UCL) and the Lower Control Limit (LCL).  The summary also displays the number of values that fall beyond those limits.  A process is in control if all the values fall within the control limits.


Range Chart

This portion of the Analysis Summary is similar to that for the Moving Average Chart portion in that it displays the values for the UCL, Centerline, and LCL.  The program uses the sigma values to calculate the UCL and LCL.  The summary also lists the number of subgroups that are beyond the control limits.  A process is in control if all the values fall within the control limits.


Subgroup Information

This portion of the Analysis Summary displays the number of subgroups used in the analysis, the size of the subgroups or the average size if the size of the subgroups differ, and the number of subgroups excluded from the study.


Estimated

This portion of the Analysis Summary displays the values for the estimated process mean, process sigma, and the mean range.  When the sizes of the subgroups are not equal, the program uses the average size to calculate the values.


Standard

This portion of the Analysis Summary displays the values for the process mean and process sigma you enter on the Moving Average Chart Options dialog box when you perform a Control to Standard analysis.  The summary also displays the value for the range of the standard mean.


Capability Indices (Moving Average Chart)

The Capability Indices tabular option displays the values for the capability indices, which is calculated using the 6.0 sigma limits.  Unlike the Process Capability Analysis, this analysis uses the estimated process sigma I the calculations.

These values help to determine the capability of the process to produce products that meet a standard.  The capability indices are not calculated until you choose or enter the USL, Nominal, and LSL values on the Process Capability Indices Options dialog box.

To choose options for this report, use the Process Capability Indices Options dialog box.


EWMA Chart
EWMA Chart – this topic is no longer used

This portion of the Analysis Summary shows the value for the Centerline, which represents the average value for the quality characteristic when a process is in control.  It also shows the values for the Upper Control Limit (UCL) and the Lower Control Limit (LCL), and the number of values that fall beyond these values.  A process is in control if all the values fall within the control limits.


Subgroup Information
Subgroup Information  - this topic is no longer used

This portion of the Analysis Summary displays the number of subgroups the program uses for the analysis, the size of the subgroups or the average size if the size of the subgroups differ, and the number of subgroups you want to exclude from the study.


Estimated
Estimated  - this topic is no longer used

This portion of the Analysis Summary displays the estimated values for the process mean, process sigma, and mean range.  When the size of the subgroups are not equal, the program uses the average subgroup size to calculate these values.


Standard
Standard – this topic is no longer used

This portion of the Analysis Summary displays the values for the process mean and sigma you enter on the EWMA Chart Options dialog box when you perform a Control to Standard study.  It also displays the values for the standard mean range.


CuSum Chart
CuSum Chart – this topic is no longer used

This portion of the Analysis Summary displays the number of standard deviations from the control mean at which a shift in the process is detected.  The summary also displays the alpha and beta values that represent the risk of having a Type I or a Type II error, and shows the sample number at which the program places the V-mask on the CuSum Chart.


Range Chart
Range Chart  - this topic is no longer used

This portion of the Analysis Summary shows the value for the Centerline, which represents the average value for the quality characteristic when a process is in control, and the values for the Upper Control Limit (UCL), and the Lower Control Limit (LCL).  It also displays the number of values that fall beyond these limits.  A process is in control if all the values fall within the control limits.


Subgroup Information
Subgroup Information  - this topic is no longer used

This portion of the Analysis Summary displays the number of subgroups the program uses for the analysis and the size of the subgroups or the average size if the size of the subgroups differ.


Estimated
Estimated – this topic is no longer used

This portion of the Analysis Summary displays the values for the estimated process mean, process sigma, and the mean range.  When the sizes of the subgroups are not equal, the program uses the average size to calculate the values.


Standard
Standard  - this topic is no longer used

This portion of the Analysis Summary displays the values for the process mean and sigma you enter on the CuSum Chart Options dialog box when you perform a Control to Standard study.  It also displays the values for the standard mean range.


Moving Average Chart
Moving Average Chart – this topic is no longer used

This portion of the Analysis Summary displays the value for the Centerline, which represents the average value for the quality characteristic when a process is in control.  It also displays the values for the Upper Control Limit (UCL), the Lower Control Limit (LCL), and the number of values that fall beyond these limits.  A process is in control if all the values fall within the control limits.


MR(2) Chart
MR(2) Chart – this topic is no longer used

This portion of the Analysis Summary displays the values for the UCL, Centerline, and LCL that the program uses in the analysis.  It also displays the sigma values the program used to calculate the UCL and the LCL, and lists the number of observations that are beyond the control limits.  A process is in control if all the values fall within the control limits.


Observation Information
Observation Information –this topic is no longer used

This portion of the Analysis Summary displays the number of observations the program used in the analysis.


Estimated
Estimated – this topic is no longer used

This portion of the Analysis Summary shows the values for the estimated process mean, process sigma, and mean MR(2).


Standard
Standard – This topic is no longer used

This portion of the Analysis Summary shows the values for the process mean and sigma you entered on the MA Individuals Chart Options dialog box.  It also displays the value for the standard mean MR(2).


Moving Average Chart

The Moving Average Chart graphical option displays a Moving Average Chart of the data.


EWMA Chart
EWMA Chart  - this topic is no longer used

This portion of the Analysis Summary shows the value for the Centeline, which represents the average value for the quality characteristic when a process is in control.  It also displays the values for the Upper Control Limit (UCL), the Lower Control Limit (LCL), and the number of values that fall within these control limits.


MR(2) Chart
MR(2) Chart  - this topic is no longer used

This portion of the Analysis Summary displays the values for the UCL, Centerline, and LCL that the program used in the analysis.  The program uses the sigma values to calculate the UCL and LCL.  The summary also lists the number of observations that are beyond these control limits.  Like the EWMA Chart, a process is in control if all the values fall within the control limits.


Observation Information
Observation Information – this topic is no longer used

This portion of the Analysis Summary displays the number of observations the program uses for the analysis.


Estimated
Estimated – this topic is no longer used

This portion of the Analysis Summary displays the values for the estimated process mean, process sigma, and the mean MR(2).


Standard
Standard – this topic is no longer used

This portion of the Analysis Summary displays the values for the process mean and sigma you enter on the EWMA Individuals Chart Options dialog box.  It also displays the value for the standard mean MR(2).


Capability Indices

The Capability Indices tabular option displays the values for the capability indices, which the program calculates using the 6.0 sigma limits.  Unlike the Process Capability Analysis, this analysis uses the value for the estimated process sigma in the calculations.  These values help to determine the capability of a process to produce products that meet a standard.  The program does not calculate the capability indices until you choose or enter the values for the USL, Nominal, and LSL on the Process Capability Indices Options dialog box.

To choose options for the capability indices, use the Process Capability Indices Options dialog box.


EWMA Chart

The EWMA Chart graphical option displays the values for the exponentially weighted moving averages for each of the measurements.  A process is out of control if points are shown outside the control limits, or if points shown within the control limits are arranged in a nonrandom sequence.

To choose options for the chart, use the EWMA Control Chart Options dialog box.


CuSum Chart

This portion of the Analysis Summary shows the number of standard deviations from the control mean at which the program detects a shift in a process.  The summary displays the values for alpha and beta that represent the risk of a Type I or a Type II error occurring.  It also displays the sample number at which the program places the V-mask on the chart.


MR(2) Chart

This portion of the Analysis Summary displays the values for the UCL, Centerline, and LCL that the program uses in the analysis.  The program uses the the sigma values to calculate the UCL and LCL.  The summary also lists the number of observations that are beyond these control limits.  Unlike the CuSum Chart, a process is in control if all the values fall within the control limits.


Observation Information

This portion of the Analysis Summary displays the number of observations the program used in the analysis.


Estimated

This portion of the Analysis Summary displays the values for the estimated process mean, process sigma, and the mean MR(2).


Standard

This portion of the Analysis summary displays the values for the process mean and sigma you enter on the CuSum Individuals Chart Options dialog box.  It also displays the values for the standard mean MR(2) and the mean deviation.


Cumulative Sum Chart (CuSum Individuals Chart Analysis)

The Cumulative Sum Chart graphical option displays the values for the cumulative sum of the deviation from target for each measurement.

A process is out of control is points are shown outside the control limits, or if points shown within the control limits are arranged in a nonrandom sequence.


MR(2) Chart (CuSum Individuals Chart Analysis)

The MR(2) Chart graphical option displays a plot that shows the values for the moving ranges for each of the measurements.  A process is out of control if points are shown outside the control limits, or within the control limits but arranged in a nonrandom sequence.

To choose options for the chart, use the Control Chart Options dialog box for either an Initial Study or a Control to Standard.


Key Glyph

The Key Glyph graphical option displays a single glyph with each ray labeled with its corresponding variable name.  The program plots the first variable, starting at the 12 o’clock position and continues clockwise.  This graph is helpful when you need to interpret smaller glyphs.


Box-and-Whisker Plot (Average and Range Method)

The Box-and-Whisker Plot graphical option displays a Box-and-Whisker Plot of the data.

The data for each sample are divided into four areas of equal frequency, with a box enclosing the middle 50 percent.  The median is drawn as a vertical line inside the box.  Horizontal lines, known as whiskers, extend from each end of the box.  The left (or lower) whisker is drawn from the first quartile to the smallest point within 1.5 interquartile ranges from the lower quartile.  The other whisker is drawn from the upper quartile to the largest point within 1.5 interquartile ranges from the upper quartile; values that fall beyond the whiskers but within 3 interquartile ranges are plotted as individual points.  Those values are suspect outliers.

The far outside outliers — those points more than 3 interquartile ranges below the lower quartile or above the upper quartile — are plotted using a special character (a point with a plus (+) through it) so they are easy to distinguish.

To choose options for the plot, use the Box-and-Whisker Plot Options dialog box.


Gage Report (ANOVA Method)

The Gage Report tabular option displays a report that contains the values for the Measurement Unit Analysis and Study Variation statistics.

If you choose the Tolerance option, a Tolerance analysis is also performed.  If you choose the Process Sigma option, a Process Sigma analysis is displayed.

Percent of Tolerance values below 10 percent indicate that the gage system is capable.  Values above 30 percent indicate that the measurement system needs considerable improvement.  Values between 10 percent and 30 percent suggest that you should monitor the measurement system.

To choose options for the report, use the ANOVA Method Options dialog box.


Operator and Part Plot

The Operator and Part Plot graphical option displays a multiple-line plot of the average measurement for each part by each operator.

The plot is helpful when you need to determine if there is an interaction between parts and operators.  Lines that cross suggest interaction.

To choose options for the plot, use the Operator and Part Plot Options dialog box.


Box-and-Whisker Plot (Multiple-Sample Comparisons Analysis)

The Box-and-Whisker Plot graphical option displays a Box-and-Whisker Plot of the data.

The program divides the data for each sample into four areas of equal frequency, with a box enclosing the middle 50 percent.  The median is drawn as a vertical line inside the box.  Horizontal lines, known as whiskers, extend from each end of the box.  The left (or lower) whisker is drawn from the first quartile to the smallest point within 1.5 interquartile ranges from the lower quartile.  The other whisker is drawn from the upper quartile to the largest point within 1.5 interquartile ranges from the upper quartile; values that fall beyond the whiskers but within 3 interquartile ranges are plotted as individual points.  Those values are suspect outliers.

The far outside outliers — those points more than 3 interquartile ranges below the lower quartile or above the upper quartile — are plotted using a special character (a point with a plus (+) through it) so they are easy to distinguish.

To choose options for the plot, use the Box-and-Whisker Plot Options dialog box.


R&R Plot

The R&R Plot graphical option displays a plot of repeatability and reproducibility with one box for each operator.

The program uses a point to indicate the amount each trial deviates from the average measurement of each part.  A vertical line connects the minimum and maximum deviations for each part; a horizontal line represents the average deviation for that operator.


Operators A and B

This portion of the Analysis Summary displays the name you choose for each operator.


Number of Parts

This portion of the Analysis Summary displays the number of parts in the study.


Mean Range

This portion of the Analysis Summary displays the average range for all the trials.


Estimated R&R Sigma

This portion of the Analysis Summary displays the estimated R&R in standard deviations.


Gage R&R

This portion of the Analysis Summary displays the number of standard deviations (sigma intervals) and the estimated sigmas.  The default is 5.15 sigma intervals.


Percent of Tolerance

This portion of the Analysis Summary displays the values that result when you divide the values in the R&R measurements by the tolerance value and then multiplying by 100.


Sigma Intervals

This portion of the Analysis Summary displays the number the program uses to obtain the values for the Gage R&R Percent of Tolerance.


Tolerance

This portion of the Analysis Summary displays the total tolerance width from the part specifications.  The program uses this value as a denominator when it calculates the percentage tolerance for combined Gage R&R.


Operator and Part Plot (Range Method)

The Operator and Part Plot graphical option displays a multiple-line plot of the average measurement for each part by each operator.

The plot helps determine if there is an interaction between parts and operators.  Lines that cross suggest interaction and indicate that you should use the ANOVA Method to analyze the data.

To choose options for the plot, use the Operator and Part Plot Options dialog box.


Range Chart by Part (Range Method)

The Range Chart by Part graphical option displays a plot of the ranges for each part that each operator measures and groups the ranges by parts.

This chart is helpful when you need to detect unusual ranges and differences in appraiser variation by part.


Box-and-Whisker Plot (Range Method)

The Box-and-Whisker Plot graphical option displays a Multiple Box-and-Whisker Plot of the data.

The data for each sample are divided into four areas of equal frequency, with a box enclosing the middle 50 percent.  The median is drawn as a vertical line inside the box.  Horizontal lines, known as whiskers, extend from each end of the box.  The left (or lower) whisker is drawn from the first quartile to the smallest point within 1.5 interquartile ranges from the lower quartile.  The other whisker is drawn from the upper quartile to the largest point within 1.5 interquartile ranges from the upper quartile; values that fall beyond the whiskers but within 3 interquartile ranges are plotted as individual points.  Those values are suspect outliers.

The far outside outliers — those points more than 3 interquartile ranges below the lower quartile or above the upper quartile — are plotted using a special character (a point with a plus (+) through it) so they are easy to distinguish.

To choose options for the plot, use the Box-and-Whisker Plot Options dialog box.


OC Curve (np Chart Analysis)

The OC Curve graphical option produces a plot that shows the probability of not detecting a shift in the true process parameter on the subgroup immediately after a shift occurs.

The X-axis shows the shift in the number of defects.  The Y-axis shows the probability of not detecting the shift.


Plot (Points or Glyphs)

These options allow you to instruct the program to plot either points or glyphs.

Points

Plots the observations as points.

Glyphs

Plots multivariate glyphs.


Control to Standard

Determines the parameters or control limits.  These options are available only when you choose Control to Standard from the Type of Study option.

Specify Parameter

Enter the value that will be used to calculate the control limits.

p

Enter a value for the process proportion.  Enter any numeric value between 0 and 1.

Specify Control Limits

Determines the control limits for the p Chart.

Upper

Enter a numeric value for the UCL.  The number must be greater than the values you enter into the Centerline and LCL text boxes.

Centerline

Enter a numeric value for the Centerline.  The number must be less than the value you enter for the UCL, and greater than the value you enter for the LCL.

Lower

Enter a numeric value for the LCL.  The number must be less than the values you enter for the UCL and Centerline.


Display

Choose the subgroups that will be included in the Subgroup Report.

All Subgroups

Includes all the subgroups in the report.

Subgroups beyond Limits

Lists the subgroups that are beyond the control limits for the p Chart.

Excluded Subgroups

Lists the subgroups that have been excluded from the analysis.


Control to Standard

Enter values for the parameters or the control limits. These options are available only when you choose the Control to Standard.option.

Specify Parameters

Enter values that will be used to calculate the parameters.

u

Enter a value for the process standard for defect rate.  Enter any numeric value greater than or equal to 0.

Specify Control Limits

Enter values that will be used to calculate the control limits.

Upper

Enter a value for the Centerline.  Enter a numeric value that is greater than the values in the Centerline and LCL text boxes.

Centerline

Enter a value for the Centerline.  Enter a numeric value that is less than the value in the UCL text box and greater than the value in the LCL text box.

Lower

Enter a value for the LCL.  Enter a numeric value that is less than the values in the UCL and Centerline text boxes.


Control to Standard (c Chart)

Enter values for the parameters or the control limits.  These options are available only when you choose the Control to Standard option.

Specify Parameters

This option allows you to enter values the program will use to calculate the parameters.

c

Enter a value for the process standard for the number of defects.  Enter any numeric value greater than or equal to 0.

Specify Control Limits

This option allows you to enter values the program will use to calculate the control limits.

Upper

This text box allows you to enter a value for the UCL.  Enter a numeric value that is greater than the values in the Centerline and LCL text boxes.

Centerline

This text box allows you to enter a value for the Centerline.  Enter a numeric value that is less than the value in the UCL text box and greater than the value in the LCL text box.

Lower

This text box allows you to enter a value for the LCL.  Enter a numeric value that is less than the values in the UCL and Centerline text boxes.


Display

Choose the observations that will be included in the report.

All Observations

Includes all the observations; it is the default.

Observations beyond Limits

Lists the observations that are beyond the control limits.

Excluded Observations

Lists the excluded observations.


Data

Choose or enter the name of the variable that contains the type of data you want to analyze.

Observations

Enter individual observations.  Use the text box to enter the observations.  If you choose this option, you must also complete the Subgroup Numbers or Size text box.

Subgroup Statistics

Enter values for the subgroup statistics.  If you choose this option, you must also complete the Means, Ranges, and Subgroup Numbers or Size text boxes.

Means

Enter values for the means of the subgroups you want to analyze.

Ranges

Enter values for the ranges of the subgroups you want to analyze.  The values you enter must correspond to the values you enter into the Means text box.


Control to Standard

Choose or enter the name of the variable that contains the parameters.  The options are available only when you choose the Control to Standard option.

Specify Parameters

Choose or enter the values that will calculate the control limits.

Mean

Enter a value for the process mean.  Enter any numeric value.

Sigma

Enter a value for the process sigma.  Enter any positive numeric value.


Display

Choose the subgroups that will be included in the MA Chart Report.

All Subgroups

Includes all the subgroups in the report.

Subgroups beyond Limits

Lists the subgroups that are beyond the control limits for the Moving Average or Range charts.

MA beyond Limits

Lists the subgroups that have moving averages beyond the control limits.

Ranges beyond Limits

Lists the subgroups that have ranges beyond the control limits.

Excluded Subgroups

Lists the subgroups that have been excluded from the analysis.


Control Chart Options Dialog Box (Initial Study)

Choose the warning limits you want to display on the Control Chart.  You can also choose a moving average and exponentially weighted moving average for the plot.

Outer Warning Limits

Inner Warning Limits

Moving Average

Exponentially Weighted Moving Average


Display

Choose the subgroups you want to include in the EWMA Chart Report.

All Subgroups

Includes all the subgroups in the report.

Subgroups beyond Limits

Lists the subgroups that are beyond the control limits for the EWMA or Range charts.

EWMA beyond Limits

Lists the subgroups that have exponentially weighted moving averages that are beyond the control limits.

Ranges beyond Limits

Lists the subgroups that have ranges that are beyond the control limits.

Excluded Subgroups

Lists the subgroups that have been excluded from the analysis.


Display

Choose the subgroups you want to include in the CuSum Chart Report.

All Subgroups

Includes all the subgroups in the report.

Subgroups beyond Limits

Lists the subgroups that are beyond the control limits for the CuSum or Range charts.

CuSum beyond Limits

Lists the subgroups that are outside the V-mask.  The first subgroup that falls outside the V-mask indicates a shift in the process.

Ranges beyond Limits

Lists the subgroups that have ranges that are beyond the control limits.

Excluded Subgroups

Lists the subgroups that have been excluded from the analysis.


Display

Choose the subgroups you want to include in the Moving Average Individuals Chart Report.

All Observations

Includes all the observations in the report.

Observations beyond Limits

Lists the observations that are beyond the control limits for the Moving Average and MR(2) charts.

MA beyond Limits

Lists the observations that have moving averages that are beyond the control limits.

MR(2) beyond Limits

Lists the observations that have moving ranges that are beyond the control limits.

Excluded Observations

Lists the observations that have been excluded from the analysis.


Control to Standard

Choose or enter values for the standard process parameters.  The options are available only when you choose the Control to Standard option.

Specify Parameters

Choose or enter values that will be used to calculate the control limits.

Mean

Enter a value for the process mean.  Enter any numeric value.

Sigma

Enter a value for the process sigma.  Enter any positive numeric value.


Display

This dialog box allows you to choose the report that will be created.

All Observations

Includes all the observations in the report.

Observations beyond Limits

Lists the observations that are beyond the control limits.

CuSum beyond Limits

Lists the observations that are outside the V-mask.  The first observation that falls outside the V-mask indicates where a shift in the process occurs.

Scale beyond Limits

Lists the observations that have moving ranges that are beyond the control limits.

Excluded Observations

Lists the observations that have been excluded from the analysis.


Analysis Summary (Range Method)

The Analysis Summary displays a summary of the analysis.  The summary includes the following information.

Operators A and B

Displays the names of the variables that contain the names you enter for each operator.

Number of Parts

Displays the number of parts in the study.

Mean Range

Displays the average range for all the trials.

Estimated R&R Sigma

Displays the values for the estimated R&R in standard deviations.

Estimated R&R Variance

Displays the values for the estimated R&R in variances.

If you choose the Tolerance option (the upper specification minus the lower specification), the program displays the following statistics display.

Gage R&R

Displays the number of standard deviations (sigma intervals) and the estimated sigma values.  The default is 5.15 sigma intervals.

Percent of Tolerance

Displays the values that result from dividing the values in the R&R measurements by the tolerance value and multiplying by 100.

Sigma Intervals

Displays the number used to obtain the Percent of Tolerance values.

Tolerance

Displays the total tolerance width from the part specifications.  This value is used as a denominator when the percent of tolerance is calculated for the combined R&R.

To choose options for the analysis, use the Range Method Options dialog box.


Lines

Enter the position and direction for up to eight lines on a Custom Chart.  Use the Text Options dialog box to change the default graphics setting for the text.

Position

Enter a value for the X- and Y-axis intercepts for the Custom Chart.  Enter any numeric value; 25 is the default.  If you enter a value that does not fit within the axis scaling, the line will not appear on the chart.

Direction

Choose a direction for each of the lines.  If you choose Horizontal, a line parallel to the X-axis is drawn.  If you choose Vertical, a line parallel to the Y-axis is drawn.


Display

Choose the subgroups you want to include in the EWMA Individuals Chart Report.

All Observations

Includes all the observations in the report.

Observations beyond Limits

Lists the observations that are beyond the control limits.

EWMA beyond Limits

Lists the observations that have exponentially weighted moving averages that are beyond the control limits.

MR(2) beyond Limits

Lists the observations that have moving ranges that are beyond the control limits.

Excluded Observations

Lists the observations that have been excluded from the analysis.

Allows you to choose options


Box-and-Whisker Plot (ANOVA Method)

The Box-and-Whisker Plot option creates multiple plots, one for each operator.  The rectangular part of the plot extends from the lower quartile to the upper quartile, covering the center half of the sample.  The centerlines within each box show the location of the sample medians.  The plus signs indicate the location of the sample means.  The whiskers extend from the box to the minimum and maximum values in the sample, except for any outside or far outside points, which are plotted separately.

Outside points are points that lie more than 1.5 times the interquartile range above or below the box and are shown as small squares.  Far outside points are points that lie more than 3.0 times the interquartile range above or below the box.  They are shown as small squares with plus signs through them.

Use the Box-and-Whisker Plot Options dialog box to indicate if the direction of the plot will be vertical or horizontal; and to choose the features for the plot: median notch, outlier symbols, or mean marker.


c Chart

The c Chart option creates a plot of the nonconformities for each of the observations.  A process is considered out of control if points are shown outside the control limits, or if points are shown within the control limits, but arranged in a nonrandom sequence.

Use the Control Chart Options dialog box to choose options for the chart.


Capability Indices (EWMA Chart Analysis)

The Capability Indices option calculates several process capability indices, based on the estimated process mean and standard deviation.  These indices help determine the capability of the process to produce products that meet a quality standard.

Use the Process Capability Indices Options dialog box to choose options for the report.


Range Chart (Moving Average Chart Analysis
Range Chart (Moving Average Chart Analysis)

The Range Chart option creates a plot of the ranges for each of the subgroups and shows the points that are beyond the control limits.

Use the Control Chart Options dialog box to choose options for the chart.


Select

[Optional]  Select a subset of subgroups.  For example, to analyze the first 50 values in each variable, enter first (50) into this text box.


Control to Standard

Determines the parameter or control limits.  The options are only available when you choose Control to Standard from the Type of Study option.

Specify Parameter

Enter the value that will be used to calculate the control limits.

np

Enter a value for the process defective count.  Enter any positive numeric value.


MA Chart

An acronym for Moving Averages Chart.


MAE

An acronym for Mean Absolute Error.


Mahalanobis Distance

A standardized form of Euclidean distance.  Data are standardized by scaling responses in terms of standard deviations and adjustments are made for intercorrelations between the variables.


Main Effect

A measure that estimates the influence of a single factor on the response when the factor is changed from one level to another.


Mann-Whitney u Test

A test that determines if two medians from two independent samples differ.


MAPE

An acronym for Mean Absolute Percentage Error.


Matrix

See Coefficient Correlation Matrix, Covariance Matrix, Design Matrix, Identity Matrix, Symmetric Matrix.


Maximum

The largest value.  In a function, the greatest value of the function, if it has such a value.


Maximum Likelihood Estimate

An estimate of a universe parameter that, if it were the true value, would maximize the probability of the sample on which the estimate is based.  See also Estimate.


ME

An acronym for Mean Error.


Mean

The sum of the observations divided by the number of observations.  Also called Arithmetic Mean or Average.  See also Control Mean, Geometric Mean, Grand Mean, Population Mean, Process Mean, Raw Mean, Sample Mean, Standard Mean.


Mean Absolute Error (MAE)

The average of the absolute values of the residuals.  A measure of forecast accuracy calculated by summing the absolute values of the individual forecast errors of the time series and dividing by the number of observations.  The MAE is appropriate when the function is linear and symmetric.  See also Error.


Mean Absolute Percentage Error (MAPE)

A measure of forecast accuracy calculated by taking the absolute value of the individual forecast errors of the time series, dividing by the actual value of the time series, multiplying by 100, and calculating the average of the resulting values.  The MAPE is not related to the scale of the observations, so it is useful in comparing the errors between distinct variables not measured in the same units.  See also Error.


Mean Error (ME)

A measure of forecast accuracy calculated by averaging the individual forecast errors across all of the time-series observations.


Mean Percentage Error (MPE)

A measure of forecast accuracy calculated by taking the individual forecast errors of the time-series forecasts, dividing by the actual value of the time series, multiplying by 100, and calculating the average of the resulting values.  The MPE is typically small because positive and negative errors tend to offset each other.  See also Error.


Mean Range

The average of subgroup ranges that is the centerline of a Range Chart.  You use the mean range to estimate the process standard deviation.  See also Interquartile Range, Range.


Mean Sigma

The average of subgroup standard deviations that is the centerline of an S Chart.  You use the mean sigma to estimate the process standard deviation.  See also Process Sigma, Sigma, Standard Sigma.


Mean Square

The result of dividing the sum of the squares by its associated degrees of freedom.  See also Interaction Mean Square, Residual Mean Square.


Mean Square for Rows

The row sum of squares divided by its degrees of freedom.


Mean Squared Error (MSE)

A measure of forecast accuracy calculated by squaring the individual forecast error for each time-series observation and then finding the average of these errors.  The MSE gives larger weight to large errors than other measures of accuracy because these values are squared before they are averaged.


Mean Variance

The average of the variances for subgroups of data when the subgroup sizes are equal.  You use the mean variance to determine the centerline for a variance control chart.


Means Plot

A plot of the mean for each sample and the intervals for the means.


Means Table

A table of the sample means and standard errors for the levels in the data.  See also Frequency Table, Multi-Way Table, Two-Way Table.


Means Test

A statistical method for testing the differences between group averages in ANOVA.


Median

With the observations arranged in order from smallest to largest, the number halfway between the smallest and largest observations; the 50th percentile.  A measure of the central tendency of the data.  See also Sample Median.


Metric Variable

A variable constant unit of measurement.  For example, if a variable is scaled from 1 to 9, the difference between 1 and 2 is the same as that between 8 and 9.


Midpoint

The point that divides a line segment or an arc into two equal parts.


Minima

The plural of minimum.


Minimum

The smallest value in a set of data or a function.


Missing Value

Information that is not available for a subject about which other information is available; for example, when a respondent does not answer a question in a survey.


Mixed Model

An analysis of variance model in which one or more factors are fixed and one or more are random.  See also Model.


Mixture Experiment

An experiment in which you assume that the response depends only on the relative proportions of the ingredients (components) in the mixture and not on the amount of the mixture.


Mode

A value with the highest frequency.  An observation in a sample which occurs most frequently; a measure of the central tendency of the data.


Models

Methods used to fit regressions.


Model Fitting

The method of using an equation to quantify a mathematical relationship among observed data and variables or combinations of variables.


Month Variable

A variable that contains numbers entered in mm/yy format or the format you set on the Windows Control Panel.


Moving Average

The absolute value of the difference between two averages.  In quality control, the absolute value of the difference between the average of a given subgroup and the average of a previous subgroup.  See also Average.


Moving Average (MA) Chart

A control chart that plots the moving averages of the subgroups.  It is useful for showing trends in the subgroup averages.


Moving Range (MR)

The absolute value of the difference between two ranges.  In quality control, the absolute value of the difference between the range of a given subgroup and the range of a previous subgroup.


Moving Range (MR) Chart

A control chart that plots the moving ranges of the subgroups.  This chart is necessary when plotting individual data (subgroup size equal to 1).


MPE

An acronym for Mean Percentage Error.


MR Chart

An acronym for Moving Range Chart.


MR(2)

The moving range calculated by taking the difference between every pair of contiguous data values.


MR(2) Chart

A control chart that plots the moving ranges for each pair of subgroup values.  The preferred chart for individual data (subgroup size equal to 1).


MSE

An acronym for Mean Square Error.


Multiple Box-and-Whisker Plot

A graphical summary of the outliers in data for two or more variables.


Multiple Regression

A Taylor series model that uses several independent variables to predict one dependent variable.


Multiple Range Tests

A table that shows the number of observations and the mean for each sample, the variables in homogeneous groups that are not significantly different, the average values for the difference and plus/minus limits for each pair of samples and the size of the interval about this difference.


Multiple X-Y Plot

A scatterplot with one variable on the X-axis and one or more variables on the Y-axis.


Multiple X-Y-Z Plot

A scatterplot for three or more variables.  One variable each is plotted on the X- and Y-axes; one or more variables are plotted on the Z-axis.  A three-dimensional line plot, scatterplot, or connected scatterplot for three or more variables.


Multiplicative Model

A calibration model used to fit a simple regression that is equivalent to taking the natural logs of Y and X; defined by the equation Y = aX^b.  See also Model.


Multivariate

An analysis that involves more than one dependent variable.


Multivariate Control Chart

A control chart for multivariate samples in which you can correlate different measurements.


Multivariate Data

Simultaneous observations or measurements on two or more variables.  See also Data.


Multivariate Normal Data

Data generated from a multivariate normal distribution.  The sampling distributions of many multivariate statistics are approximately normal, due to the central limit theorem.  See also Data.


Multivariate Normal Distribution

A normal distribution generalized to two or more dimensions.  The multivariate normal distribution has two parameters:  a vector of means, and the sums of squares and cross-product matrix.  These parameters are analogous to the mean and standard deviation for the univariate normal distribution.  See also Distribution.


Multi-Way Table

A contingency table for three or more variables.  See also Frequency Table, Means Table, Two-Way Table.


Natural Logarithm

The log, base "e," of a number.


Negative Correlation

A negative linear relationship that exists between two variables; that is, the variables vary in the opposite direction.  See also Correlation, Pearson Product-Moment Correlation, Positive Correlation, Zero Correlation.


Nested Data

Data in which the classifying factors are qualitative and no theoretical relationship exists between observations at a given level of a subsample with observations in a corresponding level of another subsample.  Also called Hierarchical Data.  See also Data.


Nested Design

A design in which the classification factors form a hierarchy.  A class of experimental design in which every level of a given factor appears with only a single level of any other factor.  See also Design.


Nested Factor

In a ANOVA design, any factor that is nested below another factor.  See also Factor.


Nested Model

An analysis of variance model in which the effects of certain factors are pyramided.  Levels of lower factors are nested in levels of factors higher up the pyramid, but do not cut across the levels of the higher factor.  Also called Hierarchical Model.  See also Model.


Newman-Keuls Method

A method for determining statistically significant differences among means if the F-ratio is significant and you want to test multiple hypotheses.  The Type I error rate is smaller when you use this method than it is when you use the Duncan method.  A multiple-comparison test similar to Tukey's Honestly Significant Differences (HSD) Test.  The program calculates the sample averages, ranks the averages, takes pairwise differences, calculates standard errors, and computes a test statistic.  The test shows significant differences more quickly than Tukey's HSD Method.


Newton-Raphson Algorithm

A powerful and well-known numerical method for solving a root-finding problem for a function.  See also Algorithm.


Noise

Any random or unexplained error or variability in the response.  All errors that are not due to assignable causes.  See also White Noise.


Nominal (Target) Value

The preferred value for an item or data value that results from a process.  Typically, the nominal value falls between the lower specification limit and the upper specification limit.  See also Lower Specification Limit, Specification Limits, Upper Specification Limit.


Nonlinear Model

A model in which the parameters enter nonlinearly.  See also Model.


Nonlinear Regression

Regression analysis that finds a least squares solution for a nonlinear model, which cannot be done using matrix algebra as it is in linear regression.  A statistical modeling technique that relates a response variable to a set of predictor variables in an equation that is not linear in the regression coefficients.  See also Linear Regression, Regression.


Nonmetric Variable

A variable that contains data that are not measured on an interval or ratio scale; a variable that contains ordinal data.


Nonparametric

Statistical procedures for data or sample statistics that have unknown or unspecified distributions.


Nonstationary

Not having a constant mean or variance.


Normal Distribution

A continuous probability distribution that is useful in characterizing a large variety and type of data.  It is a symmetric, bell-shaped distribution, completely determined by its Mean and Standard Deviation.  A common bell-shaped curve used to calculate probabilities of events that tend to occur around a mean value and trail off with decreasing likelihood.  Also called Gaussian Distribution.  See also Distribution.


Normal Equations

A synonym for Least Squares Equations.


Number of Defectives per Item Chart

A control chart that allows you to construct control limits based on an attribute that is related to frequency, such as the number of defects per item.  Also called c Chart.


Number of Defectives per Sample Chart

A control chart that allows you to analyze whether a process produces an unacceptably high proportion of defective items, based on the number of defective items you find in a particular sample or series of samples.


Numeric Variable

A variable that contains only numbers and has a floating decimal place.  Also called Floating-Point Numeric Variable.


Observation

The result of determining the presence or absence of attributes or measuring a variable.


Observed Frequency

When conducting a chi-square test, the actual data in the crosstabulation.  You compare the observed frequencies with the expected frequencies; that is, the frequencies you expect if the independent variable has no effect.  Differences between the observed and expected frequencies suggest a relationship among the variables you are studying.  See also Frequency.


Observed Value

The particular value of a characteristic you determine as a result of a test or measurement.


OC Curve

An acronym for Operating Characteristic Curve.  See also Curve.


Offset

To move an object away from a centerline or at an angle to another object.  Also, the distance the object is moved.


One-Ahead Forecast

The difference between the actual observation at time t and the observation you predict from time period t - 1.  See also Linear Forecast.


One-Factor-At-a-Time Experimentation

A highly inefficient method in which one factor setting is changed while all other factors are held constant.  The method ignores the possibility of interactions.


One-Tailed Test

A test of a hypothesis that has only one critical value, either an upper or lower rejection region.


One-Way Analysis of Variance

An analysis for determining the effect of one qualitative factor on one response variable.  See also Analysis of Variance, Two-Way Analysis of Variance.


One-Way Design

An ANOVA or experimental design in which you study the effect of one factor that has two or more levels.  See also Design.


Operating Characteristic Curve

A graph of the probability for a type II error (beta error) as a function of the hypothesized values of the parameter of interest.  In quality control, the curve that shows, for a given acceptance control chart configuration, the probability of accepting a process as a function of the process level.  Also called OC Curve.  See also Curve.


Operator Variation

The variation in measurements obtained when an operator measures an identical characteristic on the same part several times.  See also Appraiser Variation, Equipment Variation.


Order of Polynomial

The highest power of the independent variables in a polynomial equation.


Ordinate

The vertical (Y) axis of a graph.


Orthogonal

The mathematical independence of factor axes to each other; that is, at right angles or 90 degrees.


Orthogonal Design

An experimental design where the correlation between factors is 0.  See also Design.


Orthogonal Transformation

A transformation that rotates axes but maintains their perpendicular relationship.  To be strictly orthogonal, the coefficients of the transformation (that is, the elements in the transformation matrix) must be such that when the coefficients (elements) in any row are squared they sum to 1; when they are cross-multiplied row by row they sum to 0.  See also Logarithmic Transformation.


Out-of-Control Process

A process that is not in statistical control.  Indications of this condition include subgroup values that plot beyond control limits on a control chart or subgroup values that form patterns or trends on a control chart.


Outlier

Points more than three interquartile ranges below the first quartile or above the third quartile..


p Chart

A control chart that allows you to analyze the proportion of defective items that a process produces.


p-Level

The p-value below which you reject the null hypothesis; this value is the chance of making a type I (alpha) error.  See also Level.


p-Value

A component of an ANOVA table that serves as a measure of significance.  The probability of observing a value for a test statistic that is at least as inconsistent with the null hypothesis as the value of the test statistic actually observed.


Paired-Sample Test

A hypothesis-test technique for testing the difference between averages for paired data.  The test is essentially a one-sample test you perform in one-variable analysis.


Paired Samples

Samples that occur when you take two measures from the same source; for example, a pretest and posttest you administer to students before and after a lecture.  See also Independent Samples, Pooled Samples.


Pairwise Comparison

A comparison of the difference between two treatment groups.


Parameter

A constant or coefficient of a universe that describes some characteristic of its distribution; for example, standard deviation, average.


Parametric

Statistical procedures that are based on a known distribution you can write in terms of parameters.


Partial Autocorrelation

A measure of correlation that identifies the extent of relationship between the current values for a variable with earlier values of that same variable while holding the effects of all the other time lags constant.


Partial Confounding

An experimental design in which a comparison (main effect or interaction) is confounded with block effects in one but not all replications of the experiment.  See also Confounding.


Partial Correlation Coefficient

A statistic that measures the relationship between two variables while controlling for possible effects of other variables.  See also Coefficient.


Partial Derivative

The ordinary derivative for a function of two or more variables with respect to one of the variables, considering the others as constants.  See also Derivative, Higher-Order Derivative.


Partially Nested Design

An ANOVA design in which some but not all of the factors are nested.  Also called Partially Hierarchical Design and Cross-Nested Design.  See also Design.


Path of Steepest Ascent

The direction at right angles to the contours of a Response Surface Plot that is used to locate the region  in which the response increases; this area includes a local (or global) maximum or minimum on the response surface.


Path of Steepest Descent

The direction at right angles to the contours of a Response Surface Plot that is used to locate the region in which the response decreases.


Pearson's Correlation Coefficient
Pearson’s Correlation Coefficient

A statistic that shows the degree of linear relationship between two variables you measure on interval or ratio scales.  Also called Pearson’s Product-Moment Correlation, Pearson's r.  See also Coefficient.


Pearson's Product-Moment Correlation
Pearson’s Product-Moment Correlation

A statistic that shows the degree of linear relationship between two variables you measure on interval or ratio scales.  Also called Pearson’s Correlation Coefficient, Pearson's r.  See also Correlation.


Pearson's r

A statistic that shows the degree of linear relationship between two variables you measure on interval or ratio scales.  Also called Pearson’s Correlation Coefficient, Pearson’s Product-Moment Correlation.


Percentage Barchart

A barchart that displays percentages rather than frequencies.


Percentile

A value below which a certain percentage of observations in a sample fall.


Periodicity

A quality of something that recurs regularly.


Periodogram

A graph that breaks a time series into a set of sine waves of various frequencies.  A periodogram is useful for identifying randomness, seasonality, or autocorrelation in a data series.  Also known as a Line Spectrum.


Physical Acceleration Model

A model that shows the relationships between failure rates at high stress levels and normal operating levels.  See also Model.


Piechart

A circle-shaped chart segmented into shaded or colored wedges.  The chart is useful for displaying percentage breakdowns for up to 20 classification factors.


Plackett-Burman Design

An orthogonal, balanced design that has a multiple of four runs.  Used for estimating main effects only; that is, no interactions.


Poisson Distribution

A distribution that expresses probabilities that concern the number of events per unit time.  Often used to describe situations in which the probability of an event is small and the number of opportunities for the event is large.  See also Distribution.


Polynomial

An algebraic expression that contains two or more names or terms.  See also Order of Polynomial.


Polynomial Function

See also First-Degree Polynomial Function, Second-Degree Polynomial Function.


Pooled Data

Two or more sets of data you collect and combine under different conditions or from different populations.  See also Data.


Pooled Estimate

A statistic you calculate by combining two or more samples of data collected under different conditions or from different populations.  See also Estimate.


Pooled Samples

Two or more samples of data you collect and combine under different conditions or from different populations.  See also Independent Samples, Paired Samples.


Pooled Standard Error

The square root of the pooled variance multiplied by a factor of the sample sizes.  See also Internal Standard Error, Standard Error.


Pooled Variance

The common variance from two or more samples; estimated by a weighted average of the sample variances.


Pooling

Combining sums or sums of squares to achieve a combined mean.


Population Mean

The average, often unknown, for a set of data that characterizes some process or phenomenon.  See also Mean.


Population Standard Deviation

A measurement of the spread or dispersion of observations that is the positive square root of the population variance.  See also Residual Standard Deviation, Sample Standard Deviation, Standard Deviation.


Population Variance

A measurement of the spread or dispersion of observations, based on the mean of the squared deviations from the arithmetic mean.


Portmanteau Statistic

A synonym for chi-square statistic.  See also Chi-Square Statistic.


Portmanteau Test

A synonym for chi-square test.  See also Chi-Square Test.


Positive Correlation

A positive linear relationship between two variables; that is, the variables vary in the same direction.  See also Correlation.


Power

The probability that the null hypothesis will be rejected when it is false.  Power is 1 minus the beta error.


Power Curve

A plot that illustrates the probability of the null hypothesis being rejected.  See also Curve.


Power Function

Equals 1 minus the ordinate of the operating characteristic curve.  See also Function.


Predicted Value

The estimated value for the response or dependent variable at the observed values for the independent variables.


Prediction Limits

Limits for the forecast or the fitted value associated with given values of the independent variables.


Predictor Variable

A variable whose levels are selected whether or not the selection is within your control; for example, a factor level in an experiment.  Also called Independent Variable.


Prime Number

A positive integer that is not divisible without remainder by any integer except itself and 1.


Principal Components

A method for reducing the dimensionality of a set of variables by constructing uncorrelated linear combinations of them.  The combinations are computed in a way that the first component accounts for the major part of the variance; that is, it is the major axis of the points in the p-dimensional space.


Probability

The likelihood of the occurrence of any particular form of an event or result.  See also Cumulative Survival Probability, Event Probability, Survival Probability, Two-Tailed Probability.


Probability Density Function

A function of a continuous variable whose interval over a region gives the probability that a random variable falls within the region.  Also, a function of a discrete variable whose sum over a discrete set gives the probability of occurrence of a specified value.  See also Function.


Probability Distribution

The assignment of probabilities to possible values for a variable.  A distribution of the relative frequencies of a random variable.  The distribution describes the chance of a randomly chosen member of the population falling within any given range of values.  See also Distribution.


Probability Level (p-Level)

The p-value below which you reject the null hypothesis; this value is the chance of making a type I (alpha) error.  See also Level.


Probability Plot

A plot that assesses whether a set of observations could reasonably come from a normal distribution.  A plot with an arithmetic (interval) horizontal axis and a vertical axis scaled so the cumulative distribution function (cdf) of a normal distribution plots as a straight line.  The plot includes a least squares regression line for comparison.  Also called Normal Probability Plot.


Process Capability

Actual or potential capability of a process with respect to meeting specifications.  Interest may center on the standard deviation of the process, ultimately on the percentage that does not conform.


Process Fallout

The percentage of items that do not meet specifications in a production process or performance study.


Process Mean

The assumed or target average for a process.  See also Mean.


Process Sigma

The assumed or target standard deviation for a process.  See also Mean Sigma, Sigma, Standard Sigma.


Product-Moment Correlation Coefficient

A synonym for correlation coefficient.


Pure Error

The sums of squares from replicated environmental runs.  Pure error provides an opportunity to test for lack-of-fit in the fitted model.


Quadratic Line

A fitted equation that includes squared terms for one or more independent variables.  See also Fitted Line, Regression Line.


Quadratic Model

A model that includes squared terms for one or more independent variables.  See also Model.


Quadratic Exponential Smoothing

A one-parameter, triple exponential smoothing technique that places greatest weight on the most recent observations.  The forecasting equation that results is quadratic and may be appropriate to use when the underlying time-series data do not follow a nonlinear pattern.


Qualitative Factor

A synonym for categorical, nominal.  See also Factor.


Qualitative Variable

A variable, such as gender, that is nonnumeric.


Quality

The totality of features and characteristics of a product or service that bear on its ability to satisfy given needs.


Quality Control

The operational techniques and activities that sustain a quality of product or service that satisfy given needs.


Quality Improvement

The reduction of variability in a process.


Quantitative Variable

Numeric variables that contain continuous data; for example, age.


Quartile

One of four equally sized divisions of the total observations in a study.  See also Lower Quartile, Upper Quartile.


R Chart

A Range Chart.


R-Squared (Coefficient of Determination) Statistic

A statistic that measures the proportion of the variability in Y that a model accounts for.  This value ranges between 0 and 100 percent.


Random Number

Usually, a number from some table of random sampling numbers.


Random Sample

A subset of a population in which each member of the population has an equal chance of being chosen.


Random Seed

A value you submit to a random-number generator program to begin the process of producing random numbers.


Random Variable

A variable whose values are randomly determined; that is, the events, values, or subjects are chosen or occur randomly (the variable itself is not random).


Random Walk

A model that randomly forecasts the next observation based on the current observation and the mean and standard deviation of the difference of the values.


Randomization

A system for using random numbers to evenly spread the effects of factors not included in an experiment.


Randomized Block Design

A design in which you randomly assign the treatments you want to compare to positions in each of several blocks of replications.  In a complete block experiment, each block contains all treatments.  See also Design.


Randomness

An intuitive concept that refers to a condition of disorder and an unpredictability of results.


Range

The difference between the largest and smallest observed values in a sample.  A measurement of the spread or dispersion of the data.  See also Interquartile Range, Mean Range.


Range Chart

A control chart you use in statistical quality control to maintain a check on the variability of the quality of the particular product or processes.  Also called R Chart.


Rank

A numeric value assigned to an observation, that reflects the relative position of the observation among all the other observations.  Typically, the smallest observation receives rank one.


Rank Correlation Coefficient

See Kendall’s Rank Correlation Coefficient, Spearman Rank Correlation Coefficient.


Rank Test

A test that combines the data for two samples, sorts the data from smallest to largest, and compares the average ranks for the two samples of combined data.


Ratio-Scaled Data

Data that follow a graphical scale in which equal absolute variations correspond to equal proportional variations in the data.  See also Data.


Raw Data

Untabulated data.  See also Data.


Raw Mean

The sample average.  See also Mean.


Readout/Interval Data

Data for which you record failures or terminations at periodic intervals.  Also called Interval Censored Data.  See also Data.


Reciprocal

The value that results from dividing a number into 1.


Reciprocal Model

A model that is defined by the equation Y = 1/(a + bX).  See also Model.


Regression

The tendency for the mean value of one variable for given values of one or more other variables to vary with the other variables.  See also Linear Regression, Nonlinear Regression.


Regression Analysis

A mathematical tool that quantifies the relationship between a dependent variable and one or more independent variables.  The process of estimating the parameters for a model by optimizing the value for an objective function (for example, by the method of least squares), and then testing the resulting predictions for statistical significance against an appropriate null hypothesis model.


Regression Line

A graphic representation of a simple linear regression equation.  On a scatterplot, the line drawn through the pattern of points that best summarizes the relationship between the dependent and independent variables.  See also Fitted Line, Linear Line, Quadratic Line.


Rejection Region

The large and/or small values for a test statistic that lead to the rejection of the null hypothesis.  Also called Critical Region.


Relative Frequency

The proportion of the total number of occurrences to the total number of members.  See also Frequency.


Relative Frequency Polygon

A graph that is similar to a relative frequency histogram, except that the class midpoint replaces each bar and straight lines connect the midpoints.  See also Cumulative Frequency Polygon, Cumulative Relative Frequency Polygon, Frequency Polygon.


Repeatability

The variation in measurements obtained with one gage when one operator uses it several times to measure the identical characteristic on the same part.  Also called Equipment Variation, Gage Repeatability.


Repeated Measures Design

An ANOVA design in which you observe each subject under two or more conditions.  See also Design.


Replication

The number of times a specific combination of factor levels is run during an experiment.


Replicated Design

One or more complete replications of an experimental design.  See also Design.


Reproducibility

The variation in measurements obtained when several operators use one gage to measure the identical characteristic on the same part.  Also called Appraiser Variation, Gage Reproducibility.


Residual

The difference between the observed and the fitted value.  In forecasting, an error that is calculated by subtracting the forecasted value from the actual value.  See also Standardized Residual.


Residual Average

The average of the errors.  For an unbiased model, the residual average is 0.  See also Average.


Residual Mean Square

The residual sum of squares divided by its associated degrees of freedom.


Residual Plot

Any plot that includes the residuals on either the X- or Y-axis.  You can use this plot as a diagnostic tool to check model assumptions.


Residual Standard Deviation

The standard deviation of the errors.  Usually estimated by the square root of the mean squared errors.  See also Population Standard Deviation, Sample Standard Deviation, Standard Deviation.


Residual Sum of Squares

The residual after you subtract the column, row, and other special sums of squares from the total sums of squares.


Resolution

See Design Resolution.


Response

The outcome, result, or variable of a study.


Response Surface

The pattern of predicted responses based on the assumed model derived from the experimental observations.  The geometric result of plotting a response variable as a function of one or more factors.


Response Surface Methodology

A process of locating an optimal value in a higher-order model.  The methodology utilizes regression, contour plots and/or method of steepest ascent/descent.


Response Surface Plot

A plot of the predicted responses for one or more factors that use the model derived from the experimental observations.  See also Surface Plot.


Response Variable

The variable you think is influenced by the independent variables or factors.  A variable that shows the observed results of an experimental treatment.  On a plot, the values in this variable appear on the Y-axis.  Also called Dependent Variable.


Right-Sided (GT) Test

A hypothesis test in which you state the alternative hypothesis as greater than the value in the null hypothesis.


Risk

The probability of drawing the improper conclusion for a statistical test based on a sample or samples.  See also Alpha Risk, Beta Risk.


Rotatability

A design characteristic that implies that the estimated parameter variability is not a function of direction from the center of a design matrix.


Rotatable Design

A design used in the mapping of response surfaces in which fitted models estimate the response with equal precision at all points in the experimental region that are equidistant from the center of the design.


Rough

The values outside the smoothed curve.


Row Sum of Squares

The sum of squares of the deviations of the row means from their grand mean weighted by the number of cases in a row.


Runs

An experimental condition determined by a row of settings in the design matrix.  Also known as a trial.  See also Experimental Condition.


Runs Test

A statistical test you can use to check for patterns in subgroup statistics in quality control charts.


s Chart

A standard deviation chart.


S-Curve Model

A model that takes the natural log of Y and the reciprocal of X; defined by the equation Y = exp (a + b/X).  This model transforms the independent variable, linearizing the nonlinear relationship between the independent and dependent variables.  This transformation of the dependent variable helps rememdy error terms that are not normal and that do not have constant variance.  See also Model.


Sample

The subset of a population, or of all possible outcomes.  In regression, you use a random sample to make inferences about a population.


Sample Mean

The average from a set of data; usually noted as X-bar.  See also Mean.


Sample Median

The median or 50th percentile from a set of data.  See also Median.


Sample Size

The number of observations or collected items; usually noted as n.


Sample Standard Deviation

A measurement of the spread or dispersion of observations in a sample that is the positive square root of the sample variance.  See also Population Standard Deviation, Residual Standard Deviation, Standard Deviation.


Sample Variance

A measurement of the spread or dispersion of observations in a sample, based on the squared deviations from the arithmetic average divided by the degrees of freedom.


Samples

Subsets of a population.  See also Independent Samples, Paired Samples, Pooled Samples.


Sampling

The process of obtaining or selecting a subset of items from a population.  See also Sequential Sampling.


Sampling Interval

The frequency with which time-series data are collected.  For example, temperature data might be collected once each hour, making hourly the sampling interval.  Possible values for the sampling interval include daily, monthly, quarterly, hourly, each minute, each second, and so on.


Sampling Plan

A plan that designates sample size(s) and acceptance criteria.


Scatterplot

A plot of the values as point symbols along a single horizontal axis.  A plot that displays only points (no connecting lines).  See also Casement Scatterplot, Coded Scatterplot, Connected Scatterplot, Draftsman Scatterplot, Multiple Scatterplot, Three-Dimensional Scatterplot, X-Y Scatterplot, X-Y-Z Scatterplot.


Scheffe Method

A method for determining statistically significant differences among means, when the F-ratio is significant and you want to make unplanned comparisons between pairs of means.  Used for post-hoc multiple comparisons after a regression analysis or an analysis of variance.


Screening

Testing a set of factors for main effects in the hopes of reducing their numbers.


SE

An acronym for Standard Error.


Seasonality

A pattern that repeats itself over fixed intervals of time.  For example, temperature data are high in summer and low in winter, following a 12-month seasonal pattern.


Second-Degree Polynomial Function

An equation that includes squared terms or two-factor interaction terms.  Also called second-order equation.  A complete second-order polynomial includes all possible second-order terms (squared terms and two-factor interactions).  See also Function.


Second-Order Model

An equation that includes squared terms or two-factor interaction terms.  A complete second-order model includes all possible second-order terms (squared terms and two-factor interactions).  See also Model.


Sequential Sampling

Sampling inspection in which, after you inspect each unit, you decide to accept the lot, not accept it, or inspect another unit.  See also Sampling.


Shape of Data

A phrase that reflects any apparent distribution shape in a histogram for a dataset.


Shewhart Control Chart

Time sequence plots with superimposed upper and lower control limits.  See also Chart.


Sigma

The standard deviation of a population.  See also Mean Sigma, Process Sigma, Standard Sigma.


Sigma Chart

A quality control chart of the subgroup standard deviations.


Sigma Limits

Boundaries you determine by adding to and subtracting one standard deviation from the average.


Significance Level

The probability of making a wrong conclusion about the importance of a factor, based on statistics; a Type I error.  The lower the probability, the higher the statistical significance.  Also called alpha level.  See also Confidence Level, Factor Level, Probability Level.


Signs Test

A test that helps you to determine whether a hypothesized median is reasonable for a given dataset.  The test uses counts of the number of observations above and below the hypothesized value, but not the magnitudes of the differences.  See also Basic Signs Test.


Simple Exponential Smoothing

A one-parameter smoothing technique that places greatest weight on the most recent observations.


Simple Linear Regression

A model in which one independent variable is used to predict one dependent variable.


Simple Moving Average

A statistic you calculate by averaging a selected number of points on either side of a target value.  See also Average.

In Time Series, a smoothing technique that calculates smoothed values by taking the average of the previous N values of the series.  The value of N is called the order (or length) of the moving average.


Sinusoid

The sine curve, which is described by the equation y = a sin x, where the y coordinate of a point is proportional to the sine of the x coordinate.


Skewed

Asymmetrical.  The median is significantly smaller or larger than the average.


Skewed Left

In a frequency polygon, histogram, or density trace that shows the distribution of the data, the left end of the plot has a longer tail; therefore, the median is greater than the mean.


Skewed Right

In a frequency polygon, histogram, or density trace that shows the distribution of the data, the right end of the plot has a longer tail; therefore, the mean is greater than the median.


Skewness Coefficient

A measurement of the symmetry, or shape, of the data.  A skewness of 0 indicates that the data are symmetrically distributed.  Positive values of skewness tell you that the upper tail of the curve is longer than the lower tail; negative values tell you that the lower tail is longer.  See also Coefficient.


Slope

The rate at which a line or curve rises or falls across a given horizontal distance.  To calculate the slope, take any two points on the line, then divide the vertical distance (rise) between them by the horizontal distance (run) between them.


Smoothing

A methodology that combines two or more observations taken from periods during which the same causal factors were in effect, which provides a smoothed value or estimate.  The term smoothed is used because these types of combinations tend to reduce randomness by allowing positive and negative random effects to partially offset each other.


Somer's D Statistic

Statistics that show a symmetric measure of association for variables that are measured on an ordinal scale.


Spearman Rank Correlation Coefficient

A test that is equivalent to ranking each variable separately and calculating the usual correlation coefficient on the ranks.  See also Coefficient.


Specification Limits

Limits that define the conformance boundaries for an individual unit of a manufacturing or service operation.  Also called Tolerance Limits.  See also Lower Specification Limit, Nominal Specification Limit, Upper Specification Limit.


Spencer's 15-Term/21-Term Moving Averages
Spencer’s 15-Term/21-Term Moving Averages

A high-order smoothing technique used to deal with time series that exhibits substantial randomness.  In general, the greater the randomness, the larger the number of terms selected in the moving average method.


Split Plot Design

A design that subdivides (splits) the group of experimental units (plot) to which you assign the same level of a principal factor, allowing you to study one or more additional principal factors within each level of that factor.  See also Design.


Spread of Data

The variability in a group of values.  Also, a synonym for dispersion.


Square Plot

A plot of the predicted values for the dependent variable versus the high and low values for a factor.  A response plot of the estimated responses for two factors in an experimental design.  See also Plot.


Square Root

A number that, when multiplied by itself, produces the given number.


s-Squared Chart

A variables control chart with control limits based on the variances of the subgroups.


Stacked Barchart

A plot that displays categorical data in either a horizontal or vertical format and stacks associated bars on top of one another.  See also Barchart.


Standard Deviation

A measurement of the spread or dispersion of data.  A statistic that defines an average size of the deviation for a single observation from its expected value.  Also called sigma.  See also Population Standard Deviation, Residual Standard Deviation, Sample Standard Deviation.


Standard Error

The standard deviation divided by the square root of the sample size.  The standard deviation of a sampling distribution.  See also Internal Standard Error, Pooled Standard Error.


Standard Error Bars

Lines that extend from the means plus and minus one standard error.  See also Error Bars.


Standard Error of Estimate

This statistic explains the value for the standard deviation of the residuals.  You can use this value to construct prediction limits for new observations.  Explains the value for the deviations from a line, curve, or surface of regression; usually estimated by the square root of the mean squared error.


Standard Mean

The assumed or target average.  See also Mean.


Standard Order

The order of the experimental runs of the design matrix for a two-level factorial design where the first column consists of successive low and high settings, the second column consists of successive pairs of low and high settings, the third column consists of four low settings followed by four high settings, and so on.


Standard Sigma

The assumed or target standard deviation.  See also Mean Sigma, Process Sigma, Sigma.


Standardize

To put measurements on a common standard scale by subtracting the mean and dividing the standard deviation.


Standardized Kurtosis

A measurement that tests for significant deviations from the normal distribution.  With large samples, the standardized coefficient is approximately unit normal.  When the values for the standardized coefficient are outside the range -2.0 to +2.0, the data may depart significantly from a normal distribution.  See also Coefficient of  Kurtosis, Kurtosis.


Standardized Skewness

A measurement that tests for significant deviations from the normal distribution.  With large samples, the standardized coefficient is approximately unit normal.  When the values for the standardized coefficient are outside the range -2.0 to +2.0, the data may depart significantly from a normal distribution.  See also Skewness Coefficient.


Standardized Pareto Chart

A plot you can use to determine significant effects from an experimental design.  The values shown are the effects divided by the standard errors.


Standardized Residual

A residual divided by the standard deviation of the residuals.  See also Residual.


Standardized Value

A value minus the average of the sample and divided by the standard deviation of the sample.


Star Symbol Plot

A graph of multivariate data that compares different observations so you can see the relative values for all the variables at once.  Each star represents one observation in the data.


Stationary

A time series is stationary when it is based on a constant mean and variance, and when its statistical properties are independent of the time period during which it is observed.


Statistic

A numerical measure you calculate from a set of sample observations, most often to form an estimate of some population parameter.


Statistical Tolerance

Engineering tolerances based on statistical analysis of product variation.  Also, limits that have a given chance of including a specified percent of the products.


Stem-and-Leaf Plot

A table that shows the range and concentration of the values, the symmetry of the data, and if there are gaps or outliers.  In exploratory data analysis, a display for a single quantitative variable that allows you to visually examine the distribution of the data.


Stepwise Variable Selection

An automatic search method for selecting one regression model from several candidate independent variables.


Strip Plot Design

An experimental design in which you arrange the experimental units in rectangles, such as an agricultural field.  You apply the levels for one factor to the rows, and the levels for the other factor to the columns.  The design is helpful when the application method does not allow you to treat the experimental units individually.  See also Design.


Studentized Residuals Plot

A plot that scales the residuals by an estimate of the variance from the data with the observation removed.  A large studentized residual value may indicate an outlier and an influential observation.


Student's t Distribution

A distribution useful in forming confidence intervals for the mean when the variance is unknown, testing to determine if two sample means are significantly different, or testing to determine the significance of coefficients in a regression.  The distribution is similar in shape to a Normal distribution.  See also Distribution.


Subgroup

A set of groups of observations you obtain by subdividing a larger group of observations.


Subgroup Size

The number of items in a subgroup.


Subgroup Statistics

Any numeric values you calculate from a subgroup; for example, X-Bar.


Sum

The simple sum of the observations in a variable.  See also Cumulative Sum.


Sum of Squares

The sum of the squared deviations from the mean of the sample observations.  See also Error Sum of Squares, Residual Sum of Squares, Row Sum of Squares, Total Sum of Squares.


Sum of Squares between Groups

In One-way ANOVA, the amount of variance calculated across samples.


Sum of Squares within Groups

In One-way ANOVA, the amount of variance calculated inside the samples.


Summary Statistics

Statistical information about the center, spread, and shape of one or more variables.  The group includes the average, median, mode, geometric mean, variance, standard deviation, standard error, minimum, maximum, range, lower quartile, upper quartile, interquartile range, coefficients of skewness and kurtosis (with standardized values of each), coefficient of variation, and sum.


Sunray Plot

A plot that provides a visual comparison of different observations with the means for the variables.  A separate glyph is plotted for each observation in the data.


Surface Plot

A three-dimensional plot of a response surface that is useful in locating optimal regions.  It shows the relationship between the estimated dependent variable and two variables you select.  A plot that represents a three-dimensional grid surface for the function Z = f(X,Y).  You view the plot from outside the plot area at an angle oblique to the X- and Y-axes.  See also Response Surface Plot.


Survival Probability

The likelihood of remaining or surviving for a specified amount of time or value.  See also Cumulative Survival Probability, Event Probability, Two-Tailed Probability.


Survivor Function

A function that produces a plot of the survivor function for a distribution you select.  The plot shows the probability of observing a value greater than the specified value.  The survivor function is 1 - CDF.  For reliability data, the survivor function shows the probability of surviving to time x without failure.  See also Function.


Symmetric Distribution

A distribution whose left value is a mirror image of the distribution to the right of the value.  In a symmetric distribution, the mean and median are equivalent.  See also Distribution.


Symmetric Matrix

A matrix that is equal to its transpose.  See also Matrix.


t Distribution

A synonym for Student's t distribution.  See also Distribution.


t-Statistic

In a t test, the number you compare with the critical region.  Also called t-Value.


t-Test

A test that determines whether two means from two independent, normally distributed samples differ.


t-Value

A synonym for t-statistic.


Table

See Frequency Table, Means Table, Multi-Way Table, Two-Way Table.


Table of Frequencies

A tabular display of the number of items that fall within categories or numerical classes.


Tabulate

To count or categorize data.


Tabulated Data

Values you place in categories or numerical classes.  See also Data.


Tail Areas

An analysis whose results display the area under the density curve at specified points using the cumulative distribution function.  The function calculates the probability that a random variable will fall below a given value.


Taper

A bias-reducing process that damps or tapers a time-series variable at its two ends.  STATGRAPHICS Plus uses a cosine bell tapering method to calculate the transformed values.


Test Statistic

A statistic you use to test a finding for statistical significance — not to describe a sample or to estimate a population parameter.


Three-Dimensional Frequency Histogram

A three-dimensional graph that plots the first variable along one axis, the second variable on another axis, and the frequency on the vertical axis.  See also Frequency Histogram, Histogram.


Three-Dimensional Scatterplot

An X-Y-Z Scatterplot.  See also Plot.


Three-Level Factorial Design

A design that combines the low, median, and high for each factor with all three levels of every other factor.  You can reduce the number of experimental runs by fractioning the design.  See also Design.


Time-Censored Data

Data in which every item begins at the same time and in which the experiment ends after a specified amount of time.  Also called Type I Data.  See also Data.


Time Series

The values for a variable, in ordered sequence, that are observed at equally spaced time intervals.


Time Series Data

Data taken at specific time intervals.  See also Data.


Time-Weighted Charts

Control charts that incorporate the past history of a process to estimate the charted point.  They are generally more sensitive to small, gradual changes in the process than Shewhart charts.


Tolerance Interval

See Tolerance Limits.


Tolerance Limits

The values between which you can expect to find a specified proportion of a population.  See also Distribution-Free Tolerance Limits, Normal Tolerance Limits.


Tolerance Width

The range of the tolerance limits.


Total Sum of Squares

The sum of squares for the deviations of the individual items from the mean of all the data.


Trading Day

An active day in a month; that is., a business day rather than a holiday or weekend.  Trading-day adjustments are made to time-series data to reflect the fact that similar periods may not include the same number of trading days.


Transform Data

To perform a quantitative operation on a variable; for example, taking the log.  You often transform data to stabilize the variance.


Transformation

See Logarithmic Transformation, Orthogonal Transformation.


Trend

Values for a variable that has movement in one direction.  Trend can follow any of various functional forms such as linear, quadratic, exponential, S-curve, and so on.


Trial

A synonym for an experimental run.


Tukey's Honestly Significant Differences (HSD) Test

A method for determining statistically significant differences among means, based on the range distribution.  A test you can perform to determine which means are significantly different from the overall mean.


Two-Level Factorial Design

A screening design that combines the low and high levels of each factor with two levels of every other factor.  You can reduce the number of experimental runs by fractioning the design.  See also Design.


Two-Sided (NE) Test

A hypothesis test in which the alternative hypothesis is that the values are not equal.


Two-Tailed Test

A test of a hypothesis that has two critical values, both an upper and a lower rejection region.


Two-Way Analysis of Variance

A technique that determines the effect of two variables on a population.  In two-way analysis of variance, you analyze the effect of two factors on one variable.  See also Analysis of Variance, Multifactor Analysis of Variance, One-Way Analysis of Variance.


Two-Way Design

An ANOVA or experimental design in which you analyze the effects of two factors on a response variable.  See also Design.


Two-Way Table

A contingency table for two categorical variables.  See also Frequency Table, Means Table, Multi-Way Table.


Type I Data

Data in which every item started at the same time and in which the experiment ended after a specified amount of time.  Also called Time Censored Data.  See also Data.


Type I Error

The error of rejecting a hypothesis when it is true.  Also called Alpha Error.  See also Error.


Type I Sums of Squares

A method for computing the sums of squares for each factor in the order you enter the factors.  See also Sum of Squares.


Type II Error

The error of accepting a hypothesis when it is not true.  Also called Beta error.  See also Error.


Type II Data

Data gathered during an experiment that ended after a specified number of failures or deaths.  Also called Failure-Censored Data.  See also Data.


Type III Sums of Squares

Computes additional sums of squares for each factor as through that factor was the last one added to the model.  See also Sum of Squares.


u (Count per Unit)

The average count, or average number of events of a given classification, per unit (unit area of opportunity) that occurs within a sample.  More than one event can occur in a unit (unit area of opportunity); each event is counted.


u Chart

An attributes control chart that allows you to construct control limits based on an attribute that is related to frequency, such as the number of defects per item.  This chart is similar to a c Chart except that it expresses rates rather than absolute numbers.  The u Chart is especially helpful when the sample or subgroup size is not constant.


UCL

An acronym for Upper Control Limit.


Unbalanced Design

Factorial designs that contain unequal numbers of observations for different factor levels or combinations, or cells that contain unequal numbers of subjects.  Also called unbalanced experimental design.  See also Design.


Unbalanced Nested Design

A nested design in which the number of levels of the nested factor varies for the different levels of the factor above the nested factor and the number of replications for the different factor combinations are unequal.  See also Design.


Unbalanced One-Way Design

A one-factor ANOVA design in which you do not run each factor level an equal number of times.  See also Design.


Unblocked Design

An ANOVA or experimental design that does not include a blocking factor.  See also Design.


Uncertainty

An indication of the variability associated with a measured value that takes into account two major components of error:  Bias and the random error attributed to the imprecision of the measurement process.


Uncertainty Coefficient

In crosstabulation, a statistic for measuring the linear relationship between two categorical variables.  See also Coefficient.


Uniform Distribution

A distribution useful for characterizing data that range over an interval of values, each of which is equally likely.  See also Distribution.


Unit Normal

The normal distribution having a mean of zero and a standard deviation of one.  Also called Unit Gaussian.


Univariate Data

A set of data represented by a single variable.  See also Data.


Univariate Plot

A plot that allows the study of the distribution of cases for one variable.  See also Plot.


Unsaturated Model

A model that does not contain all possible factors or independent variables.  See also Model.


Unspecified Values

Values that do not fall into any of the specified recoding intervals.


Upper Capability Indices

A statistic that represents the distance from the upper specification limit to the mean divided by half the sigma range.


Upper Control Limit

The control limit for points that plot above the center level.  Also called UCL.  See also Control Limits, Lower Control Limit.


Upper Quartile

The value above which 25 percent of the data will lie; the 75th percentile.  See also Lower Quartile, Quartile.


Upper Specification Limit

A specification limit applicable to the upper conformance boundary for an individual unit of a manufacturing or service operation.  See also Lower Specification Limit, Nominal (Target) Value, Specification Limits.


Upper Tail (of a Distribution Curve)

The location of the largest values in a distribution.  See also Tail Area.


User-Defined Design

An experimental design in which you specify and enter the factor levels and runs.  See also Design.


USL

An acronym for upper-specification limit.


v-Mask

A v-shaped mask used with a CuSum Chart.  When cumulative sums cross the "arms" of the v-mask, you consider the process to be out of control.


Validation

A process for testing a model’s ability to make forecasts where some of the sample data are “held out” of the model-fitting process and used to test the model’s forecast accuracy.


Variables Control Chart

A control chart for plotting central tendency and variability.  Available charts are X-Bar and R, X-Bar and S X-Bar and S^2, and Individuals.


Variance Chart

A quality control chart of the subgroup variances.


Variation

A quantifiable measure of the deviations from a target value.  You can use control charts to detect and remove assignable causes of variation.  See also Appraiser Variation, Equipment Variation, Operator Variation.


Warning Limits

Limits on a control chart, usually drawn at 2 sigma.  If a process exceeds the warning limits, you should take more data for study.


Weibull Distribution

A distribution useful for random variables constrained to be greater than 0; characterized by the Shape and Scale parameters.  A distribution that is an appropriate model for product failures because its failure rate curves can take various shapes.  This distribution is a generalization of the exponential distribution.  See also Distribution.


Weighted Average

The result of multiplying each data value in a variable by its associated weighting factor and dividing the total by the sum of the weighting factors.  See also Average.


Whisker

The line on a Box-and-Whisker Plot that extends from each end of the box to data values within 1.5 times the interquartile range.


White Noise

Random error.  An error that does not result from an assignable cause.  See also Noise.


Wilcoxon Signed-Rank Test

A test that helps you to determine whether a hypothesized median is reasonable for a given dataset.  The test calculates the difference between the data values and the hypothesized median, and ranks the absolute values of the difference.  By comparing the sum of the ranks for observations above the median to those below the median, the program forms a test statistic for the hypothesis.


X-Axis

The horizontal axis on a graph.


X-Bar

A symbol (an uppercase X with a line over it) that represents the mean of a sample.


X-Bar Chart

A quality control chart that plots the averages of collected subgroup data.


X-Bar and R Chart

A variables control chart with control limits based on the X-bars and ranges for the subgroups in the data.


X-Bar and S Chart

A variables control chart with control limits based on the X-Bars and sigmas (standard deviations) for the subgroups in the data.


X-Bar and S-Squared Chart

A variables control chart with control limits based on the X-Bars and variances for the subgroups in the data.


X-Y Lineplot

An X-Y Plot that connects lines without points.


X-Y Scatterplot

A scatterplot that shows points only (no connecting lines).  It plots one variable versus another to examine the relationships.


X-Y-Z Lineplot

A three-dimensional X-Y-Z Plot for three or more variables that connects lines without points.


X-Y-Z Scatterplot

A three-dimensional scatterplot for three or more variables that shows points only (no connecting lines).


Y-Axis

The vertical axis on a graph.  Also called the Ordinate.


Y-Intercept

The point at which a regression line intersects the vertical (Y) axis.


Yates' Order

The standard order for a two-level factorial design.


Z-Axis

The third axis on an X-Y-Z Plot.


z-Score

The most commonly used standard score, in which the mean is 0 and a standard deviation is 1.  For example, a z-score of 1.5 is one and one-half standard deviations above the mean, and a z-score of -1 is one standard deviation below the mean.


z-Score for Kurtosis

A statistic that shows the degree of peakedness of a distribution.  Unlike the standardized kurtosis, the z-score for kurtosis is valid for small sample sizes (n is less than or equal to 20).


z-Score for Skewness

A statistic that shows whether the data are symmetrically distributed; if so, the data are likely to be normally distributed.  Unlike the standardized skewness, the z-score for skewness is valid for small sample sizes (n is less than or equal to 8).


z-Statistic

A test statistic you compare to the standard normal distribution.  Typically used for testing averages when the sample sizes are large.  Also called Test Statistic Z.


Zero Correlation

No linear relationship exists between two variables; that is, the variables are statistically independent.  See also Correlation.


3-Level Design

An experiment in which all the factors are set at one of three levels:  Low, Medium, or High.  For example, -1, 0, 1 or 1, 2, 3.


2-Level Design

An experiment in which all the factors are set at one of two levels:  Low or High.  For example, -1, +1 or 1, 2.


3 RSR

A nonlinear smoothing technique that includes a median for a value and three points around that value:  Resmoothing (R), a splitting operation to eliminate flat segments in the data (S), and a second resmoothing (R).


3 RSS

A nonlinear smoothing technique that includes a median for a value and three points around that value:  Resmoothing (R), and two splitting operations to eliminate flat segments in the data (SS).


3 RSSH

A nonlinear smoothing technique that includes a median for a value and three points around that value:  Resmoothing (R), two splitting operations to eliminate flat segments in the data (SS), and a “Hanning” weighted average with weights .25, .5, and .25 (H).


5 RSS

A nonlinear smoothing technique that includes a median for a value and five points around that value:  Resmoothing (R), and two splitting operations to eliminate flat segments in the data (SS).


5 RSSH

A nonlinear smoothing technique that includes a median for a value and five points around that value:  Resmoothing (R), two splitting operations to eliminate flat segments in the data (SS), and a “Hanning” weighted average with weights .25, .5, and .25 (H).


Algorithm

A special process for solving a problem, particularly a method that continually repeats some basic process; a set of rules or procedures, similar to an equation.  See also Newton-Raphson Algorithm.


Alias Pattern

A display that shows the main effects and interactions, and any confounding that involves the main effects or interactions.


Aliased Effects

The effects of two or more factors that cannot be separated and assigned.  Also called confounded effects.  See also Factor Effects, Row Effects.


Aliases

Two or more main or interaction factors whose effects are estimated by the same contrast and, therefore, cannot be estimated separately.


Aliasing

Confusing two or more factors so their effects cannot be separated; setting two or more factors at the same levels throughout the experiment; that is, the columns are 100 percent correlated.  Also called confounding.


Alpha Error

The error of rejecting a hypothesis when it is true.  Also called Type I error.  See also Error.


Alpha Level

The alpha risk (the probability of a Type I error); determines the probability of declaring a process out of control when, in fact, it is not.  See also Level.


Alpha Risk

The probability of a Type I error; that determines the probability of declaring a process out-of-control when, in fact, it is not.  See also Beta Risk.


Alternative Hypothesis

The alternative that you are willing to accept if you do not accept the null hypothesis.  Sometimes called the hypothesis of change.  See also Hypothesis, Null Hypothesis.


Analysis of Covariance

A technique for estimating and testing the effects of treatments when one or more concomitant variables influence the response variable.  See also Covariance.


Analysis of Variance

A technique that subdivides the total variation in a set of data into meaningful component parts that can be associated with specific sources of variation; this allows you to test a hypothesis on the parameters of the model or to estimate variance components.  See also One-Way Analysis of Variance, Two-Way Analysis of Variance.


ANOVA

Analysis of Variance.  A statistical tool based on F ratios that measures whether a factor contributes significantly to the variance of a response.  Also determines the amount of variance that is due to pure error.


Appraiser Variation

The variation in measurements obtained when several operators use one gage to measure the identical characteristic on the same part.  Also called reproducibility.  See also Equipment Variation, Operator Variation.


ARIMA

An abbreviation for Autoregressive Integrated Moving Average.  This class of forecasting model, popularized by Box and Jenkins, comprises an AR parameter that represents the order of the autoregressive portion of the model, and an MA parameter that represents the order of the moving average in the model.


Area of Opportunity

A unit or portion of a material, process, product, or service in which designated events may occur.


Asymmetric Matrix

A matrix with dependent rows and columns.  See also Matrix.


Asymptotic Normality

The property in which the coefficient estimates from regression approach normality as the sample size increases, even if the distribution of the dependent variable is far from normal.


Attribute

An inherent property usually measured by a finite number or a discrete set of values.


Attributes Control Chart

One of four charts (np, p, c, and u) that allow you to construct control limits based on a specific attribute of a sample.  See also Chart.


Autocorrelated Residuals

An indication that the forecasting method has not removed all of the pattern from the data when residual or error terms remain after you apply a forecasting method.  See also Autocorrelation.


Autocorrelation

The association of the same time series at different time periods.  You use the pattern of autocorrelation coefficients to identify seasonality in a time series and to determine an appropriate model for the data.


Autocorrelation Coefficient

A coefficient that assesses the time-lagged correlations in time series data.  See also Coefficient.


Autoregressive (AR)

A form of regression that, instead of relating the dependent variable, relates past values at varying time lags.


Autoregressive/Moving Average (ARMA) Scheme

A type of time-series forecasting model that can be autoregressive (AR) in form, moving average (MA) in form, or a combination of the two (ARMA).  In an ARMA model, the series to be forecast is expressed as a function of both previous values of the series and previous error values from forecasting.


Average

A measure of the central tendency of the data.  Also called mean.  See also EWMA, Exponentially Weighted Moving Average, Residual Average, Simple Moving Average, Weighted Average.


Axial Distance

In a central composite design, the distance from the center of a cube to a point in the star portion of the design.


Balanced Design

An ANOVA or two-level experimental design that is balanced if each factor is run the same number of times at the high and low ends.  See also Design.


Balanced Experimental Design

An experimental design in which each unique combination of factor levels are run an equal number of times.  See also Design.


Balanced Incomplete Block Design

A design in which it is not possible to include all factor combinations in every block.  However, every factor-level combination occurs an equal number of times and each pair of factors occurs together in an equal number of blocks.  See also Design.


Balanced Nested Design

A nested design in which there is an equal number of levels of the nested factor across all levels of the other factors.  In addition, the number of observations is equal at all combinations of the factor levels.


Balanced One-Way Design

A one-factor ANOVA or experimental design in which you run each factor level an equal number of times.  See also Design.


Balanced Randomized Block Design

An ANOVA or experimental design in which you consider two kinds of effects:  The treatments, which are of most interest, and a nuisance factor, which you block to eliminate its effect.  You can run the nuisance factor randomly within each block to protect against unknown sources of bias.  You can also balance the design  by running all the treatment factor levels the same number of times within each block.  See also Design.


Barchart

A graphical display of a frequency table, where each bar represents an individual row or cell in the table.  The height of the bar corresponds to the frequency, or the number of times that a value appears in the data.


Bartlett's Test

A statistical test for homogeneity of variance.  The hypothesis is that variances across different levels are equal.  If the significance level is greater than .05, accept the hypothesis (the variances are not significantly different, they are equal).


Baseline

The starting point for the bars in a Barchart or Pareto Chart, or the vertical lines in a Vertical Time Sequence Plot.


Baseline Value

The average value for a variable before you apply an experimental treatment or before you measure of the effect of a new variable.


Bernoulli Distribution

A distribution whose outcome has only two possibilities:  Success or failure.  Also known as binomial distribution.


Best-Fitting Normal Distribution

A normal distribution fit to a set of data in which the program calculates the average and standard deviation.  See also Distribution.


Beta Distribution

A distribution that is useful for random variables constrained to lie between 0 and 1; characterized by two parameters:  Shape 1 and Shape 2.


Beta Error

The probability of accepting a null hypothesis when it is not true.  Also called Type II error.  See also Error.


Beta Risk

The probability of a Type II error; determining the probability that declaring a process in control when, in fact, it is not.  See also Alpha Risk.


Beta Value

The assigned level of beta error used to determine an appropriate sample size for statistical testing techniques.


Bias

The difference between the mean value for a sample statistic and the population parameter it is used to estimate.


Biased Estimate

An estimate in which the expected value of a sample statistic overestimates or underestimates a population parameter.  See also Estimate.


Binomial Distribution

A distribution that gives the probability of observing successes in a fixed number of independent or Bernoulli trials.  Also called Bernoulli distribution.


Biplot

A plot that contains a scatterplot of principal components and a line for each variable that reflects how each of the variables contributes to the components.  The lines on a Biplot, which intersect at (0,0), represent the original variables.


Bivariate Normal Distribution

The distribution that results when each value from a pair of values comes from a normal distribution.  In correlation analysis, you assume the pair of X and Y values come from a bivariate normal distribution.  See also Distribution.


Block

In a spreadsheet, a contiguous group of selected cells in which the active cell has a dark border and all the other cells are black.  In text, a contiguous group of characters, numbers, and/or special symbols in which all the text is highlighted.


Block Effect

The change in the average response between blocks.  By estimating the block effects, you can remove the influence (variability) of the blocking from the estimates of the other effects.  See also Main Effect.


Blocked Design

An experimental design in which you group respondents into categories (blocks).  You can then treat each block as a unit in the analysis.  See also Design.


Blocking Variable

A variable (factor) that cannot be randomized.  The experiment is usually run in blocks for each level of the blocking variable and randomization is performed within the blocks.


Bonferroni Method

A method for determining statistically significant differences between means when the F-ratio is not significant, but a small number of comparisons are planned.; a method for estimating the probability of making at least one Type I error when conducting a series of t tests on the means of three or more groups.


Box-and-Whisker Plot

A graphical summary of the presence of outliers in data for one or two variables.  This plot, which is particularly useful for comparing parallel batches of data, divides the data into four equal areas of frequency.  A box encloses the middle 50 percent, where the median is represented as a vertical line inside the box.  The mean may be plotted as a point.

Horizontal lines, called whiskers, extend from each end of the box.  The lower (left) whisker is drawn from the lower quartile to the smallest point within 1.5 interquartile ranges from the lower quartile.  The other whisker is drawn from the upper quartile to the largest point within 1.5 interquartile ranges from the upper quartile.

Values that fall beyond the whiskers, but within 3 interquartile ranges (suspect outliers), are plotted as individual points.  Far outside points (outliers) are distinguished by a special character (a point with a + through it).  Outliers are points more than 3 interquartile ranges below the lower quartile or above the upper quartile.


Box-Behnken Design

A three-level design used for quantitative factors and designed to estimate all the main, quadratic, and two-way interaction effects. The design is a combination of two-level factorials and incomplete block designs.


Box-Cox Transformation

A method for transforming time-series data to stabilize the variance of the series and to make the distribution closer to normal.  There are two parameters:  The power (or strength) of the transformation, and the addend, which is the value that the program adds to the data before the power is raised.


Box-Jenkins Methodology

The application of autoregressive/moving average schemes to time-series forecasting problems and popularized by George E. Box and G. M. Jenkins.  Box and Jenkins suggested the general methodology of applying ARIMA models to time-series analysis, forecasting, and control; in time-series forecasting, the methodology is known as the Box-Jenkins Method.


Box-Pierce Test

A test for randomness that helps to determine if a set of autocorrelations differs from the null set; also known as a Portmanteau Test.


Brown's Linear Exponential Smoothing

A one-parameter, double-exponential smoothing technique that places greater weight on the most recent observations.


C (Count)

The count or number of events for a given classification that occurs in a sample.  More than one event can occur in a unit (area of opportunity); each such event counts throughout the sample.


c Chart

An Attributes Control Chart, based on the Poisson distribution, that allows you to construct control limits based on an attribute that is related to frequency, such as the number of defects per item.  See also Chart.


Capable Process

A process that is capable of performing within specified limits.


Capability Indices

Statistics that indicate the inherent capability of a process.  The available measures include:  Cp, Cpk, Cpm, Cr, and K.  See also Lower Capability Indices, Upper Capability Indices.


Casement Plot

A plot of the X and Y variables in groups determined by the Z variable.  The plots contain only those points that fall within regions that are covered by the third and/or fourth variables.  With a four-variable Casement Plot, the program arranges scatterplots in a matrix where the columns  are arranged by the values of the third variable and the rows by the values of the fourth variable.  The program draws scatterplots in the top and right margins of the matrix, which contain all the points in a given row or column.  A plot in the upper right corner contains all the points.


Categorical Data

Data that you can divide into classes.  See also Data.


Categorical Factor

A qualitative factor.  A factor, such as gender, that is nonnumeric.  See also Factor.


Causality

The assertion that changes to an input factor directly result in a specified change to an output.


Censored Data

Data that are incomplete in some way; for example, having certain values that are unknown, or having a situation in which an event does not occur during the period of observation.


Censoring

An event that occurs when you have to stop a study before every item fails or when, for various reasons, you have to withdraw items before the study ends.


Censoring Indicator

An indicator that specifies whether an item died or failed, or was censored.


Censoring Time

The time at which you stop a study before every item fails or at which you withdraw an item before the study ends.


Centerpoint

A design point in which you simultaneously run all the factors halfway between their high and low levels.  All the factors must be continuous variables.  Use centerpoints to add additional runs to the experiment, to check for curvature in screening designs, and to estimate pure error when designs are replicated.  Also called Design Centerpoint.


Central Composite Design

A three-level design that starts with a two-level factorial and some centerpoints.  Typically used for quantitative factors and designed to estimate all the main effects plus the desired quadratics and two-way interactions.  The design has two parts:  A factorial and a star.  The star portion of the design consists of an additional set of points arranged at equal distances from the center of the cube on radii that pass through the centerpoint in the face of the cube.


Central Tendency

The average, median, mode, and geometric mean measure for the central tendency of the data.


Centroid

A point whose coordinates are the mean values for the coordinates of the points in a configuration.  A two-group discriminant analysis has two centroids, one for each group.


Character Variable

A variable that contains characters and/or numbers that you treat as characters.  You cannot run calculations on character variables.


Chart

See Attributes Control Chart, BarChart, C Chart, Control Chart, Cumulative Sum Chart, Custom Chart, CuSum Chart, EWMA Chart, Exponentially Weighted Moving Averages Chart, Individuals Chart, MA Chart, Moving Averages Chart, Moving Range Chart, MR Chart, MR(2) Chart, Multivariate Control Chart, NP Chart, Number of Defectives per Item Chart, Number of Defectives per Sample Chart, P Chart, Pareto Chart, Piechart, R Chart, Range Chart, S Chart, Shewhart Control Chart, Sigma Chart, Time-Weighted Chart, U Chart, Variables Control Chart, Variance Chart, X-Bar Chart, X-Bar and R Chart, X-Bar and S Chart, X-Bar and S Squared Chart.


Chi-Square Distribution

A distribution that is useful for random variables constrained to be greater than 0; characterized by one parameter:  Degrees of Freedom.  See also Distribution.


Chi-Square Statistic

A statistic that allows you to compare observed with expected frequencies.  If none of the expected frequencies are too small, the statistic follows a chi-square distribution.  Large chi-squares can lead to the conclusion that two distributions are different (stated as a significance level less than p, typically 95 or 99 percent) that they are the same.  A small chi-square can lead to the conclusion that two distributions are similar (stated as a significance level greater that some p, typically 95 or 99 percent).  Also called Portmanteau Statistic.


Chi-Square Test
Chi-Square Test for Independence

An method that performs a hypothesis test to determine whether or not to reject the notion that two variables are independent.  A test that calculates a chi-square statistic that compares observed frequencies with the expected frequencies predicted by the fitted distribution.  The test allows you to determine whether a Normal distribution or other specified distribution type adequately represents the data.


Class (of Data)

A division of the range of the set for all the observations in a random variable.


Classical Decomposition

An approach to forecasting in which the underlying pattern of a time series is broken into cyclical, seasonal, trend, and random subpatterns.  You can then individually analyze and recombine the subpatterns to obtain forecasts for the original series.


Classification Codes

Numeric or character variables that classify data into different categories.


Classification Data

Data that contain codes that indicate the class (or category) for each observation.  See also Data.


Classification Factor

An attribute you can use to group categorical data into classes; for example, gender, age, or height.  See also Factor.


Classification Function Coefficients

The set of coefficients estimated for each category of a classification variable in Discriminant Analysis.  Use these coefficients to place new observations in an appropriate category.  See also Coefficient.


Classification Variable

A variable that contains individual observations that you have classified into categories.


Cluster

A group of similar points; a group of observations that would be close to each other if you could plot them in multi-dimensional space.


Clustered Barchart

A plot that displays categorical data (data that you can divide into classes) in either a horizontal or vertical format and in which multiple bars are placed side by side.


Clustering Method

One of several methods (Nearest Neighbor, Furthest Neighbor, Centroid, Median, Group Average, Ward’s, and K-Means) for grouping observations from a multivariate dataset into clusters of similar points.  All of the methods except K-Means are hierarchical clustering methods.  K-Means provides one nonhierarchical method.  Each method uses different criteria to measure the distances among clusters.  The analysis in each hierarchical method begins with an individual observation as its own cluster.  The program then combines observations into successively larger clusters until it reaches the number of clusters that you specify.


Cochran's C Test

A statistical test for homogeneity of variance.  The hypothesis is that the variances across different levels are equal.  If the program reports a significance level greater than .05, you accept the hypothesis; that is, you accept that the variances are not significantly different (they are equal).


Coded Scatterplot

A Scatterplot that uses only coded points (no connecting lines) to indicate the levels of a classification factor.


Coefficient

The numerical part of a term, usually written before the literal part, such as 3 in the term 3x.  See also autocorrelation coefficient, classification function coefficients, contingency coefficient, correlation coefficient, Kendall’s rank correlation coefficient, kurtosis coefficient, partial correlation coefficient, Pearson’s correlation coefficients, regression coefficient, skewness coefficient, Spearman rank correlation coefficient, standardized skewness, uncertainty coefficient.


Coefficient Correlation Matrix

A square matrix of estimated correlations between model coefficients.  See also Matrix.


Coefficient of Kurtosis

A measurement of the flatness or steepness of the distribution of the data with respect to a Gaussian or normal distribution.  For a normal distribution, the kurtosis coefficient is 0.  When the coefficient is less than 0, the curve is flat with short tails.  When the coefficient is greater than 0, the curve is either very steep at the center or has relatively long tails.  See also Kurtosis, Standardized Kurtosis.


Coefficient of Skewness

A measurement of the symmetry, or shape, of the data.  A skewness of 0 indicates that the data are symmetrically distributed.  Positive values of skewness indicate that the upper tail of the curve is longer than the lower tail; negative values indicate that the lower tail is longer.  See also Skewness, Standard Skewness.


Coefficient of Variation

A measurement that allows you to compare the amount of variance in two or more variables that are measured in different units.  A measure of the relative dispersion that is the standard deviation divided by the mean and multiplied by 100 to give a percentage value.  You cannot use this measure when the data takes both negative and positive values or when you have coded it in such a way that the value X=0 does not coincide with the origin.  See also Appraiser Variation, Equipment Variation, Operator Variation.


Collinear Independent Variables

Independent variables that are correlated.  In regression, high intercorrelation produces large standard errors for the regression coefficients, which leads to questionable conclusions regarding statistical significance.  See also Variable.


Communality

The amount of variance an original variable shares with all the other variables in an analysis.


Component-plus-Residuals Plot

A plot of the residuals around a line that is defined by the term

Bj(xij - Xj)

that multiplies the centered value of the independent variable Xj by the associated value of its regression coefficient Bj.  You can use this plot to judge the relative magnitude of the residuals with respect to the explanatory power of the variable.  Also called Component Effects Plot.


Conditional Gamma

A chi-square-based measure of association.


Confidence Bands

On a plot for a fitted line, the pair of dotted lines that appear closest to the regression line and that represent the confidence limits for the mean response at a given value of X.


Confidence Intervals

An interval that shows the precision of the estimated coefficients given the amount of available data and noise in the model; a range of values based upon a sample mean and a standard deviation that has a given probability for containing the true population parameter.


Confidence Limits

The end points of a confidence interval.  Commonly used limits are 90, 95, and 99 percent.


Confounded Effects

The effects of two or more factors that you cannot separate and assign.  The result of the factors being set at the same levels throughout the experiment.  Also called Aliased Effects.


Confounding

Confusing two or more factors so you cannot separate their effects.  Also called Aliasing.


Constant Term

A term that does not have an associated variable.


Contingency Coefficient

A version of a Chi-Square test that measures the strength of the dependency between two characteristics.  See also Coefficient.


Continuous Data

Quantitative data.  Data, such as age, that you can measure numerically.  See also Data.


Continuous Factor

A quantitative factor.  A factor, such as temperature, that you can measure numerically.  See also Factor.


Contour Plot

A two-dimensional plot of a response surface where the contours of the plot represent the height of the surface; useful for determining optimal regions.  In experimental design, the contours represent the estimated level of the response variable.  In advanced regression, the contours represent the estimated dependent variable as a function of the other variables.


Control Chart

A graph of the results from sampling the product for a manufacturing process; consists of a horizontal line that represents the expected mean value of some characteristic of quality and two lines on either side that indicate the allowable extent of sampling and/or random product deviations.


Control Limits

On a Control Chart, the lines above and below the central horizontal line that designate the area into which a stated proportion of the sample statistics should fall.  See also Lower Control Limit, Upper Control Limit.


Control Mean

The target value for the process mean.  See also Mean.


Control-to-Standard

When generating control charts for attributes or variables, a type of study that produces a chart based upon a process mean and sigma that you specify.  In this type of study, the data do not influence the control limits and you cannot exclude subgroups.


Controllable Factors

Factors the experimenter has control of during all phases of the experiment; that is, experimental, production, and operational phases.


Convergence

With a variable, the state in which the variable approaches its limit.  With a series, the state in which the sum of the first n of its terms approaches a limit as n increases without bound.  With a curve, the state in which the curve approaches a point when the distance from the curve to the point approaches 0.


Coordinate

One of a set of numbers that locate a point in space.


Correlated

Interdependent; not independent.


Correlation

A measurement of the strength of the linear relationship between random variables.  See also Negative Correlation, Pearson Product-Moment Correlation, Positive Correlation, Zero Correlation.


Correlation Coefficient

A statistic that provides a normalized and scale-free measurement of the linear association between two variables.  The coefficient values fall between -1 and +1.  A positive correlation indicates that the variables vary in the same direction while a negative correlation indicates that the variables vary in the opposite direction.  Statistically independent variables have an expected correlation of 0.  Also called Product-Moment Correlation Coefficient.  See also Coefficient.


Correlation Matrix

A table of the Pearson correlation coefficients for the estimated coefficients in a model; a table of correlation coefficients that shows all the pairs of correlations for a set of variables; a matrix in which each row and column corresponds to a variable.  Up to three numbers can appear in each cell of the matrix:  A correlation coefficient for two variables represented by the cell, the sample size (in parentheses), and the significance level of the correlation.  A table that shows the intercorrelations among all the variables.  See also Matrix.


Count Data

Data that contain a count of the number of observations in each class.  See also Data.


Covariance

A matrix of covariance measures for a set of observed values.  The covariance measures the linear association between two variables.  If both variables tend to fall above or below their means at the same time, the covariance is positive.  If one variable is typically above the mean while the other is below, the covariance is negative.  The value of the covariance is sensitive to scaling because it retains the units of the original data.  See also Analysis of Covariance.


Covariance Matrix

A matrix in which each row and column corresponds to a variable.  Two numbers appear in each cell of the matrix:  The covariance for the two variables represented by the cell and the sample size (in parentheses).  See also Matrix.


Covariate

A random variable you treat as concomitant.  (When you adjust an analysis for a random variable to allow for the effect of another variable, you refer to the latter variable as concomitant.)  In experimental design, an uncontrollable variable that influences the response but is not affected by any other experimental factors.


Cp

One of several available capability indices.  A statistic that indicates the inherent capability of a process.  In general, if the mean of the data is equal to the midpoint of the tolerances, then a Cp less than 1.00 indicates that the process is not capable.  A Cp above 1.33 indicates that the process is capable.  A Cp between 1.00 and 1.33 indicates that the process is capable, but you should monitor it as Cp approaches 1.00.


Cpk

One of several available capability indices.  A statistic that explains the capability of a process in relation to the specification mean.  Cpk is a worst-case index of the process.  It is the ratio of the smaller of the distance from the upper control limit to the mean or the lower control limit to the mean, whichever is smaller, to half of the sigma range.  Cpk is useful even if the mean of the data is not equal to the midpoint of the tolerances.  A Cpk larger than 1 indicates that both sigma limits fall within the specification limits and the process is capable of performing to specification.  A Cpk of less than 1 means that at least one of the sigma limits is outside a specification limit and the process may not be capable of performing to specification.


Cpm

One of several available capability indices.  A statistic that represents the modified Cp index.  The program calculates Cpm using the nominal values instead of the calculated mean.  It is a more conservative index than Cp, and you interpret it in the same manner.


Cr

One of several available capability indices.  A statistic that represents the capability ratio of a process.  It is the reciprocal of the Cp index.  If the mean of the data is equal to the midpoint of the tolerances, then a Cr greater than 1.00 indicates that the process is not capable.  A Cr less than 0.75 indicates that the process is capable.  A Cr between 0.75 and 1.00 indicates that the process is capable, but you should monitor it as Cr approaches 1.00.


Cramer's V

A chi square-based measure of association that are helpful in determining the relationship between variables.  Also called Cramer’s V and Conditional Gamma.


Critical Region

Large and/or small values of a test statistic that lead to rejection of the null hypothesis.  Also called Rejection Region.


Critical Value

The smallest values for the area that falls under the distribution curve; the values are no less than the values you select for a probability.  In statistical hypothesis testing, the cutoff value for a test statistic used as limits for the rejection region.


Critical Value c

For a specified area under the distribution curve, the value c that defines the upper boundary for the region.


Crosscorrelation

A measure of association between two time-series variables.  Crosscorrelations range in value from -1 to 1 and have similar interpretations as regular correlation coefficients.  Determines if two time series are correlated.


Crossed Factors

Factors in an analysis of variance in which each level of one factor appears in combination with each level of a second factor.  See also Factor.


Crosstabulation

An analysis that operates on raw data to produce frequency counts and to generate tables that show frequency and percentage breakdowns.


Cube Plot

A plot of the estimated effects for the high and low settings of three factors.


Cumulative Density Function

The synonym for cumulative distribution function.  See also Cumulative Distribution Function, Function.


Cumulative Distribution Function (cdf)

A function that calculates the probability that a random variable will fall at or below the given value.  Also called Cumulative Density Function.  See also Function.


Cumulative Forecasting

Forecasting the cumulative level for a variable over several periods.


Cumulative Frequency

The number of observations in each class or in previous classes; that is, the number of observations less than or equal to the upper limit of the class.  See also Frequency.


Cumulative Frequency Polygon

A graphic representation for a frequency distribution or a set of frequencies for the various values of a variable.  See also Cumulative Relative Frequency Polygon, Frequency Polygon, Relative Frequency Polygon.


Cumulative Normal Distribution

The cumulative frequency function (distribution function) for a normal distribution.  See also Distribution.


Cumulative Relative Frequency

The proportion of observations in each class or each previous class; calculated by dividing the cumulative frequencies by the total number of observations.  See also Frequency.


Cumulative Relative Frequency Polygon

Similar to a cumulative frequency polygon for the same data, except that the program labels the Y-axis with relative frequencies rather than counts.  Also called an ogive.  See also Cumulative Frequency Polygon, Frequency Polygon, Relative Frequency Polygon.


Cumulative Plot

A component line chart in which the program stacks the fill patterns for the variables vertically, one on top of the other.  If a plot contains positive data, the program adds the values at each time point.  If a plot contains negative data, the program subtracts the values from the previous variable.


Cumulative Sum

The sum of all preceding values after you establish a certain order.  See also Sum.


Cumulative Sum Chart

One of three Time-Weighted charts based upon subgroup statistics or observations.  This chart helps to ensure that you do not specify a process as "out of control" when it is "in control" or that you do not fail to detect a marked change in the mean.  It is also useful for detecting small, persistent drifts in a process.  Also called CuSum Chart.


Cumulative Survival Probability

The probability of surviving beyond the observed lifetime.  See also Event Probability, Survival Probability.


Curvature

The degree of curving for a line or surface.


Curvature Check

A test to determine whether curvature (quadratic) terms should be included in the response model.


Curve

See Distribution Curve, Exponential Power Curve, Fitted Curve, Fitted Normal Curve, OC Curve, Operating Characteristic Curve, Power Curve.


Curvilinear Model

A linear model that includes curvature terms.  Curvature terms are squared terms of the independent variables or higher-order independent variables.  See also Model.


Curvilinear Trend

A trend that includes curvature.  See also Trend.


Custom Chart

A blank control chart created to your specifications.


CuSum Chart

A chart that shows cumulative sums of sample data, which is useful for detecting small, persistent drifts in a process.


Daniel Plot

A plot that identifies estimated effects that are large relative to the noise in an experiment.  Large effects appear on the right side of the plot.  Also called Half-Normal Plot.


Data

See Categorical Data, Censored Data, Classification Data, Complete Data, Continuous Data, Count Data, Discrete Data, Empirical Data, Failure-Censored Data, Hierarchical Data, Interval Data, Multivariate Data, Multivariate Normal Data, Nested Data, Pooled Data, Ratio-Scaled Data, Raw Data, Readout/Interval (Interval Censored) Data, Tabulated Data, Time-Censored Data, Time Series Data, Type I Data, Type II Data, Univariate Data.


Date Variable

A variable that contains numbers in mm/dd/yy format or the format you set on the Windows Control Panel.


Decomposition

See Classical Decomposition.


Defining Relationship

A statement of one or more factor word equalities used to determine the aliasing structure in a fractional factorial design.


Definite Integral

The representation, usually in symbolic form, of the difference in values for the primitive of a given function evaluated at two designated points.


Degrees of Freedom

The number of "free" elements associated with a sum or some other function.  A parameter that, in general, is the number of independent comparisons that are available to estimate a specific parameter, and that provides a way to enter certain statistical tables.  For a fitted model, the number of independent observations minus the number of estimated parameters.  For a factor, the number of levels minus one.


Density Trace Plot

A plot of the shape or distribution of the data, especially the variations in density over the range of the data.


Dependent Variable

The presumed response in a study; known as dependent because it “depends” on other variables.  A variable whose values are characterized by the independent variable(s), whether or not a causal relationship. A variable that shows the observed results for an experimental treatment.  On a plot, the values in this variable appear on the Y-axis.  Also called Response Variable.


Derivative

The instantaneous rate of change of a function with respect to a variable.  See also Higher-Order Derivative, Partial Derivative.


Design

The complete specification of experimental runs, including blocking, randomization, replication, and the assignment of factor-level combinations.  See also Balanced Design, Balanced Experimental Design, Balanced Incomplete Block Design, Balanced One-Way Design, Balanced Randomized Block Design, Blocked Design, Box-Behnken Design, Central Composite Design, Composite Design, Draper-Lin Small Composite Design, Experimental Design, Face-Centered Design, Factorial Design, Fractional Factorial Design, Full Factorial Design, Latin Square Design, Nested Design, One-Way Design, Orthogonal Design, Partially Nested Design, Plackett-Burman Design, Randomized Block Design, Repeated Measures Design, Replicated Design, Rotatable Design, Split Plot Design, Strip Plot Design, Three-Level Factorial Design, Two-Level Factorial Design, Two-Way Design, Unbalanced Design, Unbalanced Nested Design, Unbalanced One-Way Design, Unblocked Design, User-Defined Design.


Design Centerpoint

See Centerpoint.


Design Generators

Equations that indicate the columns you must multiply together to produce the last columns in a fractional factorial design.


Design Matrix

In multiple regression, a matrix of observations for the independent variables and the constant term, if any.  In experimental design, a matrix that represents the experimental settings; usually contains values that range from -1 to 1 but can be wider.  The rows represent the runs; columns represent the factors.  See also Matrix.


Design Point

An intended experimental run.


Design Resolution (III, IV, V, or V+)

The degree of confounding in a two-level fractional design (screening design).  A design of resolution III does not confound main effects with one another, but does confound main effects with two-factor interactions.  A resolution IV design does not confound main effects and two-factor interactions, but does confound two-factor interactions with other two-factor interactions.  A resolution V design does not confound main effects and two-factor interactions with each other, but does confound two-factor interactions with three-factor interactions.


DFITS Statistic

A statistic that measures the amount of change for each estimated coefficient if the observation is removed from the data.  A statistic that estimates the influence of an individual observation on the fitted line in regression.  Both leverage and prediction error affect DFITS.  An observation has significant influence if it has an absolute value of DFITS that is greater than two times the square root of the number of coefficients divided by the number of observations.


Differencing

When a nonstationary time series can be made stationary by taking first differences of the series.  If first differences do not make the series stationary, then first differences of first differences can be created.  This is known as Second-Order Differencing.


Discrete Data

Numeric data that have a finite number of values.  See also Data.


Dispersion

The scattering of values for a variable around the mean or median of a distribution.


Distribution

See Bernoulli Distribution, Best-Fitting Normal Distribution, Beta Distribution, Binomial Distribution, Bivariate Normal Distribution, Chi-Square Distribution, Cumulative Distribution, Cumulative Normal Distribution, Exponential Dstribution, Extreme Value Distribution, F-Distribution, Frequency Distribution, Gamma Distribution, Gaussian (Normal) Distribution, Geometric Distribution, Lognormal Distribution, Multivariate Normal Distribution, Normal Distribution, Poisson Distribution, Probability Distribution, Student's t Distribution, Symmetric Distribution, t Distribution, Uniform Distribution, Weibull Distribution.


Distribution Curve

A curve or line on a graph in which the program plots cumulative frequencies on the Y-axis and values of the variate on the X-axis.  See also Curve.


Distribution Function

For any random variable, the function that assigns to each number the probability that the random variable takes a value less than or equal to the given number.  See also Function.


Distribution-Free Tolerance Limits

A method to create and displaynonparametric tolerance limits, which are used when data are non-normal.  Intervals are based on the distribution of the extreme values in a sample.  Large samples are required to construct intervals that contain a relatively large fraction of the distribution with high probability.  See also Normal Tolerance Limits, Tolerance Limits.


Draftsman Plot

A series of two-variable scatterplots for all combinations of three or more variables.


Draper-Lin Small Composite Design

A central composite design that runs a fraction rather than a full factorial.  Also called Draper-Lin Design.  See also Design.


Duncan Method

A method for determining statistically significant differences among means if you want to protect the results against Type I errors for a small number of comparisons.  It is more powerful than Tukey's Honestly Significant Differences (HSD).  However, unlike Tukey's HSD, it does not control the experiment-wide error rate.  For a small number of comparisons, it is a good compromise between the least significant differences and Tukey's HSD methods.


Durbin-Watson Statistic

A test for autocorrelation or serial correlation in the residuals of a least squares regression analysis.  As the autocorrelation increases, the Durbin-Watson statistic goes down.  The larger the correlation, the less reliable the results of the regression analysis.  Also called Durbin-Watson Coefficient.


Effect

The change in the average of the responses between two factor-level combinations or two experimental settings.  For a two-level factor, the effect of the factor is the average response at the high level of the factor minus the average of the response at the low level of the factor.  See also Confounded Effects, Block Effects, Main Effects.


Eigenvector

A scalar that has a nonzero vector where the scalar times the vector equals the value of the vector under a given linear transformation.


Empirical Data

Data that are based upon observation or experience.  See also Data.


Empirical Model

A model that uses sequential experimentation techniques to survey a domain of interest and to focus on the most important variables and their effects.  See also Model.


Endpoint

The point on either side of an interval that marks its extremity on that side.


Entry Time

The time at which an item enters a reliability or survivability study.


Equipment Variation

The variation in measurements obtained with one gage when one operator uses it several times to measure the identical characteristic on the same part.  Also called Repeatability.  See also Appraiser Variation, Operator Variation.


Error

A residual.  The difference between an observed value and an expected or predicted value.  See also Alpha Error, Beta Error, Mean Error (ME), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Mean Percentage Error (MPE), Mean Squared Error (MSE), pure error, Type I Error (H sub 0), Type II Error (H sub A).


Error Bars

Bars around data points on a graph that indicate the size of the error in the estimated value.  See also Standard Error Bars.


Error Sum of Squares

In analysis of variance, the within-group sum of squares; that is, the part that the treatment effects cannot explain.  Also called Residual Sum of Squares.


Error Term

The part of an equation that indicates what is unexplained by the independent variables and the size of the unexplained part.


Estimate

See also Biased Estimate, Interval Estimate, Least Squares Estimate, Maximum Likelihood Estimate, Pooled Estimate.


Eta

An appropriate measure of association for two variables when you measure the dependent variable on an interval scale and the independent variable on a nominal or ordinal scale.  Eta is similar to the Pearson correlation coefficient; however, it is asymmetric and does not assume a linear relationship between the variables.


Event

An occurrence of some attribute.


Event Probability

The probability associated with the success of an event in each of a series of trials.  See also Cumulative Survival Probability, Survival Probability.


EWMA

Acronym for Exponentially Weighted Moving Average.


EWMA Chart

Acronym for Exponentially Weighted Moving Averages Chart.


Exit Time

The time at which an item dies, fails, or leaves a reliability or survivability study.


Expected Frequency

In contingency tables, the frequency you predict if you know the marginal totals and if you assume the null hypothesis of independence of the variables.  See also Frequency.


Experimental Condition

A specific combination of factors and levels that you study in an experiment.  Also known as experimental trials.  See also Runs.


Experimental Design

The complete specification of experimental runs, including blocking, randomization, replication, and the assignment of factor-level combinations.  See also Design.


Experimental Factor

An independent variable that you set at different levels in an experimental design.  See also Factor.


Experimental Region

All possible factor-level combinations for which experimentation is possible.


Exploratory Data Analysis

Any of several methods you can use to discover unanticipated patterns and relationships.  For example, you can present quantitative data visually in a Stem-and-Leaf plot or a Box-and-Whisker plot.


Exponential Distribution

A continuous distribution useful for characterizing random variables that can take only positive values; completely determined by its mean.  A distribution that fits time-series data, such as arrival times, where you expect arrivals at a constant rate.  This distribution is a special case of both the Gamma and the Weibull distributions.  The Expo(b) density function is (1/b)e-x/b for x = 0, and it has mean = b and variance = b2.  This is the only continuous distribution having a "memoryless" property.  See also Distribution.


Exponential Model

A model that is equivalent to taking the natural log of Y; defined by the equation Y = exp (a + bX).  See also Model.


Exponential Power Curve

A curve based upon the function Z(t) = exp (a+bt), where t represents the time index, which fits an exponential growth curve through time-series data.  This type of trend analysis is useful for time-series data that are increasing or decreasing at a nonconstant rate.  See also Curve.


Exponential Smoothing

See also Brown’s linear exponential smoothing, Holt’s linear exponential smoothing, quadratic exponential smoothing, and simple exponential smoothing.


Exponentially Weighted Moving Average (EWMA)

The weighted average of the current observation and the estimate of the previous observation.  To calculate the weighted average, the program first multiplies the current observation by lambda then multiplies the estimate of the previous observation by 1 - lambda.  Also called EWMA.  See also Average.

In time series, it is a one-parameter smoothing technique that places greatest weight on more recent observations.


Exponentially Weighted Moving Averages (EWMA) Chart

One of three time-weighted charts that plots the exponentially weighted moving averages.  This chart helps you ensure that you do not declare a process out of control when it is in control, or one in which you do not fail to detect a marked change in the mean.  It is useful for detecting small, persistent shifts in a process.  This chart is not sensitive to the normality assumption and, therefore, is an ideal chart to use with individual data (subgroup size of 1).  Also called Geometric Moving Average Chart.


Extrapolate

To estimate values outside the tabulated or observed range.


Extreme Value

The largest and smallest values in a distribution of values.


Extreme Value Distribution

A distribution useful for random variables constrained to be greater than 0; characterized by two parameters:  Mode and Scale.  A distribution for fitting the limiting distribution for the maximum number of samples collected from a process.  This distribution applies when extremes rather than means are collected from samples from an unknown or complex underlying distribution.  See also Distribution.


F Distribution

A continuous distribution that results from the ratio of two chi-squared distributions, each divided by their associated degrees of freedom.  See also Distribution.


F-Ratio

A ratio of the variance explained by a factor (MS of the factor) to the unexplained variance (MSE).  If there is no effect, the associated p-value is close to 1.


F-Statistic

In one-way ANOVA, a ratio of the variance between groups (explained variance) to the variance within groups (unexplained variance).  In general, a numeric value that results from the ratio of mean squares.


Face-Centered Design

A central composite design with three levels rather than five, and with star points (rather than centerpoints) in the center of the faces of the factorial cube.  See also Design.


Factor

A linear combination of original variables.  Factors also represent the underlying dimensions that summarize or account for an original set of observed variables.


Factor Effects

A factor's main effect and all interactions that involve that factor.  See also Confounded Effects.


Factor Level

A given value, a specification of procedure, or a specific setting of a factor.  See also Level.


Factor Variable

A variable you can measure on an interval or ratio scale.  Also called Metric Variable.


Factorial Design

A design that combines the levels for each factor with all the levels for every other factor.  You can reduce the number of experimental runs by fractioning the design.  See also Design.


Failure

Due to one or more defects, the inability of an item, product, or service to perform its required function.


Failure-Censored Data

Data gathered during an experiment that ends after a specified number of failures or deaths.  Also called Type II Data.  See also Data.


First-Degree Polynomial Function

An equation of the form Y = b0 + b1X1 + b2X2 + ... bnXn.  See also function.


Fisher's Exact Test

A test statistic for measures of association that relate two nominal variables.


Fitted Curve

A second-order or higher polynomial model you use to estimate response values at specified independent variable values.  See also Curve.


Fitted Line

The regression line or predicted line in simple linear regression.  See also Quadratic Line, Regression Line.


Fitted Model

Any model type that you use to estimate response values at specified independent variable values.  See also Model.


Fitted Normal Curve

The curve that results from fitting the normal distribution to a sample of data that has a calculated or estimated average and standard deviation.  See also Curve.


Fitted Value

The estimated value for the response at observed values for the independent variables.


Fixed-Decimal Variable

A variable that contains only numbers that have a fixed number of decimal places.


Floating-Point Numeric Variable

Synonym for numeric variable.


Foldover Design

A way to obtain a resolution IV design based upon two designs of resolution III.  Used when confirmation runs from a resolution III design differ substantially from their prediction, and when you want to de-alias the two-way interactions from the main effects.


Forecast

A prediction generated by calculating the value of a function given a new set of values.  The estimated value of the response for a new observation.  See also Linear Forecast, One-Ahead Forecast.


Forecasting

The prediction of values for a variable based upon known past values for that variable or other related variables.  Forecasts can also be based upon nonexpert judgments, which in turn, are based upon historical data and experience.


Fractional Factorial Design

Instead of using a full factorial design, you use some subset of it assuming that some interactions will not occur and that a factor has been assigned to that interaction column of the design.  A design that does not specify all the combinations of the factors.


Frequency

The number of observations in each class.  See also Cumulative Frequency, Cumulative Relative Frequency, Expected Frequency, Observed Frequency, Relative Frequency.


Frequency Distribution

A set of all the various values that individual observations may have and the frequency of their occurrence in the sample or population.  A way of grouping data so that the important aspects of the raw data are more readily apparent.  See also Distribution.


Frequency Histogram

A graphical display of the values in a sample created by dividing the range of the data into nonoverlapping intervals and counting the number of values that fall into each interval.  The counts are called frequencies.


Frequency Polygon

A graphical display of the values for a distribution of a set of observations.  The program forms a frequency polygon by plotting the class frequency and class midpoint for each class, then using straight lines to connect the points.  See also Cumulative Frequency Polygon, Cumulative Relative Frequency Polygon, Relative Frequency Polygon.


Frequency Table

A table of the number of observations that fall within each class and the relative, cumulative, and cumulative relative frequencies.  A listing of all the observed values for a variable and the number of times the program observes each value.  For continuous data, the program places the observed values into classes of equal width.  See also Means Table, Multiway Table, Two-Way Table.


Full Factorial Design

A design that combines the levels of each factor with all the levels of every other factor.  See also Design.


Function

An equation or model that mathematically relates one variable with other variables and parameters.  See also Cumulative Density Function, Cumulative Distribution Function, Density Function, Distribution Function, First-Degree Polynomial Function, Hazard Function, Log Survivor Function, Power Function, Probability Density Function, Probability Mass Function, Second-Degree Polynomial Function, Survivor Function.


Gage Repeatability

A synonym for repeatability.


Gage Reproducibility

A synonym for reproducibility.


Gamma Distribution

A distribution useful for random variables constrained to be greater than 0; characterized by the Shape and Scale parameters.


Gaussian Distribution

A synonymn for normal distribution.  See also Distribution.


Geometric Distribution

A distribution that characterizes the number of failures before the first success in a series of Bernoulli trials, a special case of Negative Binomial distributions, where k = 1.  See also Distribution.


Geometric Mean

A measure of the the central tendency of the data.  The result of multiplying n values and taking the nth root.  See also Mean.


Geometric Moving Average Chart

The synonym for Exponentially Weighted Moving Average (EWMA) Chart.


Glyph

An alternative to displaying points on a plot, a glyph is a series of rays drawn from the centerpoint, and lines that connect the rays that (usually) form a polygon.  Each ray represents one variable, starting with the first variable at three o'clock and moving in a counterclockwise direction.  The middle represents the sample mean of the variable, the shortest ray represents the smallest value in each variable, and the longest ray represents the largest value.


Goodness-of-Fit Tests

A test whose results display a standardized chi-square statistic that compares observed frequencies with the expected frequencies predicted by the fitted distribution.  The analysis is performed using the Kolmogorov-Smirnov One-Sample Test.


Gradient

The rate of change for a variable quantity, such as temperature.  Also, a curve that represents that rate of change.


Grand Mean

An average of all the observations for a response in an experiment.  See also Mean.


Half-Normal Plot

A plot that identifies estimated effects that are large relative to the noise in an experiment.  Large effects appear on the right side of the plot.  Also called Daniel Plot.


Hartley's Test

A statistical test for homogeneity of variance.  The hypothesis is that the variances across different levels are equal.  If the significance level is greater than .05, the hypothesis is accepted; that is, the variances are not significantly different (they are equal).


Hazard Function Plot

A plot of the hazard function for the distribution you select.  The hazard function is equal to the probability density function divided by the survivor function.  When you model lifetime data, the function represents the instantaneous failure rate.


Hazard Plot

A plot of the density function divided by the survivor function.


Henderson's Weighted Moving Average
Henderson’s Weighted Moving Average

A high-order smoothing technique used with time-series data that exhibit substantial randomness.


Heteroscedasticity

A condition that exists when errors do not have a constant variance across an entire range of values.  For example, when the residuals from a time series have increasing variance with increasing time, the time series exhibits heteroscedasticity.


Hierarchical Data

Data in which the classifying factors are qualitative and no theoretical relationship exists between observations at a given level of a subsample to observations in a corresponding level of another subsample.  Also called Nested Data.  See also Data.


Hierarchical Model

An analysis of variance model in which the program pyramids the effects of certain factors.  Levels of lower factors are nested in levels of factors higher up the pyramid, but do not cut across the levels of the higher factor.  Also called Nested Model.  See also Model.


Higher-Order Derivative

A derivative of other derivatives, the latter being considered as functions of the independent variable just as was the function of which the first derivative was taken.  See also Derivative, Partial Derivative.


Histogram

A plot of data shown as a series of successive bars that represent classes.  The width of the bars is equal to the class interval.  A bar diagram that represents a frequency distribution.  A plot of a frequency distribution that displays rectangles whose bases are equal to the cell interval and whose areas are proportional to the frequencies.  See also Frequency Histogram, Three-Dimensional Frequency Histogram.


Holt's Linear Exponential Smoothing

A two-parameter, double exponential smoothing technique that places greatest weight on the most recent observations.  This method is useful in that it allows any trend in the data to be smoothed with a different smoothing parameter than that used on the original data.


Homoscedasticity

A condition that exists when the variance of a series is constant over the entire range of values of that series.  For example, when a series of residuals exhibits constant variance over the entire range of time periods, it is said to have homoscedasticity.


Homogeneous Group

Sets of data that have similar statistical characteristics.  For example, in one-way ANOVA the data from different levels of the factor must have homogeneous variances.


Hotelling t-Squared Statistic

A statistic for testing multivariate normal mean vectors.  In quality control, you use the Hotelling t-squared statistic to identify unusual observations or out-of-control points on a Multivariate Control Chart.


Hypothesis

A statement of the relationships among the variables in a study.  See also Alternate Hypothesis, Null Hypothesis.


Hypothesis Tests

Tabular results of the t-statistic, its p-value, and the recommendation to either accept or not accept the null hypothesis.


Hypothesized Value

The stated value of the null hypothesis in a statistical test.


Identity Matrix

A diagonal matrix whose elements in the principal diagonal are all unity and all other elements are 0.  See also Matrix.


Independent Samples

Groups of observations in which the value or selection of one of the observations does not influence the value or selection of any other observation.


Independent (X) Variable

A variable whose levels are selected whether or not the selection is in your control; for example, a factor level in an experiment.  Also called Predictor Variable.


Indicator Variable

A categorical variable that can place subjects into only two groups; for example, 1 = female and 2 = not female.


Individuals Chart

A control chart that plots subgroups of size 1.  The program uses the moving range of two successive observations to estimate the process variability.  The chart is sensitive to the normality assumption.


Initial Study

When generating control charts for attributes or variables, a type of study that produces an empirical chart with control limits estimated from the data.  In an initial study, you can include or exclude subgroups from the analysis.


Integer Variable

A variable that contains numbers with no decimal places.


Interaction

A multiplicative effect.  Dependence.  In analysis of variance, the tendency for the combination of factors A and B to produce a result that is different from the mere sum of their two individual contributions.  The existence of joint factor effects in which the effect of each factor depends upon the level of other factors.  In experimental design, a change in the response due to the combination of two or more factors.  An interaction involving two factors is called a two-factor interaction, three factors is a three-factor interaction, and so on.


Interaction Effect

The influence of two or more interacting factors on the response when they are changed from one level to another.


Interaction Plot

A plot of two-factor interactions.  Nonparallel trends in the plot indicate interactions.  See also Plot.


Intercept

The point at which a regression line crosses the vertical (Y) axis; that is, when the value on the horizontal axis (X) is zero.  Also called Y-Intercept.


Integrated Time-Series Models

An element of time-series models in which the model includes one or more of the differences of the time series.


Internal Standard Error

The standard deviation of the current sample divided by the square root of the sample size.  You use the internal standard error to calculate a confidence interval around the sample mean.  In ANOVA, you use the internal standard error in place of the pooled standard error when the variances of the samples are significantly different.  See also Pooled Standard Error, Standard Error.


Interpolate

To estimate an unknown value by using its position among a series of known values.


Interquartile Range

A range in which the middle 50 percent of the data will fall; a measurement of the spread or dispersion of the data; the upper quartile minus the lower quartile.  See also Mean Range, Range.


Interval

The totality of points on a line between two designated points that may or may not be included.  Also, any generalization of this to higher dimensions, such as a rectangle with sides parallel to the coordinate axes.  See also Confidence Interval, Tolerance Interval.


Interval Data

Data for which you record failures or terminations at periodic intervals.  See also Data.


Interval Depth

Used with distribution-free tolerance limits.  The interval depth specifies which extreme values you use to calculate the tolerance limits.  For example, an interval depth of two indicates that you use the second smallest and the second largest values.


Interval Estimate

An estimate that includes a range of scores.  See also Estimate.


Interval Limits

The endpoints of an interval.


Intervening Variable

A variable that explains a relationship or provides a causal link between other variables.


K

One of several available capability indices.  A statistic that represents the comparison ratio of the process mean to the nominal specification.  K is a measure of how far the center of a process is from its nominal midpoint.  If K is 0, the mean and the nominal value are identical.  If K is positive, the mean is above the nominal value.  If K is negative, the mean is below the nominal value.  When the absolute value of K is small, the process mean is close to the nominal specification.  Note that a small value of K can occur even if the process is not capable.


Kendall's Rank Correlation Coefficient
Kendall’s Rank Correlation Coefficient

A statistic that measures the relative degree of agreement or disagreement between two variables.  Also called Kendall's Tau.  See also Coefficient.


Kendall's Tau

Statistics that measure the relative degree of agreement or disagreement between two variables.  Also called Kendall’s Rank Correlation Coefficient.


Kolmogorov-Smirnov One-Sample Test

A procedure that allows you to test the overall goodness-of-fit between the distribution of the data and a distribution you select.


Kolmogorov-Smirnov Two-Sample Test

A method that tests the null hypothesis that two samples can reasonably be assumed to come from the same distribution.  The test calculates the maximum vertical distance between the cumulative distribution function of the two samples.  If this distance is large enough, you reject the hypothesis that the two samples come from the same distribution.


Kruskal-Wallis Test

A nonparametric method that tests the assumption that the medians of samples are equal.


Kurtosis

A value used to measure the flatness or steepness of a distribution with respect to a Gaussian or Normal distribution.  See also Coefficient of Kurtosis, Standardized Kurtosis.


Kurtosis Coefficient

A measurement of how flat or steep the distribution of the data is with respect to a Gaussian or normal distribution.  For a normal distribution, the kurtosis coefficient is 0.  When the coefficient is less than 0, the curve is flat with short tails.  When the coefficient is greater than 0, the curve is either very steep at the center or has relatively long tails.  See also Coefficient, Kurtosis, Standardized Kurtosis.


Labels

Numeric values or characters you use as a means of identification or classification.


Lack-of-Fit Test

A test that determines if the regression model adequately fits the data.  You can perform a lack-of-fit test only when there are replicated independent variable values or experimental runs.


Lag

A period of time.  In STATGRAPHICS Plus, a user-entered value used to estimate the autocorrelation values.


Lambda

A measure of association you can use when you are describing categorical (nominal or discrete) variables.  Lambdas range from 0, when knowing one variable tells you nothing about another, to 1.0, when knowing one variable always enables you to predict the other.


Latin Square Design

An experimental design in which the program groups the effects of one factor according to the levels of two other factors.  The program assigns the levels of the first factor at random, with the restriction that no one level of the first factor appears more than once with any given levels of either of the other two factors.  You can use this design to eliminate two extraneous sources of variability or to block in two directions.  See also Design.


LCL

The acronym for Lower Control Limit.


Least Significant Differences (LSD) Test

In analysis of variance, pairwise t-tests at the specified significance level for each pair of factor-level averages.


Least Squares

A mathematical method you use to find the linear or nonlinear regression equation by minimizing the sum of squares of the residuals.  A method for estimating a function (a point, line, or curve) that minimizes the sum of squares of the deviations from the estimate.  See also Regression.


Least Squares Equations

The equations used to derive the line or curve estimated by the method of least squares.  Also called Normal Equations.


Least Squares Regression

A method that fits a regression by finding the coefficients that minimize the sum of the squared effects.  A mathematical method used to find the linear or nonlinear regression equation by minimizing the sum of squares of the residuals.  A method for estimating a function (a point, line, or curve) that minimizes the sum of squares of the deviations from the estimate.  See also Regression.


Left-Sided Test (LT)

A hypothesis test in which you state the alternative hypothesis as less than the value in the null hypothesis.


Level

A specific value.  In experimental design, the value or setting for a factor.  See also Alpha Level, Confidence Level, Factor Level, Probability Level, Significance Level.


Level Code

The class for an observation.


Levels of Variable

The unique values of a data variable.  You consider every unique value an individual level.


Leverage

A statistic that measures the amount each estimated coefficient would change if each observation was removed from the data.  A statistic that estimates the influence of an individual observation on the fitted line in regression.  A point has significant influence when its leverage value is greater than three times the number of coefficients divided by the number of observations.


Likelihood Ratio Chi Square

A test statistic that is the ratio of two likelihoods, used especially for relations among categorical variables displayed in contingency tables.  The likelihood ratio helps you to determine whether to accept a particular model (rather than reject a null hypothesis).  The smaller the likelihood ratio, the stronger the relationship.


Limit

The endpoint of an interval.  See also Lower Control Limit, Lower Specification Limit, Nominal Specification Limit, Sigma limit, Strata Lower Limit, Strata Upper Limit, Upper Control Limit, Upper Specification Limit.


Limits

A set of endpoints from an interval.  See also Confidence Limits, Control Limits, Distribution-Free Tolerance Limits, Interval Limits, Normal Tolerance Limits, Prediction Limits, Specification Limits, Tolerance Limits, Warning Limits.


Line Plot

A plot that displays connecting lines without points.  See also X-Y Line Plot, X-Y-Z Line Plot.


Linear Combination

Representations of the weighted sum for two or more variables.  Also known as Linear Composites, Linear Compounds, and Discriminant Variables.


Linear Equation

An equation you can plot as a straight line on a graph; the equation does not contain powers higher than 1.


Linear Forecast

A predicted value calculated using a linear equation.  See also One-Ahead Forecast.


Linear Regression

A way to describe the relationship among two or more variables by calculating a best-fitting straight line on a graph.  The line averages or summarizes the relationship.  The result is a regression line you can also express in a regression equation.  See also Regression.


Log (Logarithmic) Scaling

On a graph, markings that are not the distances from the axes, but the antilogarithms of the actual distances.


Log Plot

A plot that allows you to scale one or more axes logarithmically to give a different view of the data.


Log Survivor Function

A plot that shows the probability of observing a value greater than a value you select (in log units); that is, the log of the survivor function.  See also Function.


Log-Likelihood Ratio

An alternative to the chi-square goodness-of-fit statistic for contingency tables.  See also Function.


Logarithmic Transformation

When the logarithm of X is normally distributed but X is not, a process that replaces X with the logarithm of X and allows you to use normal distribution theory.  See also Orthogonal Transformation.


Lognormal Distribution

A distribution useful for random variables constrained to be greater than 0; characterized by two parameters:  Mean and Standard Deviation.  A positively skewed distribution that can take on various shapes.


Lower Capability Indices

A statistic that represents the distance from the lower specification limit to the mean divided by half the sigma range.


Lower Control Limit

Control limit for points that plot below the center level.  Also called LCL.  See also Control Limits, Upper Control Limit.


Lower Quartile

The value below which 25 percent of the data will fall; the 25th percentile.  See also Quartile, Upper Quartile.


Lower Specification Limit (LSL)

A specification limit that defines the lower conformance boundary for an individual unit of a manufacturing or service operation.  Also called LCL.  See also Nominal (Target) Value, Specification Limits, Upper Specification Limit.


LSL

An acronym for Lower Specification Limit.


Agglomerative Methods

A hierarchical clustering procedure that begins with each variable or observation in separate clusters.  In subsequent steps, clusters that are closest together are combined to build a new aggregate cluster(s).


Analysis Sample

The group used to compute the discriminant function when constructing classification matrices by dividing the original sample randomly into two groups, one for developing the discriminant function and the other for validating it.


Average Linkage

An agglomerative algorithm that uses the average distance from individuals in one cluster to individuals in another cluster as the clustering criterion.  This approach tends to combine clusters with small variances.


Categorical Variable

A variable that contains the level codes.  When an independent variable is entered as a categorical variable, the program sets up indicator variables for each level except for the first one.


Centroid Method

An agglomerative method in which the distance between two clusters is the distance (typically, Euclidean) between their centroids (means).  Each time objects are grouped, a new centroid is computed; therefore, cluster centroids move as clusters are merged.


Chance Models

The procedure used to determine the percentage of individuals that would be correctly classified by chance.


City-Block Distance

A method for calculating distances based upon the sum of the absolute differences of the coordinates for the objects.  This method assumes that the variables are uncorrelated and that unit scales are compatible.


Classification

The placing of objects into more or less homogeneous groups in a manner so that the relation between groups is revealed.


Classification Matrix

A matrix that contains numbers that reveal the predictive ability of the discriminant function.  The numbers on the diagonal of the matrix represent correct classifications; the off-diagonal numbers represent incorrect representations.  Also referred to as a Confusion, Assignment, or Prediction Matrix.


Cluster Seeds

The initial center or starting point of a cluster.  This value is used to begin nonhierarchical clustering procedures.  Clusters are built around these pre-selected seeds.


Complete Linkage

An agglomertive method in which the clustering criterion is based on the maximum distance between objects.  All the objects in a cluster are linked to each other at some maximum distance or minimum similarity.


Component Analysis

A factor model in which the factors are based on the total variance.  In component analysis, unities are used in the diagonal of the correlation matrix, which implies that all of the variance is common or shared.


Computational Method

Two methods that can be utilized to derive a discriminant function:  the simultaneous (direct) method and the stepwise method.  See also Simultaneous Method and Stepwise Method.


Cutting Score

The score against which each individual's discriminant score is judged to determine into which group the individual should be classified.  When the analysis involves two groups, the hit ratio is determined by computing a single “cutting” score.  Those entities whose z-scores are below this score are assigned to one group, while those whose scores are above it are classified in the other group.


Dendrogram

A graphical representation of the results of a clustering procedure.  The vertical axis is made up of the objects or individuals; the horizontal axis represents the number of clusters formed at each step of the clustering procedure.  Also known as a Tree Graph.


Discriminant Analysis

The appropriate statistical technique when the dependent variables are metric.  In most cases the dependent variable consists of two groups or classifications; in others, more than two groups are involved, such as a three-group classification that involves low, medium, and high classifications.


Discriminant Function

A linear equation of the form

Z = W1X1 + W2X2 + ... + Wn Xn

where

Z = discriminant score

W = discriminant weight

X = independent variable


Discriminant Loadings

Used to measure the simple linear correlation between the independent variables and the discriminant function.  Also referred to as structure correlations.


Discriminant Score

Referred to as a z-score.  See Discriminant Loadings.


Discriminant Weight

Also known as a Discriminant Coefficient, its size is determined by the variance structure of the original variables.  Independent variables with large discriminatory power usually have large weights; those with little discrinatory power usually have small weights.  Collinearity among the independent variables cause an exception to this rule.


Divisive

A clustering procedure that begins with all the objects in a single cluster.  It is opposite of agglomerative procedures.  The procedure begins with a single large cluster that is divided into separate clusters based on the the most dissimilar objects.


Eigenvalue

The column sum of squares for a factor that represents the amount of variance.


Entropy Group

The few observations that are independent of either cluster.


Factor Analysis

A generic name given to a class of multivariate statistical methods whose primary purpose is to reduce and summarize data.  A technique particularly suitable for analyzing complex, multidimensional problems.


Factor Loadings

The correlation between original variables and factors, and the key to understanding the nature of a specific factor.


Factor Matrix

A table that displays the factor loadings of all variables on each factor.


Factor Rotation

The process of manipulating or adjusting the factor axes to achieve a simpler and more meaningful factor solution.


Factor Score

A measure of the composite of all the original variables that make up a new factor.


Hierarchical Clustering

A method used to cluster by joining the most similar observations, then successfully connecting the next most similar observations to these.


Hit Ratio

The percentage of statistical units (individuals, respondents, objects, and so forth), that are correctly classified by the discriminant function.


Hold-Out Sample

The group of subjects held out of the total sample when the function is computed.  Also known as the Validation Sample.


Icicle Plot

A graphical representation that resembles a row of hanging icicles.


Interpretation Stage

The point in a process where the characteristics of each cluster are understood and at which a name or label is developed that defines the nature of each characteristic.  See also Partitioning Stage and Profiling Stage.


K-Means Procedure

Probably the most widely used clustering procedure; uses a limited number of arbitrary cluster centers that offset computational difficulty.


Multiple Discriminant Analysis

A methodology to help explain research problems that involve a single categorical dependent variable and several metric independent variables.


Mutual Similarity Procedures

A method used to cluster by grouping together observations that have a common similarity to other observations.


Nonhierarchical Procedures

Cluster seeds are used instead of a tree-like construction to group objects that are within a pre-specified distance of the seeds.


Normalized Distance Function

A process that converts each raw data score to a standardized variate with zero mean and unit standard deviation.  The purpose of the process is to remove the bias introduced by differences in scales of several variables.


Oblique Factor Solutions

A factor solution that is computed in a way that the extracted factors are correlated.


Orthogonal Factor Solutions

A factor solution in which the factors are extracted so that the factor axes are maintained at 90 degrees thereby causing each factor to be independent of or orthogonal from all other factors.


Partitioning Stage

The point in a process that determines if and how clusters could be developed..  See also Interpretation Stage and Profiling Stage.


Percentage of Variance Criterion

A technique used in hard sciences and in social sciences where the criterion is the cumulative percentages of the variance extracted by successive factors.  In the hard sciences, the factoring procedure is usually stopped when the extracted factors account for at least 95 percent of the variance.  In the social sciences, the factoring procedure is usually stopped when the extracted factors account for at least 60 percent of the total variance.


Profiling Stage

The point in a process that describes the characteristics of each cluster to explain how they may differ on relevant dimensions.  See also Partitioning Stage and Interpretation Stage.


Rotation

A methodology used to preserve the original structure and reliability of discriminant models while at the same time making them substantively easier to interpret.


Scree Test Criterion

A technique that uses the scree tail test to extract factors.  The scree tail test is an approach that identifies the optimum number of factors that can be extracted before the amount of unique variance dominates the common variance structure.


Simultaneous Method

A methodology used to compute the discriminant function so all the independent variables are considered concurrently.  Therefore, the discriminant function(s) is computed based upon the entire set of independent variables, regardless of the discriminating power of each independent variable.  This method is appropriate to use when all of the independent variables are included in the analysis and it is not important to see intermediate results based only on the most discriminating variables.


Single Linkage Method

A hierarchical clustering procedure based on minimum distance.  The procedure locates the two  objects with the shortest distance and places them in the first cluster.  The process continues until all the objects are in one cluster.


Stepwise Method

An alternative to the simultaneous method.  Involves entering the independent variables into the discriminant function one at a time, based on the basis of their discriminating power.  The single best variable is chosen first; the initial variable is then paired with each of the other independent variables, one at a time, and a second variable is chosen, and so on.


Tolerance

The proportion of the variation in the independent variables that is not explained by the variables already in the model.


Trace

The sum of the square of the numbers on the diagonal of the correlation matrix used in the factor analysis.  The trace represents the total amount of variance on which the factor solution is based.  In component analysis, the trace is equal to the number of variables based on the assumption that the variance in each variable is equal to 1.  In common factor analysis, the trace is equal to the sum of the communalities on the diagonal of the reduced correlation matrix.


Vector

A straight line drawn from the center of a graph to the coordinates of a specific variable vector.  The length of each vector indicates the relative importance of each variable in discriminating among groups.


Ward's Method

A hierarchical cluster procedure that calculates the distance between two clusters as the sum of squares between the two clusters summed over all the variables.


Cluster Centroid

The average value of the objects in a cluster on all of the variables in an analysis.


Cluster Analysis

A technique for grouping individuals or objects into clusters so objects in the same cluster are more like each other than they are like objects in other clusters.  Also known as Q-Analysis, Typology, Classification Analysis, and Numerical Taxonomy.


Canonical Correlations Analysis

Canonical Correlations Analysis is a technique you can use to study the relationship between two sets of variables, each of which might contain several variables.  Its purpose is to summarize or explain the relationship between two sets of variables by finding a small number of linear combinations from each set.


Classical Factor Analysis

A factor model in which the communalities are replaced by the multiple R-Squared values.


Cluster Analysis Dialog Box

Cluster Analysis identifies hierarchical clusters of observations in a dataset by using one of six methods or algorithms: Nearest Neighbor, Furthest Neighbor, Centroid, Median, Group Average, or Ward’s.  K-Means provides one nonhierarchical method.

In hierarchical methods, each observation begins in its own cluster.  Two clusters are then merged to form a new cluster that replaces the two old clusters.  This process is repeated until only one cluster is left.  The algorithms used differ in how they compute the distance between the two clusters.

In the K-Means method, formation of clusters begins with an initial partition then uses a search algorithm to test other partitions to identify the one with the least error.

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

Data

Point Labels

Select (Multivariate Variables)

Sort

Delete...

Transform...

See also

Using the Analyses in the Multivariate Methods Module

Using the Cluster Analysis

Cluster Analysis Options

Seed Options

Membership Table Options

Icicle Plot Options

2D Scatterplot Options

3D Scatterplot Options


Cluster Analysis Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Cluster Analysis)

Membership Table (Cluster Analysis)

Icicle Plot (Cluster Analysis)

Agglomeration Schedule (Cluster Analysis)

See also

Cluster Analysis Options

Seed Options

Membership Table Options

Icicle Plot Options


Cluster Analysis Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Dendrogram (Cluster Analysis)

2D Scatterplot (Cluster Analysis)

3D Scatterplot (Cluster Analysis)

Agglomeration Distance Plot (Cluster Analysis)

See also

2D Scatterplot Options

3D Scatterplot Options


Save Results Options Dialog Box (Cluster Analysis)

The Save Results Options dialog box allows you to choose the results you want to save.  There are two options: Cluster Numbers and Distance Matrix.  If you save Cluster Numbers, they are stored in the same order as the original observations.  If you save the Distrance Matrix, the resulting variables can contain as many rows as there are observations.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (Cluster Analysis)

The Analysis Summary option displays the names of the variables, the number of complete cases, and the names of the clustering method and distance metric you are using.

It also displays a summary of the cluster numbers, the number of observations in each cluster, the percentages, and a summary of the centroids (means) for the cluster and for each of the variables.


Cluster Analysis Options Dialog Box

This dialog box allows you to choose the hierarchical clustering method or the nonhierarchical method that will be used to combine the observations or variables into clusters.  Each method uses different criteria to measure the distances among the clusters.

You also use the dialog box to choose the number of clusters that will be used, to choose the type of measurement method that will be used to calculate the distance between the clusters, and to choose how the data will be clustered. You can cluster observations or variables.

You can also standardize the variables or use the Seed… command to display the Seed Options dialog box, which you then use to enter the row numbers of the observations that will be used for each corresponding cluster.  The Seeds… command is available only when you use the K-Means method.

Method

Distance Metric

Cluster

Number of Clusters

Standardize

Seeds... Command


Seed Options Dialog Box

This dialog box allows you to enter the row number of the observations that will determine each corresponding cluster.  The Seeds… command is available only when you choose the K-Means method.

Row Number


Membership Table (Cluster Analysis)

The Membership Table option lists each observation and the cluster in which it was placed.


Membership Table Options Dialog Box

This dialog box allows you to indicate if the clusters should be sorted and displayed together.  For example, if you are using two clusters, the table with cluster 1s will display first, followed by cluster 2s.  The default is Unchecked, which means that the cluster elements will be intermixed.


Icicle Plot (Cluster Analysis)

The Icicle Plot option displays the number of clusters horizontally across the top of the plot and the observations vertically down the side.


Icicle Plot Options Dialog Box

This dialog box allows you to change the width of the plot.  The default is 60.


Agglomeration Schedule (Cluster Analysis)

The Agglomeration Schedule option displays the clusters as they are combined at each step.


Dendrogram (Cluster Analysis)

The Dendrogram option displays a representation (a tree graph) of the results.  The vertical axis represents the distance at each step; the horizontal axis represents the observations as they are combined.


2D Scatterplot (Cluster Analysis)

The 2D Scatterplot option displays a two-dimensional scatterplot of the clustered observations versus two variables.  A different point symbol is used for each cluster.  As an option, you can circle clusters to see them more clearly.


2D Scatterplot Options Dialog Box

This dialog box allows you to choose the names of the variables and to indicate if you want the clusters circled.

X-Axis

Y-Axis

Circle Clusters


3D Scatterplot (Cluster Analysis)

The 3D Scatterplot option displays a three-dimensional scatterplot of the clustered observations versus three variables.  A different point symbol is used for each cluster.

You can view three-dimensional graphs from different horizontal and vertical angles by spinning the graph to alter the location of the viewpoint.  The Smooth/Rotate button on the Analysis toolbar allows you to do this.


3D Scatterplot Options Dialog Box

This dialog box allows you to choose the names of the variables that will be plotted on the X-, Y-, and Z-axes.

X-Axis

Y-Axis

Z-Axis


Agglomeration Distance Plot (Cluster Analysis)

The Agglomeration Distance Plot option displays a plot of the distances as the clusters are combined at each step in a dendrogram.


Factor Analysis Dialog Box

Factor analysis is a technique useful for reducing information in a large number of variables into a smaller set, while losing only a small amount of information.

Variables in a factor analysis represent a linear function of a small number of common-factor variables and a single specific variable.  The common factors create covariances among the responses, while the specific variable adds only to the variances of specific responses.

The general purposes for factor analysis are to:

•	identify a set of dimensions you cannot easily observe in a large set of variables

•	devise a means for combining or condensing large numbers of observations into distinctly different groups within a larger population

•	create an entirely new set of a smaller number of variables to partially or to completely replace the original set of variables you can then use in regression, correlation, cluster, or discriminant analysis.

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

Data

Point Labels

Select (Multivariate Variables)

Sort

Delete...

Transform...

See also

Using the Analyses in the Multivariate Methods Module

Using the Factor Analysis

Factor Analysis Options

Estimation Options

Communalities Options

Scree Plot Options

2D Scatterplot Options

3D Scatterplot Options

2D Factor Weights Options

3D Factor Weights Options


Factor Analysis Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Factor Analysis)

Extraction Statistics (Factor Analysis)

Rotation Statistics (Factor Analysis)

Factor Scores (Factor Analysis)


Factor Analysis Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Scree Plot (Factor Analysis)

2D Scatterplot (Factor Analysis)

3D Scatterplot (Factor Analysis)

2D Factor Plot (Factor Analysis)

3D Factor Plot (Factor Analysis)


Save Results Options Dialog Box (Factor Analysis)

The Save Results Options dialog box allows you to choose the results you want to save.  There are six selections:

•	Eigenvalues (saves eigenvalues)

•	Factor Matrix (saves the unrotated factor matrix as a set of variables)

•	Rotated Factor Matrix (saves the rotated factor matrix as a set of variables)

•	Transition Matrix (saves the transition matrix as a set of variables)

•	Communalities (saves the final communalities; the variable has a length equal to the number of variables in the analysis)

•	Factor Scores (saves the factor scores; the variables contain rows that equal the number of observations).

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (Factor Analysis)

The Analysis Summary displays the name of each of the variables, the type of data, the number of cases, the name of the missing value treatment, whether the data are standardized, and the type of factoring.

The summary then displays the factor numbers, the eigenvalues, the percentage of variance, and the cumulative percentage for each factor.  The end of the summary displays the name of each variable and the initial communalities.

Communality is the amount of variance each of the original variables shares with all the other variables in the analysis.  For the Principal Components method, the communalities are all ones.  For the Classical method, the communalities are the multiple correlations of each variable when regressed against the other variables.


Factor Analysis Options Dialog Box

This dialog box allows you to:

•	choose options that will determine how the missing values will be treated

•	determine if the data will be standardized

•	determine the type of factoring that will be used

•	determine the type of rotation that will be used

•	determine the options that will be used to extract the factors from the analysis.

Missing Value Treatment

Standardize

Type of Factoring

Rotation

Extract by

Minimum Eigenvalue

Number of Factors

Estimation... Command

Communalities... Command


Estimation Options Dialog Box

This dialog box allows you to limit and stop the factor rotation process.

Stopping Criterion

Enter a number that will stop the rotation process.  The process is stopped when the change from the previous iteration is smaller than the number you enter.  Enter a number greater than or equal to 0; the default is 0.00001.

Maximum Iterations

Enter the maximum number of iterations that will be used to perform the rotation process.  Enter an integer between 1 and 1000; the default is 100.


Communalities Options Dialog Box

This dialog box allows you to enter the name of the variables that contain the communalities you want to use.


Extraction Statistics (Factor Analysis)

The Extraction Statistics option displays the factor-loading matrix that shows the loadings for each of the factors included in the analysis before the factor is rotated.


Rotation Statistics (Factor Analysis)

The Rotation Statistics option displays the rotated factor-loading matrix.  The table also displays the method of rotation you chose and the name and estimated communality for each of the variables.


Factor Scores (Factor Analysis)

The Factor Scores option displays the factor scores in table form.


Scree Plot (Factor Analysis)

The Scree Plot option helps determine the number of factors that will be extracted from an analysis.  If you use the Minimum Eigenvalue option, a horizontal line is drawn at that value on the graph.


Scree Plot Options Dialog Box

This dialog box allows you to choose the type of values that will plot on the Y-axis: Eigenvalues or Percent of Variance.  The Percent of Variance option plots the percentage of total variance explained by each factor.  The default is Eigenvalues.


2D Scatterplot (Factor Analysis)

The 2D Scatterplot option displays a two-dimensional scatterplot of the rotated factor scores for each observation.

This plot can help you interpret the factors and understand how the factors compare with each other.


2D Scatterplot Options Dialog Box

This dialog box allows you to choose the number of the factor that will plot on each axis.

X-Axis Factor

Y-Axis Factor


3D Scatterplot (Factor Analysis)

The 3D Scatterplot option displays a three-dimensional scatterplot of the rotated factor scores for each observation.

This plot is helpful for interpreting the factors and in understanding how they compare with each other.

You can view three-dimensional graphs from different horizontal and vertical angles by spinning the graph to alter the location of the viewpoint.  The Smooth/Rotate button on the Analysis toolbar allows you to spin three-dimensional graphs.


3D Scatterplot Options Dialog Box

This dialog box allows you to enter the number of the factor that will plot on each axis.

X-Axis Factor

Y-Axis Factor

Z-Axis Factor


2D Factor Plot (Factor Analysis)

The 2D Factor Plot option displays a two-dimensional plot of the loadings for each variable.  The plot is helpful in interpreting the factors.  For example, with lines at 0 you can see how each of the original variables affects the factors.


2D Factor Weights Plot Options Dialog Box

This dialog box allows you to enter the number of the factor that will plot on each axis.

X-Axis Factor

Y-Axis Factor


3D Factor Plot (Factor Analysis)

The 3D Factor Plot option displays a three-dimensional plot of the loadings for each variable.  The plot helps you to interpret the factors.

You can view three-dimensional graphs from different horizontal and vertical angles by spinning the graph to alter the location of the viewpoint.  The Smooth/Rotate button on the Analysis toolbar allows you to do this.


3D Factor Weights Plot Options Dialog Box

This dialog box allows you to enter the number that will plot on each axis.

X-Axis Factor

Y-Axis Factor

Z-Axis Factor


Principal Components Analysis Dialog Box

Principal components analysis differs from factor analysis in that you use it whenever you want uncorrelated linear combinations of variables.  That is, principal components analysis is a factor-analysis technique that reduces the dimensions of a set of variables by reconstructing them into uncorrelated combinations.

The analysis combines the variables that account for the largest amount of variance to form the first principal component.  The second principal component accounts for the next largest amount of variance, and so on, until the total sample is combined into component groups.  Each successive component explains progressively smaller portions of the variance in the total sample.  All the components are uncorrelated.

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

Data

Point Labels

Select (Multivariate Variables)

Sort

Delete...

Transform...

See also

Using the Analyses in the Multivariate Methods Module

Using the Principal Components Analysis

Principal Components Options

Scree Plot Options

2D Scatterplot Options

3D Scatterplot Options

2D Component Plot Options

3D Component Plot Options

2D Biplot Options

3D Biplot Options


Principal Components Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Principal Components Analysis)

Component Weights (Principal Components)

Data Table (Principal Components)


Principal Components Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Scree Plot (Principal Components)

2D Scatterplot (Principal Components)

3D Scatterplot (Principal Components)

2D Component Plot (Principal Components)

3D Component Plot (Principal Components)

2D Biplot (Principal Components)

3D Biplot (Principal Components)


Save Results Options Dialog Box (Principal Components)

The Save Results Options dialog box allows you to choose the results you want to save.  There are three selections:

•	Eigenvalues (saves the eigenvalues for each component)

•	Component Weights (saves each of the component weights)

•	Principal Components (saves the principal components for each of the observations).

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (Principal Components Analysis)

The Analysis Summary option displays the variables and the type of data you are analyzing, the number of complete cases, the type of missing value treatment, and if the data are standardized.  Then for each component, the summary displays its eigenvalue, percentage of variance, and the cumulative percentage.


Principal Components Options Dialog Box

This dialog box allows you to indicate how the program will treat missing values, whether or not you want to use standardized variables, and how components will be extracted from the analysis.

Missing Value Treatment

Standardize

Extract by

Minimum Eigenvalue

Number of Components


Component Weights (Principal Components)

The Component Weights option displays the component weights for all of the variables.  The component weights are used to calculate the principal components.  Each variable is multiplied by its associated component weight and summed with the other variables.


Data Table (Principal Components)

The Data Table option displays the principal components of the data.  The principal components are the result of multiplying the variables by their component weights and summing the “new” variables.


Scree Plot (Principal Components)

The Scree Plot option displays a plot of the eigenvalues or total variance accounted for by each component.  The plot shows a distinct gap between the steepest slope of the large components and a progressive downward path (the scree).  This plot identifies at least one and sometimes two or three of the most significant components.


Scree Plot Options Dialog Box

This dialog box allows you to choose the type of values that will plot on the Y-axis.

Eigenvalues

Plots eigenvalues.

Percent of Variance

Plots the percentage of total variance explained by each factor.


2D Scatterplot (Principal Components)

The 2D Scatterplot option displays a two-dimensional scatterplot of two principal components.


2D Scatterplot Options Dialog Box (Principal Components)

This dialog box allows you to enter the number of the component that will plot on each axis.

X-Axis Component

Y-Axis Component


3D Scatterplot (Principal Components)

The 3D Scatterplot option displays a three-dimensional scatterplot of three principal components.

You can view three-dimensional graphs from different horizontal and vertical angles by spinning the graph to alter the location of the viewpoint.  The Smooth/Rotate button on the Analysis toolbar allows you to spin (rotate) three-dimensional graphs.


3D Scatterplot Options Dialog Box

This dialog box allows you to enter the number of the component that will plot on each axis.

X-Axis Component

Y-Axis Component

Z-Axis Component


2D Component Plot (Principal Components)

The 2D Component Plot option displays a two-dimensional plot of component weights.  You can use the plot to interpret the component weights.


2D Component Plot Options Dialog Box

This dialog box allows you to enter the number of the component that will plot on each axis.

X-Axis Component

Y-Axis Component


3D Component Plot (Principal Components)

The 3D component Plot option displays a three-dimensional plot of component weights.  You can use the plot to interpret the component weights.

You can view three-dimensional graphs from different horizontal and vertical angles by spinning the graph to alter the location of the viewpoint.  The Smooth/Rotate button on the Analysis toolbar allows you to spin (rotate) three-dimensional graphs.


3D Component Plot Options Dialog Box

This dialog box allows you to enter the number of the component that will plot on each axis.

X-Axis Component

Y-Axis Component

Z-Axis Component


2D Biplot (Principal Components)

The 2D Biplot option displays a two-dimensional biplot with rays that represent the magnitude and direction for each variable.


2D Biplot Options Dialog Box

This dialog box allows you to enter the number of the component that will plot on each axis.

X-Axis Component

Y-Axis Component


3D Biplot (Principal Components)

The 3D Biplot option displays a three-dimensional biplot with rays that represent the magnitude and direction for each variable.

You can view three-dimensional graphs from different horizontal and vertical angles by spinning the graph to alter the location of the viewpoint.  The Smooth/Rotate button on the Analysis toolbar allows you to spin (rotate) three-dimensional graphs.


3D Biplot Options Dialog Box

This dialog box allows you to enter the number of the component that will plot on each axis.

X-Axis Component

Y-Axis Component

Z-Axis Component


Discriminant Analysis Dialog Box

Complex problems and the results of bad decisions frequently force researchers to look for more objective ways to predict outcomes.  Discriminant analysis is the statistical technique that is most commonly used to solve these types of problems.

Its use is appropriate when you can classify data into two or more groups, and when you want to find one or more functions of quantitative measurements that can help you discriminate among the known groups.

The objective of the analysis is to provide a method for predicting which group a new case is most likely to fall into, or to obtain a small number of useful predictor variables.

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

Classification Factor

Data

Point Labels

Select

Sort

Delete...

Transform...

See also

Using the Analyses in the Multivariate Methods Module

Discriminant Analysis Options

Classification Options

2D Scatterplot Options

3D Scatterplot Options

Discriminant Function Plot Options


Discriminant Analysis Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Discriminant Analysis)

Classification Functions (Discriminant Analysis)

Discriminant Functions (Discriminant Analysis)

Classification Table (Discriminant Analysis)

Group Centroids (Discriminant Analysis)

Group Statistics (Discriminant Analysis)

Group Correlations (Discriminant Analysis)


Discriminant Analysis Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

2D Scatterplot (Discriminant Analysis)

3D Scatterplot (Discriminant Analysis)

Discriminant Functions (Discriminant Analysis)


Save Results Options Dialog Box (Discriminant Analysis)

The Save Results Options dialog box allows you to choose the results you want to save.  There are five selections:

•	Discriminant Function Values (saves the value for each of the discriminant functions for each observation).

•	Coefficients (saves a set of coefficients for each class of observations;  each new case is classified by evaluating each function and assigning the case to the group that corresponds to thevalue of the highest function).

•	Standardized Coefficients (saves the standardized coefficients for each discriminant function).

•	Unstandardized Coefficients (saves the standardized coefficients for each discriminant function).

•	Prior Probabilities (saves the unstandardized coefficients for each discriminant function).

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (Discriminant Analysis)

The Analysis Summary option displays the name of the classification variable, the names of the independent variables, the number of complete cases, and the number of groups in the study.

It then summarizes the results, displaying the eigenvalues, relative percentages, canonical correlations, Wilks’ lambda, chi-square, degrees of freedom, and the p-values for one less than the number of groups.


Discriminant Analysis Options Dialog Box

This dialog box allows you to choose the option that will determine how the variables will be entered into the discriminant model, to choose the values for the F-ratio if you choose the Stepwise option, and to choose how you want to display the final results.

Fit

Stepwise

Display


Classification Functions (Discriminant Analysis)

The Classification Functions option displays Fisher’s linear discriminant function coefficients for each group.  You can use these functions to predict the group into which an observation is placed.  The function that yields the largest value for an observation represents the predicted group.


Discriminant Functions (Discriminant Analysis)

The Discriminant Functions option displays the standardized and unstandardized canonical discriminant function coefficients for each discriminant function.

The predictive results are the same as those for Fisher’s discriminant functions.


Classification Table (Discriminant Analysis)

The Classification Table option displays the actual and predicted results for the classifications.

Tabulations are made for the number of observations in each group that were correctly predicted for members of that group.  Tabulations are also made for the number of observations that were incorrectly predicted as being members of that group and that belong in other groups.  The table also displays the counts and percentages for each group.


Classification Options Dialog Box

This dialog box allows you to choose how prior probabilities will be assigned for groups when the observations are classified, whether or not you want to sort the observations, and how you want to display the observations.

Prior Probabilities

Display

Sort


Group Centroids (Discriminant Analysis)

The Group Centroids option displays the location of the centroids (means) for the unstandardized discriminant functions.

Each row in the table represents a group.  Each column contains the centroids for a single canonical discriminant function.


Group Statistics (Discriminant Analysis)

The Group Statistics option displays, by actual group and by all groups combined, the counts, means, and standard deviations for each variable.


Group Correlations (Discriminant Analysis)

The Group Correlations option displays the pooled within-group covariance and correlation matrices for all the independent variables.


2D Scatterplot (Discriminant Analysis)

The 2D Scatterplot option displays a two-dimensional scatterplot, which plots observations by two variables.  A different point symbol is used for each group.


2D Scatterplot Options Dialog Box

This dialog box allows you to choose the names of the variables that will be plotted on each axis.

X-Axis

Y-Axis


3D Scatterplot (Discriminant Analysis)

The 3D Scatterplot option displays a three-dimensional scatterplot, which plots observations by three independent variables.  A different point symbol appears for each group.

You can view three-dimensional graphs from different horizontal and vertical angles by spinning the graph to alter the location of the viewpoint.  The Smooth/Rotate button on the Analysis toolbar allows you to spin (rotate) three-dimensional graphs.


3D Scatterplot Options Dialog Box

This dialog box allows you to choose the names of the variables that will be plotted on each axis.

X-Axis

Y-Axis

Z-Axis


Discriminant Functions (Discriminant Analysis)

The Discriminant Functions option displays a plot of the values for two canonical discriminant functions.  You can plot the points using the classifications codes you entered in the Classification Factor text box on the Discriminant Analysis dialog box, or plot the predictions for the classification group for each observation using the 2D Discriminant Function Options dialog box.  Different symbols identify the points in each group.


Canonical Correlations Analysis Dialog Box

Developed by Hotelling in 1936, canonical correlation analysis is a technique you can use to study the relationship between two sets of variables, each of which might contain several variables.

Its purpose is to summarize or explain the relationship between two sets of variables by finding a small number of linear combinations from each set of variables that have the highest correlation possible between the sets.  This is known as the first canonical correlation.

The coefficients of these combinations are canonical coefficients or canonical weights.  Usually the canonical variables are normalized so each canonical variable has a variance of 1.

A second set of canonical variables is then found, which produces a second highest correlation coefficient.  This process continues until the number of pairs equals the number of variables in the smallest group in the study.

Use the dialog box to choose the sets of variables you want to analyze using the techniques available in the Canonical Correlations analysis.

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

First Set of Variables

Second Set of Variables

Point Labels

Select (Multivariate Variables)

Sort

Delete...

Transform...


Canonical Correlations Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Canonial Correlations)

Data Table (Canonical Correlations)


Canonical Correlations Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Canonical Variables Plot (Canonical Correlations)


Save Results Options Dialog Box (Canonical Correlations)

The Save Results Options dialog box allows you to choose the results you want to save.  There are four options:

•	Coefficients - First Set (save the coefficients of the variables in the first set)

•	Coefficients - Second Set (save the coefficients of the variables in the second set)

•	Canonical Correlations - First Set (save the canonical correlations of the variables in the first set)

•	Canonical Correlations - Second Set (save the canonical correlations of the variables in the second set).

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Analysis Summary (Canonial Correlations)

The Analysis Summary option displays the names of the variables in both the first and second sets, and the number of complete cases in the analysis.  It then displays information about the canonical correlations, and the coefficients for the canonical variables in both the first and second sets.

Canonical correlations with small p-values (less than .05) are significant.  Large correlations are associated with large eigenvalues and chi-square values.


Data Table (Canonical Correlations)

The Data Table option displays the values for the canonical variables in both the first and second sets of variables.


Canonical Variables Plot (Canonical Correlations)

The Canonical Variables Plot option displays a plot of the canonical variables.  The plot helps you identify the strength of the canonical correlations.  Strong correlations appear linear.


Canonical Variables Plot Options Dialog Box

This dialog box allows you to enter the number of the canonical variable that will appear on the plot.

Variable Number


MV Jump Topics

All of the topics following this divider are topics used in the popups referenced above.


Data

Enter the name of the variables that contain the raw data.

Note:  In STATGRAPHICS Plus, the default is Standardized. If you do not want to standardize the data, you must turn off the Standardize option on the Analysis Summary Options dialog box.  As an alternative, you can enter variables that form a correlation or covariance matrix.

You can also generate values to transform the data using mathematical functions (operators) to achieve better results.  To transform the data, click the Transform... button, which displays the Generate Data dialog box.


Point Labels

[Optional]  Enter the names of the variables you want to use for the observations that will appear in the data tables.

Enter one variable name for each observation in the data.  The first name is assigned to the first observation in the data, the second name to the second observation, and so on.  If you leave this text box blank, default observation labels are created.


Select (Multivariate Variables)

[Optional]  Selects a subset of the multivariate variables.  For example, to analyze the first 50 values in each variable, enter first (50) into this text box.


Sort

Sorts the variable names alphabetically; sorted is the default.


Cluster Numbers

Saves the cluster numbers, which are stored in the same order as the original observations.


Distance Matrix

Saves the Euclidean distance matrix.  The resulting variables contain as many rows as there are observations in the analysis.

Squared Euclidean

Euclidean

City Block


Method

Determines the method that that will be used to combine the observations or variables into clusters.

Nearest Neighbor

Finds the two observations that have the shortest distance between clusters and places them in the first cluster; repeats this process until all the observations are in one cluster or until the specified number of clusters is reached.  The Nearest Neighbor method is also known as the Single Linkage method.

Furthest Neighbor

Uses the maximum distance between any two observations in a cluster.  All the observations in a cluster are linked at some maximum distance or by some minimum similarity.  This method is also known as the Complete Linkage method.

Centroid

Uses the distance between the means of two clusters as the measurement between clusters.  When observations are grouped, new centroids are formed. The cluster centroids move each time a new observation or group of observations is added to an existing cluster.  The Centroid method requires you to use metric data; other methods do not.

Median

Uses the median distance from observations in one cluster to observations in another as the measurement between clusters.  This method tends to combine clusters that have small variances and may produce clusters that have the same variance.

Group Average

Calculates the distance between two clusters using the average distance from observations in one cluster to observations in another cluster.

Ward’s

Determines the distance between two clusters, which is the sum of squares between two clusters summed over all the variables.  This method combines clusters that have a small number of observations, and tends to produce clusters that have approximately the same number of observations.

K-Means

A nonhierarchical method; each cluster begins with a specified number of groups, each of which has a single random point.  A sequence of points is sampled, and each point is added, in turn, to the group whose mean it is closest to.  The group mean is then adjusted.

Number of Clusters

Enter the number of clusters you want to use.  Enter an integer greater than or equal to 1 and less than or equal to the number of observations in the dataset; the default is 1.  If you use the K-Means option, the maximum number of clusters you can enter is 16.

Distance Metric

Choose the method that will calculate the distance between clusters.

Squared Euclidean - Uses the sum of squared differences between observations.

Euclidean - Uses the square root of the sum of the squared distances between observations.  Measures the length of a straight line drawn between two objects; it is the most commonly used distance measurement.

City Block - Uses the absolute differences of the coordinates for the observations.  This is also known as the Manhattan distance.


Nearest Neighbor

Finds the two observations that have the shortest distance between clusters and places them in the first cluster, then repeats this process until all the observations are in one cluster or the specified number of clusters is reached. The Nearest Neighbor method is also known as the Single Linkage method.


Furthest Neighbor

Uses the maximum distance between any two observations in a cluster.  All the observations in a cluster are linked at some maximum distance or by some minimum similarity.  This method is also known as the Complete Linkage method.


Centroid

Uses the distance between the means of two clusters as the measurement between clusters.  When observations are grouped, new centroids are formed.  The cluster centroids move each time a new observation or group of observations is added to an existing cluster.  The Centroid method requires you to use metric data; other methods do not.


Median

Uses the median distance from observations in one cluster to observations in another as the measurement between clusters.  This method tends to combine clusters that have small variances and may produce clusters that have the same variance.


Group Average

Calculates the distance between two clusters using the average distance from observations in one cluster to observations in another cluster.

Ward's

K-Means


Ward's
Ward’s

Uses Ward's method to determine the distance between two clusters, which is the sum of squares between two clusters summed over all the variables.  This method combines clusters that have a small number of observations, and tends to produce clusters that have approximately the same number of observations.


K-Means

A nonhierarchical method; each cluster begins with a specified number of groups, each of which has a single random point.  A sequence of points is sampled, and each point is added, in turn, to the group whose mean it is closest to.  The group mean is then adjusted.


Number of Clusters

Enter the number of clusters that will be used.  Enter an integer greater than or equal to 1 and less than or equal to the number of observations in the dataset; the default is 1.  If you use the K-Means option, the maximum number of clusters you can enter is 16.


Distance Metric

Determines the type of measurement method that will be used to calculate the distance between clusters.

Squared Euclidean

Uses the sum of squared differences between observations.

Euclidean

Uses the square root of the sum of the squared distances between observations.  Euclidean distance measures the length of a straight line drawn between two objects; it is the most commonly used distance measurement.

City Block

Uses the absolute differences of the coordinates for the observations as the distance between the clusters.  This is also known as the Manhattan distance.


Squared Euclidean

Uses the sum of squared differences between observations.


Euclidean

Uses the square root of the sum of the squared distances between observations.  Euclidean distance measures the length of a straight line drawn between two objects; it is the most commonly used distance measurement.


City Block

Uses the absolute differences of the coordinates for the observations as the distance between the clusters.  This is also known as the Manhattan distance.


Cluster

Determines how the data will be clustered.

Obsevations

Clusters similar observations.

Variables

Clusters similar variables.


Observations

Clusters similar observations.


Variables

Clusters similar variables.


Standardize

Indicates if the variables will be standardized.  The mean is subtracted from each variable and the result divided by the standard deviation.  You should standardize variables when they are measured on different scales.  You can use standardization only if you are using variable data.  This option is the default.


Seeds... Command

Displays the Seed Options dialog box, which you use to enter the row numbers of the observations that will be used for each corresponding cluster.  This command is available only when you choose the K-Means option.


Row Number

Enter the row number that will be used as the values for the initial seeds in the clusters.  You can enter up to 16 row numbers.  The number of available text boxes equals the number of clusters you enter on the Cluster Analysis Options dialog box.


X-Axis

Choose the name of the variable that will appear on the X-axis.


Y-Axis

Choose the name of the variable that will appear on the Y-axis.


Z-Axis

Choose the name of the variable that will appear on the Z-axis.


Circle Clusters

Indicates whether or not clusters will be circled.


Data - Factor Analysis
Data

Enter the name of the variables that contain the data you want to analyze.  As an alternative, you can enter the names of variables that form a correlation or covariance matrix.


Point Labels - Factor Analysis
Point Labels

Enter the name that will be used as the label for the table of factor scores.  Enter one name for each point in the data.  The first name is assigned to the first observation in the data, the second name to the second observation, and so on.  If you leave this text box blank, default label names are created.


Missing Value Treatment

Determines how missing values will be treated.  A missing value is an observation used when data are missing.

Most of the analyses in STATGRAPHICS Plus perform Listwise deletion of missing values.  If a missing value is found in any of the variables in the analysis, that entire case is deleted from the analysis.  Other analyses allow optional Pairwise deletion of missing values.

To enter data that contain missing values, leave the appropriate cell blank when you complete the DataSheet.

Listwise

Includes only cases that have variables with values.

Pairwise

Includes all cases and uses nonmissing values for each variable whenever it is possible.  In Pairwise deletion, aincludes cases that have calculations that have and include values for two variables.


Listwise

Includes only cases in which all of the variables have values.  This option is the default.


Pairwise

Includes all the cases and uses nonmissing values for each variable whenever that is possible.  In Pairwise deletion, includes cases that have calculations that have and include values for two variables.


Standardize - Factor Analysis
Standardize

Standardizes the variables by subtracting the average from each variable and then dividing by the standard deviation.


Type of Factoring

Determines the factor analysis technique that will be used to estimate the values for the factors.

Principal Components

Defines new hypothetical variables that are exact transformations of the original variables, and makes no assumptions about the underlying structure.  That is, finds the set of linear combinations of the original variables that assimilate and account for the maximum possible proportion of total variation in those variables.

For example, the first principal component will be the single best summary of the total variance; the second principal component will be the best summary of the variance remaining after extracting the first principal component.  The diagonal element of the covariance or correlation matrix is left unchanged; for example, you cannot assume that unique factors exist.

Classical

Replaces the diagonals with the communalities; that is, assumes that unique factors exist.  Estimates the communality by removing the uniqueness of each variable and analyzing only the remaining portion of each that is assumed to be involved in determining the pattern of the variables.


Principal Components - Factor Analysis
Principal Components

Defines new hypothetical variables that are exact transformations of the original variables, and makes no assumptions about the underlying structure.  That is, finds the set of linear combinations of the original variables that assimilate and account for the maximum possible proportion of total variation in those variables.

For example, the first principal component will be the single best summary of the total variance; the second principal component will be the best summary of the variance remaining after extracting the first principal component.  The diagonal element of the covariance or correlation matrix is left unchanged; for example, you cannot assume that unique factors exist.


Classical

Replaces the diagonals with the communalities; that is, assumes that unique factors exist.  Estimates the communality by removing the uniqueness of each variable and analyzes only the remaining portion of each variable that is assumed to be involved in the patterning of the variables.


Rotation

Determines the type of rotation that will be used to rotate the factors.

None

The factors cannot be rotated.

Varimax

Simplifies the factor matrix by maximizing the variance of the squared loadings in each column.

Equimax

Balances between Varimax and Quartimax.

Quartimax

Simplifies the factor matrix by maximizing the variance of the squared loadings in each row.


None - Factor Analysis
None

The factors cannot be rotated.


Verimax
Varimax

Simplifies the factor matrix by maximizing the variance of the squared loadings in each column.


Equimax

Balances between Varimax and Quartimax.


Quartimax

Simplifies the factor matrix by maximizing the variance of the squared loadings in each row.


Extract by

Determines how the factors will be extracted from the analysis.

Minimum Eigenvalue

Uses the specified minimum eigenvalue to extract the factors.  If you choose this option, the Minimum Eigenvalue text box becomes active.

Number of Factors

Extracts the factors based on a predetermined number of factors; that is, you specify the number of factors you want to extract.  If you choose this option, the Number of Factors text box becomes active.


Minimum Eigenvalue Button
Minimum Eigenvalue

Extracts factors using the specified minimum eigenvalue.  If you choose this option, the Minimum Eigenvalue text box becomes active.


Number of Factors Button
Number of Factors

Extracts the factors based upon a predetermined number of factors; that is, you specify the number of factors you want to extract.  If you choose this option, the Number of Factors text box becomes active.


Minimum Eigenvalue Text Box
Minimum Eigenvalue

Indicate if you want to eliminate factors that have eigenvalues less than 1 (the default).


Number of Factors Text Box
Number of Factors

Enter the number of factors you want to include in the analysis.


Estimation... Command

Displays the Estimation Options dialog box, which limits and stops the factor rotation process.

Stopping Criterion

Enter a number at which the rotation process will stop. The process stops when the change from the previous iteration is smaller than the number you entered.  Enter a number greater than or equal to 0; the default is 0.00001.

Maximum Iterations

Enter the maximum number of iterations that should be perform the rotation process.  Enter an integer between 1 and 1000; the default is 100.


Stopping Criterion

Enter a number at which the rotation process will stop. The process stops the when the change from the previous iteration is smaller than the specified stopping criterion.  Enter a number greater than or equal to 0; the default is 0.00001.


Maximum Iterations

Enter the maximum number of iterations that will perform the rotation process.  Enter an integer between 1 and 1000; the default is 100.


Eigenvalues on a Scree Plot
Eigenvalues

Plots eigenvalues on the Scree Plot.


Percent of Variance

Plots the percentage of total variance that each factor explains.


X-Axis Factor

Enter the number of the factor that will appear on the X-axis.  The default is the first factor that is extracted.


Y-Axis Factor

Enter the number of the factor that will appear on the Y-axis.  The default is the second factor that is extracted unless you have only a single factor.


Z-Axis Factor

Enter the number of the factor that will appear on the Z-axis.


Communalities... Command

Displays the Communalities Options dialog box, which you use enter the name of the variable that contains the communalities you want to use.


Extraction by - Component
Extract by

Determines how the components will be extracted from the analysis.

Minimum Eigenvalue

Extracts only the components whose eigenvalues are greater than or equal to a specified minimum value.  If you choose this option, the Minimum Eigenvalue text box becomes active.

Number of Components

Extracts components based upon a predetermined number of components; that is, you know the number of components you want to extract.  If you choose this option, the Number of Components text box becomes active.


Minimum Eigenvalue Button - Principal Components
Minimum Eigenvalue

Extracts only the components whose eigenvalues are greater than or equal to a specified minimum value.  If you choose this option, the Minimum Eigenvalue text box becomes active.


Number of Components Button
Number of Components

Extracts components based on a predetermined number of components; that is, you know the number of components you want to extract.  If you choose this option, the Number of Components text box becomes active.


Minimum Eigenvalue

Enter the smallest eigenvalue a component can have and still be included in the analysis.  The default is 1.


Number of Components Text Box
Number of Components

Enter the number of components that will be included in the analysis.  The default is the number of variables.


Percent of Variance - Principal Components
Percent of Variance

Plots the percentage of total variance explained by each component.


X-Axis Component

Enter the name of the component that will appear on the X-axis.  The default is the first component that is extracted.


Y-Axis Component

Enter the number of the component that will appear on the Y-axis.  The default is the second component that is extracted.


Z-Axis Component

Enter the number of the component that will appear on the Z-axis.


Classification Factor

Enter the name of the variable that contains the codes that will be used to group the observations.  The length of the variable should equal the length of the variables in the Data text box.


Data - Discriminant Analysis
Data

Enter the names of the variables that contain the data that will be analyzed.  You can also generate data values.  STATGRAPHICS Plus allows you to transform data using mathematical functions (operators) to achieve better results.  Using these operators, the program is able to perform complex calculations.


Fit

Determines how the variables will be entered into the discriminant model.

All Variables

Enters all the variables.

Forward Selection

Performs a forward, stepwise discriminant analysis, which begins with no variables in the model and adds them one at a time to obtain a final model.

Backward Selection

Performs a backward, stepwise discriminant analysis, which begins with all the variables in the model and removes them one at a time to obtain a final model.


All Variables

Enters all the variables.


Forward Selection

Performs a forward, stepwise discriminant analysis, which begins with no variables in the model and adds them one at a time to obtain a final model.


Backward Selection

Performs a backward, stepwise discriminant analysis, which begins with all the variables in the model and removes them one at a time to obtain a final model.


Stepwise

Determines the values for the F-ratio at which the variables will be entered and specifies the maximum number of steps.

F-to-Enter

Enter the value for the F-ratio at or above which you want to enter the variables into the model.  This option is available when you choose the Forward or Backward Selection options.  Enter a number greater than or equal to the number in the F-to-Remove text box.

F-to-Remove

Enter the value for the F-ratio below which you want to remove the variables from the model.  This option is available when you choose the Forward or Backward Selection options.  Enter a number greater than or equal to 0 and less than or equal to the number in the F-to-Enter text box.

Max. Steps

Enter the maximum number of steps that should be performed before stopping the selection process.  This option is available when you choose the Forward or Backward Selection options.  Enter an integer greater than 0.


F-to-Enter

Enter the value for the F-ratio at or above which you want to enter the variables into the model.  This option is available when you choose the Forward or Backward Selection options.  Enter a number greater than or equal to the number in the F-to-Remove text box.


F-to-Remove

Enter the value for the F-ratio below which you want to remove the variables from the model.  This option is available when you choose the Forward or Backward Selection options.  Enter a number greater than or equal to 0 and less than or equal to the number in the F-to-Enter text box.


Max. Steps

Enter the maximum number of steps that will be performed before stopping the selection process.  This option is available when you choose the Forward or Backward Selection options.  Enter an integer greater than 0.


Display

Determines how the final results will be displayed.

Final Model Only

Displays the results for only the final model.

All Steps

Displays the results for each step in the stepwise discriminant analysis.  To view the step results, scroll down the Analysis Summary pane.


Final Model Only

Displays the results for only the final model.


All Steps

Displays the results for each step in the stepwise discriminant analysis.  To view the step results, scroll down the Analysis Summary pane.


Prior Probabilities

Determines how prior probabilities for groups will be assigned when the observations are classified.

All Groups Equal

Assumes equal prior probabilities for groups when the observations are classified.

Proportional to Observed

Assigns prior probabilities as the proportion of observations in each group.

User-Specified

Enter prior probabilities for each group.  Using this option activates the Probabilities text box.

Probabilities

Enter the name of the variable that contains the prior probabilities for each group.  The prior probabilities must be positive and sum to 1.


All Group Equal
All Groups Equal

Assumes equal prior probabilities for groups when the observations are classified.


Proportional to Observed

Assigns prior probabilities as the proportion of observations in each group.


User-Specified

Enter prior probabilities for each group.  Using this option activates the Probabilities text box, which you use to enter the name of the variable that contains the prior probabilities for each group.  The prior probabilities must be positive and sum to 1.


Display Options
Display

Determines how the observations will be displayed.

All Data

Displays all the data and their corresponding group classifications.

New Observations

Displays the classifications for only new observations.  Observations that do not have a corresponding code value are considered “new” observations.


All Data

Displays all the data and their corresponding group classifications.


New Observations

Displays the classifications for only new observations.  Observations that do not have a corresponding code value are considered “new” observations.


X-Axis

Enter the name of the variable that will appear on the X-axis.


Y-Axis

Enter the name of the variable that will appear on the Y-axis.


Z-Axis Function
Z-Axis

Choose the name of the variable that will appear on the Z-axis.


X-Axis Discriminant Function
X-Axis Function

Enter the number of the function that will appear on the X-axis.


Y-Axis Discriminant Function
Y-Axis Function

Enter the number of the function that will appear on the Y-axis.


Probabilities

Enter the name of the variable that contains the prior probabilities for each group.  The prior probabilities must be positive and sum to 1.


First Set of Variables

Enter the names of the first set of variables you want to analyze.


Second Set of Variables

Enter the names of the second set of variables you want to analyze.  The number of variables in this set must be less than or equal to the number of variables in the first set.


Point Labels

Enter the name that will be used as the label for the rows in the table of canonical variables or for the observations in discriminant analysis.  Enter one name for each point in the data.  The first name is assigned to the first label in the data, the second name to the second label, and so on.


Variable Number

Enter the number of the canonical variable that will be plotted.


Point Labels - Principal Components
Point Labels

Enter the name that will be used as the label for the rows in the table of principal components.  Enter one name for each point in the data.  The first name is assigned to the first observation in the data, the second name to the second observation, and so on.  If you leave this text box blank, default label names are created.


Save Results Options Dialog Box (Multiple Variable)

The Save Results Options dialog box allows you to choose the results that will be saved as correlation and covariance matrices.  You can use matrix data in Multivariate Methods analyses by entering them into any of these analyses: Principal Components, Factor Analysis, and Cluster Analysis.

You can use the Target Variables text boxes to enter the names of the matrices in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.  The program uses the following conventions to save the matrices:

CMAT - correlation matrix

RMAT - rank correlation matrix

VMAT - covariance matrix

PMAT - partial correlation matrix.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


3D Scatterplot (Factor Analysis)

The 3D Scatterplot option displays a three-dimensional scatterplot of the rotated factor scores.  This plot is helpful in interpreting the factors and in understanding how the factors compare.


3D Factor Plot (Factor Analysis)

The 3D Factor Plot option displays a three-dimensional plot of the loadings for each variable.  The plot is helpful in interpreting the factors.

You can view three-dimensional graphs from different horizontal and vertical angles by spinning the graph to alter the location of the viewpoint.  The Smooth/Rotate button on the Analysis toolbar allows you to do this.


3D Scatterplot (Principal Components)

The 3D Scatterplot option displays a three-dimensional scatterplot of the components.

You can view three-dimensional graphs from different horizontal and vertical angles by spinning the graph to alter the location of the viewpoint.  The Smooth/Rotate button on the Analysis toolbar allows you to do this.


3D Component Plot (Principal Components)

The 3D Component Plot option displays a three-dimensional plot of the component weights.

You can view three-dimensional graphs from different horizontal and vertical angles by spinning the graph to alter the location of the viewpoint.  The Smooth/Rotate button on the Analysis toolbar allows you to do this.


3D Biplot (Principal Components)

The 3D Biplot option displays a three-dimensional biplot with rays that represent the magnitude and direction for each variable.

You can view three-dimensional graphs from different horizontal and vertical angles by spinning the graph to alter the location of the viewpoint.  The Smooth/Rotate button on the Analysis toolbar allows you to do this.


Plot (Eigenvalues or Percent of Variance - Scree Plot)

Determines the type of values that will be plotted on the Y-axis.

Eigenvalues

Plots the eigenvalues.

Percent of Variance

Plots the percentage of total variance explained by each component.


Change Analysis Title Dialog Box

This dialog box allows you to edit or replace an automatically generated title of an analysis with one of your own choosing.  Type the title into the Title text box.


Recode Data Dialog Box

Allows you to change the format or range of the data so it conforms to the analysis you want to perform.

Note:  All the data you chose is recoded; if you want to retain the original data, copy it to another column before you use this dialog box.

Lower Limit

Upper Limit

New Value

Limit Conditions

Unmatched

Extrapolate


Multiple Box-and-Whisker Plot Analysis Dialog Box

The Multiple Box-and-Whisker Plot analysis is an extension of the Box-and-Whisker Plot analysis.  If you can subdivide the data into groups, you can use this analysis to produce separate Box-and-Whisker plots for each group on one chart.  This facilitates comparisons of the median, range, and extreme value for each group.

Each plot is a five-number statistical summary of a set of univariate observations.  It is an exploratory data-analysis tool that is useful for studying symmetry and distributional assumptions, and for detecting outliers.

Data

Level Codes

Select

Sort

Delete...

Transform...

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See Also

Using the Multiple Box-and-Whisker Plot Analysis

Multiple Box-and-Whisker Plot

Multiple Box-and-Whisker Plot Options

Box-and-Whisker Plot Analysis


Multiple Box-and-Whisker Plot Tabular Options Dialog Box

Allows you to select tabular options for the Multiple Box-and-Whisker plot analysis.

Analysis Summary (Multiple Box-and-Whisker Plot Analysis)


Analysis Summary (Multiple Box-and-Whisker Plot Analysis)

The Analysis Summary tabular option creates and displays a summary of the analysis.  The analysis includes the names of the dependent variable, the factor variable, and the number of observations and levels in the analysis.


Multiple Box-and-Whisker Plot Graphical Options Dialog Box

Allows you to select graphical options for the analysis.

Multiple Box-and-Whisker Plot


Multiple Box-and-Whisker Plot

The Multiple Box-and-Whisker plot graphical option creates and displays a Multiple Box-and-Whisker plot, which is a graphical summary of the outliers in the data.

The central box covers the middle 50 percent of the data; the sides of the box are the lower and upper quartiles, and the vertical line drawn through the box is the median.  The whiskers extend out to the lower and upper values of the data (the range).

The data are shown in four areas of equal frequency, which allows you to visually examine the shape of the distribution to detect skewness.  You can show outliers as individual points beyond the whiskers, add notches to show confidence intervals for the medians, or add markers to show the means.


Multiple Box-and-Whisker Plot Options Dialog Box

Allows you to select the direction of the plot as well as features for it.

Direction

Features


Probability Distributions Analysis Dialog Box

The Probability Distribution analysis allows you to perform three basic operations for each of 22 different probability distributions:

•	calculate probabilities

•	create plots of the probability and cumulative distributions

•	generate random numbers.

When you access this dialog box when you are using other analyses such as Uncensored Data, Censored Data, and others, two additional items appear on the dialog box:  # of Trials and # of Successes.

Distribution

# of Trials

# of Sucesses

To select options for the distributions, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Options dialog boxes for each of the distributions

Using the Probability Distribution Analysis

Using the Uncensored Data Analysis

Cumulative Distribution Options

Inverse CDF Options

Random Numbers Options


Probability Distributions Tabular Options Dialog Box

This dialog box allows you to select tabular options for the various Probability Distributions analyses.

Analysis Summary (Probability Distribution Analysis)

Cumulative Distribution (Probability Distribution Analysis)

Inverse CDF (Probability Distribution Analysis)

Random Numbers (Probability Distribution Analysis)


Analysis Summary (Probability Distribution Analysis)

The Analysis Summary tabular option creates and displays a summary for the distribution you selected.  For example, if you select a Normal Probability Distribution, the summary lists the parameters for the distribution, and shows the values for the mean and standard deviation.  This report will vary depending on the distribution you are analyzing.


{Normal} Options Dialog Box

Allows you to enter values for the parameters you select.  For example, for a Normal Probability Distribution, you will enter values for the mean and standard deviation.  You can enter up to five values.

Note:  The heading and the content of this dialog box will vary, depending on the distribution you choose; it is a common dialog box for all the tabular and graphical options.

Mean

Std. Dev.


Cumulative Distribution (Probability Distribution Analysis)

The Cumulative Distribution tabular option creates and displays a summary of the evaluation of the cumulative distribution you selected.  The summary includes the tail areas for up to five critical values of the distribution.


Cumulative Distribution Options Dialog Box

Allows you to enter values for the random variables.

Random Variable


Inverse CDF (Probability Distribution Analysis)

The Inverse CDF tabular option creates and displays a summary of the critical values for the distribution you selected.  The summary includes the tail areas for up to five critical values of the distribution.

To select options for the table, use the Inverse CDF Options dialog box.


Inverse CDF Options Dialog Box

Allows you to enter values for the tail areas of the parameters you want to use.

CDF


Random Numbers (Probability Distribution Analysis)

The Random Numbers tabular option creates and displays a summary of the random numbers for the distribution you select.  You can save the values for the random samples for future use.  For example, each time you save the results using the Save Results Options dialog box, a new random sample is generated.


Random Numbers Options Dialog Box

Allows you to enter the size (number) of observations that will be included in the random sample.

Size


Probability Distribution Graphical Options Dialog Box

Allows you to select graphical options for the various Probability Distribution analyses.

Density/Mass Function Plot (Probability Distribution Analysis)

CDF Plot (Probability Distribution Analysis)

Survivor Function Plot (Probability Distribution Analysis)

Log Survivor Function Plot (Probability Distribution Analysis)

Hazard Function Plot (Probability Distribution Analysis)


Density/Mass Function Plot (Probability Distribution Analysis)

The Density/Mass Function graphical option creates and displays a plot of the probability density function for the distribution you are evaluating.  The height of the function indicates the value for the probability density function that is evaluated using the value on the X-axis.


CDF Plot (Probability Distribution Analysis)

The CDF graphical option creates and displays a plot of the cumulative probability distribution for the distribution you are evaluating.


Survivor Function Plot (Probability Distribution Analysis)

The Survivor Function graphical option creates and displays a plot of the survivor function for the distribution you are evaluating.  The function indicates the probability of obtaining a value greater than or equal to the values on the X-axis.


Log Survivor Function Plot (Probability Distribution Analysis)

The Log Survivor Function graphical option creates and displays a plot of the log survivor function for the distribution you are evaluating.  The function indicates the probability of obtaining a value greater than or equal to the values on the X-axis.


Hazard Function Plot (Probability Distribution Analysis)

The Hazard Function graphical option creates and displays a plot of the hazard function for the distribution you are evaluating.  The hazard function is equal to the probability density function divided by the survivor function.

When you are modeling lifetime data, the hazard function represents the instantaneous failure rate.


Save Results Options Dialog Box (Probability Distribution Analysis)

The Save Results Options dialog box saves random number in target variables for later use.  Each time you save random numbers they are regenerated; therefore, the saved numbers will differ from any numbers you previously saved.

The contents of this dialog box will vary depending on the probability distribution you are using.


Contingency Tables Analysis Dialog Box

The Contingency Tables analysis is helpful when you want to determine if two classification factors are related, and if they are, how closely.

The analysis allows you to enter frequencies for each factor.  If you enter actual data instead of frequency counts, use the Crosstabulation analysis

To analyze data as a contingency table, each variable you enter represents one column of counts for each row class.  For example, if your data consist of row classes for Excellent, Average, and Poor, you might enter the following variables to represent each school grade:

grade1

grade2

grade3

grade4

….

Each variable would contain three values, one value for each of the three classes:  Excellent, Average, and Poor.

You can also use the Contingency Tables analysis to calculate various summary statistics:

•	a chi-square statistic that tests the hypothesis of independence between row and column factors (the statistic appears with the degrees of freedom and the significance level)

•	the lambda values, uncertainty coefficients, and Somer's D statistics for symmetric and asymmetric cases (that is, the rows and columns are dependent)

•	the contingency coefficient and other statistics.

Fisher's Exact test is performed for two-by-two matrices that have a total cell count of 100 or fewer.

Columns

Select

Sort

Delete...

Transform...

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Contingency Tables Analysis

Frequency Table Options

Barchart Options

Mosaic Plot Options

Skychart Options


Contingency Tables Tabular Options Dialog Box

Allows you to select tabular options for the analysis.

Analysis Summary (Contingency Tables Analysis)

Frequency Table (Contingency Tables Analysis)

Chi-Square Test (Contingency Tables Analysis)

Summary Statistics (Contingency Tables Analysis)


Analysis Summary (Contingency Tables Analysis)
Analysis Summary

The Analysis Summary tabular option creates and displays the names of the variables, the number of observations, and the number of rows and columns.


Frequency Table (Contingency Tables Analysis)

The Frequency Table tabular option creates and displays Frequency Tables, which appear in sequence.  Each column of the tables contains the counts in one of the variables you entered into the Contingency Tables Analysis dialog box.  The number of row classes determines the number of values in each variable.


Frequency Table Options Dialog Box

Allows you to indicate how the percentages that will appear in each cell of the table will be calculated.

Table Percentages From


Chi-Square Test (Contingency Tables Analysis)

The Chi-Square test tabular option creates and displays the results of a Chi-Square test that determines if the rows or the columns are dependent.

If the contingency table is a two-by-two table with less than 100 observations, the statistics will also include the results from Fisher's Exact test.


Summary Statistics (Contingency Tables Analysis)

The Summary Statistics tabular option creates and displays the results of various statistical tests.

Lambda Values

These values range from 0 (knowing that one variable shows nothing about the other variable) to 1 (knowing that one variable allows you to predict the other variable).

Uncertainty Coefficients and Pearson’s R

These statistics show the degree of linear relationship between the two variables.

Somer’s D Statistics

These statistics are for symmetric and asymmetric cases; that is, with rows and columns dependent, which show a symmetric measure of association for variables that are measured on an ordinal scale.

Eta

Eta is an appropriate measure of association for two variables when you measure the dependent variable on an interval scale and the independent variable on a nominal or ordinal scale.  Eta is similar to the Pearson correlation coefficient, however, it is asymmetric and does not assume a linear relationship between the variables.

Contingency Coefficient

This statistic is the result of measuring the strength of dependence between two characteristics.

Cramer’s V and Conditional Gamma

These statistics are chi-squared-based measures of association.

Kendall’s Tau b and c

These statistics measure the relative degree of agreement or disagreement between two variables.


Contingency Tables Graphical Options Dialog Box

Allows you to select graphical options for the Contingency Tables analysis.

Barchart (Contingency Tables Analysis)

Mosaic Plot (Contingency Tables Analysis)

Skychart (Contingency Tables Analysis)


Barchart (Contingency Tables Analysis)

The Barchart graphical option creates and displays a plot of the frequency data, which displays as a series of bars.

Barcharts make it easy to understand data that are divided into classes.  If the data contain more than 20 classes, an error message displays in the graphics pane.


Mosaic Plot (Contingency Tables Analysis)
Mosaic Plot

The Mosaic Plot graphical option creates and displays a Mosaic Plot.  Rectangles, whose areas are proportional to the cell counts, are constructed.  The width of the bars is proportional to the percentage distribution of the variable.

To select options for this plot, use the Mosaic Plot Options dialog box.


Skychart (Contingency Tables Analysis)

The Skychart graphical option creates and displays a three-dimensional histogram whose bar height is proportional to the number of observations in each cell.  The row variable is plotted along one axis, the column variable on another axis, and the frequency variable on a third axis.

This three-dimensional graph helps you to visualize the relationship between the two variables and to see the distribution of the data.

You can also use the Smooth/Rotate button on the Analysis toolbar to change the angle from which you view this plot.

To select options for this plot, use the Skychart Options dialog box.


Hypothesis Tests (Describe) Dialog Box

Hypothesis tests are a classical approach to assessing the statistical significance of findings.  Basically, the technique involves comparing empirically observed sample findings with theoretically expected findings — expected if the null hypothesis is true.  This comparison allows you to compute the probability that the observed outcomes might be due to chance alone.

You can enter sample statistics directly into this analysis, instead of first using the One-Variable analysis.

For a description of the Hypothesis Tests (Compare) Analysis, which tests hypotheses about the mean and variance for two independent samples, search for that topic in this Online Help System.

The analysis allows you to test four types of parameters:

•	Normal Mean

•	Normal Sigma

•	Binomial Proportion

•	Poisson Rate.

When you are testing the Normal Mean and Normal Sigma parameters, confidence intervals are calculated for the mean and variance using the t- and chi-square distributions, respectively.  It is assumed that the data come from a normal distribution.  You can set the percentage level for the confidence intervals.

For example, suppose you want to study how working in groups instead of working alone affects performance.  The hypothetical average is based on working alone.  Eighty subjects who volunteer for the study will work in teams of four.  You will provide the subjects with a large number of problems to solve within a 20-minute time period, then record the number of correct answers.  Your alternative or research hypothesis might be that those who work in teams are more efficient than those who work individually.

To examine this hypothesis, you try to find evidence that allows you to reject the null hypothesis, which you might indicate as:  There is no difference between the average score of those who work individually and those who work in teams.

STATGRAPHICS Plus allows for three alternative hypotheses:

•	Not Equal

•	Less Than

•	Greater Than.

Parameter

Null Hypothesis

Sample Mean

Sample Proportion

Sample Size

Sample Sigma

Sample Rate

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Hypothesis Tests (Describe) Analysis

Hypothesis Tests Options

Power Curve Options

Hypothesis Tests (Compare) Analysis


Hypothesis Tests (Describe) Tabular Options Dialog Box

Allows you to select tabular options for the Hypothesis Tests (Describe) analysis.

Analysis Summary (Hypothesis Tests - Describe Analysis)


Analysis Summary (Hypothesis Tests - Describe Analysis)

The Analysis Summary tabular option creates and displays the test results for the parameter you selected.

The summary for the Normal Mean parameter displays the sample mean, sample standard deviation, and sample size as well as the 95 percent confidence interval for the mean.

Information in the lower portion of the text pane displays the theoretical mean for the null hypothesis, the type of alternative hypothesis, the computed t-statistic, the P-value, and the results — either reject or do not reject the null hypothesis.

The summary for the Normal Sigma parameter displays the sample standard deviation and sample size as well as the 95 percent confidence interval for sigma.

Information in the lower portion of the text pane displays the theoretical standard deviation for the null hypothesis, the type of alternative hypothesis test, the computed chi-square statistic, the P-value, and the results — either reject or do not reject the null hypothesis for the given alpha.

The summary for the Binomial Proportion parameter displays the sample proportion and sample size as well as the 95 percent confidence interval for P.  Information in the lower portion of the text pane displays the name of the alternative hypothesis test, the P-value, and the results — either reject or do not reject the null hypothesis for the given alpha.

The summary for the Poisson Rate parameter displays the sample rate and sample size as well as the 95 percent confidence interval for rate.  Information in the lower portion of the text pane displays the hypothetical value for the rate, the type of alternative test, the P-value, and the results — either reject or do not reject the null hypothesis for the given alpha.


Hypothesis Tests (Describe) Options Dialog Box

Allows you to select an alternative hypothesis test.  You can also enter a value for the confidence level.

Alternative Hypothesis

Alpha


Hypothesis Tests (Describe) Graphical Options Dialog Box

Allows you to select graphical options for the Hypothesis Tests (Describe) analysis.

Power Curve (Hypothesis Tests - Describe)


Power Curve (Hypothesis Tests - Describe Analysis)

The Power Curve graphical option creates and displays a plot of the probability of the null hypothesis being rejected versus a range of values for the parameter you are testing.

The vertical axis shows the probability of detecting an effect; the horizontal axis represents the size of the effect.


Power Curve Options Dialog Box (Hypothesis Tests - Describe Analysis)
Power Curve Options Dialog Box (Hypothesis Tests)

Allows you to enter a value for the assumed standard deviation.

Assumed Sigma


Sample-Size Determination (Describe) Analysis Dialog Box

The sample size needed to adequately address the objectives of a project is a research issue that must be resolved early in the project schedule.

Many research questions involve means or proportions.  You must often either (a) estimate a population mean, proportion, or difference with a certain degree of accuracy; or (b) test the statistical significance of the difference either, between a sample mean or proportion and some hypothesized value or, between means or proportions from two different samples.

An appropriate sample size should provide the degree of accuracy you need to estimate population means, proportions, or differences.  It should also allow you to control the risk of reaching incorrect conclusions when you test for statistical significance.

When the estimates of means and proportions come from large samples, there is less sample-to-sample variation than in estimates that come from smaller samples.  Large-sample estimates tend to be more accurate than estimates from smaller samples.

One factor that affects sample-size requirements is the degree of accuracy you want to achieve — the maximum tolerable difference between the population parameter you are estimating and its true value.

The degree of accuracy attained by any sample size also depends on the spread (variability) of the variable you are testing.  Typically, the variance or standard deviation measures the variability.  In general, small variances are necessary to achieve the small number of subjects necessary to result in the degree of accuracy you desire.  It is better to err on the “high” side because this provides an estimated sample size that has, at least, the accuracy you desire.

Another factor that affects sample size is the degree of confidence that will actually achieve accuracy.  Except in trivial cases, there is no sample size, short of a census, that allows you to be certain of achieving the accuracy you want.

Parameter

Hypothesized Mean

Hypothesized Sigma

Hypothesized Proportion

Hypothesized Rate

To select options for this analysis, use the Sample-Size Determination Options dialog box.  To access the Options dialog box, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Sample Size Determination (Compare) Analysis


Sample-Size Determination (Describe) Tabular Options Dialog Box

Allows you to select tabular options for the Sample Size Determination (Describe) analysis.

Analysis Summary (Sample-Size Determination - Describe Analysis)


Analysis Summary (Sample Size Determination - Describe Analysis)

The Analysis Summary tabular option creates and displays the name of the parameter and the controls you selected. The last line displays the calculated sample size.  A separate summary is displayed, depending on the parameter you are using.


Sample-Size Determination (Describe) Options Dialog Box

Allows you to select various options to determine the required sample size.  The option you select depends on the type of analysis for which you are determining a sample size.

Control

Confidence Level

Alternative Hypothesis


Sample-Size Determination (Describe) Graphical Options Dialog Box

Allows you to select graphical options for the Sample-Size Determination (Describe) analysis.

Power Curve (Sample Size Determination - Describe)


Power Curve (Sample-Size Determination - Describe Analysis)

The Power Curve graphical option creates and displays a plot of the power versus the true value of the mean for a given sample size.


Paired Sample Comparison Dialog Box
Paired-Sample Comparison Dialog Box

The Paired-Sample Comparison analysis is appropriate to use when you want to compare two sets of data when the observations in the samples are paired.

For example, suppose you are analyzing data that contain information about the miles per gallon ratings achieved by the same automobile during highway driving and city driving.  The data represent two different sets of values for each automobile:  Miles per gallon ratings for highway driving and miles per gallon ratings for city driving.

When data are from paired samples, you analyze it by calculating the difference between each value in each pair of observations.  That is, you treat the paired differences as though they were a single sample from a population of differences

Sample 1

Sample 2

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Two-Sample Comparison Analysis

Two-Sample Comparison Analysis

Hypothesis Tests (Compare) Analysis

Summary Statistics Options

Percentiles Options

Frequency Tabulation Options

Stem-and-Leaf Options

Confidence Intervals Options

Hypothesis Tests Options

Box-and-Whisker Plot Options

Frequency Plot Options

Normal Probability Plot Options

Density Trace Options


Paired Sample Comparison Tabular Options Dialog Box
Paired-Sample Comparison Tabular Options Dialog Box

Allows you to select tabular options for the Paired-Sample Comparison analysis.

Analysis Summary (Paired-Sample Comparison Analysis)

Summary Statistics (Paired Sample Comparison)

Percentiles (Paired-Sample Comparison Analysis)

Frequency Tabulation (Paired Sample Comparison)

Stem-and-Leaf Display (Paired Sample Comparison)

Confidence Intervals (Paired Sample Comparison)

Hypothesis Tests (Paired Sample Comparison)


Analysis Summary (Paired-Sample Comparison Analysis)

The Analysis Summary tabular option creates and displays the names of the variables you selected to compare, and the number and range of the paired differences.


Summary Statistics (Paired-Sample Comparison Analysis)

The Summary Statistics tabular option creates and displays statistical information about the center, spread, and shape of the paired differences:  the number of values in each variable (Count); and the average, variance, standard deviation, the minimum and maximum values, and the sum of the pairwise differences.

This information is helpful when you need to determine if other statistical analyses might be appropriate to use with the data, or when you need to determine if the data should be transformed.


Percentiles (Paired-Sample Comparison Analysis)

The Percentiles tabular option creates and displays percentiles for the paired differences.  The results show the percentage of the values that are equal to or less than a value you select.


Frequency Tabulation (Paired-Sample Comparison Analysis)

The Frequency Tabulation tabular option creates and displays a table of relative and cumulative frequencies that summarize the distribution of the data.  The table displays values for the class, lower and upper limits, midpoint, frequency, relative and cumulative frequencies, and the cumulative relative frequency.  The paired differences are first grouped into the number of class intervals you select, then the table is created.


Stem-and-Leaf Display (Paired-Sample Comparison Analysis)

The Stem-and-Leaf Display tabular option creates and displays the range of the values, the concentration of the values, the symmetry of the data. Gaps or outliers are shown if they occur.


Confidence Intervals (Paired-Sample Comparison Analysis)

The Confidence Intervals tabular option creates and displays the confidence intervals, which show the 95 percent confidence intervals for the mean and standard deviation of the paired differences


Hypothesis Tests (Paired-Sample Comparison Analysis)

The Hypothesis Tests tabular option creates and displays the mean and median for the paired differences, the results of the t-test, the computed t statistic, and the p-value.

The last line recommends that you either reject or do not reject the null hypothesis for a given alpha.


Paired-Sample Comparison Graphical Options Dialog Box

Allows you to select graphical options for the Paired-Sample Comparison analysis.

Scatterplot (Paired Sample Comparison)

Box-and-Whisker Plot (Paired Sample Comparison)

Frequency Histogram (Paired Sample Comparison)

Quantile Plot (Paired Sample Comparison)

Normal Probability Plot (Paired Sample Comparison)

Density Trace (Paired Sample Comparison)

Symmetry Plot (Paired Sample Comparison)


Scatterplot (Paired-Sample Comparison Analysis)

The Scatterplot graphical option creates and displays a plot of the paired differences along a single axis as point symbols with no connecting lines.


Box-and-Whisker Plot (Paired-Sample Comparison Analysis)

The Box-and-Whisker plot graphical option creates and displays a plot of the paired differences.

The paired differences are divided into four areas of equal frequency (quartiles).  A box encloses the middle 50 percent, where the median is drawn as a vertical line inside the box.  Horizontal lines, known as whiskers, extend from each end of the box.

The left (or lower) whisker is drawn from the lower quartile to the smallest point within 1.5 interquartile ranges from the lower quartile.  The other whisker is drawn from the upper quartile to the largest point within 1.5 interquartile ranges from the upper quartile.


Frequency Histogram (Paired-Sample Comparison Analysis)

The Frequency Histogram graphical option creates and displays a plot of the frequency distribution for the paired differences.

STATGRAPHICS Plus divides the paired differences into sets of nonoverlapping frequencies, and plots bars for each frequency.  The height of each bar is the number of values that fall within that frequency.


Quantile Plot (Paired-Sample Comparison Analysis)

The Quantile plot graphical option creates and displays a plot where the Y-axis shows the fraction of data that are below a particular value.

Use the plot to view the cumulative distributions for the paired differences, or to estimate percentiles.


Normal Probability Plot (Paired-Sample Comparison Analysis)

The Normal Probability plot graphical option creates and displays a plot that can help you determine if the paired differences come from a normal distribution.

A Normal Probability plot consists of an arithmetic (interval) horizontal axis scaled for the data and a vertical axis scaled so the cumulative distribution function for a normal distribution appears on the plot as a straight line.  The closer the data are to the reference line, the more likely that they follow a normal distribution.


Density Trace (Paired-Sample Comparison Analysis)

The Density Trace graphical option creates and displays a plot that allows you to view the shape or distribution of the data, especially the variations in density over the range of the data.

Unlike a Histogram, the plot uses overlapping intervals and a weight function to smooth the densities, which results in a continuous line rather than a group of rectangles.


Symmetry Plot (Paired-Sample Comparison Analysis)

The Symmetry plot graphical option creates and displays a plot that is helpful in determining symmetry of the data.

Use this plot if you want to use analyses that are best applied to a symmetrical distribution.  Symmetrical data would closely follow the reference line.


Save Results Options Dialog Box (Paired-Sample Comparison Analysis)

The Save Results Options dialog box allows you to select the results you want to save.  There are six selections:  Summary Statistics, Percentiles, Frequencies, Cumulative Frequencies, Relative Frequencies, and Cumulative Relative Frequencies.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.


Hypothesis Tests (Compare) Dialog Box

Hypothesis tests are a classical approach to assessing the statistical significance of findings.  Basically, the technique involves comparing empirically observed sample findings with theoretically expected findings; expected if the null hypothesis is true.

This comparison allows you to compute the probability that the observed outcomes might be due to chance alone.  The data you use in this analysis should be sample statistics and sample sizes rather than raw data.

The Hypothesis Tests (Compare) analysis tests hypotheses about the sample means and variances for two or more random samples.

For a description of the Hypothesis Tests (Describe) analysis, which tests hypotheses about the mean and variance for a single random sample, see that section in this Online Help System.

This dialog box allows you to enter data to test four types of parameters:  Normal Means, Normal Sigmas, Binomial Proportions, and Poisson Rates.

In addition, you can use the options dialog box to control for error tolerance, power, and sample size; set confidence intervals; and choose from three alternative hypotheses:  Not Equal, Less Than and Greater Than.

Compare

Null Hypothesis for Difference of

Sample 1 Mean

Sample 2 Mean

Sample 1 Sigma

Sample 2 Sigma

Sample 1 Proportion

Sample 2 Proportion

Sample 1 Rate

Sample 2 Rate

Sample 1 Size

Sample 2 Size

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Hypothesis Tests (Describe) Analysis

Using the Hypothesis Tests (Compare) Analysis

Hypothesis Tests Options

Power Curve Options


Hypothesis Tests (Compare) Tabular Options Dialog Box

Allows you to select tabular options for the Hypothesis Tests (Compare) Analysis.

Analysis Summary (Hypothesis Tests - Compare Analysis)


Analysis Summary (Hypothesis Tests - Compare Analysis)

The Analysis Summary tabular option creates and displays a summary of the estimated test statistics for the parameter you select.

The summary for the Normal Means parameter displays the following for both Sample 1 and Sample 2:  the sample means, sample standard deviations, and sample sizes as well as the 95 percent confidence interval for the difference between the means.  Information in the lower portion of the text pane displays the difference between means for the null hypothesis, the name of the alternative hypothesis, the computed t-statistic, the p-value, and the recommendation — either reject or do not reject the null hypothesis.

The summary for the Normal Sigmas parameter displays the following for both Sample 1 and Sample 2:  the sample standard deviations and sample sizes as well as the 95 percent confidence interval for the ratio of variances.  Information in the lower portion of the text pane displays the ratio of variances for the null hypothesis, the name of the alternative hypothesis test, the computed F-statistic, the p-value, and the recommendation — either reject or do not reject the null hypothesis for the given alpha.

The summary for the Binomial Proportions parameter displays the following for both Sample 1 and Sample 2:  the sample proportions and sample sizes as well as the 95 percent confidence interval for the difference between proportions.  Information in the lower portion of the text pane displays the difference between proportions for the null hypothesis, the name of the alternative hypothesis test, the computed z-statistic, the p-value, and the recommendation — either reject or do not reject the null hypothesis for the given alpha.

The summary for the Poisson Rates parameter displays the following for both Sample 1 and Sample 2:  the sample rates and sample sizes as well as the 95 percent confidence intervals for the difference between rates.  Information in the lower portion of the text pane displays the difference between rates for the null hypothesis, the name of the alternative hypothesis test, the computed z-statistic, the p-value, and the recommendation — either reject or do not reject the null hypothesis for the given alpha.


Hypothesis Tests (Compare) Options Dialog Box

Allows you to select an alternative hypothesis test, to enter a value for alpha (the confidence level), and to indicate if you want to assume equal standard deviations.

Alternative Hypothesis

Alpha

Assume Equal Sigmas


Hypothesis Tests (Compare) Graphical Options Dialog Box

Allows you to select graphical options for the Hypothesis Tests (Compare) analysis.

Power Curve (Hypothesis Tests (Compare))


Power Curve (Hypothesis Tests - Compare Analysis)

The Power Curve graphical option creates and displays a Power Curve for the hypothesis test you select.

Power Curve (Normal Means)

Displays a graph of the power versus the true difference between the means.

Power Curve (Normal Sigmas)

Displays a graph of the power versus the true ratio of the variances.

Power Curve (Binomial Proportions)

Displays a graph of the power versus the true difference between the proportions.

Power Curve (Poisson Rates)

Displays a graph of the power versus the true difference between the rates.

To select options for the plot, use the Power Curve Options dialog box.


Power Curve Options Dialog Box (Hypothesis Tests - Compare Analysis)
Power Curve Options Dialog Box (Hypothesis Tests)

Allows you to enter a value for the:

•	assumed standard deviation if you are using the Normal Means option

•	assumed mean if you are using the Binomial Proportions option

•	assumed mean rate if you are using the Poisson Rates option.

Assumed Sigma (Normal Means Option)

Assumed Mean Proportion (Binomial Proportions Option)

Assumed Rate (Poisson Rates Option)


Variance Components Dialog Box

According to Box, Hunter, and Hunter (1978), the objective of variance components analysis is to determine the values of component variances that cannot be measured directly.  The design usually used for this analysis is a nested or hierarchical design.

The Variance Components analysis is a method used to estimate and compare the variance contributions of factors in a fully nested, random effects model.  For example, when you collect data by sampling and then subsampling to provide a comparison among the variances at each level of a hierarchy.

A good example of a nested design would be soil samples in an agricultural or geological study taken from five geographic regions, with subsamples taken from 12 areas within each region.

Another example is a study of worker productivity, which samples workers by selecting 10 factories at random, then randomly selecting four departments within each factory, then randomly selecting five workers from each department.

This dialog box allows you to enter the data you want to use to analyze the effect of one or more qualitative factors on one response variable.  The data should be fully nested or hierarchical.  The number of observations does not need to be equal at all combinations of the factor levels.

Dependent Variable

Factors in Order of Nesting

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left either Pane Options or Analysis Options.

See also

Using the Variance Components Analysis

Scatterplot Options

Residual Plot Options


Variance Components Tabular Options Dialog Box

Allows you to select tabular options for the Variance Components analysis.

Analysis Summary (Variance Components Analysis)

Summary Statistics (Variance Components)


Analysis Summary (Variance Components Analysis)

The Analysis Summary tabular option creates and displays an ANOVA table that shows the sum of squares, degrees of freedom, mean square, variance component, and percent.

The Percent column contains the percentage of variance accounted for by each factor.  If you omit the last factor, a line on the table appears with the label “ERROR.”


Summary Statistics (Variance Components Analysis)

The Summary Statistics tabular option creates and displays a summary of statistical information about the center, spread, and shape of the data:  the name of the dependent variable, the level codes, grand mean, number (count), mean, and standard deviation for each level and for each of the factors


Variance Components Graphical Options Dialog Box

Allows you to select graphical options for the Variance Components analysis.

Scatterplot (Variance Components)

Residuals versus Factor Levels Plot (Variance Componets)

Residuals versus Predicted Plot (Variance Components)

Residuals versus Row Number Plot (Variance Components)


Scatterplot (Variance Components Analysis)

The Scatterplot graphical option creates and displays a plot of the data plotted on the Y-axis versus the factor you selected for the X-axis.

Solid horizontal lines are drawn at the means of the factor.  If the factor is any other than the last one you selected, the means of the factor that is nested within the factor you selected, is plotted as points.


Scatterplot Options Dialog Box

Allows you to select the main factor for the Y-axis.

Factor


Residuals versus Factor Levels Plot (Variance Components Analysis)

The Residuals versus Factor Levels graphical option creates and displays the residuals versus any factor you select.

If an error term does not appear in the ANOVA table, all of the residuals are zero.


Residual Plot Options Dialog Box

Allows you to select the main factor for the X-axis.

Factor


Residuals versus Predicted Plot (Variance Components Analysis)

The Residuals versus Predicted graphical option creates and displays a plot of the residuals versus the predicted values for each point.


Residuals versus Row Number Plot (Variance Components Analysis)

The Residuals versus Row Number graphical option creates and displays a plot of the residuals versus the row number.


Save Results Options Dialog Box (Variance Components Analysis)

The Save Results Options dialog box allows you to select the results you want to save.  There are two selections:  Variance Components and Residuals.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results Options button on the Analysis toolbar (the fourth button from the left).


Sample-Size Determination (Compare) Dialog Box

Rarely do research projects have a single objective.  Typically, there are a number of research questions, each of which requires a separate analysis.  Also, the appropriate sample sizes are most likely to be different for each objective.

The most common applications of statistical significance tests, especially in marketing research, involve comparisons of means or proportions obtained from two or more independent samples.  Usually, the issue is if it can be concluded that two population means are different, based on an observed difference between two sample means.  You can control the risk of an incorrect conclusion by gathering an adequate number of observations.

An example of this type of significance test might be testing two different brands of cat food to be fed to two groups of cats over a two-week period.  After the two weeks, the products are rated by comparing the average weight gain of one group with that of the other group.

In other situations it might be necessary to draw two samples that are not the same size.  This is usually the case when the means you want to compare do not correspond with experimental “treatments,” but rather with groups of respondents who are classified by some demographic characteristic such as income or region.

The Sample-Size Determination (Compare) analysis has two purposes:  to help determine the number of observations required to provide sufficiently powerful estimates, and to analyze the power curve for samples already drawn.  In addition, the error tolerance or power can be tested and confidence intervals set.  You can also select an alternative hypothesis from three choices:  Not Equal, Less Than, or Greater Than.

You can calculate sample sizes for testing five types of parameters:  Two Normal Means, Two Normal Sigmas, Two Binomial Proportions, Two Poisson Rates, and Several Normal Means.

Compare

Hypothesized Difference

Hypothesized Means

Hypothesized Proportions

Percent of Data in First Sample

Hypothesized Within Group Sigmas

Hypothesized Rates

Number of Means

To select options for this analysis, use the Sample-Size Determination Options dialog box.  To access the Options dialog box, click the right mouse button on a text or graphics pane, then click the left either Pane Options or Analysis Options.

See also

Sample Size Determination (Describe) Analysis

Using the Sample Size Determination (Compare) Analysis


Sample-Size Determination (Compare) Tabular Options Dialog Box

Allows you to select tabular options for the Sample-Size Determination (Compare) analysis.

Analysis Summary (Sample-Size Determination - Compare Analysis)


Analysis Summary (Sample-Size Determination - Compare Analysis)

The Analysis Summary tabular option creates and displays a summary of the analysis, specific to the parameter you are using.

The summary includes the name of the parameter being estimated, as well as the tolerance, confidence level, and assumed sigma.  The last line displays the number of observations required for each sample.


Sample-Size Determination (Compare) Options Dialog Box

Allows you to select the type of control and its precision, to enter a value that will be determine the confidence intervals, and to select the form of alternative hypothesis.

Control

Confidence Level

Alternative Hypothesis


Sample-Size Determination (Compare) Graphical Options Dialog Box

Allows you to select graphical options for the Sample Size Determination (Compare) analysis.

Power Curve (Sample Size Determination (Compare))


Power Curve (Sample-Size Determination - Compare Analysis)

The Power Curve graphical option creates and displays a plot of the power versus the true value for the parameter currently being used.


Polynomial Regression Dialog Box

Polynomial regression analysis is regression analysis for relationships that are or are suspected to be nonlinear.  It is known as polynomial regression because the regression equation for a curvilinear (nonlinear) relationship is a polynomial equation.  The more turns in the regression line, the higher the power the terms in the equation must be.

The first degree of freedom contains the linear effect across all categories; the second degree of freedom, the quadratic effect; and so on for the higher order effects.

A polynomial equation is an equation in which one of the terms is raised to a power greater than 1.  For example, the regression equation Y = a + b1X + b2X^2 + b3X^3 is a polynomial because X is raised to the second and third powers.  The highest power of a term gives the equation its “degree” or “order.”  The equation shown above is a third-order (or degree) polynomial equation.

The analysis calculates a polynomial regression model between a single dependent variable Y, and a single independent variable X.  You can fit polynomial models up to Order 8.

Y

X

Weight

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Simple Regression Analysis

Simple Regression Analysis

Multiple Regression Analysis

Polynomial Regression Options

Confidence Intervals Options

Forecasts Options

Plot of Fitted Model Options

Residual Plot Options


Polynomial Regression Tabular Options Dialog Box

Analysis Summary (Polynomial Regression Analysis)

Conditional Sums of Squares (Polynomial Regression)

Lack-of-Fit Test (Polynomial Regression)

Confidence Intervals (Polynomial Regression)

Forecasts (Polynomial Regression)

Unusual Residuals (Polynomial Regression)

Influential Points (Polynomial Regression)


Analysis Summary (Polynomial Regression Analysis)

The Analysis Summary tabular option creates and displays the following summary of the analysis.

The model fitting results in the top portion of the pane include the estimates for the constant (intercept term) and the model coefficients for each power of the independent variable.  By default, the model is fit to an Order 2 polynomial.  Use the Order option to change the order of the model.

The table also displays several key measures you can use to judge the adequacy of the model.  The standard errors of the coefficients, the t-statistics (which are calculated by dividing the estimate by its standard error), and the p-value for each t-statistic.  The p-value corresponds to tests of hypotheses that the coefficients are equal to zero.  Small probability levels (less than .05 for a 95 percent confidence level) indicate statistically significant, nonzero coefficients.

Estimates that have a high probability level (greater than .05 for a 95 percent confidence level) have little or no effect on the dependent variable.  The F-ratio tests the overall model significance; in other words, it tests to see if the coefficients are all equal to zero.

The bottom portion of the summary displays the analysis of variance statistics for the full regression, and provides five additional values to help you judge the utility of the model.

•	The R-Squared statistic measures the proportion of variability in the model for the dependent variable.

•	The Adjusted R-Squared value is the amount of variation in the model for the dependent variable.  It adjusts the R-Squared value based on the number of coefficients in the model.  Unlike the R-Squared statistic, the adjusted R-Squared value may decrease if higher orders do not significantly add to the fit.

•	The standard error of the estimate is the square root of the residual mean square (the mean squared error).  It measures the unexplained variability in the dependent variable.

•	The mean absolute error is the average of the absolute values of the residuals.  It is the average error size you can expect in a prediction.

•	The Durbin-Watson statistic is a measure of the serial correlation of the residuals.  In general, a Durbin-Watson statistic of less than 1.3 indicates serial correlation in the residuals.  For interpretations, see Durbin and Watson (1951) or standard text books such as Draper and Smith (1981).

•	The Lag-1 Residual Autocorrelation is the first-order autocorrelation.


Polynomial Regression Options Dialog Box

Order

Enter the number of the highest power of the independent variable you want to include in the model.  Enter a number from 0 through 8; the default is 2.


Conditional Sums of Squares (Polynomial Regression Analysis)

The Conditional Sums of Squares tabular option creates and displays additional analysis of variance statistics.

The table includes the contribution made to the total regression sums of squares that can be attributed to each power of the independent variable when it entered the regression (also called Type I sums of squares).


Lack-of-Fit Test (Polynomial Regression Analysis)

The Lack-of-Fit Test tabular option creates and displays a modified ANOVA table with a line for lack-of-fit.

The test determines if the regression model adequately fits the data.  It assumes that the observations Y, for a given X, are independent and normally distributed, and that the distributions of Y have the same variance.  Significant lack-of-fit shows that the specified model does not adequately fit the response.

A p-value less than .05 indicates that the model does not adequately fit the data.


Confidence Intervals (Polynomial Regression Analysis)

The Confidence Intervals tabular option creates and displays the 95 percent confidence intervals for the coefficient estimates.

The estimates and the standard errors are identical to those shown in the initial table of model-fitting results.


Confidence Intervals Options Dialog Box

Enter the number that will be used to calculate the confidence level intervals.  Enter a number greater than 0 and less than 100.  The default is 95; other common levels are 90 and 99.


Forecasts (Polynomial Regression Analysis)

The Forecasts tabular option creates and displays the values for Y, based on the values for X.  It also displays the predictions, confidence limits, and prediction limits for the observations.  The prediction and confidence limits are based on a 95 percent confidence level.


Forecasts Options Dialog Box

Confidence Level (for Predictions and Confidence Limits)

Forecast at X


Unusual Residuals (Polynomial Regression Analysis)

The Unusual Residuals tabular option creates and displays observations that have Studentized Residuals less than -2 or greater than 2.  Also shown are the corresponding row, observed independent and dependent values, fitted value, and residual.


Influential Points (Polynomial Regression Analysis)

The Influential Points option creates a table that lists all the observations that have leverage values greater than three times the average.  Leverage is a statistic that measures the influence of each observation in determining the coefficients of the estimated model.  DFITS is a statistic that measures how much the estimated coefficients would change if each observation was removed from the data.

The table also displays values for the Mahalanobis distance, which is the square of the standardized value of X.  For more information, see Belsley, Kuh, and Welsch (1980).


Polynomial Regression Graphical Options Dialog Box

Plot of Fitted Model (Polynomial Regression)

Observed versus Predicted Plot (Polynomial Regression)

Residuals versus X Plot (Polynomial Regression)

Residuals versus Predicted Plot (Polynomial Regression)

Residuals versus Row Number Plot (Polynomial Regression)


Plot of Fitted Model (Polynomial Regression Analysis)

The Plot of Fitted Model graphical option creates and displays a plot of the curve of the fitted line.  The plot includes both confidence limits for the means (the inner pair of lines) and prediction limits (the outer pair of lines).


Plot of Fitted Model Options Dialog Box

Include

Confidence Level

X-Axis Resolution


Observed versus Predicted Plot (Polynomial Regression Analysis)

The Observed versus Predicted option creates a plot of the observed values of the independent variable versus the values predicted by the fitted model.  The closer the points are to the diagonal line, the better the model.


Residuals versus X Plot (Polynomial Regression Analysis)

The Residuals versus X option creates a plot of the residuals versus the dependent variable.  A nonrandom pattern indicates that the selected model does not adequately describe the observed data.  Any values outside the range of –3 to +3 are probably outliers.

Use the Residual Plot Options dialog box to indicate if residuals or studentized residuals will appear on the plot.


Residuals Plot Options Dialog Box
Residual Plot Options Dialog Box

Plot

Determines the type of residuals that will appear on the plot.

Residuals

Plots the difference between the observed and the fitted values.

Studentized Residuals

Plots the residuals scaled by an estimate of the variance from the data with the observation removed.  A large studentized residual value may indicate an outlier and an influential observation.  This option is the default.


Residuals versus Predicted Plot (Polynomial Regression Analysis)

The Residuals versus Predicted option creates a plot of the residuals versus the predicted values for the independent variable.  A nonrandom pattern could indicate that the selected model does not adequately describe the observed data.  The plot is especially helpful in detecting heteroscedasticity, in which the variability of the residuals changes as the values of the independent variable change.  If the model is correct and if all the assumptions are satisfied, the residuals should be structureless.

Use the Residual Plot Options dialog box to indicate if residuals or studentized residuals will appear on the plot.


Residuals versus Row Number Plot (Polynomial Regression Analysis)

The Residuals versus Row Number graphical option creates and displays a plot of the residuals versus their row number.

The residuals are plotted in the order that the observations appear in the dependent variable.  The plot  is helpful in identifying sequential correlations among the residuals.


Save Results Options Dialog Box (Polynomial Regression Analysis)

The Save Results Options dialog box allows you to select the results you want to save.  There are 12 selections:  Predicted Values, Standard Errors of Predictions, Lower Limits for Predictions, Upper Limits for Predictions, Standard Error of Means, Lower Limits for Forecast Means, Upper Limits for Forecast Means, Residuals, Studentized Residuals, Leverages, DFITS Statistics, and Mahalanobis Distances.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Erasing Graphs from the StatGallery Window

STATGRAPHICS Plus allows you to erase items from the StatGallery window.  You can erase the entire contents of the window, or erase only items that you select.

To Erase Graphs from the StatGallery Window

1.	Click the right mouse button on the StatGallery window.

2.	Click the left button on Erase Graph on the pop-up window to display the Erase Graphs Options dialog box.

3.	Complete the dialog box and click OK to erase either the entire contents of the StatGallery window or the portion of it you selected.


Random Variable

Allows you to enter up to five values (one for each of five parameters) for the random variables.


Survivor Function Plot (Probability Distribution Analysis)

The Survivor Function Plot graphical option creates and displays a plot of the survivor function for the distribution you are evaluating.

The function indicates the probability of obtaining a value greater than or equal to the values on the X-axis.


Log Survivor Function Plot (Probability Distribution Analysis)

The Log Survivor Function Plot graphical option creates and displays a plot of the log survivor function for the distribution you are evaluating.

The function indicates the probability of obtaining a value greater than or equal to the values on the X-axis.


Hazard Function Plot (Probability Distribution Analysis)

The Hazard Function Plot graphical option creates and displays a plot of the hazard function for the distribution you are evaluating.

The hazard function is equal to the probability density function divided by the survivor function.  When you are modeling lifetime data, the hazard function represents the instantaneous failure rate.


Mean

Allows you to enter a value for the hypothetical mean of the paired differences.  Enter any real number; the default is 0.


Alpha

Allows you to enter the value (as a percentage) for the confidence level.  Enter a number greater than or equal to 0 and less than 100; the default is 5.  Other common levels are 1 and 10.


Hypothesis Tests (Compare) Options Dialog Box

Allows you to select an alternative hypothesis test, to enter a value for the confidence level, and to indicate if you want to assume equal standard deviations for testing the normal means.

Alternative Hypothesis

Alpha

Assume Equal Sigmas


Residual Plot Options Dialog Box

Allows you to select the type of residual that will be included on the plot.

Residuals

Plots the difference between the observed and the fitted values.

Studentized Residuals

Plots the residuals scaled by an estimate of the variance from the data with the observation removed.  A large studentized residual value may indicate an outlier and an influential observation.


Residuals versus Factor Levels Plot (One-Way ANOVA Analysis)

The Residuals versus Factor Levels Plot graphical option creates and displays a plot of the residuals versus the factor levels.

The plot is helpful when you need to detect when the variance is not constant across different factor levels.


Percentiles Options Dialog Box

Enter the values that will be used for the Percentiles test.  Enter 0 if you do not want to calculate percentiles.


Parameter

Determines the parameter that will be used.

Normal Mean

Determines the sample size for estimating the mean of a population.  If you choose this option, enter values into the Hypothesized Mean and Hypothesized Sigma text boxes.  This option is the default.

Normal Sigma

Determines the sample size for estimating the standard deviation of a population.  If you choose this option, enter values into the Hypothesized Sigma text box.

Binomial Proportion

Determines the sample size required to estimate a population proportion (number of successes).  If you choose this option, enter a value into the Hypothesized Proportion text box.

Poisson Rate

Determines the sample size required to estimate the frequency of events occurring within a period of time.  If you choose this option, enter a value into the Hypothesized Rate text box.


Distribution

Select the name of the distribution you want to use.

Bernoulli

Fits data that follow a Bernoulli distribution.  The outcome has only two possibilities:  Success or Failure.  Data fit to this distribution should have values of only 0 or 1.

Binomial

Fits data that follow a Binomial distribution.  The distribution gives the probability of observing successes in a fixed number of independent or Bernoulli trials.  When you use this distribution, you must select the number of trials (experiments).  Data fit to this distribution should be integers greater than or equal to 0.

Cauchy

A distribution that fits data that follow a Cauchy distribution.  The distribution’s probability density function has no mean and an infinite variance.  It is characterized by two parameters:  Mode and Scale.  Data fit to this distribution should be continuous with a Mode between –infinity and +infinity and a Scale greater than 0.

Discrete Uniform

Fits data that follow a Discrete Uniform distribution.  The distribution allocates equal probabilities to all integer values between a Lower and an Upper limit.  Data fit to this distribution should be integers.

Geometric

Fits data that follow a Geometric distribution.  The distribution characterizes the number of failures that occur before the first success in a series of Bernoulli trials.  Data fit to this distribution should be integers greater than 0.

Hypergeometric

A distribution that arises when a random selection is made between objects of two distinct types (success, fail).  The sampling occurs without replacement; that is, each time an item is drawn and studied, it is not placed back into the population.  The distribution gives the probability of the number of successes.  Data fit to this distribution should be integers greater than or equal to 0.

When you use this distribution, the Number of Trials and Population Size text boxes are activated so you can enter numbers for the number of trials that will be in the analysis, as well as a number for the size of the population.

Negative Binomial

Fits data that follow a Negative Binomial distribution.  The distribution characterizes the number of failures before the kth success in a series of Bernoulli trials.  When you use this distribution, you must declare the number of successes.  Data fit to this distribution should be integers greater than 0.

Poisson

Fits data that follow a Poisson distribution.  The distribution expresses probabilities that concern the number of events per unit time; for example, the number of times a computer malfunctions per year.  Data fit to this distribution should be integers greater than or equal to 0.

Beta

Fits data that follow a Beta distribution.  The distribution is useful for random variables that are constrained to lie between 0 and 1; characterized by two parameters:  Shape 1 and Shape 2.

Chi-Square

Fits data that follow a Chi-Square distribution.  The distribution is useful for random variables that are constrained to be greater than 0; characterized by one parameter:  Degrees of Freedom.

Erlang

Fits data that follow an Erlang distribution.  The distribution is useful for random variables that are constrained to be greater than 0, such as the time required to complete a task.  The distribution is characterized by two parameters:  Shape and Scale.  This distribution is a special case of the Gamma distribution, which requires that the Shape parameter be an integer.  Data fit to this distribution should be values greater than 0.

Exponential

Fits data that follow an Exponential distribution.  This distribution fits time-series data, such as arrival times, where arrivals are expected at a constant rate, and useful for random variables that are constrained to be greater than 0.  This distribution is a special case of both the Gamma and the Weibull distributions.

Extreme Value

Fits data that follow an Extreme Value distribution.  The distribution fits the limiting distribution for the maximum number of samples collected from a process, and applies when extremes rather than means are collected from samples from an unknown or complex underlying distribution.  The distribution is useful for random variables constrained to be greater than 0; characterized by two parameters:  Mode and Scale.  It is sometimes known as a Gumbels distribution.

F (Variance Ratio)

Fits data that follow a F (Variance Ratio) distribution.  The distribution is useful for random variables that are constrained to be greater than 0.  It is characterized by two parameters:  Numerator Degrees of Freedom and Denominator Degrees of Freedom.  It is often used as the distribution for test statistics that are created as variance ratios.

Gamma

Fits data that follow a Gamma distribution.  The distribution is useful for random variables that are constrained to be greater than 0.  It is characterized by two parameters:  Shape and Scale.  This distribution is often used to model data that are positively skewed, such as the time required to complete a task.  Data fit to this distribution should be values greater than 0.

Laplace

Fits data that follow a Laplace distribution.  The distribution is useful from random variables from a distribution that is more peaked than a Normal distribution.  It is characterized by two parameters:  Mean and Scale.  This distribution is sometimes referred to as the “double-exponential” distribution because it looks like an exponential distribution with a mirror image.

Logistic

Fits data that follow a Logistic distribution.  The distribution Is useful for random variables that are not constrained to be greater than 0, and is characterized by two parameters:  Mean and Standard Deviation.

Lognormal

Fits data that follow a Lognormal distribution.  The distribution is useful for processes in which the value is a random proportion of the previous value, such as personal incomes or particle sizes from breakage processes.  The log of data that follow the lognormal distribution are normally distributed.  The distribution is positively skewed and can take on various shapes.  Data fit to this distribution should be values greater than 0.

Normal

Fits data that follow a Normal distribution.  The distribution is useful in instances when you plot a Frequency Histogram of the data and the bars form a common, bell-shaped curve.  This option is the default.

Pareto

Fits data that follow a Pareto distribution.  The distribution possesses a decreasing density function.  One parameter, Shape, is necessary to specify the distribution.  Data fit to this distribution should be values greater than 0.

Student’s t

Fits data that follow a Student’s t distribution.  The distribution is useful in forming confidence intervals when the variance is known, testing to determine if two sample means are significantly different, or testing to determine the significance of coefficients in a regression.  The distribution is similar in shape to a Normal distribution.  The mean of the t distribution is always equal to 0, while the standard deviation is usually slightly greater than 1.  One parameter, Degrees of Freedom, is necessary to completely specify the distribution.

Triangular

Fits data that follow a Triangular distribution.  The distribution is useful for random variables that are constrained to lie between two fixed limits.  Unlike the Uniform distribution, in which all the values between the limits are equally likely, the Triangular distribution peaks at some value between the two limits.  This distribution is characterized by three parameters:  Lower Limit, Central Value (Mode), and Upper Limit.

Uniform

Fits data that follow a Uniform distribution.  The distribution is useful for characterizing data that range over an interval of values, each of which is equally likely.  The distribution is completely determined by the smallest possible value, a, and the largest possible value, b.  The mean equals (a + b)/2, while the variance equals ((b - a)^2)/12.  For discrete data, there is a related discrete uniform distribution.

Weibull

Fits data that follow a Weibull distribution.  The distribution is useful for random variables that are constrained to be greater than 0.  Because its failure-rate curves can take various shapes, it is an appropriate model for product failures.  The distribution is a generalization of an Exponential distribution.


# of Trials

Allows you to enter a value for the number of independent Bernoulli trials that will be performed in an experiment.


# of Successes

Allows you to enter a value for the number of successes that will be observed in an experiment of repeated Bernoulli trials.


Residual Plot Options Dialog Box

Allows you to select the type of residuals that will be on the plot and to select the independent variable.

Plot

Plot versus:


Plot versus:

Select the independent variable that will be used for the Residuals versus X Plot.


Alpha (Hypothesis Tests Compare)

Enter a value for the alpha level, in percentages, that will be used to perform a hypothesis test for the confidence level.  Enter a number greater than or equal to 0 and less than 100; the default is 5.


Lower Limit

Enter the lowest value for each range for which values will be recoded.  For example, if the range is 1-10, enter 1.


Upper Limit

Enter the highest value for each range for which values will be recoded. For example, if the range is 1-10, enter 10.


New Value

Enter the value for which all the elements in the range will be recoded.


Limit Conditions

Select the condition that best describes the end points will be treated for for each range that will be recoded.

Lower <= Value <= Upper

The values will be inclusive.

Lower <= Value < Upper

The Lower Range values will be inclusive; the Upper, noninclusive.

Lower < Value <= Upper

The Lower Range values will not be noninclusive; the Upper, inclusive.

Lower < Value < Upper

The Lower nor the Upper range values will be inclusive.


Unmatched

Select how the values that do not fit into any of the selected ranges will be treated.

Leave As Is

Uses the values as they currently exist.

Set to Missing

Uses the values as if they were missing from the data.


Extrapolate

Determines the range of the values based on the values entered in the Limit Conditions text boxes.


Data Version 2
Data

Enter the name of the variable that contains the data that will be analyzed.


Level Codes

Enter the name of the variable that contains the level codes that will group the data. You must include one level code for each observation.  Enter a numeric or an alphanumeric variable.


Select Text Box
Select

[Optional]  Select a subset of the observations.  For example, to analyze the first 50 values in each variable, enter first (50) into this text box.


Sort

Sorts the variable names alphabetically; sorted is the default.


Transform...

Allows you to generate data values. Transformed data use mathematical functions (operators) to achieve better results, resulting in the ability to perform complex calculations.

To transform data, click the Transform... button, which displays the Generate Data dialog box.


Features on a Multiple Box-and-Whisker Plot
Features

Determines the features that will appear on the plot.

Median Notch

Adds a notch to the box around the median.  The length of the notch represents an approximate 95 percent confidence interval for the median

Outlier Symbols

Plots individual points that are beyond the whiskers as two different point symbols — Outside or Far Outside.  Outside points, which are shown as small squares, are points that lie more than 1.5 times the interquartile range above or below the box.  Far Outside points, which are shown as small squares with plus signs through them, are points that lie more than 3 times the interquartile range above or below the box.  This option is one of two defaults.

Mean Marker

Displays the location of the average; it is one of two defaults.


Bernoulli Probability Distribution

Fits data that follow a Bernoulli distribution, which has only two possibilities:  Success or Failure; for example, heads or tails, defective or nondefective.  Data fit to this distribution should have values of only 0 or 1.


Binomial Probability Distribution

Fits data that follow a Binomial distribution, which gives the probability of observing successes in a fixed number of independent or Bernoulli trials.  Select the number of trials (experiments).  Data fit to this distribution should be integers greater than or equal to 0.


Discrete Uniform Probability Distribution

Fits data that follow a Discrete Uniform distribution, which allocates equal probabilities to all integer values between a lower and an upper limit.  Data fit to this distribution should be integers.


Geometric Probability Distribution

Fits data that follow a Geometric distribution, which characterizes the number of failures that occur before the first success in a series of Bernoulli trials.  Data fit to this distribution should be integers greater than 0.


Negative Binomial Probability Distribution

Fits that that follow a Negative Binomial distribution, which characterizes the number of failures before the kth success in a series of Bernoulli trials.  When you use this distribution you must declare the number of successes.  Data fit to this distribution should be integers greater than 0.


Poisson Probability Distribution

Fits data that follow a Poisson distribution, which expresses probabilities that concern the number of events per unit time; for example, the number of times a computer malfunctions per year.  Data fit to this distribution should be integers greater than or equal to 0.


Beta Probability Distribution

Fits data that follow a Beta distribution, which is useful for random variables that are constrained to lie between 0 and 1; characterized by two parameters:  Shape 1 and Shape 2.


Chi-Square Probability Distribution

Fits data that follow a Chi-Square distribution, which is useful for random variables that are constrained to be greater than 0; characterized by one parameter:  Degrees of Freedom.


Erlang Probability Distribution

Fits data that follow an Erlang distribution, which is useful for random variables that are constrained to be greater than 0, such as the time required to complete a task; characterized by two parameters:  Shape and Scale.  This distribution is a special case of the Gamma distribution, which requires the Shape parameter be an integer.


Exponential Probability Distribution

Fits data that follow an Exponential distribution, which fits time-series data, such as arrival times, where arrivals are expected at a constant rate; useful for random variables that are constrained to be greater than 0.  This distribution is a special case of both the Gamma and the Weibull distributions.


Extreme Value Probability Distribution

Fits data that follow an Extreme Value distribution, which fits the limiting distribution for the maximum number of samples collected from a process, and applies when extremes rather than means are collected from samples from an unknown or complex underlying distribution.  The distribution is useful for random variables that are constrained to be greater than 0; characterized by two parameters:  Mode and Scale.  Also known as a Gumbel’s distribution.


F(Variance Ratio) Probability Distribution

Fits data that follow a F (Variance Ratio), which is useful for random variables that are constrained to be greater than 0; characterized by two parameters:  Numerator Degrees of Freedom and Denominator Degrees of Freedom.  It is often used as the distribution for test statistics that are created as variance ratios.


Gamma Probability Distribution

Fits data that follow a Gamma distribution, which is useful for random variables that are constrained to be greater than 0; characterized by two parameters:  Shape and Scale.  This distribution is often used to model data that are positively skewed, such as the time required to complete a task.


Laplace Probability Distribution

Fits data that follow a Laplace distribution, which is useful for random variables from a distribution that is more peaked than a Normal distribution; characterized by two parameters:  Mean and Scale.  This distribution is sometimes called the “double exponential” distribution because it looks like an exponential distribution with a mirror image.


Logistic Probability Distribution

Fits data that follow a Logistic distribution, which is useful for random variables that are not constrained to be greater than or equal to 0; characterized by two parameters:  Mean and Standard Deviation.


Lognormal Probability Distribution

Fits data that follow a Lognormal distribution, which is useful for processes in which the value is a random proportion of the previous value, such as personal incomes or particle sizes from breakage processes.  The log of data that follow the lognormal distribution are normally distributed.  The distribution is positively skewed and can take on various shapes.  Data fit to this distribution should be values greater than 0; characterized by two parameters:  Mean and Standard Deviation.


Normal Probability Distribution

Fits data that follow a Normal distribution, which is useful in instances when a Frequency Histogram of the data is plotted and the bars form a common, bell-shaped curve.


Pareto Probability Distribution

Fits data that follow a Pareto distribution with a decreasing density function.  One parameter, Shape, is necessary to specify the distribution.  Data fit to this distribution should be values greater than 0.


Student's t Probability Distribution

Fits data that follow a Student’s t distribution, which is useful in forming confidence intervals when the variance is unknown, testing to determine if two sample means are significantly different, or testing to determine the significance of coefficients in a regression.  The distribution is similar in shape to a Normal distribution.  The mean of the t distribution is always equal to 0, while the standard deviation is usually slightly greater than 1.  One parameter, Degrees of Freedom, is necessary to completely specify the distribution.


Triangular Probability Distribution

Fits data that follow a Triangular distribution, which is useful for random variables that are constrained to lie between two fixed limits.  Unlike the Uniform distribution, in which all the values between the limits are equally likely, the Triangular distribution peaks at some value between the two limits.  This distribution is characterized by three parameters: Lower Limit, Central Value (Mode), and Upper Limit.


Uniform Probability Distribution

Fits data that follow a Uniform distribution, which is useful for characterizing data that range over an interval of values, each of which is equally likely.  The distribution is completely determined by the smallest possible value, a, and the largest possible value, b.  The mean equals (a + b)/2, while the variance equals ((b - a)^2)/12.  For discrete data, there is a related discrete uniform distribution.


Weibull Probability Distribution

Fits data that follow a Weibull distribution, which is useful for random variables that are constrained to be greater than 0; characterized by two parameters: Shape and Scale.  Because its failure-rate curves can take various shapes, it is an appropriate model for product failures.  The distribution is a generalization of an Exponential distribution.


Analysis Summary (Probability Distributions Analysis)

The Analysis Summary tabular option creates a summary of the distribution you selected.  Therefore, the contents of this pane will vary.  The summary lists the parameters for the selected distribution as well as other statistics, depending on the distribution you are using.

Use the Options dialog boxes for the individual distributions to change the values for the parameters.


Cumulative Distribution (Probability Distributions Analysis)

The Cumulative Distribution tabular option creates and displays a summary of the evaluation of the selected cumulative distribution. The summary includes the tail areas for up to five critical values of the distribution.  It also displays the value for the probability density function at 0.


Inverse CDF (Probability Distributions Analysis)

The Inverse CDF tabular option creates and displays a summary of the critical values for the selected distribution.  The summary includes the tail areas for up to five critical values of the distribution.


Mean (for Probability Distributions)

Enter values for the means of the selected parameters.  Enter up to five values.


Standard Deviation for Probability Distribution
Std. Dev.

Enter values for the standard deviations of the selected parameters.  Enter up to five values.


Random Variable

Enter values for the random variables for the selected parameters.  Enter up to five values.


CDF for Probability Distribution
CDF

Enter values for the tail area of the selected parameters.  Enter up to five values.


Size for Probability Distribution
Size

Enter the number of observations that will be included in the random sample.


Density/Mass Function (Probability Distributions Analysis

The Density/Mass Function Plot graphical option creates and displays a plot of the probability density function for the selected distribution. The height of the function indicates the value for the probability density function that is evaluated using the value on the X-axis.


CDF Plot (Probability Distributions Analysis)

The CDF Plot graphical option creates and displays a plot of the cumulative probability distribution for the selected distribution.


Survivor Function Plot (Probability Distribution Analysis)

The Survivor Function Plot graphical option creates and displays a plot of the survivor function for the selected distribution.  The function indicates the probability of obtaining a value greater than or equal to the values on the X-axis.


Log Survivor Function Plot (Probability Distribution Analysis)

The Log Survivor Function graphical option creates and displays a plot of the log survivor function for the selected distribution.  The function indicates the probability of obtaining a value greater than or equal to the values on the X-axis.


Hazard Function Plot (Probability Distribution Analysis)

The Hazard Function graphical option creates and displays a plot of the hazard function for the selected distribution.  The hazard function is equal to the probability density function divided by the survivor function.  When you are modeling lifetime data, the hazard function represents the instantaneous failure rate.


Columns on Contingency Table
Columns

Enter the names of the variables that contain frequency counts for each row of a two-way table.


Analysis Summary (Contingency Tables Analysis)
Analysis Summary

The Analysis Summary tabular option creates and displays a summary of the analysis.  The summary shows the names of the variables, the number of observations, and the number of rows and columns.


Frequency Table (Contingency Tables Analysis)

The Frequency Table tabular option creates and displays the Frequency Tables in sequence.

The Frequency Table displays counts for a 10-by-2 table where the first number in each cell of the table is the count or frequency.  The second number is the percentage of the entire table that is represented by that cell.


Chi-Square Test (Contingency Tables Analysis)

The Chi-Square Test tabular option creates and displays the results of a hypothesis test to determine if the assumption that the row and column classifications are independent.

If the Contingency Table is a two-by-two table with less than 100 observations, the statistics will also include the results from Fisher’s Exact test.


Summary Statistics (Contingency Tables Analysis)

The Summary Statistics tabular option creates and displays information on the center, spread, and shape of the data:  The number of values in the variable; the average, variance, standard deviation, minimum and maximum values; and the sum of all the values.  This information is helpful when you are determining if other statistical analyses might be appropriate to use with the data, or when you need to determine if the data should be transformed.


Table Percentages From

Determines how the percentages that will appear in each cell of the table will be calculated.

Entire Table

Calculates the percentages using the sum of all the frequencies.

Row Totals

Calculates the percentages using the row frequencies.

Column Totals

Calculates a percentage for each cell based on the frequency for that column.


Barchart (Contingency Tables Analysis)

The Barchart graphical option creates and displays a plot of the frequency data, which display as a series of bars.


Mosaic Plot

The Mosaic Plot graphical option creates and displays a plot of rectangles whose areas are proportional to the frequencies in the plot (see Snee, 1974).


Skychart (Contingency Tables Analysis)

The Skychart graphical option creates and displays a three-dimensional histogram.  The row variable is plotted along one axis, the column variable on another axis, and the frequency on a third axis.  This three-dimensional graph helps to visualize the relationship between the two variables and to see the distribution of the data.


Parameters for Hypothesis Test (Describe)
Parameter

Determines the parameter that will be tested. Each of the options compares the sample parameter with a hypothetical population.

Normal Mean

Performs a t-test for the mean of a sample; it is the default.  If you choose this option, enter values into the Null Hypothesis, Sample Mean, Sample Sigma, and Sample Size text boxes.

Normal Sigma

Performs a chi-square test for the variance of a sample.  If you choose this option, enter values into the Null Hypothesis, Sample Size, and Sample Sigma text boxes.

Binomial Proportion

Tests for the number of successes in a sequence of trials. If you choose this option, enter values in the Null Hypothesis, Sample Proportion, and Sample Size text boxes.

Poisson Rate

Compares the sample frequency with which a specific event will occur during a specific period of time with a hypothetical rate. If you choose this option, enter values in the Null Hypothesis, Sample Size, and Sample Rate text boxes.


Null Hypothesis for Hypothesis Test (Describe)
Null Hypothesis

Enter a value for the hypothetical population parameter that will be tested. This text box is activated for all the parameters you test.  The default is 0.5.


Sample Mean for Hypothesis Test (Describe)
Sample Mean

Enter a value for the sample mean that will be tested. This text box is activated only if you choose the Normal Mean option.


Sample Sigma for Hypothesis Test (Describe)
Sample Sigma

Enter the actual value for the sample size in the test. This text box is activated when you choose the Normal Mean or Normal Sigma options.  Enter a number greater than 0; 0 is the default.


Sample Proportion for Hypothesis Test (Describe)
Sample Proportion

Enter a value for the sample proportion that will be tested. This text box is activated only if you choose the Binomial Proportion option.  Enter a number between 0 and 1; 0.5 is the default.


Sample Rate for Hypothesis Test (Describe)
Sample Rate

Enter a value for the sample rate that will be tested. This text box is activated only if you choose the Poisson Rate option.  Enter a number greater than 0; 1 is the default.


Sample Size for Hypothesis Tests (Describe)
Sample Size

Enter a value for the sample size in the test. This text box is activated for all the parameters you test.  Enter a number greater than 1; 100 is the default.


Analysis Summary (Hypothesis Tests - Describe Analysis)

The Analysis Summary tabular option creates and displays a summary of the test results for the selected parameter.

If you select the Normal Mean option, the summary displays the sample mean, sample standard deviation, and sample size, as well as the 95 percent confidence interval for the mean.

If you select the Normal Sigma option, the summary displays the sample standard deviation and sample size, as well as the 95 percent confidence interval for sigma.

If you select the Binomial Proportion option, the summary displays the sample proportion and sample size, as well as the 95 percent confidence interval for p.

If you select the Poisson Rate option, the summary displays the sample rate and sample size, as well as the 95 percent confidence interval for rate.


Alternative Hypothesis for Hypothesis Tests (Describe)
Alternative Hypothesis

Determines the alternative test that will be performed.

Not Equal

Performs a two-sided test.

Less Than

Performs a one-sided test with a lower rejection region.

Greater Than

Runs a one-sided test with an upper rejection region.


Alpha for Hypothesis Tests (Describe)
Alpha

Enter a value (as a percentage) that will be used to calculate the confidence level.  Enter a number greater than or equal to 0 and less than 100; the default is 5.


Power Curve (Hypothesis Tests - Describe Analysis)

The Power Curve graphical option creates and displays a plot of the probability of the null hypothesis being rejected versus a range of values for the selected parameter.

The vertical axis of the Power Curve shows the probability of detecting an effect; the horizontal axis represents the size of the effect.


Assumed Sigma for Hypothesis Tests (Describe)
Assumed Sigma

Enter a value for the assumed standard deviation; the default is 1.  This option is available only when you use the Normal Mean parameter.


Normal Mean for Sample Size (Describe)
Normal Mean

Determines the sample size for estimating the mean of a population.  Enter values in the Hypothesized Mean and Hypothesized Sigma text boxes.


Normal Sigma for Sample Size (Describe)
Normal Sigma

Determines the sample size for estimating the standard deviation for a population.  Enter a value in the Hypothesized Sigma text box.


Binomial Proportion for Sample Size (Describe)
Binomial Proportion

Determine the sample size required to estimate a population proportion (number of successes).  Enter a value in the Hypothesized Proportion text box.


Poisson Rate for Sample Size (Describe)
Poisson Rate

Determines the sample size required to estimate the frequency of events occurring within a period of time.  Enter a value in the Hypothesized Rate text box.


Hypothesized Mean for Sample Size (Describe)
Hypothesized Mean

Enter the actual value for the assumed population mean that will be used as a null hypothesis.  The default is 0.


Hypothesized Sigma for Sample Size (Describe)
Hypothesized Sigma

Enter a value for the assumed population sigma that will be used to determine the sample size for a normal mean, or use as a null hypothesis for a normal sigma.  The default is 1.


Hypothesized Proportion for Sample Size (Describe)
Hypothesized Proportion

Enter the actual value for the sample proportion that will be used to determine the sample size.  The default is 0.5.


Hypothesized Rate for Sample Size (Describe)
Hypothesized Rate

Enter the actual value for the sample rate that will be used to determine the sample size.  The default is 1.


Analysis Summary (Sample-Size Determination - Describe Analysis)

The Analysis Summary tabular option creates and displays a summary that shows the name of the selected parameter and the controls. The last line displays the calculated sample size.  A separate summary is displayed, depending on the parameter you are using.


Control for Sample Size (Describe)
Control

Select the type and quantity of control that will be used to determine the required sample size.  The option you select depends on the type of analysis for which you are determining a sample size.

Absolute Error

Enter a value for the absolute error the program should control for.  Use the text box to enter the value; the smaller the value, the larger the sample size.

Relative Error

Enter a value for the allowable amount of error the program should control for.  Use the text box to enter the value.  The allowable amount of error is the percentage of the hypothesized value of the parameter you are using.  If you use a hypothesized mean of zero, this option is dimmed.

Power

Enter a value for the desired power of the test the program will use to determine the sample size.  Enter values in the Percentage and Difference to Detect text boxes.

Sample Size

Enter a value that will be used to calculate the power curve for a given test and sample size.


Alternative Hypothesis for Sample Size (Describe)
Alternative Hypothesis

Select an alternative hypothesis that will be used to determine which of two states is true: the null hypothesis or the alternative hypothesis.

Not Equal

Uses a two-sided alternative hypothesis; tests the hypothesis that the true population parameter is not equal to a certain value.

Less Than

Uses a one-sided alternative hypothesis; tests the hypothesis that the true population parameter is less than a certain value.

Greater Than

Uses a one-sided alternative hypothesis; tests the hypothesis that the true population parameter is greater than a certain value


Power Curve (Sample-Size Determination - Describe Analysis)

The Power Curve graphical option creates and displays a graph of the power versus the true value of the mean for a given sample size.


Sample 1 for Paired Sample
Sample 1

Enter the name of the variable that contains the first set of data that will be compared.  Enter a numeric variable.


Sample 2 for Paired Sample
Sample 2

Enter the name of the variable that contains the second set of data that will be compared.  Enter a numeric variable.


Analysis Summary (Paired-Sample Comparison Analysis)

The Analysis Summary tabular option creates and displays a summary of the analysis.  The summary displays the names of the selected variables and the number and range of the paired differences.


Summary Statistics (Paired-Sample Analysis)

The Summary Statistics tabular option creates and displays statistical information about the center, spread, and shape of the paired differences:  the number of values in each variable (Count); the average, variance, standard deviation; the minimum and maximum values; and the sum of the pairwise differences.  This information is helpful when you need to determine if other statistical analyses might be appropriate to use with the data, or when you need to determine if the data should be transformed.


Percentiles (Paired-Sample Comparison Analysis)

The Percentiles tabular option creates and displays the percentiles for the paired differences.  The results show the percentage of the values that are equal to or less than the selected value.


Frequency Tabulation (Paired-Sample Analysis)

The Frequency Tabulation tabular option groups the paired differences into the number of selected class intervals, and produces a table of relative and cumulative frequencies that summarize the distribution of the data.  The table displays values for the class, Lower and Upper limits, midpoint, frequency, relative and cumulative frequencies, and the cumulative relative frequency.


Stem-and-Leaf Display (Paired-Sample Comparison Analysis)

The Stem-and-Leaf Display tabular option creates and displays a table of the range and concentration of the values, the symmetry of the data, and if there are gaps or outliers.


Confidence Intervals (Paired-Sample Comparison Analysis)

The Confidence Intervals tabular option creates and displays the Confidence Intervals report, which shows the 95 percent confidence intervals for the mean and standard deviation of the paired differences.


Hypothesis Tests (Paired-Sample Comparison Analysis)

The Hypothesis Tests tabular option calculates and displays the mean and median for the paired differences, the results of the t-test, the computed t statistic, and the p-value.  The last line recommends that you either reject or do not reject the null hypothesis for a given alpha.


Scatterplot (Paired-Sample Comparison Analysis)

The Scatterplot graphical option calculates, plots, and displays the paired differences along a single axis as point symbols with no connecting lines.


Box-and-Whisker Plot (Paired-Sample Comparison Analysis)

The Box-and-Whisker Plot graphical option calculates and displays a plot of the paired differences.  The paired differences are divided into four areas of equal frequency (quartiles).  A box encloses the middle 50 percent, where the median is drawn as a vertical line inside the box.  Horizontal lines, known as whiskers, extend from each end of the box.

The left (or lower) whisker is drawn from the lower quartile to the smallest point within 1.5 interquartile ranges from the lower quartile.  The other whisker is drawn from the upper quartile to the largest point within 1.5 interquartile ranges from the upper quartile.


Frequency Histogram (Paired-Sample Comparison Analysis)

The Frequency Histogram graphical option creates and displays a plot that shows the frequency distribution for the paired differences.

The paired differences are divided into sets of nonoverlapping frequencies, and bars are plotted for each frequency.  The height of each bar is the number of values that fall within that frequency.


Quantile Plot (Paired-Sample Comparison Analysis)

The Quantile Plot graphical option creates and displays a Quantile Plot.  The Y-axis shows the fraction of data that are below a particular value.  Use the plot to view the cumulative distributions for the paired differences, or to estimate percentiles.


Normal Probability Plot (Paired-Sample Comparison Analysis)

The Normal Probability Plot graphical option constructs and displays a plot that determines if the paired differences come from a normal distribution.

The plot consists of an arithmetic (interval) horizontal axis scaled for the data and a vertical axis scaled so the cumulative distribution function for a normal distribution appears on the plot as a straight line.  The closer the data are to the reference line, the more likely that they follow a normal distribution.


Density Trace (Paired-Sample Comparison Analysis)

The Density Trace graphical option calculates and displays a plot that allows you to view the shape or distribution of the data, especially the variations in density over the range of the data.  Unlike a Histogram, the Density Traces Plot uses overlapping intervals and a weight function to smooth the densities, which results in a continuous line rather than a group of rectangles as in a Histogram.


Symmetry Plot (Paired-Sample Comparison Analysis)

The Symmetry Plot graphical option calculates and displays a plot that is helpful in determining the symmetry of the data.  Use this plot if you want to use analyses that are best applied to a symmetrical distribution.  Symmetrical data would closely follow the reference line.


Paired Sample Save Summary Statistics
Summary Statistics

Saves the statistical information on the center, spread, and shape of the data.


Paired Sample Save Percentiles
Percentiles

Saves the percentiles of the data.


Paired Sample Save Frequencies
Frequencies

Saves the number of observations in each class.


Paired Sample Save Cumulative Frequencies
Cumulative Frequencies

Saves the sum of the frequencies for all the classes up to and including the current class.


Paired Sample Save Relative Frequencies
Relative Frequencies

Saves the frequencies as a percentage of the sum of the counts.


Paired Sample Save Cum Rel Frequencies
Cum. Rel. Frequencies

Saves the cumulative frequencies as a percentage of the sum of the counts.


Paired Sample Save Target Variables
Target Variables

Enter the names of the variables in which the values generated during the analysis will be saved.  Enter new names or accept the defaults.


Compare for Hypothesis Test (Compare)
Compare

Determines the parameter that will be tested.

Normal Means

Compares two means.  If you choose this option, enter values in the text boxes for the Null Hypothesis for Difference of Means, Sample 1 Mean, Sample 2 Mean, Sample 1 Sigma, Sample 2 Sigma, Sample 1 Size, and Sample 2 Size.

Normal Sigmas

Compares two sigmas.  If you choose this option, enter values in the text boxes for the Null Hypothesis for Ratio of Variances, Sample 1 Sigma, Sample 2 Sigma, Sample 1 Size, and Sample 2 Size.

Binomial Proportions

Compares two proportions.  If you choose this option, enter values in the text boxes for the Null Hypothesis for Difference of Proportions, Sample 1 Proportion, Sample 2 Proportion, Sample 1 Size, and Sample 2 Size.

Poisson Rates

Compares two rates.  If you choose this option, enter values in the text boxes for the Null Hypothesis for Difference of Rates, Sample 1 Rate, Sample 2 Rate, Sample 1 Size, and Sample 2 Size.


Null Hypothesis for Differences of
Null Hypothesis for Difference of . . .

Enter a value for the hypothetical difference between the two samples for the parameter you choose.  This text box is activated for all the parameters you test. The name of the text box changes depending on the parameter you choose. For example, if you choose the Normal Sigmas option, the name of the text box is Null Hypothesis for Ratio of Variances.


Sample 1 Mean for Hypothesis Test (Compare)
Sample 1 Mean

Enter a value for the mean for Sample 1. This text box is activated only if you choose the Normal Means option.


Sample Mean 2 for Hypothesis Test (Compare)
Sample 2 Mean

Enter a value for the mean for Sample 2.  This text box is activated only if you choose the Normal Means option.


Sample Sigma 1 for Hypothesis Tests (Compare)
Sample 1 Sigma

Enter a value for the sigma for Sample 1.  This text box is activated only if you choose the Normal Means or Normal Sigmas options.  Enter a number greater than 0.


Sample Sigma 2 for Hypothesis Tests (Compare)
Sample 2 Sigma

Enter a value for the sigma for Sample 2.   This text box is activated only if you choose the Normal Means or Normal Sigma options.  Enter a number greater than 0.


Sample 1 Proportion for Hypothesis Tests (Compare)
Sample 1 Proportion

Enter a value for the proportion for Sample 1.  This text box is activated only if you choose the Binomial Proportions option.  Enter a number between 0 and 1.


Sample 2 Proportion for Hypothesis Tests (Compare)
Sample 2 Proportion

Enter a value for the proportion for Sample 2.  This text box is activated only if you choose the Binomial Proportions option.  Enter a number between 0 and 1.


Sample 1 Rate for Hypothesis Tests (Compare)
Sample 1 Rate

Enter a value for the rate for Sample 1.  This text box is activated only if you choose the Poisson Rates option.  Enter a number greater than 0.


Sample 2 Rate for Hypothesis Test (Compare)
Sample 2 Rate

Enter a value for the rate for Sample 2.  This text box is activated only if you choose the Poisson Rates option.  Enter a number greater than 0.


Sample 1 Size for Hypothesis Tests (Compare)
Sample 1 Size

Enter the number of observations for Sample 1.  Thuis text box is activated for all the parameters you test.  Enter a number greater than 1.


Sample 2 Size for Hypothesis Tests (Compare)
Sample 2 Size

Enter the number of observations for Sample 2.  This text box is activated for all the parameters you test.  Enter a number greater than 1; the default is 100.


Analysis Summary (Hypothesis Tests - Compare Analysis)

The Analysis Summary tabular option creates and displays a summary of the estimated test statistics for the selected parameter.

Normal Means Option

Normal Sigmas Option

Binomial Proportions Option

Poisson Rates Option


Alternative Hypothesis for Hypothesis Tests (Compare)
Alternative Hypothesis

Determines the alternative hypothesis test.

Not Equal

Performs a two-sided test.  This option is the default.

Less Than

Performs a one-sided test with a lower rejection region.

Greater Than

Runs a one-sided test with an upper rejection region.


Alpha for Hypothesis Tests (Compare)
Alpha

Enter the value (as a percentage) for the confidence level.  Enter a number greater than or equal to 0 and less than 100; the default is 5.


Assume Equal Sigmas for Hypothesis Tests (Compare)
Assume Equal Sigmas

Indicates if you want to assume equal standard deviations for testing the normal means.  When the dialog box displays, this option is selected, which means that equal standard deviations are assumed.  This check box is activated only when you compare two means.


Power Curve for Hypothesis Tests - Compare Analysis

The Power Curve graphical option creates and displays a plot of the power for the selected test.

Power Curve for Normal Means

Power Curve for Normal Sigmas

Power Curve for Binomial Proportions

Power Curve for Poisson Rates


Power Curve for Normal Means

Displays a graph of the power versus the true difference between the means.


Power Curve for Normal Sigmas

Displays a graph of the power versus the true ratio of the variances.


Power Curve for Binomial Proportions

Displays a graph of the power versus the true difference between the proportions.


Power Curve for Poisson Rates

Displays a graph of the power versus the true difference between the rates.


Assumed Sigma Normal Means Option
Assumed Sigma

Enter a value for the assumed standard deviation.  Enter any number greater than 0; the default is 1.


Assumed Mean Proportion Binomial Proportions Option
Assumed Mean Proportion

Enter a value for the assumed mean proportion.  Enter any number between 0 and 1; the default is 0.5.


Assumed Rate Poisson Rates Option
Assumed Rate

Enter a value for the assumed mean rate.  Enter any number greater than 0; the default is 1.


Dependent Variable for Variance Components
Dependent Variable

Enter the name of the dependent variable you want to examine.  The variable must contain numeric values.


Factors in Order of Nesting

Enter the names of the variables that contain the level codes for each factor in the design.  The order in which you enter the factors determines the nesting hierarchy that will be used in the analysis.  Enter higher level factors before lower level factors; that is, factors you enter on lower rows of the dialog box are nested within the factors you enter above them.


Analysis Summary (Variance Components Analysis)

The Analysis Summary tabular option creates and displays an ANOVA table, which displays the sum of squares, degrees of freedom, mean square, variance component, and percent.  The Percent column contains the percentage of variance that each factor accounts for.  If you omit the last factor, a line on the table appears with the label “ERROR.”


Summary Statistics (Variance Components Analysis)

The Summary Statistics tabular option creates and displays a summary of statistical information about the center, spread, and shape of the data:  The name of the dependent variable, the level codes, grand mean, number (count), mean, and standard deviation for each level and for each of the factors.


Scatterplot (Variance Components Analysis)

The Scatterplot graphical option calculates, plots, and displays a plot of the data plotted on the Y-axis versus the factor selected for the X-axis.  Solid horizontal lines are drawn at the means of the factor.  If the factor is any other than the last one selected, the means of the factor that is nested within the selected factor is plotted as points.


Residuals versus Factor Level (Variance Components Analysis)

The Residuals versus Factor Levels graphical option creates and displays a plot of the residuals versus any factor you select.  If an error term does not appear in the ANOVA table, all of the residuals are zero.


Residuals versus Predicted (Variance Components Analysis)

The Residuals versus Predicted graphical option creates and displays a plot of the residuals versus the predicted values for each point.  This plot is helpful in detecting nonconstant variance.


Residuals versus Row Number (Variance Components Analysis)

The Residuals versus Row Number graphical option creates and displays a plot of the residuals versus the row number.  The plot is helpful when you need to identify sequential correlations among the residuals.


Factor for Variance Components
Factor

Determines the main factor for the X-axis.  Click the factor to select it.


Save Results Options Dialog Box (Variance Components Analysis)

The Save Results Options dialog box allows you to select the results you want to save.  There are two selections: Variance Components and Residuals.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.


Compare for Sample Size (Compare)
Compare

Select the parameter (assumed distribution) and the null hypothesis for which you want to determine sample sizes.

Two Normal Means

Determines the sample sizes necessary to estimate the difference between two normal means.  If you choose this option, enter values in the text boxes for the Hypothesized Difference, Hypothesized Means, Percent of Data in First Sample, and Hypothesized Within-Group Sigmas.

Two Normal Sigmas

Determines the sample sizes necessary to estimate the ratio between two normal sigmas.  If you choose this option, enter values in the text boxes for the Hypothesized Ratio, Percent of Data in First Sample, and Hypothesized Within-Group Sigmas.

Two Binomial Proportions

Determines the sample sizes necessary to estimate the difference between two binomial proportions.  If you choose this option, enter values in the text boxes for the Hypothesized Difference, Hypothesized Proportions, and Percent of Data in First Sample.

Two Poisson Rates

Determines the sample sizes necessary to estimate the difference between two Poisson rates.  If you choose this option, enter values in the text boxes for the Hypothesized Difference, Percent of Data in First Sample, and Hypothesized Rates.

Several Normal Means

Determines the sample sizes necessary to compare several normal means using Tukey's HSD. If you choose this option, enter values in the text boxes for the Hypothesized Difference, Hypothesized Means, Hypothesized Within-Group Sigmas, and Number of Means.


Hypothesized Difference for Sample Size (Compare)
Hypothesized Difference

Enter the value for the hypothetical difference between two populations for which you want to form the null hypothesis.


Hypothesized Means for Sample Size (Compare)
Hypothesized Means

Enter the value for the hypothetical means you want to use to form the null hypothesis.


Hypothesized Proportions for Sample Size (Compare)
Hypothesized Proportions

Enter the value for the hypothetical rates you want to use to form the null hypothesis.


Percent of Data in First Sample

Enter a value for the percentage of total observations you want to take from the first population.  For equal sample sizes, the most common size, the percentage is 50.


Hypothesized Within Group Sigmas
Hypothesized Within-Group Sigmas

Enter a value for the hypothetical sigmas you want to use to determine the sample sizes for the normal distribution.


Hypothesized Rates for Sample Size (Compare)
Hypothesized Rates

Enter a value for the hypothetical rate you want to use to form the null hypothesis.


Number of Means for Sample Size (Compare)
Number of Means

Enter the number of means the program will test if you select several normal means.


Analysis Summary (Sample-Size Determination - Compare Analysis)

The Analysis Summary tabular option creates and displays a summary of information specific to the selected parameter.  The summary includes the name of the parameter being estimated, as well as the tolerance, confidence level, and assumed sigma.  The last line displays the number of observations required for each sample.


Control for Sample Size (Compare)
Control

Determines the type of control and its precision.

Absolute Error

Enter a value for the precision of the error.  Click the option button, then enter a number into the text box.

Relative Error

Enter a value for the precision of the error as a percentage of the null hypothesis for the parameter.  Click the option button, then enter a number into the text box.  When the null hypothesis is zero, this text box is dimmed.

Power

Calculates the sample size that will be used to detect the difference you specify, while controlling for the probability of a Type II error.  Enter a number into the Power text box.  Use the Difference to Detect text box to enter the number you need to detect the difference between the null and alternative hypotheses for the parameter you are using.

Sample Size

Lets you to view the Power Curve for the sample size you choose.  Enter a number into the text box.


Alternative Hypothesis for Sample Size (Compare)
Alternative Hypothesis

Determines the form of the alternative hypothesis.

Not Equal

Calculates the sample size for a two-sided test.  This option is the default.

Less Than

Calculates the sample size for a one-sided test with a lower rejection region.

Greater Than

Calculates the sample size for a one-sided test with an upper rejection region.


Power Curve (Sample-Size Determination - Compare Analysis)

The Power Curve graphical option creates and displays a graph of the power versus the true value of the selected parameter.


Y for Polynomial Regression
 Y

Enter the name of the dependent variable whose values will be predicted by the estimated model.  Enter a numeric variable.


X for Polynomial Regression
 X

Enter the name of the independent variable whose values will be used to predict the values for the dependent variable.  Enter a numeric variable.


Weight for Polynomial Regression
Weight

[Optional]  Enter the name of the variable that contains the values for weighting the observations.  Enter a numeric variable.


Analysis Summary (Polynomial Regression Analysis)

The Analysis Summary option creates a summary of the analysis, which fits a second-order polynomial model that describes the relationship between two variables.  The model-fitting results in the top portion of the pane include the estimates for the constant (intercept term) and the model coefficients for each power of the independent variable.

The model is fit to an Order 2 polynomial by default.  Use the Order option on the Polynomial Regresson Options dialog box to change the order of the model.

The table also displays several key measures that can be used to judge the adequacy of the model: the standard errors of the coefficients, the t-statistics (which are calculated by dividing the estimate by its standard error), and the p-value for each t-statistic.  The p-value corresponds to tests of hypotheses whose coefficients are equal to zero.  Small probability levels (less than .05 for a 95 percent confidence level) indicate statistically significant, nonzero coefficients.

The estimates that have a high probability level (greater than .05 for a 95 percent confidence level) have little or no effect on the dependent variable.  The F-ratio tests the overall model significance; in other words, it tests to see if the coefficients are all equal to zero).

The bottom portion of the summary displays the analysis of variance statistics for the full regression, and provides five additional values to help you judge the utility of the model.

•	The R-Squared statistic measures the proportion of variability explained in the model for the dependent variable.

•	The Adjusted R-Squared value is the amount of variation explained in the model for the dependent variable.  It adjusts the R-Squared value based on the number of coefficients in the model.  Unlike the R-Squared statistic, the Adjusted R-Squared value may decrease if higher orders to not significantly add to the fit.

•	The standard error of the estimate is the square root of the residual mean square (the mean squared error).  It measures the unexlained variability in the dependent variability.

•	The mean absolute error is the average of the absolute values of the residuals.  It is the average error size you can expect in a prediction.

•	The Durbin-Watson statistic is a measure of the serial correlation of the residuals.  In general, a Durbin-Watson statistic of less than 1.3 indicates serial correlation in the residuals.  You can find tables that interpret the statistic in Durbin and Watson (1951) or in standard text books such as Draper and Smith (1981).

Use the Polynomial Regression Options dialog box to enter the number of the highest power you want to include in the model.


Conditional Sums of Squares (Polynomial Regression Analysis)

The Conditional Sums of Squares option creates additional analysis of variance statistics.  The table shows the statistical significance of each power as it was added to the polynomial regression model, and includes the contribution each independent variable made to the total regression sums of squares when it entered the regression (also called Type I sums of squares).


Lack-of-Fit Test (Polynomial Regression Analysis)

The Lack-of-Fit Test option creates a modified ANOVA table with a line for lack-of-fit.  The test is designed to determine if the regression model adequately fits the data.  The Lack-of-Fit test is performed by comparing the variability of the residuals for the current model with the variability between observations at replicate values of the independent variable.

The test assumes that the observations Y, for a given X, are independent and normally distributed, and that the distributions of Y have the same variance.  Significant lack-of-fit shows that the specified model does not adequately fit the response.


Confidence Intervals (Polynomial Regression Analysis)

The Confidence Intervals option creates 95 percent confidence intervals for the coefficient estimates.  The estimates and the standard errors are identical to those shown in the initial table of model-fitting results.

Use the Confidence Intervals Options dialog box to change the number used to calculate the confidence intervals.


Forecasts (Polynomial Regression Analysis)

The Forecasts option creates predicted values for the Y variable using the fitted model.  In addition to the best predictions, the table displays the prediction intervals for new observations and confidence intervals for the mean of many observations (at a given percentage).

Use the Forecasts Options dialog box to enter values to change the confidence level that will be used to calculate the confidence limits, and to enter values for X for which you want to predict a Y value.


Unusual Residuals (Polynomial Regression Analysis)

The Unusual Residuals option creates a table that displays the values for all the observations that have studentized residuals less than -2 or greater than 2 in absolute value.  Studentized residuals measure the number of standard deviations each observed value of the independent variable deviates from a model fitted using all the data excet that observation.  Take a close look at any values greater than 3 in absolute value to determine if they are outliers, which you should remove from the analysis.


Influential Points (Polynomial Regression Analysis)

The Influential Points option creates a table that lists all the observations that have leverage values above three times the average.  Leverage is a statistic that measures the influence of each observation in determining the coefficients of the estimated model.  DFITS is a statistic that measures how much the estimated coefficients would change if each observation was removed from the data.


Order as a Polynomial Regression Option
Order


Confidence Level Option for Polynomial Regression
Confidence Level

Enter the number that will be used to calculate the confidence level intervals.  Enter a number greater than 0 and less than 100.  The default is 95; other common levels are 90 and 99.


Forecast at X Forecast Option
Forecast at X

Enter the values for X for which you want to predict a Y value.


Plot of Fitted Model (Polynomial Regression Analysis)

The Plot of Fitted Model option creates a plot of the results of fitting a second-order polynomial model to describe the relationship between the dependent and independent variables.  The plot shows the curve or the fitted line, and includes both confidence limits for the means (the inner pair of lines) and prediction limits (the outer pair of lines).

Use the Plot of Fitted Model Options dialog box to indicate which limits will be shown on the plot, to enter a value for the confidence limits that will be used to calculate the confidence intervals, and to enter a number that will be used to change the resolution of the lines on the plot.

You can use the Exclude… command to refit the regression.


Observed versus Predicted Plot (Polynomial Regression Analysis)

The Observed versus Predicted Plot graphical option plots the observed values versus the predicted values for the fitted model.  The plot includes a line with slope equal to one.  If all the predictions are perfect, all the points should be on the line.  Use the plot to detect cases such as increases in variability.


Residuals versus X Plot (Polynomial Regression Analysis)

The Residuals versus X Plot graphical option plots the residuals versus the independent variable (the default is studentized).  Use the plot to detect any nonrandom pattern, which could indicate that the model does not adequately fit the data.


Residuals versus Predicted Plot (Polynomial Regression Analysis)

The Residuals versus Predicted Plot graphical option plots the residuals versus the predicted values (the default is studentized).  Use the plot to detect nonlinear relationships between Y and X, and to determine if the variance of the residuals is constant.  If the model is correct and if all the assumptions are satisfied, the residuals should be structureless.


Residuals versus Row Number Plot (Polynomial Regression Analysis)

The Residuals versus Row Number graphical option plots the residuals versus their row number.  The residuals are plotted in the order that the observations appear in the dependent variable.  The plot helps to identify sequential correlations among the residuals.


Include for Polynomial Regression
Include

Determines what will be included on the plot.

Prediction Limits

Includes the prediction limits.  If you want to include both prediction limits and confidence limits on the plot, click both options.

Confidence Limits

Includes the confidence limits.  If you want to include both prediction limits and confidence limits on the plot, click both options.


X-Axis Resolution for Fitted Model Option

Enter the number that will determine the resolution of the lines on the graph.  Enter an integer between 20 and 200; the default is 30.  Higher values give smoother lines.


Plot as a Polynomial Regression Option
Plot

Determines the type of residuals that will appear on the plot.

Residuals

Plots the difference between the observed and the fitted values.

Studentized Residuals

Plots the residuals scaled by an estimate of the variance from the data with the observation removed.  A large studentized residual value may indicate an outlier and an influential observation.  This option is the default.


Save Results Options Dialog Box (Polynomial Regression Analysis)

The Save Results Options dialog box allows you to select the results you want to save.  There are 12 selections:  Predicted Values, Standard Errors of Predictions, Lower Limits for Predictions, Upper Limits for Predictions, Standard Errors of Means, Lower Limits for Forecast Means, Upper Limits for Forecast Means, Residuals, Studentized Residuals, Leverages, DFITS Statistics, and Mahalanobis Distances.

You can also use the Target Variables text boxes to enter the names of the variables in which the values generated during the analysis will be saved.  Enter new names or accept the defaults.


Target Variables for Polynomial Regression
Target Variables

Enter the names of the variables in which the values generated during the analysis will be saved.  Enter new names or accept the defaults.


Arrangement (for StatGallery)

Adds additional splitter windows to the StatGallery window or arranges the placement of the splitter windows within the window

Two by Two

Arranges the window into four equally sized panes; two on the top and two on the bottom; it is the default.

Top and Bottom

Arranges the window into two equally sized, horizontal panes; one on the top and one on the bottom.

Left and Right

Arranges the window into two equally sized, side-by-side panes.

Two Left, One Right

Arranges the window into two equally sized, top and bottom panes on the left and one pane on the right.

One Left, Two Right

Arranges the window into two equally sized, top and bottom panes on the right and one pane on the left.  The arrangement is the opposite of Two Left, One Right.

Three by Three

Arranges the window into nine equally sized panes.

One Position Only

Arrange the window into nine different sized panes within the columns of the window.


Position for Erasing StatGallery
Position

Select the position of the items that will be erased from the StatGallery window.

Top Left

Places the item in the top-left portion of the StatGallery window.

Top Center

Places the item in in the top-center portion of the StatGallery window.

Top Right

Places the item in the top-right portion of the StatGallery window.

Center Left

Places the item in the center-left portion of the StatGallery window.

Center

Places the item in the center of the StatGallery window.

Center Right

Places the item in the center-right position of the StatGallery window.

Bottom Left

Places the item in the bottom-left portion of the StatGallery window.

Bottom Center

Places the item in the bottom-center portion of the StatGallery window.

Bottom Right

Places the item in the bottom-right portion of the StatGallery window.


Gallery Arrangement One Left, Two Right
StatGallery Arrangement One Left, Two Right

Places three items within the window; two placed one on top of the other in the upper and lower panes of the right half of the window, and the third placed in the center of the left half of the window.


Gallery Arrangement Three by Three
StatGallery Arrangement Three by Three

Places nine items within the window; three across the top third of the window beginning from the left side of the window; three across the middle third of the window beginning from the left side of the window; and three across the bottom third of the window beginning from the left side of the window.


Gallery Arrangement One Position Only
StatGallery Arrangement One Position Only

Places one item within the center of the window.


Gallery Erase Top Left
StatGallery Erase Top Left

Erases the item in the top-left portion of the window.


Gallery Erase Top Center
StatGallery Erase Top Center

Erases the item in the top-center portion of the window.


Gallery Erase Top Right
StatGallery Erase Top Right

Erases the item in the top-right portion of the window.


Gallery Erase Center Left
StatGallery Erase Center Left

Erases the item in the center-left portion of the window.


Gallery Erase Center
StatGallery Erase Center

Erases the item in the center portion of the window.


Gallery Erase Center Right
StatGallery Erase Center Right

Erases the item in the center-right portion of the window.


Gallery Erase Bottom Left
StatGallery Erase Bottom Left

Erases the item in the bottom-left portion of the window.


Gallery Erase Bottom Center
StatGallery Erase Bottom Center

Erases the item in the bottom-center portion of the window.


Gallery Erase Bottom Right
StatGallery Erase Bottom Right

Erases the item in the bottom-right portion of the window.


Normal Means Option
Normal Means

The Analysis Summary for the Normal Means test displays the following for both Sample 1 and Sample 2:  The sample means, sample standard deviations, and sample sizes as well as the 95 percent confidence interval for the difference between the means.

Information in the lower portion of the text pane displays the difference between means for the null hypothesis, the name of the alternative hypothesis, the computed t-statistic, the p-value, and the recommendation — either reject or do not reject the null hypothesis.


Normal Sigmas Option
Normal Sigmas

The Analysis Summary for the Normal Sigmas test displays the following for both Sample 1 and Sample 2:  The sample standard deviations and sample sizes as well as he 95 percent confidence interval for the ratio of variances.

Information in the lower portion of the text pane displays the ratio of variances for the null hypothesis, the name of the alternative hypothesis test, the computed F-statistic, the p-value, and the recommendation — either reject or do not reject the null hypothesis for the given alpha.


Binomial Proportions Option
Binomial Proportions

The Analysis Summary for the Binomial Proportions test displays the following for both Sample 1 and Sample 2:  The sample proportions and sample sizes as well as the 95 percent confidence interval for the difference between proportions.

Information in the lower portion of the text pane displays the difference between rates for the null hypothesis, the name of the alternative hypothesis test, the computed z-statistic, the p-value, and the recommendation — either reject or do not reject the null hypothesis for the given alpha.


Poisson Rates Option
Poisson Rates

The Analysis Summary for the Poisson Rates test displays the following for both Sample 1 and Sample 2:  The sample rates and sample sizes as well as the 95 percent confidence intervals for the difference between rates.

Information in the lower portion of the text pane displays the difference between rates for the null hypothesis, the name of the alternative hypothesis test, the computed z-statistic, the p-value, and the recommendation — either reject or do not reject the null hypothesis for the given alpha.


By Columns

These options arrange the StatGallery window into different sized panes within the columns of the window.

Rows

Changes the number of panes that will be displayed within each column.

For example, if you enter 3 for Column 1, 2 for Column 2, and 1 for Column 3, the StatGallery window will contain Top, Middle, and Bottom panes in Column 1; Top and Bottom panes in Column 2, and a One Position Only pane in Column 3.


Learning the Program

These topics provide step-by-step instructions for learning the basics about the program.

Learning the Basics

Using Menus

Using Commands

Using Toolbars

Using Taskbars

Using Different Types of Windows

Using Dialog Boxes

Working with Analyses


Learning the Basics

The topics in this section help you navigate through STATGRAPHICS Plus by explaining basics such as the structure of the menus; how to use commands, toolbars, and taskbars; how to use different types of windows; how to use dialog boxes; and how to work with analyses.

Basic information about Windows is not included in the manuals or in this Online Help program.  If you have questions, please see the applicable Windows documentation.


Using Menus

Application programs in the Windows environment make extensive use of menus.  The standards for the menu structure in STATGRAPHICS Plus are consistent with those of other Windows products; that is, the Menu bar provides access to most of the user commands.  When you choose a selection on the Menu bar, a menu pops down.

STATGRAPHICS Plus provides a Menu bar across the top of the Application window, which lets you access files, perform file-management tasks, and access editing tools and statistical analyses.

STATGRAPHICS Plus contains the following menus: File, Edit, Plot, Describe, Compare, Relate, Special, View, Window, and Help.

Application programs in the Windows 95 environment make extensive use of menus.  The standards for the menu structure in STATGRAPHICS Plus are consistent with those of Windows 95; that is, a Menu bar contains the titles of commands on pull-down menus of varying levels.

STATGRAPHICS Plus provides a Menu bar across the top of the Application window, which lets you access files, editing tools, and statistical analyses.

STATGRAPHICS Plus contains the following menus:

File Menu

Edit Menu

Plot Menu

Describe Menu

Compare Menu

Relate Menu

Special Menu

View Menu

Window Menu

Help Menu


File Menu

The File Menu contains commands to open and close files, print, open recently used files, and exit the program.  Specifically, the File menu allows you to:

•	Open, close, save and save as StatFolios, a StatGallery, a StatReporter, and/or data files with a different name; query a database; and read a Clipboard directly from STATGRAPHICS Plus.

•	Use StatLink, a feature that can tie StatFolios directly to other data sources such as spreadsheets, databases, and measuring devices such as digital micrometers via linking software.  StatLink queries the data source when a StatFolio is opened.  Tasks you can perform include connecting to another data source, displaying status, starting and stopping polling, updating, and disconnecting a data source.  See Using Special Features for more information about these topics.

•	Print files and preview a page before you print it; use Print Setup to select printers other than the default; and Page Setup to select values other than the defaults for page attributes; and use Save Graph to save a graph as a metafile.  See, Printing, for more information about this topic.

•	Combine StatFolios and/or data files; use Send, an interface to e-mail programs that requires the use of Microsoft's Exchange program; and use Links to edit spreadsheet links.  For information about the Links command, see Working with Data and DataSheets.

The last section of the menu lists the files you most recently used and allows you to exit the program.


Edit Menu

The Edit Menu contains commands that allow you to:

•	Use editing commands such as Undo, Cut, Copy, Paste, and Paste Link.

•	Set system-wide edit preferences for system options, graphics, and link behavior.

•	Change a text font and its attributes; change the title of an analysis; and create a duplicate of an analysis.

•	Insert a new column into or delete an existing column from a DataSheet.

•	Update a formula-type column in a DataSheet.

•	Modify a column in a DataSheet; generate data values by using operators to transform the data; recode data into a STATGRAPHICS Plus format; and sort the data in a file.

Note:  STATGRAPHICS Plus uses a “spreadsheet-like” worksheet — a DataSheet — within the DataEditor.  The DataSheet is a document you use to store and manipulate data.  See Working with Data and DataSheets, for detailed information about how to use the DataEditor and a DataSheet.


Plot Menu

The Plot Menu allows you to access basic analyses through the use of various common plots.

Scatterplots

Contains analyses you use to create basic types of scatterplots. The analyses are: Univariate Plot, X-Y Plot, X-Y-Z Plot, Multiple X-Y Plot, Multiple X-Y-Z Plot, and Polar Coordinates Plot. See Using Basic Plots for more information.

Exploratory Plots

Contains analyses you use to create exploratory plots, which are useful for studying symmetry, checking distributional assumptions, and detecting outliers.  The analyses are: Box-and-Whisker Plot, Multiple Box-and-Whisker Plot, Normal Probability Plot, Frequency Histogram, Dot Diagram, Multiple Dot Diagram, Bubble Chart, and Radar/Spider Plot.

Business Charts

Contains analyses that produce business charts, which are useful for presenting relative quantities in an easily understood visual format.  The analyses are: Barchart, Multiple Barchart, Piechart, Component Line Chart, and High-Low-Close Plot.

Probability Distributions

Contains 24 distributions that are useful for generating and saving random numbers, calculating probabilities, and plotting the probability and cumulative distributions.

Response Surfaces Plots

Contains an analysis that creates response plots and contour plots based on a user-defined function.  These plots are helpful when you need to visualize the relationship between factors and a response variable.

Custom Charts

Contains an analysis for creating charts that are useful when circumstances require the use of a customized chart; usually in a manufacturing environment.


Describe Menu

The Describe Menu allows you to access analyses used to investigate and summarize data.

Numeric Data

Contains analyses used to describe and summarize a set of data: One-Variable Analysis, Multiple-Variable Analysis, Subset Analysis, Row-Wise Statistics, Power Transformations, and Statistical Tolerance Limits.

Categorical Data

Contains analyses that work with data that contain numeric codes representing discrete categories: Tabulation, Crosstabulation, and Contingency Tables.

Distributions

Allows you to create probability distributions, produce probability plots to test distributional assumptions, or fit a specific distribution to a set of data.  The analyses are: Probability Distributions, Probability Plots, and Distribution Fitting for Uncensored and Censored Data.

Life Data

Contains analyses that are useful for analyzing and summarizing lifetime data.  The analyses include Life Tables (Intervals and Times), Weibull Analysis, and Arrhenius Plots.

Hypothesis Tests (Describe)

Performs hypothesis tests on a variety of parameters that involve a single sample.

Sample-Size Determination

Determines the proper size for a sample.


Compare Menu

The Compare Menu allows you to access analyses used to create and compare descriptive statistics.

Two Samples

Performs analyses that compare two or more samples of data: Two-Sample Comparison, Paired-Sample Comparison, Hypothesis Tests, and Sample-Size Determination.

Multiple Samples

Performs analyses that compare several sets of data: Multiple-Sample Comparison, Comparison of Proportions, and Comparison of Counts.

Analysis of Variance

Performs one of three different analyses on data typically collected in a designed experiment.  The purpose is to determine the effect of one or more experimental factors on the values for a response variable.  The analyses are: One-Way ANOVA, Multifactor ANOVA, and Variance Components.


Relate Menu

The Relate Menu allows you to access statistical analyses that model the relationship between dependent and independent variables.

Simple Regression

Fits a model that relates one dependent variable to one independent variable by minimizing the sum of the squares of the residuals for the fitted line.

Polynomial Regression

Performs a special case of simple linear regression, whose models contain higher-order terms of the predictor variable.

Box-Cox Transformations

Determines an optimal transformation in the context of fitting a simple regression model.

Multiple Regression

Analyzes the relationship between one dependent variable and one or more independent variables.


Special Menu

The Special Menu allows you to access analyses in other STATGRAPHICS Plus products: STATGRAPHICS Plus Quality and Design and analyses in Advanced Regression, Multivariate Methods, and Time Series.

Quality Control Analyses

Contains analyses that cover all aspects of quality control: determining statistical control of variable, attribute, and multivariate data; identifying defects; determining the capability of a process, including Gage R&R; using time-weighted and special-purpose control charts; optimizing processes, and acceptance sampling.

Experimental Design Analyses

Contains a built-in catalog of designs that include a wide range of choices, including screening, response surface, mixture, multilevel factorial, inner/outer arrays, single and multifactor categorical, and variance component.

Advanced Regression Analyses

Contains analyses that let you fully explore the data by formulating complex multiple regression models and validating methods, to choosing the best regression model.

Multivariate Methods

Contains analyses that help to sort and group data, determine relationships between variables, and construct and test hypotheses.

Time-Series Analyses

Contains a complete set of analyses for building models to handle data that change over time.


View Menu

The View Menu controls the appearance of visible items in STATGRAPHICS Plus; that is, you use it to select and deselect the Toolbar, Status Bar, and StatAdvisor.


Window Menu

The Window Menu allows you to cascade, tile, and arrange icons; refresh panes; and move open items to the top viewing position.


Help Menu

The Help Menu accesses the Contents window for the Online Help program; accesses the StatWizard; and accesses the About window.


Using Toolbars

Toolbars are a set of buttons on the Application window placed immediately below the Menu bar.  The buttons correspond to a menu command.  Clicking a button is the same as choosing a corresponding menu command.  If you move the mouse pointer to a button on a toolbar and leave it there for a few seconds, a small tag displays a terse description of the button's purpose.

STATGRAPHICS Plus has two toolbars: the Application toolbar and the Analysis toolbar.

Application Toolbar

The Application toolbar displays the buttons you use to gain access to features you use to perform common tasks, such as opening and saving files, or performing editing tasks.

This toolbar also accesses Analysis dialog boxes for basic plots, such as Scatterplots and Box-and-Whisker plots.  Most functions that you can access using toolbar buttons you can also access using menus.  For example, when you click the first button in the last set of buttons on the toolbar, the Analysis dialog box for the X-Y Plot Analysis displays; the pop-up identifier label says “Scatterplots.”  See the Visual Glossary in Online Help.

Analysis Toolbar

The Analysis toolbar appears below the Application toolbar and displays buttons you use to redisplay Analysis dialog boxes, access tabular and graphical options, save the results of certain statistical analyses, and when applicable, access additional graphics options.


Using Commands

STATGRAPHICS Plus lets you choose commands from menus and submenus, from Analysis dialog boxes and Options dialog boxes.  For example, after you complete an Analysis dialog box, you use its command buttons to advise the program of the action you want to perform by clicking command buttons such as OK or Help.

Most dialog boxes in STATGRAPHICS Plus contain at least three commands, which appear as buttons: OK, Cancel, and Help.  Like these, most command names are self-explanatory..

Name:	All

Usage:	Selects all the options available on a dialog box.

Name:	Back

Usage:	Returns to and displays the previous dialog box.

Name:	Cancel

Usage:	Cancels an action.  When you click the Cancel button, the program closes the dialog box without performing an action.

Name:	Change Analysis Title…

Usage:	Changes the title of an analysis.

Name:	Change Text Font…

Usage:	Changes a font and its attributes.

Name:	Close…

Usage:	Closes a StatFolio, a data file, or the StatGallery.

Name:	Colors…

Usage:	Displays the Windows Color dialog box that lets you change colors.  For information about this dialog box and how you use it, see the Windows documentation.

Name:	Communalities

Usage:	Displays the Communalities Options dialog box, which lets you enter the name of the variable that contains the communalities you want to use.

Name:	Combine

Usage:	Allows you to combine StatFolios or data files.

Name:	Components…

Usage:	Displays the Response Plot Components dialog box, which lets you select the components you want to plot on a Response plot.

Name:	Copy

Usage:	Copies a highlighted entry.

Name:	Cut

Usage:	Cuts a highlighted entry.

Name:	Define

Usage:	Displays the Generate Data dialog box, which lets you enter an expression the program will use for the formula or for transforming the data.

Name:	Delete

Usage:	Allows you to delete text you highlighted in the Effects list box.

Name:	Display…

Usage:	Displays the Generate Data dialog box.

Name:	Enter

Usage:	Allows you to enter another term on the next line of the dialog box.

Name:	Estimation…

Usage:	Displays the Estimation Options dialog box, which allows you to limit and stop a factor-rotation process or a model-estimation process, depending on the analysis you are using.  In the Forecasting analysis in the Time Series module, the command is available when you select Simple Exponential Smoothing, Brown’s Linear Exponential Smoothing, Holt’s Linear Exponential Smoothing, Quadratic Exponential Smoothing, Winter’s Exponential Smoothing, or ARIMA Model.

Name:	Exclude…

Usage:	Displays the Exclude Interactions Options dialog box, which allows you to highlight terms you want to exclude from an analysis.

Name:	Exclude…

Usage:	Displays the Exclude Effects Options dialog box, which allows you to exclude factors from an analysis.

Name:	Exclude

Usage:	Displays the Exclude Options dialog box, which allows you to select the variables you want to exclude from a model.  Use this command when you have multiple independent variables and/or you select Second Order and want to use only certain second-order terms.  Initially, all the variables are shown in the Include text box.  When you highlight the variables you want to exclude, then click the Exclude button, the variables you highlighted move to the Exclude text box.

Name:	Exclude…

Usage:	Displays the Exclude/Include Options dialog box, which allows you to exclude a subgroup from an analysis.

Name:	Factors…

Usage:	Displays the Response Plot Factors dialog box, which allows you to select the factors you want to include on a Response plot.

Name:	Factors

Usage:	Displays the Plot of Fitted Model Options dialog box, which allows you to choose the two quantitative variables that will appear on the plot, change the limits for those variables, choose a level at which to hold any other quantitative variables.

Name:	Fonts…

Usage:	Displays the Windows Font dialog box, which lets you change the attributes for a font or change to a different font. Displays the Windows Font dialog box that lets you change the attributes for a font or change to a different font.  For information about this dialog box and how you use it, see the Windows documentation.

Name:	Generate Data

Usage:	Displays the Generate Data dialog box, which lets you generate values for variables by using operators to transform the data.

Name:	Generators…

Usage:	Displays the Design Generators dialog box when you select a fractional factorial design.  The dialog box lists the design generators used to create the last column(s) of the design matrix.  You can chanabe the signs (plus or minus) of the design generators.  When you click OK, the Blocked Composite Design Options dialog box displays.

Name:	Grid…

Usage:	Displays the Grid Options dialog box, which lets you change the attributes for a grid on a graph.

Name:	Help

Usage:	Accesses Online Help.  When the click the Help button, the program opens a Help window.

Name:	Hold

Usage:	Allows you to set the level of the quantitative factors when you are plotting a fitted model; that is, holds the categorical factors for the plot at 0.

Name:	Insert

Usage:	Inserts a new column into a DataSheet.

Name:	Links

Usage:	Allows you to edit spreadsheet links.

Name:	Modify Column…

Usage:	Allows you to modify the name of a column and the type of data in a DataSheet.

Name:	OK

Usage:	Uses the information you supply in a dialog box to perform an action.  When you click OK, the program processes the action.

Name:	Open

Usage:	Opens a StatFolio, a data file, real-time data, the StatGallery, or queries databases (ODBC).

Name:	Page Setup…

Usage:	Uses default settings to define the print attributes, and allows you to select different values for the attributes.

Name:	Paste

Usage:	Copies a highlighted entry into a new location.

Name:	Paste Link

Usage:	Links data from a spreadsheet in another application to a DataSheet in STATGRAPHICS Plus.

Name:	Preferences

Usage:	Allows you to set and save user-defined graphics options and graphics settings.

Name:	Print…

Usage:	Allows you to print pages.

Name:	Print Preview…

Usage:	Allows you to view pages to see their format before you actually print them.

Name:	[Print] Setup…

Usage:	Allows you to print to a printer other than the default printer.

Name:	Recode Data…

Usage:	Recodes data you import into STATGRAPHICS Plus by changing its format.

Name:	Undo

Usage:	Allows you to reverse (undo) the last editing action.

Name:	Save

Usage:	Saves a StatFolio, data file, a StatGallery, or the StatReporter.

Name:	Save As

Usage:	Saves a StatFolio, a data file, a StatGallery, or the StatReporter using a different name or a different file format.

Name:	Save Graph

Usage:	Saves a graph as a metafile.

Name:	Seeds…

Usage:	Displays the Seed Options dialog box, which you use to enter the row numbers of the observations you want to use for each corresponding cluster in a Cluster analysis.  This command is available only when you select the K-Means option.

Name:	Send

Usage:	Provides an enterface to e-mail programs.

Name:	Setup…

Usage:	Displays the Print Setup dialog box, which lets you select a different printer, choose a paper size and source.

Name:	Sort File…

Usage:	Allows you to reorder the data in a DataSheet.

Name:	Transform…

Usage:	Allows you to generate values to use in an Analysis dialog box.  STATGRAPHICS Plus lets you transform data using mathematical functions (operators) to achieve better results.  Using operators, the program is able to perform complex calculations.

When you click the Transform… button, the Generate Data dialog box displays.  Use this dialog box to create values for the data.

Name:	Update Formulas

Usage:	Allows you to update a formula-type column in a DataSheet.


Using Taskbars

The long horizontal bar at the bottom of the desktop is a taskbar. In STATGRAPHICS Plus, your desktop will show two taskbars, one for the Application, and one for STATGRAPHICS Plus analyses, which are separated by the status bar.

The Application taskbar contains three elements: the Start menu button; taskbar buttons for open applications, and the time of day indicator at the right end.  The Analysis taskbar contains taskbar buttons that represent open windows in STATGRAPHICS Plus.  For example, when you first open the program, five taskbar buttons appear: Untitled Comments, Untitled DataSheet, StatAdvisor, StatGallery, and StatReporter.


Using Different Types of Windows

A window can represent many objects.  In STATGRAPHICS Plus there are eight distinct types of windows:

•	Analysis window

•	Application window

•	Comments window

•	DataSheet window

•	Preview window

•	StatAdvisor window

•	StatGallery window

•	StatReporter window.

To learn more about using these windows, choose a topic from the list.

Using the Analysis Window

Using the Application Window

Using the Comments Window

Using the DataSheet Window

Using the Preview Window

Using the StatAdvisor Window

Using the StatGallery Window

Using the StatReporter Window


Using the Application Window

The Application window appears when you first start STATGRAPHICS Plus.  At least some of the components that make up the window appear on most, if not all, the windows.

When the Application window initially displays, it contains the Title bar and its icon, the Menu bar, the Application toolbar and its icons and buttons, and the Taskbar and its buttons.

Initially, the Taskbar buttons include: Untitled Comments button, Untitled Data button, StatAdvisor button, StatGallery button, and StatReporter button.  Each of these buttons contains their own icon.  The Status bar appears between the Analysis and Application taskbars.


Using the Comments Window

The Comments window appears when you click the Untitled Comments taskbar button, then click the Restore option on the pop-up menu.  You use this window to record important information about the created StatFolios or you can use it like a notebook to make notations about information you need to remember about the StatFolio.

Using this window is much like using a word processor: you can cut, copy, and paste information, even information about text panes in an Analysis window.  You can also customize the look of the text by changing the font.


Using the DataSheet Window

The DataSheet window appears in the Application window when you click the Untitled Data taskbar button, then click the Restore command.  You use the window to create new DataSheets, to modify existing DataSheets, and to modify data using the Data Editor.


Using the Analysis Window

The Analysis window appears after you select a plot or statistical analysis from the Menu bar and provide appropriate information in the Plot or Analysis dialog box.

An Analysis window contains these components: Analysis icon title bar, Analysis toolbar, and text and graphics panes.

Analysis Icon Title Bar

Displays the icon and title for the analysis.

Analysis Toolbar

Displays the buttons you use to redisplay dialog boxes, to access the tabular and graphical options, to save the results of certain statistical analyses, and, when applicable, to access additional graphics options.

Text and Graphics Panes

Displays the text and graphics in one or more panes in the Analysis window.  You can display both text and graphics in single panes; text in the left pane, graphics in the right, each one singly in a maximized pane; or display both text and graphics in minimized panes.


Using the StatAdvisor Window

If a statistical interpretation is available for either an analysis or a graph, it will appear in this window.  If an interpretation is not available, a message to that effect appears in the window instead.

The StatAdvisor window appears when you click the StatAdvisor button on the Analysis toolbar.

For detailed information about the StatAdvisor, see Using Special Features in STATGRAPHICS Plus.


Using the StatGallery Window

The StatGallery window appears when you click the StatGallery taskbar button, then click Restore on the pop-up menu.

Use the window to arrange text and graphics that you will either view or print.

For detailed information about the StatGallery, see Using Special Features in STATGRAPHICS Plus.


Using the Preview Window

The Preview window becomes active when you use the Print Preview… command on the File menu.

When the Preview window displays, it contains the Application title bar, and the Window toolbar with seven buttons: Print, Next Page, Prev Page, Two Page, Zoom In, Zoom Out, and Close.


Using the StatReporter Window

The StatReporter window appears when you click the StatReporter taskbar button, then click Restore on the pop-up menu.

Using this window is much like using a word processor.  You can create customized reports by copying and pasting text and/or graphics panes, and adding your own text.


Using Dialog Boxes

This topic covers setting system-wide edit preferences, accessing analyses and the different types of Options dialog boxes, and performing some basic tasks involving analyses.

Modifying Dialog Box Appearance

Setting System-Wide Edit Preferences

Using and Accessing Dialog Boxes and Options


Combining Existing Files

Sometimes you need to combine several files into a single file.  You can combine data files or StatFolio files.  You can also combine as many files as you like, but you must combine them two at a time.

Use the Combine... command on the File menu to combine the files.  When you select the command and press OK, the Combine Data Files or Combine StatFolios dialog box appears.

After you access the Combine [n] dialog box you need to provide information about the files you want to combine.

To Combine Existing Files

1.	Open the first file you want to combine; for example, cardata.

2.	Choose FILE... COMBINE... COMBINE [n]... to display the Combine [n]... dialog box.

3.	Open the second file you want to combine; for example, QCDATA; the program loads the data and combines the files.

4.	Click the cardata taskbar button, then click Restore... to display the DataSheet that contains the files you combined.

5.	To retain the cardata name for the combined file, save the DataSheet as either a data file or as a StatFolio, using the directions above.  Use FILE... SAVE AS... SAVE DATA FILE AS... to save the combined file with a new name.

If you want to combine more files with the new file, repeat the process.


Recoding Data

The Recode data feature allows you to change the upper and lower limits of the data to create a new value.  For example, suppose you are using the Tabulation Analysis to create a Piechart.  Because your dataset contains 50 values and STATGRAPHICS Plus allows you to use only 20, you must change the limits to create fewer values, which would allow you to create the Piechart.  You will use the Recode Data feature to create four categories of:

0-20
20-30
30-40
40-50.

1.	Copy the mpg variable into Column 1 of a new DataSheet.

2.	Type Groups into the Name text box on the Modify Column dialog box to name the new variable.

3.	Click the left mouse button on the column of data, then click the right button on Recode Data... on the DataSheet pop-up menu to display the Recode Data dialog box.

4.	Enter the following data into the Lower Limit, Upper Limit, and New Value text boxes.

0           20          20
20.1      30          30
30.1      40          40
40.1      50          50

5.	Click OK to recode the data.

6.	Access the Tabulation Analysis.  From the menus, choose: DESCRIBE... CATEGORICAL... TABULATION... to display the Tabulation Analysis dialog box.

7.	Enter the Groups variable into the Data text box, then click OK to display the Analysis Summary and a Barchart in the Analysis window.

8.	Click the Piechart option on the Graphical Options dialog box, then click OK to display the Barchart.  Notice that the data have been plotted into four groups within the new ranges.


Printing Various Types of Windows

STATGRAPHICS Plus contains several types of windows you can print: Comments, DataSheet, Analysis, StatAdvisor, StatGallery, and StatReporter.

To print any of these windows, you first complete a dialog box that is specific to the type of window you want to print.  The dialog boxes are: Print Comments, Print DataSheet, Print Analysis, Print StatAdvisor, Print StatGallery, and Print StatReporter.

There are several methods you can use to access these dialog boxes:

•	Choose FILE... PRINT... from the Menu bar.

•	Click the Print button on the Application toolbar.

•	Click the Print... command on the pop-up menu that appears whenever you click the right mouse button on a pane.

In Online Help, the step-by-step instructions use the first method.

Printing a [StatFolio] Comments Window

Printing a DataSheet Window

Printing an Analysis Window

Printing a StatAdvisor Window

Printing a StatGallery Window

Printing a StatReporter Window


Printing a [StatFolio] Comments Window

The [StatFolio] Comments window contains a record you can create for a StatFolio.  You use it much like you would a notebook.  Printing the window provides a hard-copy record of the information.

To Print a [StatFolio] Comments Window

1.	Click the Comments icon on the Taskbar button, then click Restore on the pop-up menu to display the Comments window.

2.	Choose FILE… PRINT… from the Menu bar to display the Print StatFolio Comments dialog box.

3.	Choose the print range, select the print quality, indicate the number of copies, and if you want to print to a file.  If your printer allows you to collate, indicate if you want the copies collated.

4.	Click OK to print the window.

The Setup… command on the dialog box displays the Print Setup dialog box, which allows you to select a different printer, and choose a paper size and source.

See the topic, Using the [Print] Setup… Command, for complete information.


Printing a DataSheet Window

The DataSheet window contains the data for the file you select.  You can print the entire sheet, or only the portions you highlight.

To Print a DataSheet Window

1.	Choose FILE… OPEN… OPEN DATA FILE… from the Menu bar to display the Open Data File dialog box.

2.	Select the file you want to open by clicking its name, then clicking the Open button.  The program opens the file and displays the Data icon with the file name in a Taskbar button.

3.	Click the Taskbar button that contains the name of the file you just opened.

4.	Click Restore… on the pop-up menu to load the data and display the DataSheet.

5.	Choose FILE… PRINT… from the Menu bar to display the Print DataSheet dialog box.

6.	Choose the print range, select the print quality, indicate the number of copies, and if you want to print to a file.  If your printer allows you to collate, indicate if you want the copies collated.

7.	Click OK to print the window or the portion of it you highlighted.


Printing an Analysis Window

An Analysis window is the window that appears after you complete an Analysis dialog box for an analysis you select from one of the five STATGRAPHICS Plus menus.

You can print a single maximized Analysis pane, all panes, visible panes, all text panes, or all the graphics panes.

To Print an Analysis Window

1.	Select the analysis you want to use from one of the five menus.

2.	Complete the Analysis dialog box and click OK to display the Analysis Summary and the first graph in the text and graphics panes of the Analysis window.

3.	Choose FILE… PRINT… from the Menu bar to display the Print Analysis dialog box.

4.	Choose the print range, select the print quality, indicate the number of copies and if you want to print to a file.  If you want to print all the analyses in a StatFolio, click that check box.

5.	Click OK to print the window.


Printing a StatAdvisor Window

The StatAdvisor window contains information that helps you understand and interpret the results of a statistical analysis.  You can print this information.

To Print a StatAdvisor Window

1.	Open and click on the StatAdviso window you want to print.

2.	Choose FILE… PRINT… from the Menu bar to display the Print StatAdvisor dialog box.

3.	Choose the print range, select the print quality, indicate the number of copies and if you want to print to a file.  If your printer allows you to collate, indicate if you want the copies collated.

4.	Click OK to print the StatAdvisor window.


Printing a StatGallery Window

STATGRAPHICS Plus allows you to copy text text and graphics to the StatGallery window so you can either view or print them.  You can print the current page, all the pages, or a range of pages.

To Print a StatGallery

1.	Complete, then click the StatGallery window you want to print.

2.	Choose FILE… PRINT… from the Menu bar to display the Print StatGallery dialog box.

3.	Choose the print range, select the print quality, indicate the number of copies, and if you want to print to a file.


Using the Print Preview... Command

The Print Preview… command on the File menu allows you to view pages to see their format before you actually print them.  Among the command’s features are the capabilities to display multiple pages, to zoom in and out of the pages, and to print from the command.

You can preview one pane at a time; for example, if the text and graphics options for an analysis are an Analysis Summary and a Scatterplot, you can preview only one of them at a time.

There are two methods you can use to access this command.

•	Choose FILE… PRINT PREVIEW… from the Menu bar.

•	Click the Print Preview… command on the pop-up menu that appears whenever you click the right mouse button on a pane.

To Use the Print Preview… Command

1.	Access the analysis you want to use from one of the five menus.

2.	Complete the Analysis dialog box, then click OK to display the Analysis Summary and the first graphical option.

3.	Click the Tabular and/or Graphical Options button on the Analysis toolbar to select the other options you want to create.

4.	Click OK to redisplay the Analysis window with the new options.

5.	Choose FILE… PRINT PREVIEW… from the File menu on the Application toolbar to display the first page in the Print Preview window.

6.	Click the Next button on the Preview window toolbar to preview the remaining paages, if there are any.

7.	Click one of the other buttons on the Preview window toolbar to perform other actions.

8.	Click either Close or Print on the Preview window toolbar when you finish previewing the pages; the program will either close the Preview window and redisplay the Analysis window or display the Print Analysis dialog box.

Using the Buttons on the Preview Window


Using the [Print] Setup... Command

If you want to print to a printer other than the default printer (the printer you designated as the default when you installed your Windows program), use the Print Setup… command from the File menu or the Setup… command on the Print [n] dialog box(es).

To Use the [Print] Setup… Command

1.	Choose FILE… PRINT SETUP… from the Menu bar or click the Setup… button on a Print dialog box to display the Print Setup dialog box.

2.	Choose the name of the printer you want to switch to, the paper size and source, and the print orientation, then click OK to save the settings.


Using the Page Setup... Command

STATGRAPHICS Plus uses default settings to define the print attributes, however, you can choose different values for the attributes.  The changes you make remain in effect until you change them again.  The settings are retained even when you start and end other sessions.

To Use the Page Setup… Command

1.	Choose FILE… PAGE SETUP… from the Menu bar to display the Page Setup dialog box.

2.	Change the settings for the top, bottom, left, and right margins; then enter the text that will be used for the header.  Indicate if the date, time, and file name should be part of the heading.  Choose the number of panes that will be printed per page.  Enter values for the horizontal and vertical graphics scaling and indicate if the graphics should be converted to a gray scale; if the background should be printed, and if the line width should be doubled.

3.	Click OK to save the settings.


Printing a StatReporter Window

After you create a StatReport, you can print it.

1.	Create the StatReport, then click the window you want to print.

2.	Choose FILE... PRINT... from the Menu bar to display the Print dialog box.

3.	Choose the print range, indicate the number of copies and if you want to print to a file.  If your printer allows you to collate, indicate if you want the copies collated.  This is a standard Windows Print dialog box.

4.	Click OK to print the report.


Modifying Dialog Box Appearance

Most dialog boxes in STATGRAPHICS Plus have several kinds of controls, including textboxes, command buttons, checkboxes, and option (radio) buttons.  Some contain labeled tabs you use by clicking the tab to turn to its page.

Microsoft Windows contains three settings that control the size of the type in the desktop: Windows Standard, Windows Standard (extra large), and Windows Standard (large).  If the title on a dialog box truncates, you will need to reset that control.  A truncated title will end abruptly followed by a series of dots; for example,

Box-and-Whisker Plot Op.....

To reset the control:

1.	Click START... to display the Start menu.

2.	Click SETTINGS... CONTROL PANEL... to display the Control Panel window.

3.	Double-click DISPLAY... to display the Display Properties dialog box.

4.	Click the APPEARANCE... TAB to display the Appearance page.  The top portion of the page shows the inactive window in the background, the active window in the foreground, and an OK message box in the front.

5.	From the Scheme options, choose Windows Standard as the setting, then click OK.


Setting System-Wide Edit Preferences

Before you begin to use STATGRAPHICS Plus you might want to set system-wide edit preferences that will override the defaults for various aspects of the program.  The Edit Preferences dialog box allows you to set behavioral preferences for some system, graphics, and link options.  To access the dialog box, click Preferences on the Edit menu.

The System options portion of the dialog box lets you either retain or not retain settings for sorting variable names on dialog boxes, using four-digit dates, and enabling Autosave and setting specific times, in minutes.  By default, variable names are sorted on dialog boxes.  You can change that setting system-wide using this dialog box instead of changing it one by one later on, or changing it on the individual dialog boxes.  Changing the setting for four-digit dates allows you to enter four-digit dates when you create or modify DataSheets instead of using the default of two-digit dates.  The change takes place after you exit the current STATGRAPHICS Plus session, and re-enter the program.

The Graphics options portion of the dialog box lets you either retain or not retain a graphics aspect ratio of 1:1, which means that graphs will be created in a square shape.  You can retain or not retain black and white graphs, which means you can override the default setting on the Profile page of the Graphics Options dialog box.  You can determine the number of decimal places that will appear in labels on charts.

The Link Behavior options portion of the dialog box lets you either update or not update analyses while they are in the nature of an icon, and update or not update analyses whenever a new data value is generated.


Using and Accessing Dialog Boxes and Options

To analyze data in STATGRAPHICS Plus, you will use a variety of dialog boxes and options.  Some of the dialog boxes contain special list or text boxes that give you quick access to the variables in the open data file.  You can type directly into an active text box or you can use the variables’ list to choose a variable name.  A black arrow on a button indicates an active text box; a grey arrow indicates an inactive one.  In addition to dialog boxes, each analysis has a varying array of options from which you can choose to create reports and graphs, as well as pane and analysis options that are tied specifically to a report or graph.  The dialog boxes and options are defined below.

Analysis Dialog Boxes

These dialog boxes are specific to an analysis.  You use them to enter or choose the data that will be initially analyzed.

Analysis Options Dialog Boxes

These dialog boxes allow you to enter or choose options to vary the way the data are analyzed.  These are named specifically for an analysis; for example, for the Weibull Analysis, this dialog box is called the Weibull Analysis Options dialog box.  You access it by clicking the right mouse button on a text or graphics pane, then choosing Analysis Options... or Pane Options... from the pop-up menu.  Analysis Options... are always specific to the analysis; the changes affect the analysis globally.  Pane Options... are always specific to the pane that is currently open; the changes affect only that specific pane.

Tabular and Graphical Options Dialog Boxes

These dialog boxes contain a list of reports or graphs that are available for a specific analysis.  You access them by clicking the Tabular or Graphical Options buttons on the Analysis toolbar.

Accessing dialog boxes is easy.  First, choose the menu you want to use; then the submenu, if applicable; then the analysis.  For example, to access the Weibull Analysis, which is part of the Life Data submenu, the access path is:  DESCRIBE... LIFE DATA... WEIBULL ANALYSIS....

Accessing Analysis Dialog Boxes

Accessing Tabular or Graphics Options Dialog Boxes

Accessing Pane Options... or Analysis Options...


Working with Analyses

The Edit menu contains several commands you can use to modify an analysis at any time.  These commands are: Change Text Font, Change Analysis Title, Copy Analysis.

To Change a Text Font

1.	Access the analysis and maximize a text pane.

2.	Choose EDIT... CHANGE TEXT FONT... to display the Font dialog box.

3.	Make the changes.  Choose a new font; change the font style from Regular, Italic, Bold, or Bold Italic; and view the changes.

4.	Click OK.

To undo the changes, you must return to the Font dialog box and reverse your changes.

To Change Analysis Title

1.	Access the analysis.

2.	Choose EDIT... CHANGE ANALYSIS TITLE... to display the Change Analysis Title dialog box.

3.	Type a new title into the Title text box, then click OK.  The new title displays in the Analysis titlebar.

To Copy An Analysis

1.	Choose EDIT... COPY ANALYSIS...; the program copies the analysis and displays the Analysis icon and name in a taskbar button.


Creating New Data Files

If the data you are analyzing are not already in files, use the DataEditor to enter the data and create a STATGRAPHICS Plus data file.


Working with Existing Files

Note:  In the sections that follow, there is discussion about the dialog boxes you use to open, close, and save a data file, StatFolio, StatGallery, or StatReporter.  Because all these dialog boxes are similar except in specific name, the convention is to refer to them as [n], where [n] equals the name of your selection; that is StatFolio, Data File, StatGallery, or StatReporter.  The name file in the text is used interchangeably for all four types of files.  The use of ellipses is to show the progression path.

Opening Existing Files

Saving Files

Closing a File and Exiting

Combining Existing Files

Sorting a File


Opening Existing Files

If you want to edit, add to, delete from, or perform an analysis on existing data, you must first retrieve the file that contains the data.  An existing file is one you previously saved and includes data files, and files in StatFolios, the StatGallery, and the StatReporter.  One way to open an existing file, is to use the Open command on the File menu.

After you access the Open [n]... dialog box, you need to provide information about the file.  Online Help contains detailed descriptions of the options on all the dialog boxes, including the defaults and explanations of what you enter into the fields.  This is a change from previous versions of the product, where the manual as well as Online Help contained this information.

If you are using STATGRAPHICS Plus on a network, any number of users on the network can open the file and work with its contents.  If multiple users have read/write priviledges, processes should be established to ensure that concurrent use does not result in data loss.

To Open an Existing File

1.	Choose FILE... OPEN... OPEN [n]..., which displays the appropriate Open dialog box.

2.	Choose or type the name of the file you want to open, then click Open.  The program opens the file and places the appropriate icon in a Taskbar button.

Note:  If you make any recorded changes to a file, then try to open another file or close the current file, a message displays asking if you want to save the current StatFolio, Data File, StatGallery, or StatReporter.

If you click Yes, and the file is yet untitled, another message box tells you to rename the file before you save it.  Click OK and proceed as usual.  When you click OK, the Save Data File As... dialog box displays, which you use to select or enter a name for the file.


Saving Files

You can save a file anytime during a working session or when you finish a session of STATGRAPHICS Plus.  You can save the file using the same name, or save it using a different name.  Two commands on the File menu allow you to perform these tasks: Save... and Save As....

Save...

The Save... command saves changes to an existing file using the name with which it was last saved; that is, the file retains the name of the previously saved file.  You can save a file as a StatFolio, a data file, a StatGallery, or a StatReporter.  If you are saving a data file, you can also use the shortcut keys, Shift+F11.

Save As...

The Save As... command saves a file for the first time after you create it, saves it with a new name, saves it in a different format or a different directory or folder, or saves it on another disk.  You can save a file as a StatFolio, a data file, a StatGallery, or a StatReporter.  If you are using Save As... with a data file, you can also use the shortcut keys, Shift+12.

To Save a File Using the Same Name

1.	Choose FILE... SAVE... SAVE [n].... The program saves the file using the same name, and allows you to continue working.

The only exception to the above is for StatFolios.  Using the path: FILE... SAVE... SAVE STATFOLIO..., a message displays asking you to rename the data file before saving the StatFolio.  After you click OK, the Save Data File As... dialog box displays, which you use as usual.

To Save a File Using a Different Name

1.	Choose FILE... SAVE AS... SAVE [n] AS... to display the Save [n] As... dialog box.

2.	Enter a new name for the file into the File Name text box, then click Save.  The program saves the file and redisplays the data icon with the new file name in a Taskbar button.


Closing a File and Exiting

To Close a File

1.	Choose FILE... CLOSE... CLOSE [n]....

To Close a File and Exit STATGRAPHICS Plus

1.	Choose FILE... CLOSE... CLOSE [n]...; the program closes the file and removes the Taskbar buttons from the applicable window.

2.	Choose FILE... EXIT STATGRAPHICS....  The program displays a dialog box that asks if you want to save the current StatFolio.

3.	Click Yes, No, or Cancel, depending on the action you want to take, and proceed accordingly.


Sorting a File

Regardless of the order in which you enter values into the columns of a DataSheet, you can sort them into one column, two or more adjacent columns, or sort the entire DataSheet into ascending or descending order.  You can sort the values on an entire DataSheet or by only the portion of it that you highlight.

To sort a file, use the Sort File Options dialog box, which you access by first accessing the DataSheet, then choosing EDIT... SORT FILE... from the Edit menu.  You can also access the dialog box by right clicking on a column of data, then choosing Sort File... from the pop-up menu.


Importing Files

When you “import” data, you are actually opening data in a file created as another file type.  Refer to Table 3-1 in the User Manual to review the file types that STATGRAPHICS supports.

If you are importing native files, the data are transferred directly into a DataSheet format.  If you are importing files other than native files, you will have to specify parameters before you can import the data.  To do this, use dialog boxes specific to the type of data you are importing.  For example, if the file is in ASCII format, you will supply the parameters using the Read ASCII File dialog box; if the file is in Excel format, you will use the Read Excel File dialog box.  STATGRAPHICS Plus now lets you read Excel spreadsheets through Excel `97.  The Read Excel File dialog box also lets you define a character or string as the missing value parameter.  During the import, that character or string is converted by STATGRAPHICS Plus into missing values (blanks).

To import spreadsheet data from noncompatible programs, first save the spreadsheet as an ASCII text file, then import the text file.

In addition to importing files, you can also use ODBC as another type of import capability.

Importing Excel Files

Importing ASCII Files

Using ODBC


Using ODBC

Open Database Connectivity (ODBC) is a database-dependent interface from Microsoft Corporation.  STATGRAPHICS Plus includes support for ODBC for 32-bit applications.  The interface allows you to read data from a database file, such as one from Microsoft's Access or Excel, or from any other SQL-compliant database format for which you have an ODBC driver.

If you have never used ODBC, check the Windows Control Panel to see if you have the proper setup.  If an ODBC icon appears, double-click it to see which data sources are set up.  If the ODBC icon does not appear in the Windows Control Panel or if double-clicking the icon does not indicate you have the data sources you need, the ODBC command in STATGRAPHICS Plus will not work.

You can install ODBC drivers from disks available with Microsoft's 32-bit applications such as Office 95 or Office 97.  ODBC drivers may also be available on disks you purchase from other vendors.

As you complete the Query Database (ODBC) - Use Rows dialog box, keep these tips in mind.

•	If you do not make changes in the Use Rows text box, when you click OK, STATGRAPHICS Plus brings all the data into the DataEditor.

•	A semicolon is not necessary at the end of the statement you enter into the Use Rows text box.

•	STATGRAPHICS Plus uses implied Select and Where statements, so if you repeat them, a syntax error occurs.

•	If you use a text variable, use this syntax:  “Description”=`software', where Description is the name of the variable, which appears in double quotation marks.  Use single quotation marks with the text string, software.

•	If you use a text variable, use this syntax:  “temperature”100, where temperature is the name of the variable, which appears in double quotation marks; the numeric, 100, does not need single quotation marks.

•	If you use Boolean operators, you must use an ampersand (&) for the AND statement.

Note:  To complete the SQL Data Sources, Query Databases Dialog Box, and Query Database (ODBC)  - Use Rows dialog boxes, see their individual entries in Online Help where details for each of the items on all the dialog boxes are fully discussed.


Using OLE

OLE is a mechanism that allows you to create and edit documents that contain items or “objects” created by multiple applications.  OLE was originally an acronym for Object Linking and Embedding.  However, it is now referred to simply as OLE.

OLE documents, historically called compound documents, seamlessly integrate various types of data or components.  Sound clips, spreadsheets, and bitmaps are typical examples of components found in OLE documents.  In supporting OLE, STATGRAPHICS Plus allows you to use OLE documents without worrying about switching between different applications; OLE does the switching for you.

You use container applications  to create compound documents and a server application or component application to create the items within the container documents.  Any application you write can be a container, a server, or both.

OLE incorporates many different concepts that all work toward the goal of seamless interaction between applications.  These areas include the following.

Linking and Embedding

Linking and embedding are the two methods for storing items inside an OLE document that was created in another application.

In-Place Activation

Activating an embedded item in the context of the container document is called in-place activation or visual editing.  The container application's interface changes to incorporate the features of the component application that created the embedded item.  Linked items are never activated “in-place” because the actual data for the item is contained in a separate file, out of the context of the application containing the link.

Note:  Linking and embedding and in-place activation provide the main features of OLE visual editing.

Automation OLE

OLE Automation allows one application to drive another application.  The driving application is known as an automation client or automation controller, and the application being driven is known as an automaton server or automation component.

Compound Files

Compound files provide a standard file format that simplifies structured storing of compound documents for OLE applications.  Within a compound file, “storages” have many features of directories and “streams” have many features of files.  This technology is also called structured storage.

Uniform Data Transfer

Uniform Data Transfer (UDT) is a set of interfaces that allow data to be sent and received in a standard fashion, regardless of the actual method chosen to transfer the data.  UDT forms the basis for data transfers by drag and drop.  UDT now serves as the basis for existing Windows data transfer, such as the Clipboard and dynamic data exchange (DDE).

Drag and Drop

Drag and drop is an easy-to-use, direct-manipulation technique used to transfer data between applications, between windows within an application, or even within a single window in an application.  You simply select the data to be transferred and drag it to the desired destination.

Component Object Model

The Component Object Model (COM) provides the infrastructure used when OLE objects communicate with each other.  The MFC OLE classes simplify COM for the programmer.

You can also use OLE with DDE to link and exchange files.

Using DDE and OLE to Link and Exchange Files


Using DDE and OLE to Link and Exchange Files

STATGRAPHICS Plus supports two functions for linking and exchanging data with other applications:

•	Dynamic Data Exchange (DDE)

•	OLE (formerly Object Linking and Embedding).

DDE allows you to establish a link to data in another application using the Paste Link command.  For example, you can copy a portion of a spreadsheet and paste-link it into a STATGRAPHICS Plus DataSheet.  When the data in the source application is changed, the data will update in STATGRAPHICS Plus.  The source application can remain open when STATGRAPHICS Plus updates, which differs from the StatLink... command, which updates from a closed file.

STATGRAPHICS Plus also supports OLE as a server application.  In practice, this means that STATGRAPHICS Plus objects (text blocks or graphics) can be pasted or paste-linked into other applications.  For example, you can copy a STATGRAPHICS Plus graphics pane and use the Paste Special... command to paste-link it into a word processing application.  When changes are made to the graphic, they will also be made in the copy paste-linked into the word processor.

You can create a link by:

•	using the Paste Link... command.

•	using the Paste Special... command.

•	using the StatLink... command to tie StatFolios directly to data from spreadsheets, databases, and measuring devices such as digital micrometers via linking software.

When an item has been linked, it will reflect changes that are made in STATGRAPHICS Plus.  For example, if a scatterplot is paste linked to a word processor page, change the number of points used to generate the plot in STATGRAPHICS Plus, then return to the word processor page, the plot is also updated there.

Note:  If the StatFolio you want to link was saved in versions of STATGRAPHICS Plus earlier than Version 3, you will need to resave it in Version 4 before you can use it in a link.

Creating a Link Using Paste Link...

Creating a Link Using Paste Special...


Accessing and Using Files

STATGRAPHICS Plus is designed to handle a variety of file formats, including, STATGRAPHICS files created in other operating systems (DOS); spreadsheet files created in Lotus and Excel; database files created in SQL formats; and ASCII text files.  In addition to data files, STATGRAPHICS Plus also handles files created using three special features in the product — StatFolios, the StatGallery, and the StatReporter — that are designed to speed up the way you work and cut down on time spent on repetitious data-entry tasks.

The associated topics explain the tasks of opening, saving, and closing files; combining data files or StatFolios; and sorting files.  The remaining topics explain how you import files from other applications, how you use ODBC to query databases, and how to link and exchange files between other applications and STATGRAPHICS Plus.

Creating New Data Files

Working with Existing Files

Importing Files

Using OLE


Working with Variables

Regardless of the type of statistical analysis you plan to perform, before you begin work you must organize the data.  Organizing data includes collecting, classifying, and tabulating it.  The related topics look at the classification process; and how you create variables and DataSheets.

In STATGRAPHICS Plus, data are stored in variables, which are stored in DataSheets.  A variable is defined as a characteristic or property of an individual population unit.  A variable describes any finding (an attribute or a characteristic), that can change, can vary, or can be expressed as more than one value, or in various values or categories.  A variable contains observations, or data values, that measure a certain characteristic of a population.

It is extremely important that you know the type of data you are working with because, although you can process various types of data in the analyses in STATGRAPHICS Plus, the results may be partially or totally meaningless if the analysis is not appropriate for that data.  In some cases, the use of inappropriate data may cause the program to shut down.

Assigning Formats to Variables

Naming Variables


Assigning Formats to Variables

The format of a variable affects the way the data appear in a DataSheet.  When you are creating a new DataSheet, you can create variables in 10 different formats: Numeric, Character, Integer, Date, Month, Quarter, Time (in two formats), Fixed Decimal, and Formulas.  The variables are shown on the Modify Column dialog box, which you use to assign a format to a variable.

The format includes the name, a comment that identifies the variable, the width required for the variable in the DataSheet, and a classification type, such as numeric or month.

Note:  To change the width of a column, you simply enter another value for the width in the Width text box on the Modify Column dialog box.

Numeric

Numeric variables contain only numbers and have a floating decimal place.  You can type as many numbers as you need after the decimal.  You can also create numeric variables that contain numbers as codes, then store them in a single variable or use them to divide data into classes.

Character

Character variables contain characters and/or numbers that are treated as characters.  You cannot run calculations on character variables.  You can use character variables to define subgroups.

Integer

Integer variables contain numbers without decimal places.

Date

Date variables contain numbers in MM/DD/YY format.  If you prefer to use a four-digit date, the format is MM/DD/YYYY.  Use the Edit Preferences dialog box from the Edit menu to change the data format.  You can use date variables as labels on a graph.

Month

Month variables contain numbers in MM/YY format.  If you prefer to use a four-digit date, the format is MM/YYYY.  Use the Edit Preferences dialog box from the Edit menu to change the data format.

Quarter

Quarter variables contain data in Q1/YY, Q2/YY, Q3/YY, and Q4/YY format. If you prefer to use a four-digit date, the format is Q1/YYYY, Q2/YYYY, Q3/YYYY, and Q4/YYYY.  Use the Edit Preferences dialog box from the Edit menu to change the data format.  You can use quarter variables as labels on a graph.

Time (HH:MM)

This type of Time variable contains numbers in a hour and minute format (HH:MM).  You can use this Time variable as a label on a graph.

Time (HH:MM:SS)

This type of Time variable contains numbers in a hour, minute, and second format (HH:MM:SS).  You can use this Time variable as a label on a graph.

Fixed Decimal

Fixed-decimal variables contain only numbers that have a fixed number of decimal places.

Formula

Formula variables contain data from existing columns you can use to perform calculations.  The program greys out the resulting values and creates a link between the values used in the formula and those in the columns.  You can also use the Formula column as a calculator and use numbers like 2145/3 to create a numeric answer for the first row of a column.

You cannot edit the data in the Formula column.  But If you change the data in the columns used in the formula, the formula is updated.  You can also update a formula using the Update Formulas... command on the Edit menu and the DataSheet pop-up menu.


Naming Variables

Follow these conventions when you name variables for STATGRAPHICS Plus.

•	Each column (variable) in a DataSheet has a unique name that can contain from one to 32 characters.

•	The name must begin with a letter (A-Z or a-z), an underscore (_), or a number sign (#).

•	The name can consist of letters (A-Z or a-z), digits (0-9), an underscore (_), a period  (.), a blank ( ), as well as any of the following symbols:  @, #, $, %, and &.

•	Embedded blanks in variable names are ignored; for example, Flow Rate and FlowRate are equivalent.


Creating a DataSheet

When you enter STATGRAPHICS Plus for the first time, you will begin work with a blank untitled DataSheet you use to set up and enter the data that will become the variables for an analysis.

Opening a Blank DataSheet

Setting Up a DataSheet


Opening a Blank DataSheet

The first step in creating a DataSheet, is to open a blank form.

To Open a Blank DataSheet

1.	Open STATGRAPHICS Plus.

2.	Click the data icon taskbar button.

3.	Click Restore... on the pop-up menu to display the untitled DataSheet.


Setting Up a DataSheet

A DataSheet is a “spreadsheet-like” worksheet in the DataEditor that contains rows and columns.  Cells in the rows and columns contain the values for the variables you will create.  A DataSheet does not behave like a true spreadsheet (such as Microsoft's Excel), because it does not have the functionality necessary to create results.

There are many ways you can set up a DataSheet.  The steps below provide one way, which is to first create names for all the variables.  You use the Modify Column dialog box to do this.

To Create Names for Variables

1.	Access a blank DataSheet.

2.	Position and click the mouse pointer on Col_1 of the untitled DataSheet to highlight the column.

3.	Choose EDIT... MODIFY COLUMN... from the Menu bar to display the Modify Column dialog box.

4.	Type a name for the first variable (the title of the first column) in the Name text box.

5.	Type a description about the variable in the Comment text box.  The comment serves as a note to yourself (or to future users of this file), which explains something about the variable you are creating.

6.	Enter an integer between 1 and 70 for the width of the first variable.  See Online Help for the range of values you can use for each individual variable type.

7.	Use Type options to choose the type of data you will be entering, then click OK to update and redisplay the DataSheet with the name of the variable appearing instead of Col_1.

At this point you can either continue creating titles for the remaining variables or enter the values for the first variable, then create the next new variable name by following the steps above.


Entering Data

When you enter the values, use the mouse or the arrow keys to move up and down through the cells.  Use the mouse or the Tab and Shift+Tab keys to move right and left through the cells.  If you enter more values than will display in a cell at one time, the DataSheet automatically scrolls the display across the cell.

The program organizes the values in the DataSheet (the representations of the variables) into a table of rows and columns.  Each column represents a variable; each row represents one observation for each variable.

For information about importing data from other software applications, see the topic, Accessing and Using Files.

Entering Data by Rows and Columns

Entering Data by Typing the Values

Entering Data Using Copy and Paste

Generating Data for a DataSheet

Updating a Formula


Entering Data by Typing the Values

When you enter data by typing it, you enter the values directly into the cells of the DataSheet.  If you need to enter an observation that does not contain data (missing values), enter the missing value by leaving the appropriate cell empty (blank).


Entering Data Using Copy and Paste

Using this option you can create a new DataSheet by copying all or portions of data from other DataSheets in STATGRAPHICS Plus or from other applications.

To Enter Data from Other DataSheets

1.	Open the DataSheet in STATGRAPHICS Plus that contains the data you want to use.

2.	Highlight the data.

3.	Choose EDIT… COPY… from the Menu bar.

4.	Close the DataSheet; open the DataSheet that will contain the copied data.

5.	Click the cell where you want to begin pasting the data.

6.	Choose EDIT… PASTE… from the Menu bar.  The program places the data into the cells of the new DataSheet.

7.	Name and save the DataSheet.

To Enter Data from Other Applications

1.	Access a new untitled DataSheet in STATGRAPHICS Plus.

2.	Access amd p[em the spreadsheet in another application that contains the data you want to use.

3.	Highlight the data you want to copy.

4.	Choose EDIT… COPY… from the Menu bar.

5.	Click the cell of the new STATGRAPHICS Plus DataSheet where you want to begin pasting the data.

6.	Choose EDIT… PASTE… from the Menu bar.  The program places the new data into the cells of the DataSheet.

7.	Name and save the DataSheet.


Generating Data for a DataSheet

If you are an experienced user, you can also use operators to transform data to create values for a variable.  The Generate Data dialog box lets you use variables, operators, and/or a keypad to create a mathematical expression.

The mathematical expression can perform specific functions ranging from basic math to complex calculations.  You create the expression by using, individually or in combination, the variable names and operators, as well as the keypad, which you can use to insert or delete numeric values.

In addition to the operator name, each item in the list of operators includes the current syntax for the operator.  For example, ABS(?) indicates that the ABS operator takes a single right argument, (?).  Doublle-click the operator to display it in the Expression text box.  See Using Operators in the Reference section for descriptions and examples of all the operators.

You can access the Generate Data dialog box by:

•	using the DataSheet pop-up menu (the method used in the steps below).

•	choosing EDIT… GENERATE DATA… from the Menu bar

•	pressing the Transform… command button on Analysis dialog boxes.

To Access the Generate Data Dialog Box

1.	Place the mouse pointer on an open DataSheet and click the left button on the column heading to highlight a column.

2.	Click the right button to display the DataSheet pop-up menu.

3.	Click Generate Data… on the pop-up menu to display the Generate Data dialog box.

4.	Use the variable names, operators, and/or keypad, either individually or in combination, to create a function in the Expression text box.

5.	Click OK to generate the data.


Updating a Formula

If a column in a DataSheet is made up entirely of numbers, you can use that data with the Update Formulas… command like a calculator to create numeric answers for that column.

To Update a Formula

1.	Access an untitled DataSheet.

2.	In Column 1, enter a column of numbers, then click on the Column 1 heading to select the column.

3.	Access the Modify Column dialog by either clicking it on the Edit menu or on the DataSheet pop-up menu.

4.	Enter a name for the column in the Name text box.

5.	From the Type otions, choose Formula.

6.	In the Formula text box, type the name of the column, followed by a mathematical symbol indicating addition, subtraction, multiplication, or division (+, - *, / ) and a number that will be used with the mathematical symbol.  For example, if you want to subtract 1 from each value in the column, you would enter the name of the column, followed by –1.

Each time you access the Modify Column dialog box and click OK, the numbers are recalculated using the formula.  This is repeated until you change the formula.


Modifying and Editing a DataSheet

After you create, name, and save a DataSheet, you can modify or edit it in several ways.

Modifying a DataSheet

If you are modifying a variable using the Modify Column dialog box, you can rename it, change the comments about it, change the column width, change the classification type, or change the formula.

Editing a DataSheet

If you are using commands on the Edit menu or the DataSheet pop-up menu, there are basic editing tasks you can perform using either of them.  This includes undoing the last editing action or modification; cutting, copying, or pasting a highlighted entry; inserting or deleting a cell, row, or column; and sorting a file.

Undoing an Entry in a DataSheet

Cutting an Entry in a DataSheet

Copying and Pasting an Entry in a DataSheet

Inserting a Column Into a DataSheet

Deleting a Column in a DataSheet


Working with Data and DataSheets

To work with data, it is important that you understand variables, how to assign formats to them, and name them.  You also need to know how to create, modify, and edit a DataSheet; and how to recode data.

Working with Variables

Creating a DataSheet

Entering Data

Modifying and Editing a DataSheet

Recoding Data


Undoing an Entry in a DataSheet

To Undo an Entry

Whenever possible, you can undo (reverse) the last editing action or modification.

1.	Click the right button to display the DataSheet pop-up menu.

2.	Click Undo... to reverse the last change and redisplay the DataSheet with the original data entered into the cell.


Cutting an Entry in a DataSheet

To Cut an Entry

1.	Select the entry you want to cut by clicking on the cell or group of cells.

2.	Click Cut... on the DataSheet pop-up menu to cut the entry or entries you selected and redisplay the DataSheet with the selected entry(ies) removed.


Copying and Pasting an Entry in a DataSheet

To Copy and Paste An Entry

1.	Select the entry you want to copy by clicking on the cell or group of cells.

2.	Click Copy... on the DataSheet pop-up menu to copy the entry and place it on the clipboard but leave it unchanged in the DataSheet.

3.	Place the mouse pointer in the first position of the location into which the program will copy the entries.

4.	Click Paste... on the DataSheet Pop-up menu to copy the entry into its new location.


Inserting a Column Into a DataSheet

To Insert a Column

1.	Place the mouse pointer on the column that appears after the location in which you want to insert the new column.

2.	Click the left mouse button to highlight the column, then click the right mouse button to display the DataSheet pop-up menu.

3.	Click Insert... on the DataSheet pop-up menu to insert a new column before the selected column.


Deleting a Column in a DataSheet

To Delete a Column

1.	Place the mouse pointer on the column that you want to delete.

2.	Click the left mouse button to highlight the column, then click the right mouse button to display the DataSheet pop-up menu.

3.	Click Delete... on the DataSheet Pop-up menu to delete the column.


Entering Data by Rows and Columns

To Enter Data by Columns or Rows

1.	Access the DataSheet.

2.	Click the cell in which you want to begin entering data, then enter the first value.

3.	Press the down arrow if you are entering the data by column, then continue entering the values in a downward- or upward-column fashion.

Press the right arrow if you are entering data by rows, then continue entering the values in a cross-wise right or left direction.


Using the Buttons on the Preview Window

To Use the Buttons on the Preview Window

Print

Closes the Preview window and displays a Print dialog box.  The name of the dialog box varies, depending on the type of material you are previewing.

Next Page

Displays the next page of the material you are previewing if there is more than one page.

Prev Page

Displays the previous page of the material you are previewing if there is more than one page.

Two Page

Displays two side-by-side pages of preview material.

Zoom In

Moves the focus closer to the material on the page.  You can click the button twice in one sequence.

Zoom Out

Returns the preview material closer to its original size.

Close

Closes the preview material without printing it.


Importing Excel Files

To Import Excel Files

1.	Open STATGRAPHICS Plus.

2.	Choose FILE... OPEN... OPEN DATA FILE... to display the Open Data File dialog box.

3.	Using the Look In drop-down list, if necessary, choose the directory where the Excel file resides.

4.	Choose EXCEL (*.XLS)... from the Files of Type... drop-down list.

5.	Enter the name of the file into the File Name text box, then click OK to display the Read Excel File dialog box.

6.	Complete the Read Excel File dialog box, then click OK to import the data.  The dialog box lets you indicate if the variable names you want to import are stored in the first row of the Excel spreadsheet or if STATGRAPHICS should create default names.  You can also enter the number of the worksheet you are importing, and/or provide a character or character string to be interpreted as a missing value.


Importing ASCII Files

To Import An ASCII File

1.	Open STATGRAPHICS Plus.

2.	Choose FILE... OPEN... OPEN DATA FILE... to display the Open Data File... dialog box.

3.	Using the Look In drop-down list, if necessary, choose the directory where the ASCII file resides.

4.	Choose ALL FILES (*.*)... from the Files of Type... drop-down list.

5.	Enter the name of the file into the File Name text box, then click OK to display the Read ASCII File dialog box.

6.	Complete the Read ASCII File dialog box, then click OK to import the data.


Reading SQL Databases

Important Note: The step-by-step instructions document the STATGRAPHICS Plus implementation of ODBC accessing Microsoft's Access database.  If you previously used ODBC, the instructions and the names of the dialog boxes and the items on them may differ, depending on how ODBC was set up.

To Read SQL Databases

Note:  The steps follow one set of dialog boxes.  The dialog boxes will vary, depending on the ODBC setup on your machine.

1.	Choose FILE... OPEN... QUERY DATABASE (ODBC)... to display the SQL Data Sources dialog box.

2.	Choose the data source you want to open by clicking on the name, then clicking OK to display the Query Database dialog box.

Depending on the set up, a prompt may ask you to provide information such as a login ID and/or password, directory, and/or file information.

3.	Enter the information, then click OK to display the Query Database dialog box.

Note:  If you are working on a network and need help, see your system administrator.

4.	Choose the name of the table (database) you want to open from the Table drop-down list.  When you choose a table, the program displays the names of the fields in the Available Fields list box.

5.	Choose the names of the fields you want to read into STATGRAPHICS Plus by double-clicking the field name.  As you choose the names of the fields, they appear in the Selected Fields list box.

6.	Click OK to display the Query Database (ODBC) - Use Rows dialog box.

7.	Complete the dialog box if you want to import a subset of the fields, then click OK.  If you do not want to select a subset of the fields, click OK.  The program imports the data you want to save and displays the name of the database in brackets in a data icon Taskbar button.


Accessing Analysis Dialog Boxes

To Access Analysis Dialog Boxes

1.	Choose DESCRIBE... LIFE DATA... WEIBULL ANALYSIS... to display the Weibull Analysis dialog box.

2.	Complete the dialog box, then click OK to display the first text and graphics panes of the Weibull Analysis.


Accessing Tabular or Graphics Options Dialog Boxes

To Access Tabular or Graphical Options Dialog Boxes

1.	Click the Tabular or Graphical Options button on the Analysis toolbar to display the dialog box.

2.	Click the name of the Tabular or Graphical option you want to use, then click OK to display the report or graph.


Accessing Pane Options... or Analysis Options...

To Access Pane Options... or Analysis Options...

1.	Click the right mouse button on a report or graph.

2.	Choose either Pane Options... or Analysis Options... on the pop-up menu to display the appropriate Options dialog box.


Creating a Link Using Paste Link...

To Create a Link Using the Paste Link... Command

1.	Open a STATGRAPHICS Plus session.

2.	Maximize a DataSheet.

3.	Open a spreadsheet application and load a spreadsheet file containing data.  Highlight a section of data with the cursor.

4.	Choose EDIT... COPY... from the Edit menu in the spreadsheet application to copy the data.

5.	Return to STATGRAPHICS Plus and choose EDIT... PASTE LINK... from the Edit menu or DataSheet popup menu.  The data is displayed in the open DataSheet.

After an item has been linked, changes to the data made in the other application will also be made in the DataSheet.  Any analysis or StatFolio using that DataSheet will also reflect the change.

6.	When a DDE link is established, the FILE... LINKS... menu item is activated.  You can use the dialog box associated with that menu item to update or change the links.

Note:  If the StatFolio you want to link was saved in versions of STATGRAPHICS Plus earlier than Version 3, you will have to resave it in Version 3 or 4 before you can use it in this type of link.

7.	Choose SAVE AS... SAVE DATA FILE AS... to save the DataSheet and preserve the DDE link.


Creating a Link Using Paste Special...

To Create a Link Using the Paste Special... Command

1.	Save a STATGRAPHICS Plus analysis as a StatFolio.

2.	Maximize the text or graphics pane in STATGRAPHICS Plus.

3.	Choose EDIT... COPY... from the Edit menu.

4.	Open the destination application and choose EDIT... PASTE SPECIAL... from the Edit menu.  A dialog box asks you to select the type of object you want to paste.

5.	Ensure that the PASTE LINK radio button is selected and SGWIN StatFolios Object is highlighted.  When you click OK, the pane in STATGRAPHICS Plus is now displayed and linked with the destination application.


Printing

Associated topics about printing include how you print the various types of windows in STATGRAPHICS Plus; how you use the Print Preview…, [Print] Setup…, and Page Setup… commands.

Printing Various Types of Windows

Printing a [StatFolio] Comments Window

Printing a DataSheet Window

Printing an Analysis Window

Printing a StatAdvisor Window

Printing a StatGallery Window

Printing a StatReporter Window

Using the Print Preview... Command

Using the [Print] Setup... Command

Using the Page Setup... Command


Using the StatAdvisor Pop-Up Menu

The pop-up menu that displays when you click the right mouse button on a StatAdvisor pane, contains three commands: Print..., Print Preview..., and Copy to Gallery....

The first two are self-explanatory; however, the latter is important because it lets you copy this interpretation into a StatGallery where it can add credibility to the results.


Using Special Features

STATGRAPHICS Plus contains six unique features.  They are all easy to use, yet powerful in the results they offer.

StatAdvisor

This tool lets you display and print a short and easy-to-understand interpretation of the reports and graphics in a statistical analysis.

StatFolios

StatFolios are designed to eliminate the need for re-entering data and information you use on a regular basis.

StatGallery

This tool lets you copy an unlimited number of text panes and up to 100 graphics panes on multiple pages so you can view or print them.

StatLink

This tool provides the ability to tie a StatFolio directly to a data source so when you open the StatFolio, the data source is automatically queried and the analyses in the StatFolio are automatically updated.

StatReporter

An intermediate tool between a notepad and a “complete” word processor, this feature allows you to combine reports, created using tabular options, with graphics and your own notes in a report format that is available from within STATGRAPHICS Plus.

StatWizard

This new tool aids new or casual users by helping them select the correct analysis for their data using one of two options: selecting analyses from a standard menu or choosing an option from a Quick Pic list.

Using the StatAdvisor

Using StatFolios

Using the StatGallery

Using StatLink

Using the StatReporter

Using the StatWizard


Using the StatAdvisor

The StatAdvisor provides statistical advice that

•	helps you interpret the results of an analysis

•	highlights possible flaws and problem areas

•	determines if the results are statistically significant

•	adds credibility to reports.

The interpretation is a simple explanation of the data-sensitive results; that is, the interpretation varies according to the variables you use in an analysis.  For example, when you use the StatAdvisor after you perform a Multiple Regression analysis, the interpretation indicates which variables appear to add significantly to the fitted model.

You can access the StatAdvisor by clicking the:

•	StatAdvisor icon button on the Application toolbar.

•	StatAdvisor taskbar in the Application window.

Displaying the StatAdvisor in Text Panes

Using the StatAdvisor Pop-Up Menu


Displaying the StatAdvisor in Text Panes

The View menu on the Application toolbar determines whether or not the StatAdvisor appears in the text panes.

To Display the StatAdvisor in Text Panes

1.	Choose VIEW... from the Menu bar to display the drop-down menu, which has three choices: Toolbar, Status Bar, and StatAdvisor.

2.	Click the option you want to use; a check mark appears in front of your selection.  In this case, click the StatAdvisor option.

The next analysis you run will display the StatAdvisor in the text pane.


Using StatFolios

StatFolios eliminate the need for creating macros for repetitive tasks, for re-entering data, or for re-creating an analysis you will use another time.  StatFolios let you perform the same analyses on numerous sets of data, or rerun analyses using new data or a new variable.  You can save an entire set of analyses, which also saves the variables, graphics settings, and results from the various options.  When you print the StatFolio, you can print one analysis at a time, or all of the analyses at once.

Using StatFolios greatly improves productivity because there is no need to repeat the same steps year after year.  Instead, you can use them to automatically update analyses to reflect new data.  When you save individual StatFolios with unique names, you can compare them yearly.  And copying StatFolios into a StatGallery makes it easy to compare year-to-year data and to view graphics side-by-side.

Creating a StatFolio


Using the StatGallery

The StatGallery is a flexible tool you use primarily for archival purposes, while the StatReporter lets you “publish” reports that can include a StatGallery plus text you customize for the report.  The StatGallery feature provides many benefits, including the ability to:

•	Archive graphics for any given dataset; for example, you can make a text change in the Analysis Summary and copy the summary into a StatGallery; return to the DataEditor, change the data, refresh the Analysis Summary by minimizing it to a taskbar button, then restore it.  The text pane will reflect the new data and the “custom” text will be gone.

•	Copy analyses to the StatGallery and use the Save Graph... command from the File menu to save the StatGallery as a metafile.

•	Perform the same analysis on the same data for a consecutive interval of time, save the analyses with unique names, then copy the same graph from the time intervals into the StatGallery and compare them side by side, perhaps on a monthly, quarterly, or yearly basis.

The StatGallery also lets you to copy up to 100 graphics pane and an unlimited number of text panes (on multiple pages) to panes in the StatGallery window so you can view or print them.

A StatGallery window consists of nine panes, known as splitter windows, which are arranged in three columns.  The panes are numbered in this order:

1     2     3

     4     5     6

   7     8     9

and grouped into columns in this order:

Column 1 = Panes 1, 4, 7

Column 2 = Panes 2, 5, 8

Column 3 = Panes 3, 6, 9

Four panes are usually visible, but using the Arrange Panes... command on the StatGallery pop-up menu allows you to use the StatGallery Options dialog box to change the arrangement of the panes and the columns.  The bars separating the nine splitter windows allow you to change the pane height and width.

The program copies the text and graphics panes you select to a secondary clipboard known as the Gallery clipboard, then allows you to place the panes in a variety of positions in the splitter windows within the StatGallery window.  You can place items on the Gallery clipboard from within an analysis, within the StatAdvisor, or within a Comments window.

Each splitter window can contain:

•	a single page of text from an analysis, the StatAdvisor, or the Comments window

•	a single graph or multiple overlaid graphs from an analysis.

To access the StatGallery, click the StatGallery icon taskbar button in the Application window.

Creating a StatGallery

Using the Buttons on the StatGallery Window

Modifying the Arrangement of Panes

Overlaying Graphs


Using the StatGallery Pop-Up Menu

This pop-up menu displays when you click the right mouse button on a pane in the StatGallery window.

Undo

Cancels the last action.

Cut

Removes the current contents of the pane and places it on the Gallery clipboard.

Copy

Copies individual StatGallery panes and places them on the Gallery clipboard or lets you paste them into the StatReporter or into other software applications.

Paste

Places the current contents of the Gallery clipboard into the selected pane.  If you placed the item on the clipboard using the Cut... or Copy... commands, the item retains the properties it had before you placed it on the clipboard.

Paste Link

Maintains a link between the text or graph you place into the StatGallery and the analysis.  If you make changes to the analysis, the linked text and the graphics pane are automatically updated.

Add Item

Opens a drawing toolbar that lets you to place lines, unfilled or filled rectangles and ellipses, or text on a graph.  Click one of the drawing buttons then click on the graph to use all but the last button.  The Text Options dialog box displays when you click the last button (it looks somewhat like the letter A); it lets you enter the text you want to add.  You must maximize the graphics pane before you can use the Add Item... command.  Note:  This option is available only for unlinked panes.

Modify Item

Allows you to select an option that you want to change on an unlinked graph, then access a graphics Options dialog box; for example, if you want to change the layout, points, or point fills, the Layout Options, Point Options, or Fills Options dialog box would display.

Delete Item

Deletes items you select in the StatGallery window; for example, lines, titles, legends, and added items.

Unlink

Unlinks text or graphs you linked to an analysis using the Paste Link... command.

Clear Page

Clears the contents of the current page of the StatGallery window.

Delete Page

Deletes the current page from the StatGallery window.

Insert Page

Inserts a 2x2 page before the current page of the StatGallery window.

Arrange Panes

Displays the StatGallery Options dialog box, which allows you to select different arrangements for the panes on the current page of the StatGallery.

Clear Gallery

Erases the entire contents of the StatGallery.

Print

Displays the Print StatGallery dialog box, which allows you to select printing options.  See Printing for information about this dialog box and printing in general.

Print Preview

Displays the Print Preview window, which allows you to view pages to see their format before you actually print them. See Printing for information about Print Preview.

Save StatGallery

Saves the current StatGallery.

Save StatGallery As

Saves the current StatGallery with a different name.

You can use the Copy to Gallery... command to place the text and graphs onto the Gallery clipboard, then use the Paste... or Paste Link... commands to copy the items into a splitter window.

Using the Paste Link... command automatically updates the StatGallery when you make changes within an analysis.  The program checks the analysis to see if changes were made to the data, then automatically updates the data already there.  For example, if you create a StatFolio one week and copy it into a StatGallery, then the next week make changes to that data, the program recalculates the analysis within the StatFolio, then automatically updates the StatGallery.


Creating a StatGallery

To Create a StatGallery

1.	Access the text or graphics pane you want to move into a StatGallery window.

2.	Click the left mouse button on the item you want to copy to the window, click the right to display the pop-up menu, then click the left on Copy Pane to Gallery... on the pop-up menu.

3.	Click the left button on the StatGallery icon taskbar button, then click Restore... on the pop-up menu to display the StatGallery window.

4.	Click the right button in one of the splitter windows to display the pop-up menu, then choose the task you want to perform.


Modifying the Arrangement of Panes

To Modify the Arrangement of Panes in a StatGallery Window

1.	Click the right mouse button on a StatGallery window.

2.	Click the left on Arrange Panes... on the pop-up menu to display the StatGallery Options dialog box.

The dialog box lets you choose from seven pane positions, or from column and row positions.  If you choose the By Column option, in the Row text boxes, enter the number of panes you want to appear in each of the three columns.

3.	Choose one of the arrangement options, then click OK to rearrange the panes.


Overlaying Graphs

Overlaying one graph on top of another in a StatGallery can be beneficial, especially in evaluating the results of an analysis.  For the overlay to be helpful, use graphs that have approximately the same scaling.

To Overlay Graphs

1.	Open and perform an analysis, choosing plots that will have approximately the same scaling.

2.	Click the Copy Pane to Gallery... command from the pop-up menu.

3.	Click the StatGallery taskbar button, then Restore... on the pop-up menu.

4.	Click either the Paste or Paste Link command to copy the first graph into the StatGallery.

5.	Minimize the StatGallery window.

6.	Create the second plot.

7.	Click the Copy Pane to Gallery... command on the pop-up menu.

8.	Click the StatGallery taskbar button, then Restore... on the pop-up menu.

9.	On the same pane that contains the first graph, click either the Paste or Paste Link command to copy the second graph into the StatGallery; the Paste to Gallery Options dialog box displays.

10.	Click the Overlay option, then OK to overlay the second plot on top of the first.


Using StatLink

StatLink is a key enhancement to STATGRAPHICS Plus.  It provides the ability to tie a StatFolio directly to a data source so when a StatFolio is opened, an automatic query begins and an automatic update is made to the analyses in the StatFolio.  In addition, the feature provides the capability to poll the data source automatically at regular intervals.

To use StatLink, from the menus, choose: FILE... STATLINK..., which displays a submenu of items:  Change Data Source, Display Status, Start Polling, Stop Polling, and Update Now.

Using the Change Data Source Item

Using the Display Status Menu Item

Using the Start and Stop Polling Menu Item

Using the Update Now Menu Item


Using the Change Data Source Item

This option displays the Open Data Source dialog box that lets you choose the

data source you want to use.  You have five options.

SG Plus DataSheet

Links data to a DataSheet.  To check to see if the link was made, use StatLinks to display the Status message box.

File

Displays the Open Data File dialog box so you can select the file you want to use.

ODBC Query

Displays the Select Data Source dialog box).  Use the dialog box to select the data source that describes the driver you want to connect to.  You can use any data source that refers to an ODBC driver that is installed on your computer.

Clipboard

Displays the Read Clipboard dialog box that lets you indicate if the variable names will be from the first row of data or if defaults should be created by the program.

Demo

Generates a single column of random numbers.

After you make a selection, the program reads the data and locks the DataSheet to prevent other users from making changes.


Using the Display Status Menu Item

This item displays a message box that shows the last time the data was read and the number of rows and columns obtained from the data source.


Using the Update Now Menu Item

This item immediately rereads the data and updates all the analyses.


Using the StatReporter

The StatReporter feature lets you “publish” a customized report.  Described as an “intermediate” tool between a notepad and a “complete” word processor, it lets you combine reports generated from tabular options, graphics, your own notes, and even interpretations from the StatAdvisor, into a report format.  Your report can be further customized by using Cut... and Paste... to rearrange the text and graphs, changing the style of the text font, as well as its point size and color.

When you make changes to graphs in an analysis, the changes are automatically made in the StatReporter.  You can also use the StatReporter to copy captions, annotate items, copy items, and work back and forth between Word and STATGRAPHICS Plus.

To access the StatReporter, click the StatReporter taskbar on the Application window.

The StatReporter window has its own special toolbar.  The items on the toolbar let you select a font and change its point size; use bold, italic, underlining, or color; indicate if the text will be aligned left, right, or centered; use bullets; add the data and time; and find words or phrases in the document you are creating.  The buttons follow standard Windows usage.

Using the StatReporter Pop-Up Menu

Creating a StatReport

Copying One Pane to the StatReporter


Using the StatReporter Pop-Up Menu

When you click the right mouse button on the StatReporter window, the StatReporter pop-up menu displays.

Undo

Cancels the last action.

Cut

Removes the current contents of the pane and places it on the Gallery clipboard.

Copy

Copies an element in the StatReporter and pastes it into other applications.

Paste

Places the current contents of the Gallery clipboard into the StatReporter.  If you placed the item on the clipboard using the Copy... command, the item retains the properties it had before you placed it on the clipboard.

Paste Special

Available only after you save a StatFolio.  Lets you insert StatFolios, pictures (metafile format), or unformatted text using the Paste Special dialog box.

Find

Displays the Find dialog box that lets you enter the word or phrase that you are trying to locate.  You can indicate if you want to match the whole word or if you want to match the case.  Find is case sensitive when you select Match Case; for example, to find StatAdvisor, be sure to specify Match Case and StatAdvisor.

Find Next

Finds the next occurrence of the last search.  The behavior is the same as that for the Find dialog box.

Replace

Displays the Replace dialog box that lets you enter the word or phrase you want to find and the word or phrase that it will be replaced with.  You can indicate if you want to match the whole word or if you want to match the case.

Print

Displays the Print dialog box, that lets you choose the print range, indicate the number of copies and if you want to print to a file.  If your printer allows you to collate, indicate if you want the copies collated.  This is a standard Windows Print dialog box.  For more information, see Printing.

Print Preview

Displays the Print Preview window that shows the first page in the Print Preview window.  For more information, see Printing.

Save StatReporter

Saves the current document.

Save StatReporter As

Saves the current document using a different name.

Clear StatReporter

Clears the StatReporter window.


Using the StatWizard

The StatWizard feature is especially useful to novice or new users who need help matching data with analyses.  The default behavior is that the StatWizard opens every time you open STATGRAPHICS Plus.  To turn it off, click the Show the StatWizard at Startup checkbox on the initial dialog box. One of the preliminary dialog boxes lets you choose analyses from a standard menu or from a Quick Pic list.  Depending on the task you choose, a different series of dialog boxes will display.

Selecting Analyses from the StatWizard Standard Menu

Selecting Analyses from the StatWizard Quick Pic List


Creating a StatFolio

To Create a StatFolio

1.	Open and perform an analysis using the tabular and graphical options.

2.	Save the analysis by using FILE... SAVE AS... SAVE STATFOLIO AS..., which displays the Save StatFolio As... dialog box.

3.	Type a name for the StatFolio in the File Name text box, and make any necessary changes, such as the directory and drive in which the file will reside.

4.	Click Save to save the StatFolio.


Using the Buttons on the StatGallery Window

The area under the StatGallery title bar displays the current page number and four page buttons: Next Page, Prev Page, First Page, and Last Page.

Next Page

Adds another page to the StatGallery window.

Prev Page

Returns to the previous page of the StatGallery.

First Page

Returns to the first page of the StatGallery.

Last Page

Moves to the last page of the StatGallery.


Creating a StatReport

To Create a StatReport

1.	Access the text or graphics pane you want to move into a StatReporter window.

2.	Click the right mouse button, then choose Copy Analysis to StatReporter... from the StatReporter pop-up menu.

3.	Click the left button on the StatReporter icon taskbar button, then click Restore... on the pop-up menu to display the StatReporter with the text and graphics panes from the analysis copies into the window.


Using the Start and Stop Polling Menu Item

The first item displays the Set Update Interval dialog box, which lets you choose the duration of time between updates.  After it reads the data, the program automatically updates the data in all the views of the Analysis windows and StatGalleries.

The Stop Polling menu item immediately and automatically halts the polling.


Copying One Pane to the StatReporter

To Copy One Pane to the StatReporter

1.	Access the text or graphics pane you want to move into a StatReporter window.

2.	Click the right mouse button, then choose Copy... from the pop-up menu.

3.	Click the left button on the StatReporter icon taskbar button, then click Restore... on the pop-up menu to display the StatReporter window.

4.	Click the right button, choose Paste... or Paste Special... from the pop-up menu.  The analysis pane is copied into the StatReporter.


Selecting Analyses from the StatWizard Standard Menu

When you choose this option, you complete a series of dialog boxes that describe the data you are using.  Because the dialog boxes are data-driven, they are too numerous to document separately, but four that are typical are described here.

The StatWizard - Data Selection dialog box lists the names of the variables in the file you have chosen.  You are asked to enter a variable name for the Response Variable, Quantitative Explanatory Factor, the Categorical Explanatory Factor, and the Labels.  You also choose the type of variable you are using — general numeric, counts (integers), proportions (0-1), or categorical.

You use the StatWizard - Row Selection dialog box when you want to analyze all the rows in the DataSheet or when you want to select a subset of the rows.

The StatWizard - Variable Transformations dialog box is used when it is necessary to transform data to achieve an approximate normality.  You first choose the name of the variable you want to transform, then choose the method that will be used to perform the transformation.

The StatWizard - Analysis Selection dialog box displays the type of variable you have chosen and asks you to choose the analyses you want to perform.


Selecting Analyses from the StatWizard Quick Pic List

The Quick Pic list contains 12 tasks, such as “Summarize a Single Column of Data,” “Compare Two Data Columns,” and “Fit a Multiple Regression Model.”

When you choose a task, then click OK, the appropriate Analysis dialog box displays.  For example, when you choose, “Summarize a Single Column of Data,” the One-Variable Analysis dialog box displays.


Resizing Graphs

You can change the vertical, horizontal, and/or diagonal dimensions of a graph to make it larger or smaller, wider or thinner.

To Resize a Graph

1.	Maximize the graph, then click to choose it; markers appear at the corners of the graph.

2.	(a) For Vertical Changes: Place the mouse pointer on the top or bottom of the graph.

(b) For Horizontal Changes: Place the mouse pointer on either side of the graphs.

(c) For Diagonal Changes: Place the mouse pointer on any corner of the graph.

When the shape of the pointer changes to a double-headed arrow, click and hold down the left button.

3.	Drag the arrow until the graph is the size and/or shape you want, then release the button.

4.	Repeat this process as many times as necessary to achieve the size you want.


Accessing and Opening Graphs

After starting STATGRAPHICS Plus, open the data file, then choose an analysis from the menus on the Application toolbar.  Although you can access and open graphs using several methods, the steps below provide general instructions.

To Access and Open Graphs

1.	From the Plot…, Describe…, Compare…, Relate…, or Special… menus, choose the analysis you want to use.

2.	Complete the Analysis dialog box, then click OK to display the Analysis Summary in a text pane in the Analysis window.

3.	Click the Graphics Options button on the Analysis toolbar to display the Graphics Options dialog box.

4.	Choose the graphs you want to create, then cllick OK to display the graphs in the graphics panes of the Analysis window.


Working with Graphs and Graphics Options

Statistical graphics, like statistical calculations, are only as good as what goes into them.  Excellent statistical graphics should not only communicate complex ideas clearly, precisely, and efficiently, they should also provide powerful analytical tools for exploring the data.  Tufte (1983) says that graphical displays should:

•	show the data

•	cause [you] to think about substance rather than methodology

•	present many numbers in a small space

•	make large datasets coherent

•	encourage the comparison of different pieces of data

•	reveal data at several levels of detail.

The first topic explains how you access, open, and save graphs.  The second discusses the Graphics Options tabbed dialog box that replaces the multiple graphics dialog boxes in previous versions of STATGRAPHICS Plus.  Other topics explain how you use buttons to add text; jitter, brush, smooth, identify, display, include, and exclude points; and how you perform basic graphics tasks, such as resize a graph and use zoom features.  The final topic explains how you set system-wide graphics preferences and how you set and save user preference profiles.

See also

Accessing, Opening, and Saving Graphs

Changing and Enhancing Graphs

Performing Miscellaneous Graphics Tasks

Setting System-Wide Graphics Preferences

Setting and Saving User Preference Profiles


Accessing, Opening, and Saving Graphs

After starting STATGRAPHICS Plus, open the data file you want to use, then choose an analysis from the menus on the Application toolbar.

Accessing and Opening a GraphAlthough you can access and open graphs using several methods, the steps below outline one easy method.

To Access and Open a Graph

1.	Choose the analysis you want to use from the Plot, Describe, Compare, Relate, or Special menus to display the appropriate Analysis dialog box.

2.	Complete the Analysis dialog box, then click OK to display a text and a graphics pane in an Application window.

Saving a GraphThere may be times when you want to save a graph in a standard format so you can re-create it in other software programs.  Currently, STATGRAPHICS Plus only allows you to save graphs in a metafile format (*.wmf).  This format saves the image as well as all the information you used to create the graph.  Use the Save Graph dialog box to save the graph.

To Save a Graph

1.	Double-click the graph to maximize it.

2.	Choose FILE... SAVE GRAPH... from the Menu bar to display the Save Graph dialog box.

3.	Complete the dialog box, then click Save... to save the graph.


Changing and Enhancing Graphs

The most effective way to describe, explore, and/or summarize a set of numbers is to look at pictures of the numbers.  “A picture is worth a thousand words” has particular significance in statistics because a graph or chart provides the simplest and most efficient display of data.  Being able to customize graphs and charts through the use of points, lines, numbers, symbols, words, and color make them the simplest and most powerful way to visualize statistical information.

After you create and view a graph, you may want to change it, add information to it, or enhance it in other ways.  You can change or enhance all the attributes that make up a graph such as its title, legends, axes, grid, points, or lines.

See also

Using the Graphics Options Tab Dialog Box


Using the Graphics Options Tab Dialog Box

STATGRAPHICS Plus contains a Graphics Options dialog box you use to access different pages through the use of tabs.  The tabs are graph-specific; for example, if you are creating a Piechart and want to make changes to it, you first create the Piechart, then access the Graphics Options dialog box, which displays with all the Tab Pages applicable for modifying a Piechart.

If you make changes to a graph, leave any tab page, then decide you do not want to make the changes, clicking the right mouse button, then Undo on the pop-up menu, reverses all the changes.

See also

Using the Fill Tab Page

Using the Grid Tab Page

Using the Label Tab Page

Using the Layout Tab Page

Using the Legend Tab Page

Using the Line Tab Page

Using the Point Tab Page

Using the Profile Tab Page

Using the Right Axis Tab Page

Using the Spinning Tab Page

Using the Text Tab Page

Using the Top Title Tab Page

Using the X-axis, Y-Axis, and Z-Axis Tab Pages


Using the Fill Tab Page

If you view and print a graph in color, you can coordinate the color of the outline and fill area of a graph.  If you view and print the graph in black and white, you can use different fill patterns to achieve the same effect.

You use the Fill tab page on the Graphics Options dialog box to change the style and color of fill patterns to distinguish the bars, boxes, wedges, and other fill areas on a graph.

See also

Changing the Style and Color of Fill Patterns


Using the Grid Tab Page

A grid, which is a series of lines that extend from an axis to an area on a plot, helps guide your eye from a point on a graph to its corresponding value or category on an axis.  Using the proper grid, or using no grid, can make points easier to see, which visually enhances a graph.

The Grid tab page allows you to change the appearance of a grid by changing its direction, changing the type of the lines on it, changing its color and/or line thickness, and indicating if a back grid should display on three-dimensional plots.

See also

Changing the Direction, Style, and Color of Grid Lines


Changing the Style and Color of Fill Patterns

To Change the Style and Color of Fill Patterns

1.	Double-click the graph to maximize it.

2.	Place the mouse pointer on a fill area on the graph.

3.	Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box, which should open to the tab page that corresponds to the area of the graph you chose in Step 2.

4.	In the Fill options portion of the dialog box, click the number of the area you want to change.

5.	Choose one of the eight Fill styles: Empty (no fill pattern), Solid, Horizontal Lines, Vertical Lines, Left- and Right-Facing Diagonal Lines, Cross-Hatch Lines, or Diagonal Cross-Hatch Lines.

6.	For the Color option, click either Fill or Outline to indicate whether you want color applied to the fill pattern or to the outline of the filled area.

7.	Click the Colors... button to display the Color dialog box.


Changing the Direction, Style, and Color of Grid Lines

To Change the Direction, Style, and Color of Grid Lines

1.	Double-click the graph to maximize it.

2.	Place the mouse pointer on an empty portion inside the graph frame.

3.	Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box.  Click the Grid tag page.

4.	Choose one of the four Direction styles: Horizontal, Vertical, Both, or None.

5.	Click the Colors… button to display the Color dialog box.

6.	Choose the color you want to use.

7.	Place the mouse pointer on the slider control for the line thickness and move the control from Thinnest to Thickest to change the width of the line.  Release the control.

Note:  The line thickness feature is available only for solid lines.

8.	If the Back Grid on 3D Plots option is active and you are using a 3D plot that would look better with a back grid, click the box.

9.	Click Apply, then OK on the Grid tab page to process these changes.


Using the Label Tab Page

The Label tab page is available for plots, such as the Pareto Chart in the Quality and Design product, for which you want to create labels.  Labels refer to text that appears on a graph as an identifier.

A series of text boxes appear on the page, which allow you to enter names for the labels.  The letter between the braces, for example, {A}, is an internal system reference to variable names.  The Fonts... command lets you change the font.

See also

Changing the Name of a Label


Changing the Name of a Label

To Change the Name of a Label

1.	Double-click the graph to maximize it.

2.	Move the mouse pointer to the label you want to change.

3.	Click the left button to choose the name of the label; markers appear at the corners of the chosen label.

4.	Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the Label tab page.

5.	In the Label text box, enter the new name for the label, then click OK to process the change.

6.	Continue entering names until you finish.

7.	Click the Fonts... button to display the Windows Font dialog box.

8.	Choose the font, font style, size, color, and other attributes, then click OK.

9.	Click Apply and OK on the Label tab page to process the changes.


Using the Layout Tab Page

The Layout tab page allows you to customize a graph by choosing a style and color for the tickmarks, the type of frame that will surround the graph, the color of the background and/or border of the graph, and the thickness of the axis line.

See also

Changing Tickmarks

Changing the Background and/or Border of a Graph

Changing the Shape of a Graph


Changing Tickmarks

To Change Tickmarks

1.	Double-click the graph to maximize it.

2.	Place the mouse pointer on an empty portion inside the graph frame.

3.	Click the left button, then the right on Graphics Options on the pop-up menu to display the Graphics Options dialog box opened to the Layout page.

4.	Click the option that corresponds to the axis whose tickmarks you want to change (X-, Y-, or Z-Axis).

5.	Choose one of the three Tickmark styles: No Tickmarks, Tickmarks Inside, or Tickmarks Outside.

6.	Click the Colors... button to display the Color dialog box.

 7.	Choose the color you want to use, then click OK on the Color dialog box.

8.	Click Apply, then OK on the Layout tab page to process all the changes.


Changing the Background and/or Border of a Graph

To Change the Background and/or Border of a Graph

1.	Double-click the graph to maximize it.

2.	Place the mouse pointer on an empty portion inside the graph frame.

3.	Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box, opened to the Layout page.

4.	Click either the background or the border option.

5.	Click the Colors... button to display the Color dialog box.

6.	Choose the color you want to use, then click OK on the Color dialog box.

7.	Click Apply, then OK on the Layout tab page to process all the changes.


Changing the Shape of a Graph

To Change the Shape of a Graph

1.	Double-click the graph to maximize it.

2.	Place the mouse pointer on an empty portion inside the graph frame.

3.	Click the left button, then the right on Graphics Options on the pop-up menu to display the Graphics Options dialog box opened to the Layout tab page.

4.	Choose one of the two shape styles: L-Shape or Square.

5.	Click Apply, then OK on the Layout tab page to process the change.


Using the Legend Tab Page

Many of the analyses you use to plot data for two or more variables contain a legend; for example, a Multiple X-Y-Z Plot or a Barchart.  A legend lists and explains the symbols on a graph.

You use the Legend tab page on the Graphics Options dialog box to change the title of a legend, change the names of the individual variables that apply to a legend, and to change the font attributes such as the style, point size, and color.  A series of text boxes appear on the page, which allow you to enter names for the legends.  The letter between the braces, for example, {A}, is an internal system reference to variable names.  The Fonts... command lets you change the font.

See also

Changing a Legend Title and Variable Names


Changing a Legend Title and Variable Names

To Change a Legend Title and Variable Names

1.	Double-click the graph to maximize it.

2.	Move the mouse pointer to the legend title you want to change.

3.	Click the left button, then the right on Graphics Options on the pop-up menu to display the Graphics Options dialog box opened to the Legend tab page.

4.	Enter a title into the Title text box.

5.	Click in the {A} Legend text box, then enter a name for the first variable.

6.	Continue entering names until you finish.

7.	Click the Fonts... button to display the Windows Font dialog box.

8.	Choose the color you want to use, then click OK.

9.	Click Apply and OK on the Legend tab page to process the changes.


Using the Line Tab Page

Changing the look of the lines that appear on a graph is useful when you need to enhance and clarify the graphical results.

You use the Line tab page on the Graphics Options dialog box to set the style and color of the lines on a graph.

See also

Changing the Type, Thickness, and Color of Lines


Changing the Type, Thickness, and Color of Lines

To Change the Type, Thickness, and Color of Lines

1.	Double-click the graph to maximize it.

2.	Place the mouse pointer on the line you want to change.

3.	Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the Line tab page.

4.	In the Line options portion of the dialog box, click the number of the line you want to change.

5.	Choose one of the five Line styles: Solid, Dashed, Dotted, Dash-Dot, or Dash-Dot-Dot.

6.	If you chose a Solid line, place the mouse pointer on the slider control for the line thickness and move the control from Thinnest to Thickest to change the width of the line.  Release the control.

7.	Click the Colors... button to display the Color dialog box.

8.	Choose the color you want to use, then click OK.

9.	Click Apply, then OK on the Lines tab page to process the changes.


Using the Point Tab Page

When you create two- and three-dimensional scatterplots or similar types of plots, it is helpful to be able to change the shape, size, and color of the individual points.

You use the Point tab page on the Graphics Options dialog box to set the style and color of points.

See also

Changing the Shape, Size, and Color of Points


Changing the Shape, Size, and Color of Points

To Change the Shape, Size, and Color of Points

1.	Double-click the graph to maximize it.

2.	Place the mouse pointer on the point you want to change.

3.	Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the Points tab page.

4.	In the Point options portion of the dialog box, click the number of the point you want to change.

5.	Choose one of the eight Point styles: Square, Plus, X, Star, Diamond, Up Arrowhead, Down Arrowhead, or Circle.

6.	Click the Fill Point check box or leave it blank to indicate if you want filled points.  An unchecked box (the default) means the points will not be filled.

7.	Place the mouse pointer on the slider control for the Point Size and move the control from Smallest to Largest to change the size of the point, then release the control.

8.	Place the mouse pointer on the slider control for the Point Thickness and move the control from Thinnest to Thickest, then release the control.

9.	Click the Colors... button to display the Color dialog box.

10.	Choose the color you want to use, then click OK.

11.	Click Apply, then OK on the Points tab page to process the changes.


Using the Profile Tab Page

The Profile tab page on the Graphics Options dialog box lets you set up and save graphics profiles.  The first two options, System (Color, White Background) and System (Color, Dark Background) describe the two predefined choices for choosing the color and background of the graphs you produce; the choices are self-explanatory.  System (Black and White) means that the graphs will always display in black and white format.

You can set up or edit up to 12 user profiles.  When you set them up or edit them, you can either use numbers, letters, names, or a combination of them to create the name of the profile.

See also

Setting Up a User Profile


Setting Up a User Profile

To Set Up a User Profile

1.	Access the Graphics Options dialog box.

2.	Choose your graphics preferences using the tabs on the Graphics Options dialog box.

3.	Return to the Profile tab page; use Load..., Save..., or Save As....  Load loads the profile; Save, saves it; and Save As saves the profile as a specific name.

For example, you might set up one profile for scatterplots, and another one for 3-dimensional plots.  After choosing your preferences for each type of plot:

4.	Click the first User # option.

5.	Click Save As... to display the Save Profile dialog box.

6.	In the text box, type Scatterplot to save the profile for scatterplots; click OK; the program displays the current graphics settings saved in a saved profile message.  Click OK.

7.	Repeat Steps 4, 5, and 6, using 3-D Plots as the name for the User #2 option.  When you click OK, names are displayed on the Profile tab page as the names for the two user options. If you want to make one of the profiles the default:

8.	Click the option button next to the setting you want to make the default.

9.	Click Make Default..., then Load.... The D default indicator to the left of the option buttons, moves to the left of the new profile, indicating the default.


Using the Right Axis Tab Page

Some plots, such as the Multiple X-Y-Z Plot, contain a right axis.  The Right Axis tab page lets you change the scale for this axis.

Changing the Scaling for the Right Axis


Changing the Scaling for the Right Axis

To Change the Scaling for the Right Axis

1.	Double-click the graph to maximize it.

2.	Position the mouse pointer on one of the values on the right axis.

3.	Click the left button to choose the axis; markers appear at the corners of the axis.

4.	Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the Right Axis tab page.

5.	In the From text box, enter a number that will determine the minimum value for the axis.

6.	In the To text box, enter a number that will determine the maximum value for the axis.

7.	In the By text box, enter a number that will determine the distance between each tickmark on the axis scale.

8.	In the Skip text box, enter the number of tickmarks that should be skipped when the axis is created.

9.	Use the No Power check box to indicate if the axis scale for the tickmarks should be calculated using a power of 10.

10.	Use the Log check box to indicate if the axis scale for the tickmarks should be calculated using decimal log scaling.

11.	Use the Hold check box to indicate if the current scaling should be retained, even if you change the data in the Analysis dialog box.

12.	Click the Tickmark Fonts... button to display the Font dialog box, then choose the font you want to use for the tickmarks, and click OK.

13.	Click Apply and OK on the Right Axis tab page to process the changes.


Using the Spinning Tab Page

You can view three-dimensional graphs from different horizontal and vertical angles by spinning a graph to change the location of the viewpoint.  To set preferences for spinning, use the Spinning tab page of the Graphics Options dialog box.

You can set your preferences to indicate if text should be displayed on the graph while it is spinning; and to enter values that control the number of frames per second (fps) and the degrees per frame the graph will display while it is spinning.

To actually spin the graph, click the Smooth/Rotate button on the Analysis toolbar.

See also

Spinning Graphs


Using the Text Tab Page

On certain graphs or if you add text to a graph, the Text tab page allows you to edit the text.

See also

Adding Miscellaneous Text to a Graph


Adding Miscellaneous Text to a Graph

To Add Miscellaneous Text to a Graph

1.	Double-click the graph to maximize it.

2.	Place the mouse pointer on an empty portion inside the graph frame.

3.	Click the left button, then the right on Graphics Options on the pop-up menu to display the Graphics Options dialog box opened to the Text tab page

4.	In the Text text box, enter the text you want to add to the graph.

5.	Click one of the Direction options to choose the way the text will display; either horizontally or vertically.

6.	Click the Fonts... button if you want to make changes to the font or its attributes.

7.	Click OK to process the changes.


Using the Top Title Tab Page

Top title refers to the title that displays at the top of a graph.  You can change the entire name of the title or add or delete words from it.

You use the Top Title tab page in the Graphics Options dialog box to:

•	make the text changes

•	indicate the direction in which the title will appear

•	change fonts for the one- or two-line title

•	indicate if the font should be changed for both titles if you are using a two-line title.

See also

Changing the Top Title of a Graph


Changing the Top Title of a Graph

To Change a Top Title

1.	Double-click the graph to maximize it.

2.	Place the mouse pointer on the title you want to change.

3.	Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the Top Title tab page.

4.	In the first Title text box, enter either a new title or make changes to the current title.

Note:  If the plot you are working with contains a title on a second line, the second text box will be activated and you can make changes there also.

5.	Click the Vertical check box if you want the title to display vertically on the graph.  If the box is checked, the title will display in that direction

6.	Click the Line 1 Fonts... button to display the Font dialog box you use to change the font for the text in line 1.

7.	Click the Line 2 Fonts... button to display the Font dialog box you use to change the font for the text in line 2.

8.	Click the Change Font for All Titles check box if you want to change to a font that will be used for all the titles on the graph.

9.	Click Apply and OK to process the changes.


Using the X-Axis, Y-Axis, and Z-Axis Tab Pages

The scales against which a graph is plotted are known as axes.  The X- Y-, and Z-Axis tab pages are identical except for defaults.

You must change each axis independently; for example, if you want to make changes to the X-axis and the Y-axis, you must first access the X-Axis tab page, make the necessary changes, then access the Y-Axis tab page and make the necessary changes on that page.

See also

Changing Axis Scaling


Changing Axis Scaling

To Change the Axis Scaling

1.	Double-click the graph to maximize it.

2.	Position the mouse pointer on one of the values on the axis whose scale you want to change (the X-, Y-, or Z-axis).

3.	Click the left button to choose the axis; markers appear at the corners of the chosen axis.

4.	Click the left on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the n Axis tab page (n indicates the chosen axis).

5.	Enter a title for the axis in the Title text box.

6.	Indicate if the title should display vertically or horizontally.

7.	In the From text box, enter a number that will determine the minimum value for the axis.

8.	In the To text box, enter a number that will determine the maximum value for the axis.

9.	In the By text box, enter a number that will determine the distance between each tickmark on the axis scale.

10.	In the Skip text box, enter the number of tickmarks that should be skipped when the axis is created.

11.	In the No Power check box, indicate if the axis scale for the tickmarks should be calculated using a power of 10.

12.	In the Log check box, indicate if the axis scale for the tickmarks should be calculated using decimal log scaling.

13.	In the Hold check box, indicate if the current scaling should be retained, even if you change the data in the Analysis dialog box.

14.	Click the Title Fonts... button to display the Font dialog box you use to change the font for the title.

15.	Click the Tickmark Fonts... button to display the Font dialog box you use to change the font for the tickmarks.

16.	Click Apply and OK on the <M>n Axis tab page to process the changes.


Using Graphics Task Buttons

In addition to using the Graphics Options tab pages to change and enhance graphics, you can use the special graphics task buttons located on the Analysis toolbar: Add Text, Jittering, Brushing, Smooth/Rotate, Set Points Labels, Locate Labels, Locate Row, and Include/Exclude.

See also

Using the Add Text Button

Using the Jittering Button

Using the Brushing Button

Using the Smooth/Rotate Button

Using the Set Point Labels Button

Using the Exclude/Include Button


Using the Add Text Button

The Add Text button becomes available when you maximize a graph in an Analysis window.  When you click the button, the Text Options dialog box displays that lets you enter the miscellaneous text you want to add and indicate the direction in which the text will display.

Use the Text tab page on the Graphics Options dialog box to edit the text.


Using the Jittering Button

The Jittering button is available when you maximize a Scatterplot in an Analysis window.  When you plot data that contain many repeated values, it is likely that some points will occupy the same position.  This causes two or more points to be plotted one on top of the other, which makes the scatterplot difficult to interpret.

Jittering prevents this and also allows you to see the density of the points in various locations on the plot.  Jittering adds a small, random offset to each point.  You can control the amount of horizontal and/or vertical offset that will affect each point. Use the Jittering dialog box to set the offsets.

See also

Jittering Points on a Graph


Using the Brushing Button

The Brushing button becomes available when you maximize a Scatterplot in an Analysis window.  Clicking the button displays the Brushing dialog box, which lets you choose the variable that will be used to brush the points.

Brushing shows the influence an added variable has on the data or a range of data.  The added variable is shown in red.  The red points should fall between the intervals if the left value is less than the right.  If the right value is less than the left, the red points should fall outside the intervals.

The Brushing dialog box lets you choose or enter the name of a variable that will be used to brush the data.  Label and Row text boxes on the Analysis toolbar are also replaced with horizontal and vertical slider controls and text boxes that display the minimum and maximum values.

See also

Brushing Points on a Graph


Using the Smooth/Rotate Button

This button lets you smooth points on a plot or rotate (spin) a three-dimensional graph; it is available when you maximize a two- or three-dimensional plot in an Analysis window.

The Spinning tab page on the Graphics Options dialog box explains how you use the spinning option and lets you set preferences for it.  This section explains how you use the button to smooth points.

The pattern of points on two-dimensional plots, such as an X-Y Scatterplot, is often easier to see if you use a smoothing technique.  The goal of smoothing is to reduce the fluctuations in the data to make long-term trends more apparent.

You use the Smooth/Rotate button and the Scatterplot Smoothing Options dialog box to choose smoothing options for these types of scatterplots.

Each of the smoothing options uses a slightly different method to estimate the relationship between Y and X.  For each value of X, the program chooses k points in the neighborhood of X, where k is determined from the smoothing fraction you enter into the Scatterplot Smoothing Options dialog box.  For example, if the smoothing fraction is 30 percent, and there are 100 observations, 30 points in the neighborhood of X are chosen.  The Y values at the chosen points are used to estimate the smoothed line for that value of X.  The first two steps are repeated for each value of X.

The smoothing options differ in how they define the “neighborhood” of X and also in the way they estimate the smoothed line.

See also

Smoothing Points on a Graph


Using the Set Point Labels Button

This button becomes available when you maximize a Scatterplot in an Analysis window.  Clicking the button displays the Point Identification dialog box that you use to enter or choose the name of a variable that will be used to identify the point.

When you create two- and three-dimensional scatterplots or similar types of plots, it is helpful to be able to identify and display individual points.  For example, you may want to identify a point by its row number or by its label.  In addition to displaying the values you use to create the plot (for example, the X-, Y-, and Z-axes), you can also choose another variable to use as a label for each of the points.  You can also highlight a row in the DataSheet that corresponds to a point on a plot to see other related values in the dataset.

See also

Identifying a Points by Its Label

Displaying a Label by Its Point

Locating a Point by Its Row and Axis


Using the Exclude/Include Button

This button becomes available when you maximize a scatterplot in an Analysis window.  Clicking the button excludes from the analysis, the point you choose.  When you choose a point, then click the button, the program marks the point with a colored X.  You can exclude as many points as you like.  If you choose a point that you previously excluded and click the button, that point is included in the analysis.

Note:  This button is available for scatterplots where the point values are used in a calculation.


Identifying a Point by Its Label

To Identify a Point by Its Label

1.	Double-click the plot to maximize it.

2.	Click the Set Point Labels button on the Analysis toolbar (the scatterplot with a question mark) to display the Point Identification dialog box.

3.	Enter or choose the name of the variable that contains the labels for the points.

4.	Click OK to redisplay the plot.

5.	Enter the name of the label in the Label (Lbl:) text box on the Analysis toolbar.  You must enter the name exactly as it appears in the variable.  For example, if you want to see the points that represent names of automobiles, choose the make variable, then enter the name of an automobile (Ford, for instance) in the Label text box.

6.	Click the Locate Label button on the Analysis toolbar (the binoculars to the right of the Label (Lbl:) text box.  The color or shape of the points that represent the label whose name you entered, changes and the row number of the DataSheet displays in the Rows text box.  If more than one point has the same label, more than one point will change; however, the row number will not display in the Row text box.

If you want to identify points for additional labels, repeat Steps 3, 4, and 5, except enter the name of a different label in the Label text box.


Displaying a Label by Its Point

To Display a Label by Its Point

1.	Double-click the plot to maximize it.

2.	Click the Set Point Labels button on the Analysis toolbar to display the Point Identification dialog box.

3.	Enter or choose the name of the variable that contains the labels for the points.

4.	Click OK to redisplay the plot.

5.	Click the point whose label you want to display; the label for the point appears in the Label (Lbl:) text box.

If you want to display additional labels for the same point, repeat Steps 2 and 3, except enter or choose a different variable name on the Point Identification dialog box.

To display several labels at the same time, you can use operators in the dialog box.  For example, for a file that contains the makes and models of cars, you could enter:

Juxtapose (make,model)

to display both the make and model of the chosen point.  For more information on operators, see Appendix B, Using Operators, in the User Manual or Operators in the Reference portion of Online Help.


Locating a Point by Its Row and Axis

To Locate a Point by Its Row and Axis

1.	Double-click the plot to maximize it.

2.	Click the left mouse button on a point to choose it.  As you do this, a pop-up box displays that contains the Row number then the point's location on the axis or axes.

This behavior is similar to that of the Locate... command on the Graphics pop-up menu.  In the latter case, when you click Locate..., a light blue line appears on the plot.  You can move the line in either a left or right direction to see the location of the points in the pop-up box.


Smoothing Points on a Graph

To Smooth Points

1.	Double-click the plot to maximize it.

2.	Click the Smooth/Rotate button on the Analysis toolbar to display the Scatterplot Smoothing Options dialog box.

3.	Choose one of the smoothing methods: None, Running Means, Running Lines, Locally Weighted Regression, or Robust Lowess.

4.	Enter a number into the Smoothing Fraction text box that will be used to determine the size of the smoothing window.

5.	Click OK to apply the smoothing method and redisplay the plot.


Brushing Points on a Graph

To Brush Points

1.	Double-click the plot to maximize it.

2.	Click the Brushing button on the Analysis toolbar (a paint brush with scattered points) to display the Brushing dialog box.

3.	Choose or enter the name of the variable that will be used for brushing.

4.	Click OK to redisplay the plot with the values for the added variable shown on the plot in red.  Notice that the Label and Row text boxes on the Analysis toolbar have been replaced with two slider controls and text boxes.

5.	Move the slider controls or enter values into the text boxes to minimize or maximize the amount of brushing.  The minimum and maximum values appear in the text boxes next to the slider controls.  As you move the slider controls, the values for the brushing variable increase or decrease.

Note:  This feature is not available if you choose the black and white option on the Edit Preferences dialog box,


Jittering Points on a Graph

To Jitter Points

1.	Double-click the plot to maximize it.

2.	Click the Jittering button on the Analysis toolbar (the button with four outward-pointing arrows) to display the Jittering dialog box.

3.	Click and move the slider control horizontally and/or vertically until you reach the point on the bar that represents the offset you want to use for the points.  Release the slider control.

4.	Click OK to redisplay the plot with the points jittered.


Performing Miscellaneous Graphics Tasks

In addition to using the tab pages on the Graphics Options dialog box to modify graphs, you can also perform other miscellaneous graphics tasks, such as repositioning text, resizing graphs, and using the Zoom and Locate features.

See also

Repositioning Text on a Graph

Resizing a Graph

Using Zoom Features


Repositioning Text on a Graph

You can reposition text you added to graphs or existing text.

To Reposition Text on Graphs

1.	Double-click the graph to maximize it.

2.	Move the mouse pointer to the text you want to reposition.

3.	Click the left button to choose the text; markers appear at the corners of the chosen text.

4.	Click and drag the text to its new position.

5.	Release the mouse button to release the markers, then click the button a second time outside the text area to remove the markers.


Resizing a Graph

You can change the vertical, horizontal, and/or diagonal dimensions of a graph to make it larger or smaller.

To Resize a Graph

1.	Double-click the graph to maximize it, then click the graph to choose it; markers appear at the corners of the graph.

2.	For Vertical Changes: Place the mouse pointer on the top or bottom of the graph, then click.

For Horizontal Changes: Place the mouse pointer on either side of the graph, then click.

For Diagonal Changes: Place the mouse pointer on any corner of the graph, then click.

3.	When the shape of the pointer changes to a double-headed arrow, drag the mouse until the graph is the size and/or shape you want, then release the button.

Repeat this process as many times as necessary to achieve the size you want.


Using Zoom Features

The Graphics pop-up menu contains two commands that make it easier to view graphs: Zoom In... and Undo Zoom....

To Use Zoom In...

1.	Access a plot that contains points such as a Scatterplot.

2.	Click the right button on the portion of the graph that contains the points you want view at a closer range, then click Zoom In... from the pop-up menu.  When you make the selection; a check mark appears in front of the command name and enables a zoom rectangle or rubber-band box.

3.	Draw a rectangle around the points you want to view.  You can use Zoom In... 10 times in a sequence.

To Use Undo Zoom...

1.	Access the Graphics pop-up menu, then click Undo Zoom... to cancel the action.

You can use Undo Zoom... in a sequence of 10 times.  When you reach the maximum number, the Undo Zoom... feature is grayed out on the pop-up menu.


Using the Locate Feature

You access the Locate feature from the right mouse button Pop-Up menu.  When you choose the Locate menu item, the program places a single line on graphs that have a scalable X-axis, or two lines that form a cross-hair, on graphs that have both a scalable X-axis and a scalable Y-axis.


Setting System-Wide Graphics Preferences

The Edit Preferences dialog box contains options you use to choose specific system-wide preferences about the graphics you create.  For example, you can choose to always maintain a 1:1 aspect ratio, always display graphs in black and white, and indicate the number of decimal places that will appear in numeric legends.

These options appear in the Graphics portion of the Edit Preferences dialog box, which you access from the Edit menu.  The settings you choose affect all the analyses and remain in effect system-wide until you change them from this dialog box or override them.


Setting and Saving User Preference Profiles

Often the type of task you perform on a regular basis requires that you set specific preferences for the graphics you produce.  The Profile tab page on the Graphics Options dialog box allows you to choose and save your preferences.

The Profile page contains options you use to choose preferences about the graphics you create.  You can indicate if the profile will display, system-wide, graphs in color with a white background, in color with a dark background, or black and white.  You cannot override the black and white setting indicated on the Edit Preferences dialog box.


Reference Information

These topics answer common questions, answer Year 2000 readiness questions, provide a guide to shortcuts you can use from the keyboard, explain operators and how to use them.  There are two glossaries: an alphabetical statistical glossary and a visual glossary of the buttons and icons in the program.

Commonly Asked Questions

Year 2000 Readiness Disclosure

Keyboard

Operators

Statistical Glossary

Visual Glossary


Technical Support

Manugistics offer many types of support to its STATGRAPHICS Plus for Windows customers.  For information on available support, click on one of the terms below.

When You Have a Question

Registering for Product Support

Using Software Support Services

Calling Manugistics' HelpLine in the U.S.

Calling Manugistics' HelpLine Worldwide

Requesting Replacement Items

Using the 24-Hour Information Line

Using the Web Page

Using the STATGRAPHICS Plus Documentation Set

Registering for Product Training

Providing Feedback


Commonly Asked Questions

Following are some of the most commonly asked questions about STATGRAPHICS Plus.  Before you call the HelpLine, please scan this list to see if your question is included.

Each question below is followed by the word ANSWER.  To display the answer to a question, click on ANSWER.

 1.	When I view some plots like the Density Trace Plot or the Plot of Fitted Models and try to change the line type nothing seems to happen.  Why?  ANSWER

 2.	When I try to change the font used for the text, why do I seem to have fewer fonts available?  ANSWER

 3.	When I print, why do "white" lines appear in STATGRAPHICS Plus?  ANSWER

 4.	Why does my computer need virtual memory?  ANSWER

 5.	Why am I able to change the thickness of a solid line, but not dashed or dotted lines?  ANSWER

 6.	What are the guidelines for adding additional text in a text pane?  ANSWER

 7.	How can I print multiple graphs on a page? ANSWER

 8.	Can I fit a curve to my data? ANSWER

 9.	How do I convert a text pane in STATGRAPHICS Plus to a generic text file? ANSWER

10.	How do I export graphs from STATGRAPHICS Plus into other software packages?  ANSWER

11.	How do I save the colors and fonts on my graphs?  ANSWER

12.	What is the difference between a StatFolio and a data file?  ANSWER

13.	How do I obtain the latest maintenance release?  ANSWER

14.	When I open a Lotus or Excel file that contains dates, the date variables are not correct.  What is wrong?  ANSWER

15.	I am having difficulty printing to an HP LaserJet 4 printer.  What can I do?  ANSWER

16.	How do I generate descriptive statistics for several different groups?  ANSWER

17.	Can I change the border of a graph from black to another color?  ANSWER

18.	I have recently upgraded to Windows 95 and can no longer run STATGRAPHICS Plus for Windows. What is wrong?  ANSWER

19.	I do not have access to some (or all) of the analyses listed under the “Special” menu. Why?  ANSWER

20	Will STATGRAPHICS Plus have problems with the Year 2000 transition?  ANSWER

21.	I am running an international version of STATGRAPHICS Plus for Windows under NT 4.0,  I receive “copy protection” errors even though the sentinel device is properly installed.  What is wrong?  ANSWER


Answer to Question 1

If you change the line type from solid to dash or dotted, you may notice a difference right away.  This is due to the resolution of the graph.  To better view the line, change the X-axis resolution from 50 to a lower number; for example, 20.


Answer to Question 2

STATGRAPHICS Plus displays only nonproportional fonts.  This ensures that text and labels always align correctly.


Answer to Question 3

All lines, points, and text will always print, even if you change the color to white.


Answer to Question 4

STATGRAPHICS Plus uses WIN32S when running under Windows 3.1 and 3.11.  The program does not use WIN32S when it runs under Windows 95 or Windows NT.  Virtual memory is required if you use WIN32S.


Answer to Question 5

This situation is due to Microsoft's graphics editor.  When Microsoft makes the technique available, we will update our version.


Answer to Question 6

Since STATGRAPHICS Plus allows you to perform analyses in a StatFolio with different variables, the text is regenerated each time an analysis is run.  In Version 3, you can modify the text, then copy it to the StatGallery.  This provides a way for you to make changes that you can permanently save.


Answer to Question 7

The StatGallery window in STATGRAPHICS Plus is an area you can use to place one or multiple text and graphic panes in a variety of positions so you can view or print them.  Or you can save graphs as metafiles and import them into a word processing document.

See the section, “Using the StatGallery,” in the Special Features section for more information about the expanded capabilities of the StatGallery in Version 3.


Answer to Question 8

STATGRAPHICS Plus is not able to fit curves to data.  However, you can fit a regression line to a dataset.


Answer to Question 9

You will need to install a generic text print driver.

1.	Select the Main Program Group from Windows.

2.	Select the Control Panel and Printers icons.

3.	Click the Add button, then choose Generic/Text Only from the list box.

Note:  You will need to use the original Windows diskettes to do this.

Whenever you print a text pane in STATGRAPHICS Plus, you have to first choose the Generic/Text Only driver, then at the prompt enter a file name.


Answer to Question 10

You can copy the graph to the clipboard and paste it into another software package.  Or you can save the graph as a Windows metafile (*.wmf).


Answer to Question 11

After you make all your changes to the colors and fonts on the graph, choose WINDOWS... GRAPHICS DEFAULT… from the Menu bar to display the Graphics Defaults dialog box.   Choose the User-Defined and Save options, then click OK.

The program saves the colors and fonts you chose as the new graphics defaults.


Answer to Question 12

A file contains lists of observations by variable.  A StatFolio contains a file, comments, and analyses you performed on variables in the file, with the tabular and graphical results.  For example, CARDATA is a file that contains variables such as mpg, horsepower, and accel.  A StatFolio would contain the CARDATA data file and various analyses you performed such as Multiple Regression, Process Capability, and One-Variable Analysis.


Answer to Question 13

To receive a maintenance release, call the STATGRAPHICS Helpline at 301-984-5489 or send us an e-mail message:  Answer@manu.com.


Answer to Question 14

STATGRAPHICS Plus imports internal numbers that Lotus or Excel use to represent dates rather than the actual dates.  Each date is 50 years (18,263 days) greater than the internal number.

To Convert the Number to a Date

1.	Choose the numeric date column in the STATGRAPHICS Plus DataSheet.

2.	Choose EDIT... GENERATE DATA …from the Menu bar to display the Generate Data dialog box.

3.	In the Expression text box, type the date variable name and subtract 18263.  That is, type date - 18263.

4.	Click OK.

5.	With the column on the DataSheet still highlighted, choose EDIT... MODIFY COLUMN … from the Menu bar to display the Modify Column dialog box.

6.	Click the Date option, then click OK to display the column with the correct dates.


Answer to Question 15

You may not be using the appropriate driver.  Change the print driver to a LaserJet 3 series.


Answer to Question 16

The best approach is to create two columns.  Column 1 should contain the measurement data; Column 2 the codes that distinguish the various groups.  For example:

Date	Code

  10	    1

  12	    1

  15	    1

  18	    2

  20	    2

  25	    2

    .	     .

    .	     .

    .	     .

1.	Choose COMPARE... ANALYSIS OF VARIANCE… ONE-WAY ANOVA… from the Menu bar to display the One-Way ANOVA dialog box.

2.	Enter the name of the dependent variable into the Dependent Variable text box.

3.	Enter the name of the variable that contains the level codes into the Factor text box, then click OK to display the Analysis Summary.

4.	Click the Tabular Options button on the Analysis toolbar to display the Tabular Options dialog box.

5.	Click the Summary Statistics option on the Tabular Options dialog box.  The program displays a summary of the statistics for each group.


Answer to Question 17

1.	Double-click the graph to maximize it.

2.	Place the mouse anywhere within the frame of the graph and click the left mouse button.  Anchors should appear in the four corners of the graph.

3.	Click the right mouse button, then click the left on Layout Options to display the Axis Options dialog box.

4.	Click the Border option.

5.	Click the color you want to use, then click OK on the Color and Axis Options dialog boxes to display the graph with the border in the new color.


Keyboard

Keyboard equivalents provide shortcuts you can use in place of mouse actions.  Tables 1 and 2 group keyboard equivalents into Application keystrokes and Spreadsheet keystrokes.  Most keystrokes appear next to their corresponding items on the pull-down menus.

Table 1.  General Shortcut Keys

Keystroke	Purpose

   F1	Access Online Help

   F10	Access File Menu

   Alt	Access File Menu

   Ctrl-F11	Access Open StatFolio Dialog Box

   Shift-F11	Access Save StatFolio Dialog Box or automatically saves if the StatFolio has a name

   F11	Access Save StatFolio As Dialog Box

   Ctrl-F12	Access Open Data File Dialog Box

   Shift-F12	Access Save Data File Dialog Box or automatically saves if the data file has a name

   F12	Access Save Data File As Dialog Box

   F3	Access Save Graph Dialog Box

   Shift-F3	Access Print Preview

   F4	Access Print Dialog Box

   Shift-F4	Access Print Setup Dialog Box

   Alt-F4	Access Exit STATGRAPHICS Plus Dialog Box

   F7	Redisplay Analysis Dialog Box

   F5	Access Tabular Options Dialog Box

   F8	Access Graphical Options Dialog Box

   F9	Access Save Results Dialog Box

   Shift-F5	Access Modify Column Dialog Box (when column selected)

   Shift-F7	Access Generate Data Dialog Box (when column selected)

   Ctrl-X	Cut Highlighted Text

   Ctrl-C	Copy Highlighted Text

   Ctrl-V	Insert Highlighted Text (Paste)

   Ctrl-Z	Undo Previous Change

   F2	Access Font Dialog Box

   Ctrl-F4	Delete an Analysis

   Ctrl-F5	Restore the highlighted Taskbar/Icon

   Ctrl-F6	Navigate among the Taskbars/Icons

   Ctrl-F7	Display Move Icon; Use Arrow Keys to Move

   Ctrl-F8	Display Size Icon; Use Arrow Keys to Resize

   Ctrl-F9	Minimize a Window

   Ctrl-F10	Maximize a Window

Table 2.  Spreadsheet Keystrokes

Keystroke	Purpose

   Ins	Inserts a blank block of cells before a tagged block which provides the row and column specifications

   Del	Deletes a tagged block

   Arrow Keys	Moves one cell in the specified direction

   PgUp	Moves up one page

   PgDn	Moves down one page

   Home	Moves to the first column of the current row

   End	Moves to the last column of the current row

   Ctrl-PgUp	Moves one page to the left

   Ctrl-PgDn	Moves one page to the right

   Ctrl-Home	Moves to the first column in the first row

   Ctrl-End	Moves to the last column in the last row

   Ctrl-Arrow Key	Moves to the last nonblank cell in the specified direction

   Tab	Moves one cell to the right

   Shift-Tab	Moves one cell to the left

   Shift-Arrow Key	Selects cells in the specified direction

   Shift-PgUp/PgDn	Selects one page of cells in the specified direction

   Shift-Spacebar	Selects the current row

   Ctrl-Spacebar	Selects the current column

   Shift-Ctrl-Spacebar	Selects the entire spreadsheet

   Shift-Ctrl-Arrow Key	Selects cells between the active cell and the end of the spreadsheet in the specified direction


Operators

The following list describes each operator in the program.  To use the table, look in the Operator column for the name of the operator you want to use, then read the description in the Function column.  For details on how to use the operator in an expression, click on the Example button ( [image]).

Operator	Function

x + y 	Add

x - y 	Subtract

x * y 	Multiply

x / y 	Divide

x ^ y 	Raise to a power

x = y 	Equal to

x <> y 	Not equal

x > y 	Greater than

x >= y 	Greater than or equal to

x < y 	Less than

x <= y 	Less than or equal to

x & y 	Both of two conditions must be true (AND)

x | y 	Either of two conditions must be true (OR)

~ x 	Negate a Boolean (NOT)

ABS (x )	Take the absolute value

ACOS (x )	Calculate the inverse cosine of an angle in degrees

ACOSR (x )	Calculate the inverse cosine of an angle in radians

ASIN (x )	Calculate the inverse sine of an angle in degrees

ASINR (x )	Calculate the inverse sine of an angle in radians

ATAN (x )	Calculate the inverse tangent of an angle in degrees

ATANR (x )	Calculate the inverse tangent of an angle in radians

AVG (numvar)	Calculate the average

BETA (n ,m ,l )	Calculate the probability of the cumulative beta distribution at a given point

CELL (var,n )	Select a row from a specific column

CHISQUARE (n ,df)	Calculate the probability of the cumulative chi-square distribution at a given point

COMPRESS (var,logical)	Select the rows that meet a condition

COS (x )	Calculate the cosine of an angle in degrees

COSR (x )	Calculate the cosine of an angle in radians

COUNT (start,end,step)	Create a sequential numeric vector

CV (numvar)	Calculate the coefficient of variation

DATENUM (datevar)	Convert a date variable to a number equivalent to the STATGRAPHICS Plus date code

DIFF (numvar)	Calculate the differences between the consecutive values

DROP (var,n )	Select all but the first n rows

DROPLAST (var,n )	Select all but the last n rows

EXCLUDE (n )	Excludes row n.

EXP (x )	Raise the constant e (2.71828) to a power

EXP10 (x )	Raise 10 to a power

FACT (x )	Calculate the factorial

FIRST (n )	Generate a 1 for the first n rows in the file and 0 for all the other rows

FIRSTROWS (var,n )	Select the first n rows and replace the other rows with the missing value codes

GEOMEAN (numvar)	Calculate the geometric mean

INVBETA (n ,m ,l )	Calculate the critical value of the beta distribution given a probability

INVCHISQUARE (n ,df)	Calculate the critical value of the chi-square distribution given a probability

INVNORMAL (n ,mean,sdev)	Calculate the critical value of the normal distribution given a probability

INVSNEDECOR (n ,df1,df2)	Calculate the critical value of the Snedecor's-F distribution given a probability

INVSTUDENT (n ,df)	Calculate the critical value of the Student's-t distribution given a probability

IQR (numvar)	Calculate the interquartile range

JOIN (var,var)	Join the columns end to end

JOIN3 (var,var,var)	Join three numeric or three character variables end to end

JOIN4 (var,var,var,var)	Join four numeric or four character variables end to end

JUXTAPOSE (charvar,charvar)	Join the character variables side by side, expanding the width

KURTOSIS (numvar)	Calculate the coefficient of kurtosis

LAG (numvar,n )	Shift the values n positions forward or backward

LAST (n )	Generate a 1 for the last n rows in the file and 0 for all the other rows

LASTROWS (var,n )	Select the last n rows and replace the other rows with the missing value codes

LOG (x )	Take the natural logarithm

LOG10 (x )	Take the base-ten logarithm

MAX (numvar)	Find the largest value

MDIFF (numvar,n )	Calculate the multiple backward differences

MEDIAN (numvar)	Calculate the median

MIN (numvar)	Find the smallest value

MODE (numvar)	Find the most frequent observation

NORMAL (n ,mean,sdev)	Calculate the probability of the cumulative normal distribution at a given point

PERCENTILE (numvar,n )	Calculate the percentile

Q25 (numvar)	Calculate the lower quartile

Q75 (numvar)	Calculate the upper quartile

RANDOM (n )	Generate a 1 for n randomly selected rows and 0 for all the other rows

RANGE (numvar)	Calculate the range

RANK (numvar)	Calculate the rank of each row

RECODE (var)	Recode the numeric or character values to integers

REP (var,n )	Repeat each value n times

REPLACE (numvar ,old,new)	Replace all occurrences of a number with a different number

RESHAPE (var,n )	Expand or compress a constant or variable to have a specified number of values

REXPONENTIAL (n ,mean)	Generate random numbers from an exponential distribution

RGAMMA (n ,alpha,beta)	Generate random numbers from a gamma distribution

RINTEGER (n ,lower,upper)	Generate random numbers (integer values) from a discrete uniform distribution

RLOGNORMAL (n ,mean,sdev)	Generate random numbers from a lognormal distribution

RNORMAL (n ,mean,sdev)	Generate random numbers from a normal distribution

ROUND (x )	Round to the nearest integer

ROUNDTO (numvar,decimal)	Round to the specific number of decimal places

ROWS (n ,m )	Generate a 1 for rows n to m and 0 for all the other rows

RUNIFORM (n ,lower,upper)	Generate random numbers from a continuous uniform distribution

RUNTOT (numvar)	Calculate a running total

RWEIBULL (n ,alpha,beta)	Generate random numbers from a Weibull distribution

SD (numvar)	Calculate the standard deviation

SDIFF (numvar,n )	Calculate the seasonal differences

SELECT (var,logical)	Choose the rows that meet a condition

SERROR (numvar)	Calculate the standard error

SIN (x )	Calculate the sine of an angle in degrees

SINR (x )	Calculate the sine of an angle in radians

SIZE (numvar)	Count the total number of nonmissing observations

SKEWNESS (numvar)	Calculate the coefficient of skewness

SKURT (numvar)	Calculate the standardized kurtosis

SNEDECOR (n ,df1,df2)	Calculate the probability of the cumulative Snedecor's-F distribution at a given point

SQRT (x )	Calculate the square root

SSKEW (numvar)	Calculate the standardized skewness

STANDARDIZE (numvar)	Subtract the average from each value and then divide by the standard deviation

STRIPBLANKS (charvar)	Remove the double blanks from a character variable

STUDENT (n ,df)	Calculate the probability of the cumulative Student's-t distribution at a given point

SUM (numvar)	Calculate the sum of the observations

TAKE (var,n )	Select the first n rows

TAKELAST (var,n )	Select the last n rows

TAN (x )	Calculate the tangent of an angle in degrees

TANR (x )	Calculate the tangent of an angle in radians

TRUNCATE (x )	Find the largest integer greater than or equal to n

VARIANCE (numvar)	Calculate the variance


Answer to Question 18

To run under Windows 95, you need version 1.4 or higher of STATGRAPHICS Plus..  Call 301-984-5489 to upgrade.


Answer to Question 19

Check your disks.  If you have only the base program, you must purchase additional analyses to have access to these special analyses.  The add-on analyses are:

•	Quality and Design

•	Time Series

•	Multivariate Methods

•	Advanced Regression.

Call 301-984-5489 to purchase the analyses you need.


Answer to Question 20

Year 2000 Disclosure Statement:

When interpreting two-digit year formats (YY), all versions of STATGRAPHICS Plus support a 100-year date range, which is from January 1, 1950 (1/1/50 in STATGRAPHICS Plus format) through December 31, 2049 (12/31/49 in STATGRAPHICS Plus format.  Within this range, STATGRAPHICS Plus appropriately handles dates and will transition to the Year 2000 correctly, calculating leap years and handling forward and backward date calculations spanning the century boundaries.

All versions of STATGRAPHICS Plus (DOS and Windows) manage dates in this manner.

In addition, Version 4 of STATGRAPHICS Plus supports a four-digit year format (YYYY).  You can choose a format using the Preferences dialog box, which is accessed from the Edit menu.

The foregoing statement is being designated a year 2000 readiness disclosure pursuant to Section 7(3)(b)(1)(ii) of the Year 2000 Information and Readiness Disclosure Act.


Answer to Question 21

You will need to download the latest driver available for the sentinel device.  You can download it from the web site for Rainbow Technologies: http://www.rnbo.com/nt4.html.


Year 2000 Readiness Disclosure

Year 2000 Disclosure Statement:

When interpreting two-digit year formats (YY), all versions of STATGRAPHICS Plus support a 100-year date range, which is from January 1, 1950 (1/1/50 in STATGRAPHICS Plus format) through December 31, 2049 (12/31/49 in STATGRAPHICS Plus format).  Within this range, STATGRAPHICS Plus appropriately handles dates and will transition to the Year 2000 correctly, calculating leap years and handling forward and backward date calculations spanning the century boundaries.

All versions of STATGRAPHICS Plus (DOS and Windows) manage dates in this manner.

In addition, Version 4 of STATGRAPHICS Plus supports a four-digit year format (YYYY).  You can choose a format using the Preferences dialog box, which is accessed from the Edit menu.

The foregoing statement is being designated a year 2000 readiness disclosure pursuant to Section 7(3)(b)(1)(ii) of the Year 2000 Information and Readiness Disclosure Act.


Using the Analyses in the Plot Menu

STATGRAPHICS Plus contains the tools necessary for creating six basic types of plots: Scatterplots, Exploratory Plots, Business Charts, Probability Distributions, Response Surface Plots, and Custom Charts.  To view the topics for a specific plot, click its name in the list.

Scatterplots

Using the Univariate Plot Analysis

Using the X-Y Plot Analysis

Using the X-Y-Z Plot Analysis

Using the Multiple X-Y Plot Analysis

Using the Multiple X-Y-Z Plot Analysis

Using the Polar Coordinates Plot Analysis

Exploratory Plots

Using the Box-and-Whisker Plot Analysis

Using the Multiple Box-and-Whisker Plot Analysis

Using the Normal Probability Plot Analysis

Using the Frequency Histogram Analysis

Using the Dot Diagram Analysis

Using the Multiple Dot Diagram Analysis

Using the Bubble Chart Analysis

Using the Radar/Spider Plot Analysis

Business Charts

Using the Barchart Analysis

Using the Multiple Barchart Analysis

Using the Piechart Analysis

Using the Component Line Chart Analysis

Using the High-Low-Close Plot Analysis

Probability Distributions

Using the Probability Distributions Analysis

Response Surface Plots

Using the Response Surface Plots Analysis

Custom Charts

Using the Custom Charts Analysis


Using the Univariate Plot Analysis

The Univariate Plot Analysis lets you create a scatterplot for a single numeric variable.  It applies to a method of grouping data that involves one characteristic of the members of a population or sample, otherwise known as univariate data.  For example, you might examine the age of welfare recipients but not examine their gender or ethnicity.  You can enter point codes to show the levels of the classification factor.

To Create a Univariate Plot Analysis

1.	Choose PLOT… SCATTERPLOTS… UNIVARIATE PLOT… from the Menu bar to display the Univariate Plot Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary, Scatterplot, and Time Sequence Plot in the Analysis window.


Using the X-Y Plot Analysis

The X-Y Plot Analysis creates a two-dimensional scatterplot for one variable versus another, which you use to examine their relationships.  You can produce lineplots, scatterplots, connected scatterplots, coded scatterplots, and plots with standard error bars.

An X-Y lineplot displays connecting lines without points, while an X-Y scatterplot shows points only (no connecting lines).  A connected X-Y scatterplot connects lines with points; a coded X-Y scatterplot is more informative than the basic X-Y scatterplot because it uses coded points to show the levels of a classification factor.  You can designate the point codes.

When the points in a scatterplot represent means rather than individual values, you may find it useful to illustrate the uncertainty surrounding the points.  You can plot standard error bars for the X- or Y-variables, or both.  Standard error bars are lines that extend from the means, plus and minus one standard error.

To Create an X-Y Plot Analysis

1.	Choose PLOT… SCATTERPLOTS… X-Y PLOT… from the Menu bar to display the X-Y Plot  Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Scatterplot in the Analysis window.


Using the X-Y-Z Plot Analysis

The X-Y-Z Plot Analysis plots three variables instead of two and produces three-dimensional graphs with the X-axis plotted horizontally along the bottom of the screen, the Y-axis extending back into the screen, and the Z-axis aligned vertically.  The plot provides options for lineplots, scatterplots, connected scatterplots, and coded scatterplots.  You can also plot standard error bars.

An X-Y-Z lineplot displays connecting lines without points, while an X-Y-Z scatterplot shows points only (no connecting lines).  A connected X-Y-Z scatterplot connects points with lines.  A coded X-Y-Z scatterplot is more informative than the basic X-Y-Z scatterplot because it uses coded points to show the levels for a classification factor.  You can designate the point codes.

Because large numbers of points and lines can blend together and make it difficult to read the graph, use this analysis only with small datasets.  You can plot more values if you use a high-resolution graphics adapter.

To Create an X-Y-Z Plot Analysis

1.	Choose PLOT… SCATTERPLOTS… X-Y-Z PLOT… from the Menu bar to display the X-Y-Z Plot Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and X-Y-Z Scatterplot in the Analysis window.


Using the Multiple X-Y Plot Analysis

The Multiple X-Y Plot Analysis produces scatterplots with one variable on the X-axis and one or more variables on the Y-axis.  You can choose to plot X-axis variables with the scale on the left or the right.  The program automatically adjusts the size of the scales to reflect the range of the values.  You can generate scatterplots with lines, points, or both.

To Create a Multiple X-Y Plot Analysis

1.	Choose PLOT… SCATTERPLOTS… MULTIPLE X-Y PLOT… from the Menu bar to display the Multiple X-Y Plot Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Scatterplot in the Analysis window.


Using the Multiple X-Y-Z Plot Analysis

The Multiple X-Y-Z Plot Analysis produces a standard three-dimensional scatterplot for three or more variables.  One variable each is plotted on the X- and Y-axes, while one or more is plotted on the Z-axis.  The scale for the Z-axis can appear on the left or the right.  The size of the scales is automatically adjusted to reflect the range of the values.

To Create a Multiple Y-Y-Z Plot Analysis

1.	Choose PLOT… SCATTERPLOTS… MULTIPLE X-Y-Z PLOT… from the Menu bar to display the Multiple X-Y-Z Plot Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and X-Y-Z Plot in the Analysis window.


Using the Box-and-Whisker Plot Analysis

The Box-and-Whisker Plot Analysis is a way of summarizing a set of univariate data measured on an interval scale.  It is often used in exploratory data analysis to illustrate the major features of the distribution of the data and to compare means and ranges and show outliers and the shape of the distribution.  It is particularly useful when large numbers of observations are involved and when you are comparing two or more datasets.

The data are divided into four areas of equal frequency.  A box encloses the middle 50 percent, where the median is represented as a vertical line inside the box.  The mean may be plotted as a point.

Horizontal lines, called whiskers, extend from each end of the box.  The lower (left) whisker is drawn from the lower quartile to the smallest point within 1.5 interquartile ranges from the lower quartile.  The other whisker is drawn from the upper quartile to the largest point within 1.5 interquartile ranges from the upper quartile. Values that fall beyond the whiskers, but within 3 interquartile ranges (suspect outliers), are plotted as individual points.

Far outside points (outliers) are distinguished by a special character (a point with a + through it).  Far outside points are points more than 3 interquartile ranges below the lower quartile or above the upper quartile.

To Create a Box-and-Whisker Plot Analysis

1.	Choose PLOT… EXPLORATORY PLOTS… BOX-AND-WHISKER PLOT… from the Menu bar to display the Box-and-Whisker Plot Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Box-and-Whisker Plot in the Analysis window.


Using the Multiple Box-and-Whisker Plot Analysis

The Multiple Box-and-Whisker Plot Analysis is simply an extension of the Box-and-Whisker Plot analysis.  If you can subdivide the data into groups, this analysis lets you produce separate Box-and-Whisker plots for each group on one chart.  This facilitates comparisons of the median, range, and extreme value for each group.

Each of the plots is a statistical summary of a set of univariate observations.  It is an exploratory data-analysis tool that is useful for studying symmetry and distributional assumptions, and for detecting outliers.

The data are shown in four areas of equal frequency.  A box encloses the middle 50 percent, where the median is represented as a horizontal line inside the box.  Vertical lines, called whiskers, extend from each end of the box.  The lower whisker is drawn from the first quartile to the smallest point within 1.5 interquartile ranges from the first quartile.  The other whisker is drawn from the third quartile to the largest point within 1.5 interquartile ranges from the third quartile.

Individual points are plotted beyond the whiskers.  Far outliers (points that lie more than 3 interquartile ranges below the first quartile or above the third quartile), are plotted using a special character (+) that makes the points easier to identify.

To Create a Multiple Box-and-Whisker Plot Analysis

1.	Choose PLOT… EXPLORATORY PLOTS… MULTIPLE BOX-AND-WHISKER PLOT… from the Menu bar to display the Multiple Box-and-Whisker Plot Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Multiple Box-and-Whisker Plot in the Analysis window.


Using the Probability Plot Analysis
Using the Probability Plot Analysis- not used in Version 4

The Probability Plot Analysis allows you to generate a Normal Probability plot to determine if a set of observations could reasonably come from a normal distribution.

A Normal Probability plot consists of an arithmetic (interval) horizontal axis and a vertical axis scaled so the cumulative distribution function (cdf) of a normal distribution plots as a straight line.  The plot includes a least squares regression line for comparison purposes.

The Probability Plot analysis contains one tabular option and one graphical option:  Analysis Summary and Normal Probability Plot, respectively.

Another dialog box you may want to use is:

Normal Probability Plot Options

To Create a Probability Plot

1.	Choose PLOT… EXPLORATORY PLOTS… PROBABILITY PLOT… from the Menu bar to display the Analysis dialog box, which allows you to choose the data you want to plot.

2.	Complete the dialog box and click OK to display the Analysis Summary.


Using the Frequency Histogram Analysis

The Frequency Histogram Analysis provides a way to summarize data that are measured on a discrete or continuous interval scale.  It is used to illustrate the major features of the distribution of the data, such as the number of school-age children in each of n families (Weiss and Hassett, 1991).

The range of possible values is divided into classes or groups.  For each group, a rectangle is drawn with a base height equal to the frequency of the values in that specific group, and an area proportional to the number of observations that fall into that group.

To Create a Frequency Histogram Analysis

1.	Choose PLOT… EXPLORATORY PLOTS… FREQUENCY HISTOGRAM… from the Menu bar to display the Frequency Histogram Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Frequency Histogram in the Analysis window.


Using the Dot Diagram Analysis

The Dot Diagram Analysis is way of summarizing data in an exploratory data analysis, to show the primary features of the distribution of the data in a convenient form.  The graph provides another type of graphical display for numeric data, which is particularly useful for showing the relative positions of data in a dataset, or for comparing two or more datasets.  The plot is also helpful in detecting unusual outliers or gaps in the data.

The plot is similar to a barchart or a histogram, with the bars or rectangles replaced by a series of dots.  Each dot represents a fixed number of individuals.

To Create a Dot Diagram Analysis

1.	Choose PLOT… EXPLORATORY PLOTS… DOT DIAGRAM… from the Menu bar to display the Dot Diagram Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Dot Diagram in the Analysis window.


Using the Bubble Chart Analysis

The Bubble Chart Analysis allows you to create an X-Y scatterplot consisting of circles, which is another way of plotting three parameters on two axes — two variables are represented by the X- and Y-coordinates of the plotted points, and a third variable is portrayed by a plotted circle or “bubble.”   The size of the bubble depends on the numeric value of the third variable.  The larger the value, the larger the bubble.  This approach is a basic graphics tool that is helpful when you are looking for a fairly direct way to view data in higher dimensions.

For example, suppose you are analyzing a product's competitive standing; that is, top-rated products and lower-rated products.  Each product in the study is represented by a bubble that moves in relation to its market position.  Each bubble represents a point, allowing you to quickly spot important shifts in market position.

The chart shows the location of X and Y as well as their relative sizes; the size of each bubble is based on the size of the third numeric variable.  You can use different colors for different bubbles, indicate if you want filled bubbles, and enter the maximum size for the largest bubbles.

To Create a Bubble Chart Analysis

1.	Choose PLOT… EXPLORATORY PLOTS… BUBBLE CHART… from the Menu bar to display the Bubble Chart Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary Bubble Chart in the Analysis window.


Using the Barchart Analysis

The Barchart Analysis is a way of summarizing a set of categorical data, often a frequency table.  It is used in exploratory data analysis to illustrate the major features of the distribution of data in a convenient form.  It displays the data using a number of rectangles, of the same width, each of which represents a particular category.  The length (area) of each rectangle is proportional to the number of cases in the category it represents.

For example, you might use barcharts to present the Republican affiliation of members of various religious categories: 31 percent of Protestants surveyed reported affiliation with the Republicans, roughly 17 percent of Catholics did, and so on.

You can display the barcharts either horizontally or vertically; they can include horizontally or vertically stacked bars, clustered bars, or percentages.  The variable you use should contain tabulated data (counts) — a count of the number of observations in each class.  If the data contain more than 20 classes, an error message displays.

To Create a Barchart Analysis

1.	Choose PLOT… BUSINESS CHARTS… BARCHART… from the Menu bar to display the Barchart Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Barchart in the Analysis window.


Using the Multiple Barchart Analysis

The Multiple Barchart Analysis creates a plot with one or more frequency bars for each classification factor (row).  The analysis is helpful when you need to graphically represent a secondary classification factor within a primary classification factor.

The variable you use should contain tabulated data (counts) — a count of the number of observations in each class.  If the data contain more than 20 classes, an error message displays.

To Create a Multiple Barchart Analysis

1.	Choose PLOT… BUSINESS CHARTS… MULTIPLE BARCHART… from the Menu bar to display the Multiple Barchart Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Multiple Barchart in the Analysis window.


Using the Piechart Analysis

The Piechart Analysis creates a plot that is a way of summarizing a set of categorical data.  The plot contains a circle divided into segments where each segment is proportional to the number of cases in that category.  You can offset a segment of the chart to display it more prominently.

The variable you use should contain tabulated data (counts) — a count of the number of observations in each class.  If the data contain more than 20 classes, an error message displays.

A Piechart is useful for displaying breakdowns of percentages.  For example, you could use a Piechart to show how an athletic-shoe manufacturer spent its advertising budget of 6 million dollars: 3 million for television advertisements, 2 million for sponsorships, and 1 million for newspaper advertisements.

To Create a Piechart Analysis

1.	Choose PLOT… BUSINESS CHARTS… PIECHART… from the Menu bar to display the Piechart Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Piechart in the Analysis window.


Using the Probability Distributions Analysis

The Probability Distribution Analysis contains 24 different probability distribution functions that allow you to perform three basic operations:

•	Calculate probabilities

•	Create plots of the probability and cumulative distributions

•	Generate random numbers.

The 24 distributions are:

•	Bernoulli

•	Binomial

•	Discrete Uniform

•	Geometric

•	Hypergeometric

•	Negative Binomial

•	Poisson

•	Beta

•	Cauchy

•	Chi-Square

•	Erlang

•	Exponential

•	Extreme Value

•	F (Variance) Ratio

•	Gamma

•	Laplace

•	Logistic

•	Lognormal

•	Normal

•	Pareto

•	Student’s t

•	Triangular

•	Uniform

•	Weibull

The first six distributions are appropriate for discrete data; that is, data that can take only integer values.  For discrete variables, the probabilities are relative frequencies.

The other distributions are appropriate for continuous variables that can take any value over a continuous interval.

To Create a Probability Distribution Analysis

1.	Choose PLOT… PROBABILITY DISTRIBUTIONS… from the Menu bar to display the Analysis dialog box.

2.	Choose the distribution you want to use and click OK to display the Analysis Summary and Density/Mass Function Plot for the distribution you chose.


Using the Response Surface Plots Analysis

The Response Surfaces Plot Analysis allows you to create Surface and Contour plots for functions that you specify.  You must write the functions involving X and Y; for example,

10+2*X+3*Y-10*X*Y

The plots are helpful when you need to visualize the shape of a response surface and when you need to locate optimal settings.

To Create a Response Surfaces Plot Analysis

1.	Choose PLOT… RESPONSE SURFACES… from the Menu bar to display the Response Surfaces Plot Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Surface Plot in the Analysis window.


Using the Custom Charts Analysis

The Custom Charts Analysis allows you to create charts with custom titles, scaling, and horizontal and vertical lines.  Its primary purpose is to let you create charts you can use to overlay on other plots when you use the StatGallery.  A control chart is an example of a customized chart you could create.

To Create a Custom Charts Analysis

1.	Choose PLOT… CUSTOM CHART… from the Menu bar to display the Custom Charts Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Custom Chart in the Analysis window.


Using the Polar Coordinates Plot Analysis

The Polar Coordinates Plot Analysis creates a two-dimensional scatterplot or line plot for pairs of points that are defined by radius and angle positions.  In other words, it provides information about the location of a point on a graph; for example, finding (x,y) in polar coordinates.  This type of plot is useful in manufacturing environments where a polar coordinate system, rather than or in addition to a rectangular coordinate system, might be used to label points on the plane.

A polar coordinate system differs from a rectangular coordinate system in the way it represents points on the plane.  In a rectangular coordinate system, a point, (x,y), is defined as the point derived from moving from the origin horizontally x units and vertically y units.  In a polar coordinates system, a point, (x,y), is defined by beginning at the origin, finding the ray that comes from the origin that is an angle of y with the positive X-axis, and goes out a distance of y, on this ray (The Math Formum, 1997).

To Create a Polar Coordinates Plot Analysis

1.	Choose PLOT… SCATTERPLOTS… POLAR COORDINATES PLOT… from the Menu bar to display the Polar Coordinates Plot Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and the Polar Coordinates Plot in the Analysis window.


Using the Radar/Spider Plot Analysis

The Radar/Spider Plot Analysis is a simple visualization technique often considered valuable in meeting the demands of multivariate data bcause of its ability to simultaneously portray numerous aspects of the data.

This technique plots multiple measurements on equally spaced radii that are linked to create a star-like form.  The radii extend from the center of a circle and give the impression of changing values across subjects.

A Radar plot is much like a Star plot.  In a Radar plot, the value of the measurement is represented by radii reaching from the center of a circle; however, each radius stands for a subject instead of a variable.  Points of different colors represent the response for each variable.  When there are too many variables and subjects, the pattern of the data is concealed.

To Create a Radar/Spider Plot Analysis

1.	Choose PLOT… EXPLORATORY PLOTS… RADAR/SPIDER PLOT…	from the Menu bar to display the Radar/Spider Plot Analysis dialog box.

2.	Complete the Analysis dialog box and click OK to display the Analysis Summary and Overlay Plot in the Analysis window.


Using the Multiple Dot Diagram Analysis

The Multiple Dot Diagram Analysis creates a dot diagram for data that are divided into more than one group.  It displays summary statistics and confidence intervals for each group.

This plot is a way to summarize data that are often used in exploratory data analysis to illustrat the major features of the distribution of data in a convenient form.  A Multiple Dot Diagram can also help detect any unusual observations (outliers), or gaps in the dataset.

To Create a Multiple Dot Diagram Analysis

1.	Choose PLOT… EXPLORATORY PLOTS… MULTIPLE DOT DIAGRAM… from the Menu bar to display the Multiple Dot Diagram Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Multiple Dot Diagram in the Analysis window.


Using the Component Line Chart Analysis

The Component Line Chart Analysis is useful for displaying one or more sets of time-series data, which are useful for investigating trends, patterns, or other nonrandom behavior in the time series; for example, stock prices.  You can plot original values individually or cumulatively.

To Create a Component Line Chart Analysis

1.	Choose PLOT… BUSINESS CHARTS… COMPONENT LINE CHART… from the Menu bar to display the Component Line Chart Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Component Line Chart in the Analysis window.


Using the High-Low-Close Plot Analysis

The High-Low-Close Plot Analysis is valuable when you want to display stock, commodity, currency, and other market data that fluctuate greatly from hour-to-hour, day-to-day, or week-to-week.  To convey a sense of short-term change while also viewing long-term change requires that each category of data show a range of values.

To Create a High-Low-Close Plot Analysis

1.	Choose PLOTS... BUSINESS CHARTS... HIGH-LOW-CLOSE PLOT... to display the High-Low-Close Plot Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and High-Low-Close Plot in the Analysis window.


Using the Normal Probability Plot Analysis

The Normal Probability Plot Analysis is used to test a single sample to determine whether or not it is likely to be a sample taken from a normally distributed population.  The purpose of the test is to produce a graph and to determine if the shape of the plotted points form a linear pattern (that is, if the points roughly follow a straight line).

The plot also provides an easy way to identify outliers.  Outliers clearly highlight potential performance bottlenecks.  The points (effects) are arranged in ascending order of their value.  The plot consists of an arithmetic (interval) horizontal axis and a vertical axis scaled so the cumulative distribution function (cdf) plots as a straight line.

To Create a Normal Probability Plot Analysis

1.	Choose PLOT… EXPLORATORY PLOTS… NORMAL PROBABILITY PLOT… from the Menu bar to display the Normal Probability Plot Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Normal Probability Plot in the Analysis window.


Using the Analyses in the Describe Menu

This menu allows you to access analyses you use to investigate and summarize data.  There are five types of analyses:

Describing Numeric Data

Using the One-Variable Analysis

Using the Multiple-Variable Analysis

Using the Subset Analysis

Using the Row-Wise Statistics Analysis

Using the Power Transformations Analysis

Using the Statistical Tolerance Limits Analysis

Describing Categorical Data

Using the Tabulation Analysis

Using the Crosstabulation Analysis

Using the Contingency Tables Analysis

Working with Probability Distributions

Using the Probability Distributions Analysis

Using the Probability Plots Analysis

Using the Distribution Fitting (Uncensored Data) Analysis

Using the Distribution Fitting (Censored Data) Analysis

Performing Analyses Using Life Data

Using the Life Tables (Intervals) Analysis

Using the Life Tables (Times) Analysis

Using the Weibull Analysis

Using the Arrhenius Plot Analysis

Performing Hypothesis Tests and Determining Sample Size

Using the Hypothesis Tests (Describe) Analysis

Using the Sample-Size Determination (Describe) Analysis


Using the One-Variable Analysis

The One-Variable Analysis allows you to summarize a single column of numeric data.  It calculates statistics, performs hypothesis tests, and constructs a variety of graphs.  For example, options in this analysis allow you to calculate specific summary statistics, such as standard deviation and average, percentiles, and confidence intervals.  You can plot the data in a scatterplot, histogram, probability plot, or symmetry plot, among others.

To Create a One-Variable Analysis

1.	Choose DESCRIBE… NUMERIC DATA… ONE-VARIABLE ANALYSIS… from the Menu bar to display the One-Variable Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Scatterplot in the Analysis window.


Using the Multiple-Variable Analysis

The Multiple-Variable analysis allows you to summarize several columns of quantitative data by producing descriptive statistics for each variable.  For example, the options allow you to calculate summary statistics, correlations, covariances, and partial correlations.  The plots in the analysis provide different views of the data; for example, as a Scatterplot Matrix, as a Star Plot or Sunray Plot, or as a Key Glyph.  The StatAdvisor provides suggestions for using this analysis to build statistical models.

To Create a Multiple-Variable Analysis

1.	Choose DESCRIBE… NUMERIC DATA… MULTIPLE-VARIABLE ANALYSIS… from the Menu bar to display the Multiple-Variable Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Scatterplot Matrix in the Analysis window.


Using the Distribution Fitting Analysis

not used in version 4


Using the Tabulation Analysis

The Tabulation Analysis summarizes the distribution of a single categorical variable through a frequency tabulation.  You enter untabulated raw data, then the tabulation counts the number of times each value occurs.  The numerical results include a summary of the analysis and a frequency table.  The graphic results include a barchart and a piechart.

To Create a Tabulation Analysis

1.	Choose DESCRIBE… CATEGORICAL DATA… TABULATION… from the Menu bar to display the Tabulation Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Barchart in the Analysis window.


Using the Crosstabulation Analysis

The Crosstabulation Analysis is often used simply to understand patterns of association and partial association.  The analysis creates a two-way table that shows data arranged so each cell represents a unique combination of values of the two crosstabulated variables and the number of observations that fall into each combination of the values.

For example, you might conduct a study in which adults and teens were asked to choose one of two different brands of bath soap (Soap A and Soap B.  The data file would look like this:

Observation	Age Group	Soap

1	Adult	A
2	Teen	A
3	Teen	B
4	Teen	B
5	Adult	A
6	Adult	B

The crosstabulation would look like this:

Soap:A	Soap:B	Total

Age Group: Adult	20 (40%)	30 (60%)	50 (50%)

Age Group: Teen	30 (60%)	20 (40%)	50 (50%)

Total	50 (50%)	50 (50%)	100 (100%)

Each cell in the table represents a combination of unique values for the two crosstabulated variables (row Age Group, and column Soap).  The numbers in each cell show the number of observations that fall into each combination of values.

The crosstabulations count the number of times each unique value occurs in the first variable, then in the second.  This is a useful first step in studying the relationship between two variables. To quantify or test the relationship, the analysis also allows you to create various indexes that measure the extent of association, as well as create statistical tests of the hypothesis that an association does not exist.

To Create a Crosstabulation Analysis

1.	Choose DESCRIBE… CATEGORICAL DATA… CROSSTABULATION… from the Menu bar to display the Crosstabulation Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Barchart in the Analysis window.


Using the Contingency Tables Analysis

The Contingency Tables Analysis creates separate two-way tables for each combination of the variables, which determines if two classification factors are related, and if so, how closely.  You can enter frequencies for each factor.

When you analyze data as a contingency table, each variable you enter represents one column of counts for each row class.  For example, if your data consists of row classes for Excellent, Average, and Poor you might enter the following variables to represent each school grade:

grade1

grade2

grade3

grade4

 . . .

Each variable would contain three values, one value for each of the three classes: Excellent, Average, and Poor.

You can use this analysis to calculate various summary statistics, such as:

•	a chi-square statistic that tests the hypothesis of independence between row and column factors (the statistic appears with the degrees of freedom and the significance level)

•	the lambda values, uncertainty coefficients, and Somers' d statistics for symmetric and asymmetric cases (that is, the rows and columns are dependent)

•	the contingency coefficient and other statistics.

Fisher's Exact test is performed for two-by-two matrices that have a total cell count of 100 or fewer.

To Create a Contingency Tables Analysis

1.	Choose DESCRIBE… CATEGORICAL DATA… CONTINGENCY TABLES… from the Menu bar to display the Contingency Tables Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Barchart in the Analysis window.


Using the Fitting Distributions Uncensored Data Analysis

Raw data are seldom suitable for performing an analysis, so it is necessary to convert it into a suitable form that can undergo meaningful analysis.  The goal is to understand the random variability that exists in each measurement of the data.  Uncensored data are data that are present throughout the entire duration of an experiment, or data that do not have to be excluded from an experiment for any reason.

The Uncensored Data Analysis allows you to create a relevant summary by fitting one of the 24 probability distribution functions in STATGRAPHICS Plus to a set of data.  The analysis provides a way to determine if uncensored data follow a Normal (the default), or another type of distribution.  The analysis calculates and displays estimated parameters for each distribution you choose.

To Create a Distribution Fitting (Uncensored Data) Analysis

1.	Choose DESCRIBE… DISTRIBUTIONS… DISTRIBUTION FITTING (UNCENSORED DATA)… Analysis from the Menu bar to display the Distribution Fitting (Uncensored Data) Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Density Trace in the Analysis window.


Using the Distribution Fitting (Censored Data) Analysis

Censored data are data or samples that are incomplete in some way, such as when certain values are unknown or ignored.  For example, in a study of the 1993 college graduation rate of individuals born in 1970, some of those born then may not have completed college by 1993; however, they could easily have done so after the end of the study.  The data in the study would be censored because the number of individuals from the 1970 group who finished their degrees after 1993 would be unknown.

The Censored Data Analysis fits censored data to one of the 24 probability distribution functions available in STATGRAPHICS Plus.  The analysis fits a given distribution to a set of data, then calculates the estimated parameters for the distribution.

To Create a Distribution Fitting (Censored Data) Analysis

1.	Choose DESCRIBE... DISTRIBUTIONS... DISTRIBUTION FITTING (CENSORED DATA)... from the Menu bar to display the Distribution Fitting (Censored Data) Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Frequency Histogram in the Analysis window.


Using the Life Tables (Intervals) Analysis

Sample items lost from a study are called censored data, which means you only know that the sample items survive until they leave the study.  For example, imagine studying a sample of 100 automobile tires to determine their average expected tread life.  During the study, some tires are lost because they are pierced and flattened; therefore, they can no longer be used for the duration of the study.  Or, suppose you are studying 100 individuals to determine the effects of a pain-relieving medication.  During the study some portion of the sample group moves to other cities and you lose contact; they can no longer be used for the duration of the study.

The Life Tables (Intervals) Analysis creates a life table from the counts of failures in a set of intervals.  Using a random sample of censored data, the program creates the life table, which estimates the survival probabilities for a population over time; that is, it calculates the probability that items in the sample group will survive at least as long as the beginning of an interval.

To Create a Life Tables (Intervals) Analysis

1.	Choose DESCRIBE...  LIFE DATA... LIFE TABLES (INTERVALS)... from the Menu bar to display the Life Tables (Intervals) Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Survival Function in the Analysis window.


Using the Life Tables (Times) Analysis

The Life Tables (Times) Analysis creates a life table from the failure times of items, which provides a nonparametric estimate of an empirical survival function.

The analysis is helpful when you must obtain survival probabilities for multicensored data.  It is also particularly useful in reliability studies when there is need to estimate the lifetime of products and when, for various reasons, items must be withdrawn from a test.  Another use is for studying and comparing clinical trials of survival rates for patients who are undergoing different treatments for the same medical condition.

To Create a Life Tables (Times) Analysis

1.	Choose DESCRIBE... LIFE DATA... LIFE TABLES (TIMES)... from the Menu bar to display the Life Tables (Times) Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Survival Function in the Analysis window.


Using the Weibull Analysis

Weibull analysis originated in 1951 when Weibull claimed that his distribution or his “family” of distributions were applicable to a wide variety of problems that ranged from the yield strength of steel to the size of adult males born in the British Isles.  Weibull never claimed that the distributions always worked or that they were always the best choice; however, time has shown that his statements were correct (Abernethy, Breneman, Medlin, and Reinman, 1983).

Today his analyses are used in numerous applications, particularly in fitting failure-time distributions to lifetime data.  The flexible shape of the distribution makes it an appropriate fit for modeling the failure times of many different and diverse processes; therefore, the distribution can accurately describe most observed lifetimes.

The Weibull Analysis in STATGRAPHICS Plus handles various types of censored lifetime data.  The data can include time-to-failure for manufactured items or survival times for individuals undergoing medical treatment in clinical trials.  The basis for most applications of the analysis is a single failure class or mode from a single part or component.  Usually the analysis begins with a few failures embedded in a large number of successful, unfailed, or “censored” units.

The analysis creates estimates for distribution parameters that are based on three estimation methods: Rank Regression, Maximum Likelihood, or Weibayes.  It then calculates a variety of goodness-of-fit tests, as well as tail areas and critical values, and graphic displays that help determine how the survival rate will change over time.

To Create a Weibull Analysis

1.	Choose DESCRIBE... LIFE DATA... WEIBULL ANALYSIS...from the Menu bar to display the Weibull Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Weibull Plot in the Analysis window.


Using the Hypothesis Tests (Describe) Analysis

Hypothesis tests are based on a sample of data that determine which of two different states is true.  The two states are commonly called the null hypothesis and the alternative hypothesis.

Hypothesis tests are a classical approach to assessing the statistical significance of findings, a technique that involves comparing empirically observed sample findings with theoretically expected findings — expected if the null hypothesis is true.  This comparison allows you to compute the probability that the observed outcomes might be due to chance alone.

A simple example is testing a coin toss for fairness.  Toss a coin a number of times, and note the number of heads.  The sample data are the sequence of heads and tails, while the statistic is the number of heads divided by the number of tosses (10).  If the proportion of heads is around 0.5, you can conclude that the evidence agrees with the hypothesis that the true probability of heads is 0.5.

You can use the hypothesis tests explained in this chapter to estimate and test hypotheses on four parameters that involve a single sample:  normal mean, normal sigma, binomial proportion, or poisson rate for a single random sample.  This means you can enter sample statistics directly into the analysis instead of first using the One-Variable Analysis.

When you are testing the normal mean and normal sigma parameters, the program calculates confidence intervals for the mean and variance using the t- and chi-square distributions, respectively, and assumes that the data come from a normal distribution.  You can set the percentage level for the confidence intervals.

For example, suppose you want to study how working in groups instead of working alone affect performance.  The hypothetical average is based on working alone.  Eighty subjects volunteered for the study and worked in teams of four.  You provided the subjects with a large number of problems to solve within a 20-minute time period, then recorded the number of correct answers.  Your alternative or research hypothesis was that those who worked in teams were more efficient than those who worked individually.  To examine this hypothesis, you tried to find evidence that allowed you to reject the null hypothesis, which was stated as: There is no difference between the average score of those who worked individually and those who worked in teams.

STATGRAPHICS Plus contains three alternative hypotheses:

•Not Equal

•	Less Than•	Greater Than.

To Create a Hypothesis Tests (Describe) Analysis

1.	Choose DESCRIBE… DISTRIBUTION FITTING… HYPOTHESIS TESTS… from the Menu bar to display the Hypothesis Tests (Describe) Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Power Curve in the Analysis window.


Using the Sample-Size Determination (Describe) Analysis

In many statistical procedures, particularly in the planning stages and before data have been collected, it is important to determine the size of the sample required to adequately address the objectives of the study.  Many research questions involve means or proportions where you must either

-	estimate a population mean, proportion, or difference with a certain degree of accuracy, or

-	test the statistical significance of the difference, either between a sample mean or proportion and some hypothesized value, or between means or proportions from two different samples.

An appropriate sample size should provide the degree of accuracy you need to estimate population means, proportions, or differences.  It should also allow you to control the risk of reaching incorrect conclusions when you test for statistical significance.

When the estimates of means and proportions come from large samples, there is less sample-to-sample variation than in estimates that come from smaller samples.  Large-sample estimates tend to be more accurate than estimates from smaller samples.

One factor that affects sample size requirements is the degree of accuracy you want to achieve — the maximum tolerable difference between the population parameter you are estimating and its true value.

The degree of accuracy attained by any sample size also depends on the spread (variability) of the variable you are testing.  Variability is typically measured by the variance or standard deviation.  In general, the smaller the variance, the smaller the number of subjects necessary to achieve the degree of accuracy you desire.  It is better to err on the “high” side because this provides an estimated sample size that has, at least, the accuracy you desire.

Another factor that affects sample size is the degree of confidence that will actually achieve accuracy.  Except in trivial cases, there is no sample size, short of a census, that allows you to be certain of achieving the accuracy you want.

The Sample Size Determination (Describe) Analysis in STATGRAPHICS Plus calculates sampling sizes for four parameters: Normal Mean, Normal Sigma, Binomial Proportion, and Poisson Rate.

For a Normal distribution, STATGRAPHICS Plus calculates the sample size required to test hypotheses, while controlling for absolute or relative error (alpha).  You can also use this analysis to determine the sample size necessary for a given power (beta) for a specific null hypothesis, alternative hypothesis, alpha level, and standard deviation, or you can use it to determine the power curve for given sample sizes.

Alpha represents the risk of a Type I error, rejecting the null hypothesis when in fact it is correct.  Beta is the risk of a Type II error; for example, accepting a false null hypothesis.  To estimate a normal sigma, STATGRAPHICS Plus detects certain differences when you specify an absolute or relative error, or when you specify a power.

The analysis for a Binomial distribution uses a normal approximation; therefore, you should not use this distribution for very small samples.  For proportions near 0.5, the analysis provides useful approximations with sample sizes of 20 or more.  For proportions less than 0.4, the analysis provides useful approximations with sample sizes of 50 or more.

For a Poisson distribution, the program estimates the mean of the distribution.  Because it uses a normal approximation, you should not use it for very small samples.  The approximation is reasonably close to normal when the mean of the Poisson distribution is 10 or larger (for example, when n = 50 and p = 0.2).  Using a Poisson distribution is advantageous because it relies only on the mean frequency, which is applicable in situations where the probability of an event occurring is very small compared with the size of the sample.

To Create a Sample-Size Determination Analysis

1.	Choose DESCRIBE… SAMPLE-SIZE DETERMINATION… from the Menu bar to display the Sample Size Determination Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Power Curve in the Analysis window.


Using the Subset Analysis

The Subset Analysis provides the ability to calculate statistics for a single column of data at each level of a second code variable.  You can calculate separate summary statistics and plot means and confidence intervals for the subsets of data.

You define the subsets using the values in any variable that can partition the observations into subsets; for example, country, fiscal year, age, sex.  Doing this allows you to compare the central tendency, spread, and shape among the groups of data.  For example, using the Cardata sample dataset, you might want to calculate statistics on miles per gallon ratings for each of three levels of origin.  This is easily done using this analysis, which can calculate summary statistics for each level of a variable.

To Create a Subset Analysis

1.	Choose DESCRIBE… NUMERIC DATA… SUBSET ANALYSIS… from the Menu bar to display the Subset Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and the Scatterplot in the Analysis window.


Using the Row-Wise Statistics Analysis

The Row-Wise Statistics Analysis provides the capability to calculate and save statistics on a row-wise basis for data that are in two or more columns.  The analysis calculates summary statistics for each row in a set of columns.  It is designed to save the statistics so you can use them in other analyses when the data are not arranged in the usual column-wise manner.

To Create a Row-Wise Statistics Analysis

1.	Choose DESCRIBE… NUMERIC DATA… ROW-WISE STATISTICS… from the Menu bar to display the Row-Wise Statistics Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Scatterplot in the Analysis window.


Using the Power Transformations Analysis

If, after performing an exploratory analysis on a set of data, the normality of the data appears to be questionable, a transformation of the data is in order even though it is often difficult to determine what type of transformation will have the most beneficial effect.  The Box-Cox power transformation automatically identifies the optimal transformations.

The program determines the optimal Box-Cox transformation by finding the value of the Lambda1 parameter, which minimizes the mean squared error.  The StatAdvisor displays the transformation for the value of Lambda 1 you chose.  You can compare the results of the transformation with other values of Lambda1 by choosing the MSE Comparison Table option.

To Create a Power Transformations Analysis

1.	Choose DESCRIBE… NUMERIC DATA… POWER TRANSFORMATIONS… from the Menu bar to display the Power Transformations Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Scatterplot in the Analysis window.


Using the Statistical Tolerance Limits Analysis

The Statistical Tolerance Limits Analysis computes statistical tolerance limits, given a sample size, mean, and standard deviation.  The analysis also determines the sample size needed to obtain nonparametric limits for a given proportion of the population.

Statistical tolerance limits are limits that contain a certain proportion of the distribution of a quality characteristic.  When the parameters of a distribution are known, these limits are easily calculated.  However, usually the distribution and its parameters are unknown, and you must estimate the tolerance limits from a sample of population data.

This analysis provides both normal tolerance limits and nonparametric tolerance limits.  Use normal tolerance limits when it can reasonably be assumed that the data collected are well described by a normal distribution.  When the normality of the data cannot be assumed, use Nonparametric limits.

To Create a Statistical Tolerance Limits Analysis

1.	Choose DESCRIBE... NUMERIC DATA... STATISTICAL TOLERANCE LIMITS... from the Menu bar to display the Statistical Tolerance Limits Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Tolerance Plot in the Analysis window.


Using the Probability Distributions Analysis

Before you can understand or apply methods of inferential statistics to data, you need to be familiar with the science of uncertainty or probability.  Probability is a mathematical model describing the probability of observing various values of a random variable so you can evaluate and control the likelihood that a statistical inference is correct.  A random variable, also called a statistical variable, is a function that maps the outcome of an experiment to a real number.

In daily life, probability is normally defined as the relative frequency of the occurrence of an event that can be repeated many times.  For example, you might say that the chance of winning the lottery is “one in a million.”  Or, if you repeatedly sample temperatures from a process, and get values below 150 degrees half the time, the probability of a reading below 150 degrees is equal to 0.5 or 50 percent.

Just as a table of frequencies is called a frequency distribution, a table of probabilities is called a probability distribution.  The distribution is determined by probabilities associated with the underlying sample space, and by the sampling design.  Many statistical applications involve estimating the mean and standard deviation of a probability distribution based on sample data, while the probability distribution of a discrete random variable is based on the probability associated with each possible value assumed by the random variable.

The probability distributions in STATGRAPHICS Plus contain functions that let you perform three basic operations for each of 24 different distributions:

•	generate random numbers

•	calculate probabilities

•	create plots of probability and cumulative distributions.

The 24 distributions are:

Bernoulli

A distribution whose outcome has only two possibilities: Success or failure; for example, heads or tails; good or bad; defective or nondefective.  The probability of a success remains the same from trial to trial.  Data fit to this distribution should have values of only 0 or 1.

Binomial

A distribution for observing the number of successes in a fixed number (sequence) of independent or Bernoulli trials.  There are only two possible outcomes for each trial.  When you use this distribution you must choose the number of trials (experiments).  Data fit to this distribution should be integers greater than or equal to 0.

When you use this distribution, the Number of Trials text box is activated so you can enter the number of trials that will be in the analysis.

Discrete Uniform

A distribution that allocates equal probabilities to all integer values between a Lower and an Upper limit.  Data fit to this distribution should be integers.

Geometric

A distribution that characterizes the number of failures that occur before the first success in a series of Bernoulli trials; a special case of Negative Binomial distribution, where k = 1.  Data fit to this distribution should be integers.

Hypergeometric

A distibution that arises when a random selection is made between objects of two distinct types (success, fail).  The sampling occurs without replacement; that is, each time an item is drawn and studied, it is not placed back into the population.  The distribution gives the probability of the number of successes.  Data fit to this distribution should be integers greater than or equal to 0.

When you use this distribution, the Number of Trials and Population Size text boxes are activated so you can enter numbers for the number of trials that will be in the analysis, as well as for the size of the population.

Negative Binomial

A distribution that characterizes the number of failures before the kth success in a series of Bernoulli trials.  When you use this distribution you must declare the number of successes.  Data fit to this distribution should be integers greater than 0.

When you use this distribution, the Number of Successes text box is activated so you can enter the number of successes that will be in the analysis.

Poisson

A distribution that counts the number of times a certain event occurs during a given unit of time or in a given area of volume (or weight, distrance, or any other unit of measurement).  The probability that an event occurs in a given unit of time, area, or volume is the same for all the units.  The number of events that occur is independent of the number that occur in other units.  Data fit to this distribution should be integers greater than or equal to 0.

Beta

A distribution useful for random variables that are constrained to lie between 0 and 1; characterized by two parameters: Shape 1 and Shape 2.

Cauchy

A distribution that fits data that follow a Cauchy distribution.  The distribution's probability density function has no mean and an infinite variance.  It is characterized by two parameters:  Mode and Scale.  Data fit to this distribution should be continuous with a Mode between -infinity to +infinity and a Scale greater than 0.

Chi-Square

A distribution useful for random variables that are constrained to be greater than 0; characterized by one parameter: Degrees of Freedom.  This distribution is used most often as the sampling distribution for various statistical tests.

Erlang

A distribution useful for random variables that are constrained to be greater than 0, such as the time required to complete a task; characterized by two parameters: Shape and Scale.  This distribution is a special case of the Gamma distribution, which requires that the Shape parameter be an integer.

Exponential

A distribution that fits time-series data, such as arrival times, where arrivals are expected at a constant rate; useful for random variables that are constrained to be greater than 0.  This distribution is a special case of both the Gamma and the Weibull distributions.

Extreme Value

A distribution useful for random variables that are constrained to be greater than 0; characterized by two parameters: Mode and Scale.  Also known as a Gumbels' distribution.

F (Variance Ratio)

A distribution useful for random variables that are constrained to be greater than 0; characterized by two parameters: Numerator Degrees of Freedom and Denominator Degrees of Freedom.  It is often used as the distribution for test statistics that are created as variance ratios.

Gamma

A distribution useful for random variables that are constrained to be greater than 0; characterized by two parameters: Shape and Scale.  This distribution is often used to model data that are positively skewed, such as the time required to complete a task.

Laplace

A distribution useful for random variables from a distribution that is more peaked than a Normal distribution; characterized by two parameters: Mean and Scale.  This distribution is sometimes called the double exponential distribution because it looks like an exponential distribution with a mirror image.

Logistic

A distribution useful for random variables that are not constrained to be greater than or equal to 0; characterized by two parameters: Mean and Standard Deviation.

Lognormal

A distribution useful for processes in which the value is a random proportion of the previous value, such as personal incomes or particle sizes from breakage processes.  The log of data that follow the lognormal distribution are normally distributed.  The distribution is positively skewed and can take on various shapes.  Data fit to this distribution should be values greater than 0; characterized by two parameters: Mean and Standard Deviation.

Normal

A distribution useful in instances when you plot a Frequency Histogram of the data and the bars form a common, bell-shaped curve.

Pareto

A distribution with a decreasing density function.  One parameter, Shape, is necessary to specify the distribution.  Data fit to this distribution should be values greater than 0.

Student's t

A distribution useful in forming confidence intervals when the variance is unknown, testing to determine if two sample means are significantly different, or testing to determine the significance of coefficients in a regression.  The distribution is similar in shape to a Normal distribution.  The mean of the t distribution is always equal to 0, while the standard deviation is usually slightly greater than 1.  One parameter, Degrees of Freedom, is necessary to completely specify the distribution.

Triangular

A distribution useful for random variables that are constrained to lie between two fixed limits.  Unlike the Uniform distribution, in which all the values between the limits are equally likely, the Triangular distribution peaks at some value between the two limits.  This distribution is characterized by three parameters: Lower Limit, Central Value (Mode), and Upper Limit.

Uniform

A distribution useful for characterizing data that range over an interval of values, each of which is equally likely.  The distribution is completely determined by the smallest possible value, a, and the largest possible value, b.  The mean equals (a + b)/2, while the variance equals ((b - a)^2)/12.  For discrete data, there is a related discrete uniform distribution.

Weibull

A distribution useful for random variables that are constrained to be greater than 0; characterized by two parameters: Shape and Scale.  Because its failure-rate curves can take various shapes, it is an appropriate model for product failures.  The distribution is a generalization of an Exponential distribution.

To Create a Probability Distribution Analysis

1.	Choose DESCRIBE... DISTRIBUTIONS... PROBABILITY DISTRIBUTIONS... from the Menu bar to display the Probability Distributions Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Density/Mass Function Plot for the distribution you chose.


Using the Probability Plots Analysis

The Probability Plots Analysis allows you to create seven different types of probability plots to help determine if one variable comes from a particular type of distribution.  After you create and examine the plots, you can fit a distribution using a Distribution Fitting Analysis for either uncensored or censored data.

To Create a Probability Plots Analysis

1.	Choose DESCRIBE... DISTRIBUTIONS... PROBABILITY PLOTS... from the Menu bar to display the Probability Plots Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Uniform Plot in the Analysis window.


Using the Arrhenius Plot Analysis

When operating under normal conditions, it is often not possible to obtain sufficient amounts of data for fitting life distributions.  However, by increasing stress levels, you can fail an adequate number of items, collect the data you need, and attempt to fit the distribution.

The Arrhenius Plot Analysis in STATGRAPHICS Plus fits an Arrhenius model to a set of percentiles taken at two or more study temperatures.  The fitted model is then used to predict the corresponding percentile at a normal temperature.  The analysis models the relationships between failure rates at high stress levels and normal operating levels.  This analysis is a Physical Acceleration model that is useful when thermal stresses are significant.  You can use this analysis to estimate the constants in an Arrhenius model.

The form of the Arrhenius model is:

P = ΑeΔ/kT

where

P = the estimated percentile

A and Δ = the unknown constants to be estimated

k = Boltzmann's Constant (8.617 10-5 EV/degrees Kelvin)

T = the temperature in degrees (Kelvin)

Using the estimated percentiles at the temperature at which it carries out the tests, the program calculates the unknown constants in the Arrhenius model.

To Create An Arrhenius Plot Analysis

1.	Choose DESCRIBE... LIFE DATA... ARRHENIUS PLOTS... from the Menu bar to display the Arrhenius Plot Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Arrhenius Plot in the Analysis window.


Using the Analyses in the Compare Menu

This menu allows you to access analyses you use to generate and compare descriptive statistics.  There are four types of analyses:

Comparing Two Data Samples

Assessing the Problem

Using the Two-Sample Comparison Analysis

Using the Paired-Sample Comparison Analysis

Using the Hypothesis Tests (Compare) Analysis

Using the Sample-Size Determination (Compare) Analysis

Comparing Multiple Samples

Using the Multiple-Sample Comparison Analysis

Using the Comparison of Proportions Analysis

Using the Comparison of Counts Analysis

Performing Analysis of Variance Tests

Using One-Way ANOVA

Using Multifactor ANOVA

Using Variance Components Analysis


Using the Two-Sample Comparison Analysis

The primary purposes of the Two-Sample Comparison Analysis are to:

-	calculate confidence intervals for the difference between the population means and the ratio of the population variances

-	compare hypothesis tests of the means, variances, and medians.

The analysis runs tests to determine if there are statistically significant differences between the two two samples, then creates various reports and graphs that contain the results for each data sample.

To Create a Two-Sample Comparison Analysis

1.	Choose COMPARE… TWO-SAMPLE… TWO-SAMPLE COMPARISON… from the Menu bar to display the Two-Sample Compaison Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Frequency Histogram in the Analysis window.


Using the Paired-Sample Comparison Analysis

The Paired-Sample Comparison Analysis parallels the Two-Sample Comparison Analysis except, it compares data collected in pairs; that is, you want to compare two sets of data because the observations in the samples are paired.  For example, suppose you are analyzing data that contain information about the miles per gallon ratings achieved by the same automobile during highway driving and city driving.  The data represent two different sets of values for each automobile: miles per gallon ratings for highway driving and miles per gallon ratings for city driving.

When data are from paired samples, you analyze it by calculating the difference between each value in each pair of observations.  That is, you treat the paired differences as though they were a single sample from a population of differences.

To Create a Paired-Sample Comparison Analysis

1.	Choose COMPARE… TWO SAMPLES… PAIRED-SAMPLE COMPARISON… from the Menu bar to display the Paired-Sample Comparison Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Scatterplot in the Analysis window.


Using the Hypothesis Tests (Compare) Analysis

Hypothesis tests are based on a sample of data to determine which of two different states is true.   The two states are commonly called the null hypothesis and the alternative hypothesis.  Hypothesis tests are a classical approach to assessing the statistical significance of findings, a technique that involves comparing  empirically observed sample findings with theoretically expected findings — expected if the null hypothesis is true.  This comparison allows you to compute the probability that the observed outcomes might be due to chance alone.

Hypothesis tests are a classical approach for assessing the statistical significance of findings.  Basically, the technique involves comparing empirically observed sample findings with theoretically expected findings; expected if the null hypothesis is true.  This comparison allows you to compute the probability that the observed outcomes might be due to chance alone.  The data you use in this analysis should be sample statistics and sample sizes rather than raw data.

The Hypothesis Tests (Compare) Analysis in STATGRAPHICS Plus tests hypotheses about the sample means and variances for two or more random samples.

The analysis allows you to test four types of parameters: Normal Mean, Normal Sigma, Binomial Proportions, and Poisson Rate.  In addition, you can control for error tolerance, power, and sample size; set confidence intervals; and choose from three alternative hypotheses: not equal, less than, or greater than.

To Create a Hypothesis Tests (Compare) Analysis

1.	Choose COMPARE… TWO SAMPLES… HYPOTHESIS TESTS… from the Menu bar to display the Hypothesis Tests (Compare) Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Power Curve in the Analysis window.


Using the Multiple-Sample Comparison Analysis

The Multiple-Sample Comparison Analysis compares two or more samples to test the probability that when the null hypothesis is true, at least one of the observed significance levels will be less than a specified number.  The more comparisons you make, the more likely it is that one or more pairs will be statistically different, even if all the population means are equal.  Special tests in the analysis determine the means that are different, and/or the means that are the smallest or largest.

To Create a Multiple-Sample Comparison Analysis

1.	Choose COMPARE… TWO-SAMPLES… MULTIPLE-SAMPLE COMPARISON… from the Menu bar to display the Multiple-Sample Comparison Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Scatterplot in the Analysis window.


Using One-Way ANOVA

One-Way ANOVA is a statistical technique that produces a one-way analysis of variance for an interval-level dependent variable by an independent variable.  The analysis examines the effect of one qualitative factor on one response variable where the design can be balanced or unbalanced.

Assumptions of the analysis are that the:

-	populations from which you collect the samples must be normally or approximately normally distributed

-	samples must be independent

-	variances of the populations must be equal.

The analysis tests the null hypothesis that all population means are equal, versus the alternative hypothesis, that at least one population mean is different.

This analysis requires all response data to be within a single column with a factor or code column that defines the sample that a particular observation is taken from.  Each observation is classified into groups according to one factor.  For example, you might examine how three different reading textbooks produce different reading levels for children, or how cylinders in an automobile engine affect its mileage rate.

To Create a One-Way ANOVA

1.	Choose COMPARE… ANALYSIS OF VARIANCE… ONE-WAY ANOVA… from the Menu bar to display the One-Way ANOVA dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Scatterplot in the Analysis window.


Using Multifactor ANOVA

Multifactor ANOVA is basically the same as One-Way ANOVA, except that it examines the effects of two or more factors on one variable, and you typically use data you collect for a designed experiment.  The design can be balanced or unbalanced and can also include covariates.

You can use the default values and perform a standard analysis, or you can customize the analysis in a variety of ways, such as using either Type I or Type III sums of squares, or choosing the order of interactions.

The Multifactor ANOVA Analysis is useful in a range of disciplines.  For example, in marketing studies you might test how product sales are affected by alternative pricing, advertising techniques, and different packaging options.  In medical studies, you might test how disease is combated using different combinations of drugs, varying dosages of drugs, and alternative treatment schedules.  In agricultural studies, you might measure how weight gain and the overall health of cattle are affected by brands of feed, amounts of medication, and type of breed.

To Create a Multifactor ANOVA

1.	Choose COMPARE… ANALYSIS OF VARIANCE… MULTIFACTOR ANOVA… from the Menu bar to display the Multifactor ANOVA dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Scatterplot in the Analysis window.


Using the Variance Components Analysis

The Variance Components Analysis uses fully nested, random effects models, which are classification effects where the levels of the effect are assumed to be randomly chosen from an infinite population of possible levels.  The analysis estimates the contribution each of the random effects makes to the variance of the dependent variable, and analyzes the effect of one or more qualitative factors on one response variable. The number of observations does not need to be equal at all combinations of the factor levels.

An example of a nested design would be soil samples in an agricultural or geological study taken from five geographic regions, with subsamples taken from 12 areas within each region.  Another example, a study of worker productivity, samples workers by choosing 10 factories at random, then randomly chooses four departments within each factory, then again randomly chooses five workers from each department.

To Create a Variance Components Analysis

1.	Choose COMPARE… ANALYSIS OF VARIANCE… VARIANCE COMPONENTS… from the Menu bar to display the Variance Components Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Scatterplot in the Analysis window.


Using the Sample-Size Determination (Compare) Analysis

In many statistical procedures, particularly in the planning stages and before data have been collected, it is important to determine the size of the sample required to adequately address the objectives of the study.  Many research questions involve means or proportions where you must either

-	estimate a population mean, proportion, or difference with a certain degree of accuracy

-	test the statistical significance of the difference, either between a sample mean or proportion and some hypothesized value, or between means or proportions from two different samples.

An appropriate sample size should provide the degree of accuracy you need to estimate population means, proportions, or differences.  It should also allow you to control the risk of reaching incorrect conclusions when you test for statistical significance.

When the estimates of means and proportions come from large samples, there is less sample-to-sample variation than in estimates that come from smaller samples.  Large-sample estimates tend to be more accurate than estimates from smaller samples.

One factor that affects sample size requirements is the degree of accuracy you want to achieve — the maximum tolerable difference between the population parameter you are estimating and its true value.

The degree of accuracy attained by any sample size also depends on the spread (variability) of the variable you are testing.  Variance and/or standard deviation are typically used to measure variability.  In general, a small variance requires a small number of subjects to achieve the degree of desired accuracy.  It is better to err on the “high” side because this provides an estimated sample size that has, at least, the accuracy you desire.

Another factor that affects sample size is the degree of confidence that will actually achieve accuracy.  Except in trivial cases, there is no sample size, short of a census, that allows you to be certain of achieving the accuracy you want.

The Sample-Size Determination (Compare) Analysis in STATGRAPHICS Plus has two purposes: to help determine the number of observations required to provide sufficiently powerful estimates; and to analyze the power curve for samples you have already drawn.

You can calculate sample sizes for testing five types of parameters: Two Normal Means, Two Normal Sigmas, Two Binomial Proportions, Two Poisson Rates, and Several Normal Means.  In addition, you can control for error tolerance or power; set the confidence interval; and choose from three alternative hypotheses: not equal, less than, or greater than.

To Create a Sample-Size Determination (Compare) Analysis

1.	Choose COMPARE… TWO SAMPLES… SAMPLE-SIZE DETERMINATION… from the Menu bar to display the Sample-Size Determination Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Power Curve in the Analysis window.


Using the Comparison of Proportions Analysis

The Comparison of Proportions Analysis uses an ANOM (analysis of means) statistical technique, which is conceptually similar to a control chart.  The plot shows the observed proportions plotted against the decision limits.  This type of analysis uses critical values from a sampling distribution, which lend power that is comparable to an ANOVA under similar conditions.  While an ANOM is not the best test from a mathematical perspective, it is easier to use and understand, which gives it an advantage over ANOVA.

The Comparison of Proportions Analysis compares the proportion of items that have a particular characteristic of an attribute.  For example, at some time or another, manufacturers face the problem of having a variable that turns out to also be an attribute such as a light bulb that will or will not light or a battery whose life is or is not below standard (Ott, 1979).

The data for this analysis should meet these criteria:

-	the sampling distribution of the proportion should be a binomial distribution

-	if np and n (1 - p ) are both greater than 5, you should be able to use a normal distribution to approximate the sampling distribution of a portion.

If the variable you are using consists of attribute data, you can use an ANOM to compare the proportion of the items to test for differences between the proportions.

The analysis uses three or more proportions to test the hypothesis that all the proportions are equal.  The results include several reports as well as an ANOM (analysis of means) plot.

To Create a Comparison of Proportions Analysis

1.	Choose COMPARE… MULTIPLE SAMPLES… COMPARISON OF PROPORTIONS… from the Menu bar to display the Comparison of Proportions Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Analysis of	 Means Plot in the Analysis window.


Using the Comparison of Counts Analysis

The Comparison of Counts Analysis uses an ANOM (analysis of means) technique for comparing several populations you use when the response is count data.  This analysis is essentially the same as the Comparison of Proportions Analysis, except that the sample size is such that the analysis uses a normal approximation to the Poisson distribution.

Ott (1979) provides this example of a quality control environment, where workers are monitoring the number of defective items from a production line.  An inspection unit is first defined for each of the populations, which might be defined as a period of time, a fixed number of items, or a fixed unit of measurement; for example, an inspection unit of a square-foot section of material from a weaving loom.

Periodically, a square-foot section of the material is examined and the number of flaws is recorded.  The number of items with the defect is noted as c1,...,k.  The results are then calculated and plotted to see if any count falls outside the decision lines, which means there is a statistically significant difference among the counts.

To Create a Comparison of Counts Analysis

1.	Choose COMPARE... MULTIPLE SAMPLES... COMPARISON OF COUNTS...from the Menu bar to display the Comparison of Counts Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Analysis of Means Plot in the Analysis window.


Assessing the Problem

Whether the problem you are solving is simple or complex, making a detailed examination of the data is required.  Examining data involves investigating the distribution of the values, and testing for normality and measures of variation, including the mean, standard deviation, and confidence intervals.  Looking at the distribution of the values is important for determining the appropriateness of the statistical methods you are planning to use for either testing hypotheses or building models.

When data are normally distributed, calculating basic descriptive statistics may be an appropriate way to summarize the data.  These types of statistics provide basic information such as the mean, minimum and maximum values, different measures of variation, as well as information about the shape of the distribution.  The shape of the distribution is important because it provides information about the frequency of the values from different ranges of the variable, and researchers are typically interested in how well a distribution approximates a normal distribution.

What do you do when you know nothing about the assumptions underlying the population, or when the assumptions are questionable?   In these cases, nonparametric tests are often more powerful than statistical tests based on the assumption of normality.  For example, when you compare two independent samples, the Wilcoxon Mann-Whitney test does not assume that the difference between the samples is normally distributed, whereas its parametric counterpart, the two-sample t-test does.  At least one nonparametric test exists for each of its parametric counterpart.


Using the Analyses in the Relate Menu

This menu allows you to access analyses you use to model the relationship between dependent and independent variables.

Using the Simple Regression Analysis

Using the Polynomial Regression Analysis

Using the Box-Cox Transformation Analysis

Using the Multiple Regression Analysis


Using the Simple Regression Analysis

The Simple Regression Analysis estimates a linear or nonlinear regression between two variables.  The model relates one dependent variable to one independent variable by minimizing the sum of the squares of the residuals for the fitted line.  In addition to a straight line, you can also use the analysis to estimate a number of standard nonlinear models.  The analysis calculates and compares the goodness of fit for each model.

The analysis can automatically fit any of 12 models.  The preferred model is the linear model unless another model type significantly increases the R-Squared value.  To choose the best model, you must fit the data to all the models and compare the statistics.  You can also use the Comparison of Alternative Models tabular option to compare correlation coefficients and R-Squared values for several transformed model types.

You can plot the fitted line and the residuals for all the models.  STATGRAPHICS Plus also creates and plots predictions for given values of X.  You can also save the residuals and predictions for use in future analyses.

To Create a Simple Regression Analysis

1.	Choose RELATE… SIMPLE REGRESSION… from the Menu bar to display the Simple Regression Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Plot of Fitted Model in the Analysis window.


Using the Polynomial Regression Analysis

Polynomial regression analysis is regression analysis for relationships that are or are suspected to be nonlinear.  It is known as polynomial regression because the regression equation for a curvilinear (nonlinear) relationship is a polynomial equation.  The more turns in the regression line, the higher the power the terms in the equation must be.

The first degree of freedom contains the linear effect across all categories; the second degree of freedom, the quadratic effect; and so on for the higher order effects

Table 1.  Polynomial Regression Degrees of Freedom

Turns of	Order of	Number of	Type of

Regression Line	Degree	Terms	Analysis

0	First	1	Linear

1	Second	2	Quadratic

2	Third	3	Cubic

3	Fourth	4	Quartic

4	Fifth	5	Quintic

A polynomial equation is an equation in which one of the terms is raised to a power greater than 1.  For example, the regression equation Y = a + b1X + b2X2 + b3X3 is a polynomial equation because X is raised to the second and third powers.  The highest power of a term gives the equation its “degree” or “order.”  The equation shown above is a third-order (or degree) polynomial equation.

The Polynomial Regression Analysis calculates a polynomial regression model between a single dependent variable Y and a single independent variable X.  Use this analysis if you believe your model fits a polynomial instead of a linear model.  You can fit polynomial models up to Order 8.

To Create a Polynomial Regression Analysis

1.	Choose RELATE… POLYNOMIAL REGRESSION… from the Menu bar to display the Polynomial Regression Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Plot of Fitted Model in the Analysis window.


Using the Multiple Regression Analysis

There are times in regression analysis when you want to draw conclusions about the relationship of variables as well as have a description of the observed data.  Multiple regression is appropriate to use when the data consist of two or more numeric independent variables and a numeric dependent variable.  The ability to include several independent variables also provides a method to use when there is a need to avoid the risk of oversimplifying the effect of one independent variable on one dependent variable.

Real explanatory power comes from the way interpretations are made about the regression coefficients.  Multiple regression lets you estimate the effect of an independent variable on a dependent variable and, at the same time, control for the effects of all the other independent variables in the model.  In other words, because there are multiple independent variables in the model, you can compare their effects, and in doing so, estimate which independent variable has the most explanatory power.

Basically, multiple regression includes specifying the model, interpreting the regression statistics, comparing the independent variables, and interpreting the model.  Multiple regression analysis also allows you to use weights to force the intercept to 0 (regression through the origin), or to perform a stepwise regression.  Like simple regression, multiple regression uses least squares to estimate the regression model.

To Create a Multiple Regression Analysis

1.	Choose RELATE… MULTIPLE REGRESSION… from the Menu bar to display the Multiple Regression Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Component Effects Plot in the Analysis window.


Using the Box-Cox Transformation Analysis

In the context of fitting a simple regression model, it is assumed that the error variances in the different groups are homogeneous and uncorrelated with the means.  It is also assumed that the error terms are normally distributed.  If there are departures from the simple regression model, it is helpful to transform the data to stabilize stabilize the error variances and normalize the error terms.  Transforming the data can also help linearize a curvilinear regression relation.

The Box-Cox Transformations Anlaysis automatically identifies a transformation from a family of power transformations.  The analysis determines the appropriate transformation parameter, Lambda1, which minimizes the mean squared error (MSE) of the fitted model.

To Create a Box-Cox Transformations Analysis

1.	Choose RELATE… BOX-COX TRANSFORMATIONS ANALYSIS…from the Menu bar to display the Box-Cox Transformations Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Plot of Fitted Model in the Analysis window.


Using Analyses for Quality Control

Quality Control for STATGRAPHICS Plus provides analyses you use for statistical quality control.

Overview of Quality Control

Identifying Defects

Using Pareto Analysis

Analyzing the Capability of a Process

Using Process Capability Analysis

Determining Statistical Control of Variable Data

Using Variables Control Charts

Using X-bar and R Charts

Using X-bar and S Charts

Using X-bar and S-Squared Charts

Using Individuals Charts

Determining Statistical Control of Attribute Data

Using Attributes Control Charts

Using p Charts

Using np Charts

Using u Charts

Using c Charts

Using Time-Weighted Charts

Using Moving Average (MA) Chart Analysis

Using Moving Average (MA) Individuals Chart Analysis

Using EWMA Chart Analysis

Using EWMA Individuals Chart Analysis

Using CuSum Chart (V-Mask) Analysis

Using CuSum Individuals Chart (V-Mask) Analysis

Using CuSum Chart (H-K) Analysis

Using CuSum Individuals Chart (H-K) Analysis

Using Multivariate Control Chart Analysis

Using ARIMA Analysis

Using ARIMA Individuals Chart Analysis

Using Toolwear Chart Analysis

Using  Toolwear Individuals Analysis

Using Acceptance Chart Analysis

Using the Acceptance Individuals Control Chart Analysis

Using Gage R&R Analysis

Using Custom Chart Analysis

Using Fishbone Diagram Analysis

Using Acceptance Sampling

Using Acceptance Sampling by Attributes Analysis

Using Acceptance Sampling by Variables Analysis


Using X-bar and R Charts

The X-bar and R charts are the most commonly used pairs of variables charts.  X-bar is the average of the values in small subgroups — a measure of location, while R is the range of values within each subgroup (highest minus lowest) — a measure of spread.

To Create a X-bar and R Charts Analysis

1.	Choose SPECIAL... QUALITY CONTROL... VARIABLES CONTROL CHARTS... X-BAR AND R… from the Menu bar to display the X-bar and R Charts Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and X-bar Chart in the Analysis window.


Using X-bar and S Charts

X-bar and S charts were developed for the times when it is desirable to estimate the process standard deviation directly instead of using the range.  For example, the S Chart is generally more appropriate than the R Chart when the subgroup size is eight or more.  The process standard deviation, S, is more difficult to calculate, and usually is less sensitive in detecting special causes of variation when only a single value in a subgroup is unusual.  These charts are also always used as a pair.

To Create a X-bar and S Charts Analysis

1.	Choose SPECIAL... QUALITY CONTROL... VARIABLES CONTROL CHARTS... X-BAR AND S… from the Menu bar to display the X-bar and S Charts Analysis dialog box

2.	Complete the dialog box and click OK to display the Analysis Summary and X-bar and S Chart in the Analysis window.


Using X-bar and S-Squared Charts

Montgomery (1997) notes that most quality engineers prefer to use either an R Chart or an S Chart to monitor process variability, using the S Chart with moderate to large sample sizes.  Others recommend using a control chart that uses limits based on the sample variances — the S-Squared Chart.

To Create a X-bar and S-Squared Charts Analysis

1.	Choose SPECIAL... QUALITY CONTROL... VARIABLES CONTROL CHARTS... X-BAR AND S-SQUARED… from the Menu bar to display the X-bar and S-Squared Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and X-bar Chart in the Analysis window.


Using Individuals Charts

There are instances when it is necessary for process control to be based on individual readings, instead of subgroups.  This usually happens when the sample is made up on a single unit.  Montgomery (1997) provides some examples; for example, when:

•	automated inspection and measurement technology is used and every unit that is manufactured is analyzed

•	the production rate is very slow and it is inconvenient to let sample sizes of n > 1 accumulate before they are analyzed

•	repeat measurements on a process differ only because of laboratory or analysis error (chemical processes).

The control process uses the moving range of two successive observations to estimate the variability.

To Create an Individuals Charts Analysis

1.	Choose SPECIAL... QUALITY CONTROL... VARIABLES CONTROL CHARTS... INDIVIDUALS… from the Menu bar to display the Individuals Chart Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Individuals Chart in the Analysis window.


Using p Charts

A p Chart measures the proportion of defective or nonconforming items in a group of items being inspected.  The items could refer to a sample of 25 pieces, taken three times a day; some percentage of production grouped on an hourly or daily basis; or the proportion of on-time deliveries.

A fraction rejected p is defined as the ratio of the number of defective (nonconforming) items found in any inspection to the total number of items actually inspected.  A fraction rejected is almost always expressed as a decimal fraction.

This chart is the most versatile and widely used attributes control chart.  It can be applied to quality characteristics that are considered to be attributes, even though they might also have been measured as variables.  If the classification of an individual article is accepted or rejected as the result of an inspection, a p chart can be applied to one or more quality characteristics.

To Create a p Chart Analysis

1.	Choose SPECIAL... QUALITY CONTROL... ATTRIBUTES CONTROL CHARTS... p CHART... from the Menu bar to display the p Chart Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and p Chart in the Analysis window.


Using np Charts

An np Chart is appropriate for use whenever the subgroup size varies and the control chart must show the actual number of rejected items rather than the fraction or proportion rejected.  If the actual numbers of rejects were to be plotted, the central line on the chart as well as the control limits would have to be changed each time there was a change in the size of the subgroup.  If the subgroup size remains constant, a chart for actual numbers can be used.

To Create a np Chart Analysis

1.	Choose SPECIAL... QUALITY CONTROL... ATTRIBUTES CONTROL CHARTS... np CHART... from the Menu bar to display the np Chart Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and np Chart in the Analysis window.


Using c Charts

A c Chart has a much more restricted area of usefulness than other control charts in that it is mostly used for nonconformities.  However, in certain manufacturing and inspection situations the chart is definitely needed.  It must first be determined if its use is appropriate from the viewpoint of statistical theory, then it is necessary to determine if it is really the best technique to use for the intended purpose.

A nonconforming or defective item is one that fails in some way to conform to one or more specifications.  Each time the item fails to conform is a nonconformity, therefore, every nonconforming item contains one or more nonconformities.  When it is necessary to make a total count of the nonconformities in each item, or in each group of an equal number of similar items, it may be reasonable to use a technique based on a Poisson distribution, which means using either a c Chart or a u Chart.

To Create a c Chart Analysis

1.	Choose SPECIAL... QUALITY CONTROL... ATTRIBUTES CONTROL CHARTS... c CHART... from the Menu bar to display the c Chart Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and c Chart in the Analysis window.


Using u Charts

A u Chart measures the number of nonconformities (defects) per inspection reporting unit in subgroups that can have varying sample sizes.  It is similar to a c chart except that the number of nonconformities is expressed on a per unit basis.  Both u and c charts are appropriate for the same type of information; however, a u Chart can be used if the sample includes more than one unit and it must be used if the sample size varies from period to period.

To Access the u Chart Analysis

1.	Choose SPECIAL... QUALITY CONTROL... ATTRIBUTES CONTROL CHARTS... u CHART... from the Menu bar to display the Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and the c Chart in the Analysis window.

The u Chart Analysis contains three tabular options and two graphical options. The tabular options are: Analysis Summary, Subgroup Reports, and Runs Tests. The graphical options are: u Chart and OC Curve.


Using Pareto Analysis

A defect or nonconformity is the unit of a product that does not satisfy one or more specifications for a product; that is, each specific point at which a unit does not meet the specification is known as a defect or nonconformity (Montgomery, 1997).  This type of data is informative because there will usually be more than one type of nonconformity.  By analyzing the defects by type, you often gain valuable information about the cause.

In Montgomery’s printed circuit board example, there were 16 different types of defects.  Plotting those defects on a Pareto Chart points out the major types of the defects (those that occur most frequently).

The Pareto Analysis in STATGRAPHICS Plus attempts to sort out the vital few causes to gain an understanding of where to begin an improvement process.   The analysis plots the frequency of each defect type, which helps identify the most frequently occurring type of defects.  The analysis does not identify the most important defects; it simply reveals the most frequent defects.

The Pareto Chart is a histogram for categorical data.  This chart, together with attributes control charts, helps to identify and rank order the most important causes of a problem within a process, or to track the progress of changes to a process.

To Create a Pareto Analysis

1.	Choose SPECIAL... QUALITY CONTROL... PARETO ANALYSIS... from the Menu bar to display the Pareto Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and the Pareto Chart in the Analysis window.


Using Process Capability Analysis

Process capability studies in STATGRAPHICS Plus estimate process capability for processes that generate data from one of eight distributions: Normal, Exponential, Extreme Value, Gamma, Laplace, Logistic, Lognormal, and Weibull.  You can run the analysis with specifications that are one-sided, two-sided, or asymmetric.  Normal and distribution-free tolerance limits, and nonnormal capability indices are available as options.

To Create a Process Capability Analysis

1.	Choose SPECIAL... QUALITY CONTROL... PROCESS CAPABILITY ANALYSIS... from the Menu bar to display the Process Capability Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and the Capability Plot in the Analysis window.


Using Moving Average (MA) Chart Analysis

The primary purpose of the analysis is to control current processes; however, you can also use the analysis to incorporate past history of a process into charted points.  A moving average chart is particularly useful in production lines that require longer times to produce a single item.  By adding each new item to the subgroup as the item is produced, you always have an up-to-date picture of the process.

A moving average is a way to smooth a curve that represents data.  STATGRAPHICS Plus replaces individual observations with the mean of each observation and the observations on either side of it.  For example, if a variable has 10 observations, the program averages the first five observations.  It then creates a second subgroup by dropping the first observation, adding the sixth, and calculating the average.  The third subgroup drops the second observation, adds the seventh, and calculates the average; and so on.

To Create a Moving Average Chart Analysis

1.	Select SPECIAL... QUALITY CONTROL... TIME-WEIGHTED CHARTS... MOVING AVERAGE CHART… from the Menu bar to display the MA Chart Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Moving Average Chart in the Analysis window.


Using EWMA Chart Analysis

EWMA (Exponentially Weighted Moving Average) Charts are generally used for detecting small shifts in the process mean — detecting shifts of .5 sigma to 2 sigma — much faster than Shewhart charts with the same sample size (Montgomery, 1991).  However, they are slower in detecting large shifts in the process mean.  In addition, you cannot use typical run tests because of the inherent dependence of data points.

You might also prefer to use an EWMA Chart when the subgroups are of size n=1.  The advantage of CuSum, EWMA and Moving Average charts is that each plotted point includes several observations so you can use the Central Limit Theorem to say that the average of the points (or the moving average) is normally distributed and the control limits are clearly defined.

EWMA charts are also used to smooth the affect of known, uncontrollable noise in the data.  Many accounting and chemical processes fit into this categorization; for example, while day-to-day fluctuations in accounting processes may be large, they are not purely indicative of process instability.

As with other control charts, EWMA charts are used to monitor processes over time.  The charts’ X-axes are time based, so the charts show a history of the process.  Therefore, your data must be time-ordered; that is, centered in the sequence from which is was generated.  If the data are not time-ordered, trends or shifts in the process may not be detected but instead attributed to random variation.

These time-weighted charts incorporate the past history of a process to estimate the charted point.  In this analysis, the program plots the exponentially weighted moving averages that are the weighted average of the current observation and the estimate of the previous observation.  To calculate the weighted average, the current observation is multiplied by lambda and the estimate of the previous observation is multiplied by 1 - lambda.

To Create an EWMA Chart Analysis

1.	Choose SPECIAL... QUALITY CONTROL... TIME-WEIGHTED CHARTS... EWMA CHART... from the Menu bar to display the EWMA Chart Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and EWMA Chart in the Analysis window.


Using CuSum Chart (V-Mask) Analysis

The CuSum or Cumulative Sum Charts are generally used for detecting small shifts in the process mean — detecting .5 sigma to 2 sigmas — in about half the time of Shewhart charts with the same sample size (Montgomery, 1991).  An inflection in the plotted points makes the point at which the shift occurs easy to detect.  Large shifts in the process mean are slower in detecting.

The time-weighted chart is based on all the data instead of only the last few samples.  The cumulative sums for the deviations of the sample values from the target value are plotted.

The analysis helps to maintain current control of a process.  An upward or downward trend in the data indicates that the process mean has shifted and the process is out of control.  The analysis also helps detect sudden and persistent changes in the process average more rapidly than variables control charts do.  By detecting the change in the process sooner, you can adjust the process before large variations occur.

To Create a CuSum Chart (V-Mask) Analysis

1.	Choose SPECIAL... QUALITY CONTROL... TIME-WEIGHTED CHARTS... CUSUM CHART (V-MASK)... from the Menu bar to display the CuSum Chart (V-Mask) Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Cumulative Sum Chart in the Analysis window.


Using Moving Average (MA) Individuals Chart Analysis

The Moving Average Individuals Chart Analysis is a time-weighted chart that allows you to analyze the moving averages of individual observations. You use this analysis to produce a Moving Average Chart and an MR(2) Chart for the moving ranges of two successive observations at one time.  You can perform an initial study to estimate the control limits and set a standard by which the process will be measured.  Then you use a control-to-standard study and enter parameters to test whether the process meets the standard.

To Create a Moving Average Individuals Chart Analysis

1.	Select SPECIAL... QUALITY CONTROL... TIME-WEIGHTED CHARTS... MA INDIVIDUALS CHART… from the Menu bar to display the MA Individuals Chart Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Moving Average Chart in the Analysis window.


Using EWMA Individuals Chart Analysis

The EWMA Individuals Chart Analysis is a time-weighted chart that allows you to analyze the exponentially weighted moving averages of individual observations.

The analysis is insensitive to data that are not normally distributed, making it an ideal tool for individual data (subgroup size = 1).  Like the EWMA Chart Analysis, you use this analysis to produce an EWMA Chart for moving averages.  You can perform an initial study to estimate the control limits and set a standard by which the process will be measured.  Then you use a control-to-standard study and enter parameters to test whether the process meets the standard.

To Create an EWMA Individuals  Chart Analysis

1.	Select SPECIAL... QUALITY CONTROL... TIME-WEIGHTED CHARTS... EWMA CHART… from the Menu bar to display the EWMA Individuals Chart Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and EWMA Chart in the Analysis window.


Using the CuSum Individuals Chart (V-Mask) Analysis
Using CuSum Individuals Chart (V-Mask) Analysis

The CuSum or Cumulative Sum charts are generally used for detecting small shifts in the process mean — detecting .5 sigma to 2 sigmas — in about half the time of Shewhart charts with the same sample size (Montgomery, 1991).  An inflection in the plotted points makes the point at which the shift occurs easy to detect.  Large shifts in the process mean are slower in detecting.

The time-weighted chart is based on all the data instead of only the last few samples.  The cumulative sums for the deviations of the sample values from the target value are plotted.

The analysis helps to maintain current control of a process.  An upward or downward trend in the data indicates that the process mean has shifted and the process is out of control.  The analysis also helps detect sudden and persistent changes in the process average more rapidly than variables control charts do.  By detecting the change in the process sooner, you can adjust the process before large variations occur.

The CuSum Individuals Chart (V-Mask) Analysis produces a time-weighted chart of the individual observations.  This analysis plots the cumulative sums of the deviations of the sample from the target value.  Use this analysis when the subgroup size is 1.

You can use the analysis to maintain current control of a process.  An upward or downward trend in the data indicates that the process mean has shifted and the process is out of control.  The CuSum Individuals Chart allows you to detect sudden and persistent change in the process average more rapidly than variables controls charts.  By detecting the changes sooner, you can adjust the process before large variations occur.  This analysis is particularly useful in chemical and process industries where individual items may be difficult to form into subgroups.

To Create a CuSum Individuals Chart (V-Mask) Analysis

1.	Choose SPECIAL... QUALITY CONTROL... TIME-WEIGHTED CHARTS... CUSUM INDIVIDUALS CHART (V-MASK)... from the Menu bar to display the CuSum Individuals Chart (V-Mask) Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Cumulative Sum Individuals Chart in the Analysis window.


Using Multivariate Control Chart Analysis

Process-monitoring problems that involve several related variables are sometimes called multivariate quality control or process monitoring problems.  The original work in multivariate quality control was done by Hotelling (1947), who applied his procedures to bombsight data during World War II.  The subject is important today, because automatic inspection procedures make it relatively easy to measure many parameters on each unit of product manufactured.

Typically, process monitoring applies to processes in which only one variable is measured and tested.  One disadvantage is that for a single process, many variables can be monitored and even controlled.  Multivariate quality control methods overcome this disadvantage by monitoring several variables simultaneously.  Engineers and manufacturers who use multivariate quality control methods can more effectively monitor the stability of their process.

Multivariate quality control is more complex than univariate SPC, but it is a more realistic representation because in the real world, processes usually have more than one variable that is measured independently.  One way to see the advantages of multivariate quality control is to superimpose univariate control charts on top of each other, to create a graph of all the points on each control chart in the same area of space.  However, if the variables are correlated, as they often are when they are from the same process, superimposing univariate charts is not a very accurate method for monioring processes.

In multivariate situations, the probability that a process is completely in control is less than in the univariate case.  Similarly, the likelihood of a multivariate process being completely out of control is less than that in univariate situations.  Using multivariate control charts, it is possible to maintain a specific error rate, while taking advantage of cross correlation between the variables, and the process can be analyzed for stability without the complication of maintaining many control charts at once (Montgomery, 1997).

The Multivariate Control Chart Analysis in STATGRAPHICS Plus lets you construct a single control chart for two or more variables.  The intent of the analysis is to determine if all of the cases come from a single multivariate normal distribution.

To Create a Multivariate Control Chart Analysis

1.	Choose SPECIAL... QUALITY CONTROL... MULTIVARIATE CONTROL CHARTS... from the Menu bar to display the Multivariate Control Chart Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Multivariate Control Chart in the Analysis window.


Using the Gage R&R Analysis
Using Gage R&R Analysis

In modern industry, being able to interchange uniform parts is vital for cost-effective manufacturing.  If a machine part fails or wears out, a replacement must be available and it must fit.  When failures occur, data on the replacement parts and the manufacturing processes are analyzed to determine if they conform to product specifications, then the data are fed back to the manufacturing process to prevent further production problems.

Two types of variability can occur in the manufacturing processes: repeatability and reproducibility (R&R).  Repeatability or equipment variation, measures the precision of the gage or the measurement tool, and is the variation obtained when one person, using the same measuring instrument, measures the same dimension two or more times.  Reproducibility or inspector variation, is the variation in measurement averages obtained when several operators, using one gage, measure the same characteristic on the same part.

The Gage R&R Analysis in STATGRAPHICS Plus allows you to set up and perform an analysis of the repeatability and reproducibility components of gage variability.  Three analysis methods are provided: Average and Range, ANOVA, and Range.  Before you actually perform the analysis, you begin by using Gage R&R Data Setup to build a file that can be used with any of the three methods.

See also

Setting Up Data for a Gage R&R Analysis

Using the Average and Range Method

Using the ANOVA Method

Using the Range Method


Using the Custom Chart Analysis
Using Custom Chart Analysis

The Custom Chart Analysis allows you to create charts with custom titles, scaling, and horizontal and vertical lines.  Its primary purpose is to create charts that can be used to overlay other plots when the StatGallery is used.  You can also create quality control chart templates for monitoring processes.

For example, if you are trying to determine if a dispensing machine that fills boxes is in statistical control, supervisors on the plant floor might be asked to collect the data on the weight dispensed into a sample of boxes.  To ensure that all the supervisors chart the data the same way, you create a blank chart that all the supervisors can use to plot the data.

To Create a Custom Chart Analysis

1.	Choose SPECIAL... QUALITY CONTROL... CUSTOM CHART... from the Menu bar to display the Custom Chart Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Custom Chart in the Analysis window.


Using Time-Weighted Charts

Time-weighted charts are similar to control charts except in the following ways:

•	time-weighted charts incorporate past history of a process into charted points

•	time-weighted charts generally are more sensitive to small, gradual changes in a process than control charts

•	control limits for time-weighted charts are based on moving statistics.

You can overlay moving averages or moving ranges onto a control chart using the Control Chart Options dialog box in any of the analyses for variables control charts or attributes control charts.  For more information on control charts, see Determining Statistical Control of Variable Data, Determining Statistical Control of Attribute Data, and Determining Statistical Control of Special-Purpose Control Charts.


Using Variables Control Charts

Because variables charts can explain process data in terms of both its spread (piece-to-piece variability) and its location (process average), they are always prepared and analyzed in pairs — one for location and another for spread.  STATGRAPHICS Plus contains the following variables control charts: X-bar and R, X-bar and S, X-bar and S-Squared, and Individuals charts (X and MR(2).  If the data are observations arranged in subgroups, use one of the first three analyses; if the data contain individual items, use the Individuals charts.  Each of the analyses is summarized next.

X-bar and R Charts Analysis

Produces two charts, X-bar and Range, which are constructed by estimating two parameters: mean and standard deviation.  The X-bar Chart plots the averages of the sampled subgroup means; the Range Chart plots the variation via the sampled subgroup ranges; that is, the general variability.

X-bar and S Charts Analysis

Produces two charts, X-bar and S, when there is an ordered set of standard deviations on which to base the control limits, or when there are large subgroup sizes (eight or greater).

X-bar and S-Squared Charts Analysis

Produces two charts, X-bar and S-Squared, with control limits based on variances, which is useful when subgroup sample sizes are large (eight or greater).

Individuals Chart Analysis

Produces a chart that is used for individual items that are difficult to form into subgroups.  For example, if:

•	the manufacturing process is very slow and it is inconvenient to accumulate subgroup samples before the process is analyzed

•	every unit that is manufactured must be analyzed

•	measurements repeated in a process differ because of laboratory or analysis error

•	measurements on some parameter in the processing environment differ very little and produce a standard deviation that is much too small.

Under any of these circumstances, it is best to use this analysis to analyze the individual items (subgroup size = 1).  The topic, Using Time Weighted Charts, contains information about analyses that are also appropriate to use when you are analyzing individual items: the EWMA (Exponentially Weighted Moving Average) and CuSum charts.

In each of these analyses, you can include warning limits or moving averages, and exclude subgroups without altering the data when you run an Initial Study.  When a Control to Standard study is run, you can specify a mean and standard deviation or the control limits for a process.

See also

Using X-bar and R Charts

Using X-bar and S Charts

Using X-bar and S-Squared Charts

Using Individuals Charts


Determining Statistical Control of Attribute Data

Manufactured products are routinely inspected by attributes, where each item inspected is classified as either accepted or rejected.  In this type of inspection, it is also common to record the number of items that are rejected.  If a quality performance comparison is being made, it is also necessary to record the number of items rejected.  The ratio of the rejected items to the number of inspected items is known as the fraction rejected, which is commonly expressed as a decimal fraction.  To convert thedecimal fraction into the percent rejected, it is often multiplied by 100 (Grant and Leavenworth, 1980).

Usually control charts are thought of in terms of variables, however, they have also been developed for attributes.  Attributes data have only two values; for example,  conforming/nonconforming, present/absent, or pass/fail such as errors in a word processing document, or the presence of a required label.  Grant and Leavenworth (1980), provide other examples such as characteristics that are measurable, but where the results are recorded with a simple yes/no.

Attributes control charts are important because:

•	Attribute data already exist in many situations, especially where inspections currently exist.  In these cases, no additional data collection is necessary, just the effort of converting the data into control chart format.

•	Attribute information is usually quick and inexpensive to obtain in cases where new data must be collected, and it requires no special skills to obtain.

•	Data collected for management summaries are usually in attribute form and benefit from control chart analysis, which, because of its ability to distinguish between special and common causes, can be valuable in interpreting management reports.

With all Attributes control charts (except the c Chart) you must also indicate whether the data come from equal- or unequal-sized samples.  It is also important that the data meet these guidelines:

•	for a p Chart, all the values must be between 0 and 1.

•	for an np Chart, all the values must be integers between 0 and the size of the subgroup.

•	for a u Chart, all the values must be greater than or equal to 0.

•	for a c Chart, all the values must be greater than or equal to 0.


Determining Statistical Control of Variable Data

An important tool in statistical quality control is the Shewhart control chart.  The Shewhart technique is powerful in that it has the ability to separate out assignable causes of quality variation.  This makes it possible to diagnosis and correct many production problems while bringing about substantial improvements in product quality.  Because control charts tell when to leave a process alone, they prevent unnecessary process adjustments that tend to increase process variability rather than to decrease it (Grant and Leavenworth, 1980).

Control charts are an indispensable tool because they provide information that needs to be known before an action plan is set in place.  The information they provide consists of knowledge about the:

•	basic variability of the quality characteristic

•	consistency of performance

•	average level of the quality characteristic.

In the production environment, some variability is unavoidable because no process is good enough to produce every product exactly alike.  The amount of variability depends on various characteristics of the production process, such as machines, materials, and operators.  Once a control chart shows that a process has been brought under control at a satisfactory level and with acceptable limits of variability, process capability analyses can be performed to determine whether the the product meets specifications.

All manufactured products must meet certain requirements and many of these requirements are stated as variables.  Montgomery (1997) defines variables as quality characteristics that are measured on a numerical scale.  Examples include dimensions such as length or width, temperature, and volume.  Most specifications for variables include both upper and lower limits for the measured value.  For many requirements, however, it is necessary to state the characteristics in terms of attributes rather than variables.  This applies to things that can be judged only by visual examination, such as a glass cover on a pressure gage that is either cracked or not cracked.  Generally, the item being examined either conforms or does not conform to the specifications (Grant and Leavenworth, 1980).

Shewhart control charts are “usually necessary to monitor both the mean value of the quality characteristic and its variability. . . . Control of the process average or mean quality level is usually with the control chart for means, or the X-bar Chart.  Process variability can be monitored with either a control chart for the standard deviation (the S Chart), or a control chart for the range (the Range Chart)” (Montgomery, 1997).  The topic, Determining Statistical Control of Attribute Data, deals with quality characteristics that are either conforming or nonconforming — attributes control charts.

See also

Using Variables Control Charts Analyses

Using Attributes Control Charts Analyses


Setting Up Data for a Gage R&R Analysis

In the Gage R&R Data Setup feature, you create variables that contain different combinations of operators, parts, and trials.  You can create new variables using the DataEditor, or use existing variables.  To save the setup in a DataSheet, click the Save Results button, then save all the results in an empty DataSheet.

To Create a Gage R&R Data Setup

1.	Choose SPECIAL... QUALITY CONTROL... GAGE R&R... DATA SETUP... from the Menu bar to display the Gage R&R - Data Setup dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary in the Analysis window.

3.	Click the Save Results button on the Analysis toolbar (the fourth button from the left), to display the Save Results Options dialog box.

4.	Choose the option that indicates the type of results you want to save, then click OK to save the data for analyzing with one of the three methods.


Using the Average and Range Method

The Average and Range method (sometimes referred to as the Long Method), is a mathematical method for assessing a measurement system.  This method allows the measurement system to “decompose” into two separate components: repeatability and reproducibility.

This method is a full gage repeatability and reproducibility analysis involving multiple operators, parts, and replications that estimates both repeatability and reproducibility.

To use this method, you must set up variables that contain operator names, part numbers, trial numbers, and measurements.  The design must be balanced; that is, each operator must measure each part the same number of times.

To Create an Average and Range Method Analysis

1.	Choose SPECIAL... QUALITY CONTROL... GAGE R&R... AVERAGE AND RANGE METHOD... from the Menu bar to display the Average and Range Method dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and the Operator and Part Plot in the Analysis window.


Using the ANOVA Method

The Average and Range method (sometimes referred to as the Long Method), is a mathematical method for assessing a measurement system.  This method allows the measurement system to “decompose” into two separate components:  repeatability and reproducibility.

This method is a full gage repeatability and reproducibility analysis involving multiple operators, parts, and replications that estimates both repeatability and reproducibility.

To use this method, you must set up variables that contain operator names, part numbers, trial numbers, and measurements.  The design must be balanced; that is, each operator must measure each part the same number of times.

To Create an Average and Range Method Analysis

1.	Choose SPECIAL... QUALITY CONTROL... GAGE R&R... AVERAGE AND RANGE METHOD... from the Menu bar to display the Average and Range Method dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and the Operator and Part Plot in the Analysis window.


Using the Range Method

The Range Method is a quick analysis that involves only two operators who each make one measurement on two or more parts.  In this analysis, you cannot separate repeatability and reproducibility.

To Access the Range Method

1.	Choose SPECIAL... QUALITY CONTROL... GAGE R&R... RANGE METHOD... from the Menu bar to display the Range Method dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Operator and Part Plot in the Analysis window.


Identifying Defects

Pareto analysis is a simple method for separating the major causes (the “vital few”) from the minor causes (“trivial many”) of product defects.  The analysis helps in prioritizing and focusing resources where they are most needed.  It can also help measure the impact of an improvement by comparing the before and after.

The Pareto principle came about when a nineteenth-century Italian economist, Vilfredo Pareto, observed that 80 percent of Italy’s wealth was owned by 20 percent of the population; therefore, the analysis is often referred to as the 80/20 rule.  In general, the rule is that 80 percent of a company’s problems result from 20 percent of the causes.  The split may not always be exactly 80/20, but the principle is the same: a few causes are usually responsible for a majority of the problems.

The principal objective of quality-cost analysis is cost reduction by identifying improvement opportunities, which is the goal of Pareto analysis.  The analysis identifies costs by product, category, defect, or type of nonconformity.  Montgomery (1997), provides an example of defects or nonconformities in the assembly of electronic components onto printed circuit boards.  The study revealed that insufficient solder was the highest quality cost incurred in the operation, where insufficient solder accounted for 42 percent of the total defects in a particular board, and for almost 52 percent of the total scrap and rework costs.

Montgomery found that it was unrealistic to expect that cost of quality could be significantly reduced.  However, he did believe that a quality-cost program combined with good quality-improvement efforts had the capability of reducing quality costs by 50 to 60 percent, provided that no organized effort had previously existed.

Today’s consumer dissatisfaction, due in part to the large number of failures in consumer products, has contributed most to the recent rise in the re-emergence of quality-assurance programs.  Decreases in quality directly affect the corporate bottom line.  These decreases, plus the increased risk of product liability, have become major social, market, and economic forces (Montgomery, 1997).

See also

Overview of Quality Control

Using the Pareto Analysis


Analyzing the Capability of a Process

One of the basic problems in process quality control is establishing control over a manufacturing process, then maintaining that control through time.  Equally important is the problem of adjusting the process to a point where the output meets the specifications.  Then two questions are relevant: Is the output meeting specifications?  If not, can the process be adjusted to a level where it will?

Process capability analysis is the general activity that occurs during or prior to manufacturing when statistical techniques are utilized to analyze and quantify process variability.  Process capability is a statistical measure of the common-cause variation exhibited by a process, and a process capability study is a problem-solving tool used to determine if established specifications are being met.

Variability can be divided into two types:

•	variability due to common (random) causes

•	variability due to assignable (special) causes.

The first type of variability occurs naturally within a process and can usually be attributed to common causes.   This type of variability can never be completely eliminated from a process.  Variability due to assignable causes refers to variation that can be linked to specific or special causes.  If these causes or factors are modified or controlled properly, the process variability associated with them can be eliminated.

A process capability study measures the performance potential of a process when no assignable causes are present (when a process is in statistical control).  Performance studies are useful for examining incoming lots of materials or one-time only production runs.  In the case of incoming lots, a performance study cannot determine if the process that produced the material was in control, but it may determine the shape of the distribution and the percentage of parts that were out of specification.

Process capability studies have considerable impact on many management decision problems, including make or buy decisions, plant and process improvements that reduce process variability, and contractural agreements with customers or vendors regarding product quality (Montgomery, 1997).

See also

Using the Process Capability Analysis


Using the CuSum Chart (H-K) Analysis
Using CuSum Chart (H-K) Analysis

The CuSum Chart (H-K) Analysis is also called the algorithmic or tabular CuSum.  The technique accumulates deviations above the target separately from deviations below the target.  Those accumulated deviations above the target become the one-sided upper CuSums.  The accumulated deviations below the target become the one-sided lower CuSums.  The process is determined to be out of control when other types of CuSum exceed the decision interval, called H.

To Create a CuSum Chart (H-K) Analysis

1.	Choose SPECIAL... QUALITY CONTROL... TIME-WEIGHTED CHARTS...   CUSUM CHART (H-K)... from the Menu bar to display the CuSum Chart (H-K) Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Cumulative Sum Chart in the Analysis window.


Using the CuSum Individuals Chart (H-K) Analysis
Using CuSum Individuals Chart (H-K) Analysis

The CuSum Chart (H-K) Analysis is also called the algorithmic or tabular CuSum.  The technique accumulates deviations above the target separately from deviations below the target.  Those accumulated deviations above the target become the one-sided upper CuSums.  The accumulated deviations below the target become the one-sided lower CuSums.  The process is determined to be out of control when other types of CuSum exceed the decision interval, called H.

The CuSum Individuals Chart (H-K) Analysis produces a time-weighted chart of the individual observations.  This analysis plots the cumulative sums of the deviations of the sample from the target value.  Use this analysis when the subgroup size is 1.

You can use the analysis to maintain current control of a process.  An upward or downward trend in the data indicates that the process mean has shifted and the process is out of control.  The CuSum Individuals Chart allows you to detect sudden and persistent change in the process average more rapidly than variables controls charts.  By detecting the changes sooner, you can adjust the process before large variations occur.  This analysis is particularly useful in chemical and process industries where individual items may be difficult to form into subgroups.

To Create a CuSum Individuals Chart (H-K) Analysis

1.	Choose SPECIAL... QUALITY CONTROL... TIME-WEIGHTED CHARTS... CUSUM INDIVIDUALS CHART (H-K)... from the Menu bar to display the CuSum Individuals Chart (H-K) Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and CuSum Chart in the Analysis window.


Measuring More Than One Variable
Measuring More Than One Variable – duplicate of Multivariate Control Chart – don’t use

Process-monitoring problems that involve several related variables are sometimes called multivariate quality control or process monitoring problems.  The original work in multivariate quality control was done by Hotelling (1947), who applied his procedures to bombsight data during World War II.  The subject is important today because automatic inspection procedures make it relatively easy to measure many parameters on each unit of product manufactured.

Typically, process monitoring applies to processes in which only one variable is measured and tested.  One disadvantage is that for a single process, many variables can be monitored and even controlled.  Multivariate quality control methods overcome this disadvantage by monitoring several variables simultaneously.  Engineers and manufacturers who use multivariate quality control methods can more effectively monitor the stability of their process.

Multivariate quality control is more complex than univariate SPC, but it is a more realistic representation because in the real world, processes usually have more than one variable that is measured independently.  One way to see the advantages of multivariate quality control is to superimpose univariate control charts on top of each other, to create a graph of all the points on each control chart in the same area of space.  However, if the variables are correlated, as they often are when they are from the same process, superimposing univariate charts is not a very accurate method for monioring processes.

In multivariate situations, the probability that a process is completely in control is less than in the univariate case.  Similarly, the likelihood of a multivariate process being completely out of control is less than that in univariate situations.  Using multivariate control charts, it is possible to maintain a specific error rate, while taking advantage of cross correlation between the variables, and the process can be analyzed for stability without the complication of maintaining many control charts at once (Montgomery, 1997).

See also

Using Multivariate Control Charts


Using the Fishbone Diagram Analysis
Using Fishbone Diagram Analysis

After a defect, error, or problem is identified and isolated for further study, manufacturing personnel must analyze the potential causes of the undesirable effect (Montgomery, 1997).  A Fishbone Diagram, also known as a cause and effect diagram, is often constructed by a quality-improvement team that is responsible for dissecting a problem or process.  Doing this in a brainstorming session forces team members to organize their thoughts and provide a plan of action at the same time.

Montgomery (1997) suggests that these diagrams be constructed following a seven-step plan:

1.	Define the problem or effect to be analyzed.

2.	Form the team that will perform the analysis.

3.	Draw the effect box and the centerline.

4.	List the major potential cause categories and join them as boxes connected to the centerline.

5.	Identify the possible causes and classify them into the categories in Step 4; create new categories, if necessary.

6.	Rank order the causes to identify those that seem most likely to impact the problem.

7.	Take corrective action.

A noted Japanese quality expert, Dr. Kaoru Ishikawa, originally developed the diagram for solving quality problems.  A major benefit of the diagram is that it forces all that is known about a subject to be noted, which is also a major weakness because its accuracy depends on the person or group who creates the diagram.  It is critical that input be gathered from everyone involved with the process because the varying ideas often lead to a better picture of the actual causes.

There are other benefits for using this type of diagram.

•	All the factors are known, instead of only those suspected.

•	The diagram provides a plan of attack that allows deletion of causes that may not turn out to be important.

•	The diagram provides an ongoing record of when the actual relationships occur and when they are corrected.

•	When the analysis is complete, it is reasonable to assume that you have accounted for all the information.

Setting Up a DataSheet for Creating a Fishbone Diagram

STATGRAPHICS Plus lets you create a Fishbone Diagram using the computer rather than pencil and paper; however, you must know how to correctly enter the data.

1.	Access a blank untitled DataSheet.

2.	Access the Modify Column dialog box, and define a single character column 	with a width adequate for the labels you will be entering.

3.	Enter primary-cause category names flush with the left edge of the column.  Enter rank-ordered, secondary-cause categories with a beginning period (.) preceding the name; and enter rank-ordered, tertiary-cause categories with double periods (..) preceding the name.

After you create the diagram, you can use the graphics editing options to change its look.  For example, you could change the primary-cause category names to a larger point size, make them bold, or change their color to make them stand out.  You can also move the labels to provide more or less white space.

To Create a Fishbone Diagram Analysis

1.	Choose SPECIAL... QUALITY CONTROL... FISHBONE DIAGRAM... from the Menu bar to display the Fishbone Diagram dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Fishbone Diagram in the Analysis window.


Using the Acceptance Sampling by Attributes Analysis
Using Acceptance Sampling by Attributes Analysis

Acceptance sampling for attributes includes developing sampling plans for attribute data based on the Binomial and Poisson distributions.  The metric for the Operating Curve (OC) can be either the fraction defective, as in the Binomial case of Go/No-Go data, or counts, as in the Poisson case of defect count.

The Acceptance Sampling for Attributes Analysis has several useful applications.  It can:

•	determine if a process can meet a proposed quality requirement

•	determine the required inspection effort

•	improve tough recall decisions

•	calculate one- and two-sided confidence limits based on fraction defectives and counts.

A description of standard sampling procedures for inspection by attributes that were developed during World War II are discussed in Montgomery (1997) and are the basis for the Acceptance Sampling by Attributes Analysis in STATGRAPHICS Plus.  Today the most widely used version of the standard is MIL STD 105E and its civilian counterpart standard ANSI/ASQC Z14, which is quite similar.

To Create an Acceptance Sampling - Attributes Analysis

1.	Choose SPECIAL... QUALITY CONTROL... ACCEPTANCE SAMPLING... ATTRIBUTES... from the Menu bar to display the Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and the OC Curve in the Analysis window.


Using Acceptance Sampling

There are several ways to categorize acceptance-sampling plans; however, the most common is by variables and attributes.  Montgomery (1997) defines variables as “quality characteristics that are measured on a numerical scale”; and attributes as “quality characteristics that are expressed on a go/no go basis.”  STATGRAPHICS Plus contains tools that let you create and use both types.

Acceptance sampling is a procedure used to inspect raw materials, semi-finished, and finished products to accept or reject a product, based on adherence to a standard. The underlying philosophy is that acceptance sampling is not a substitute for adequate process controls.  In fact, the successful use of process-control techniques at the early stages of manufacturing can greatly reduce and, in some cases, eliminate the need for extensive sampling inspection (Montgomery, 1997).

Acceptance sampling does not lead to process improvement unless causes for rejected lots are found and corrected.  Rather, its purpose is for use as an auditing-process tool to sentence lots, not to estimate the proportion of bad items produced by the process.

You would use acceptance sampling when:

•	inspection destroys the product

•	handling is likely to induce the defects

•	time will not permit 100 percent inspection

•	inspection costs will be high

•	misjudgment costs will be low.

In quality inspection, using the acceptance sampling approach is likely to cause two types of errors: rejection of a good lot and acceptance of a bad lot.

Acceptance sampling requires the selection of a sampling plan, which will determine the size of a sample and the number of defectives permitted in the sample.

STATGRAPHICS Plus contains two Acceptance Sampling analyses:

•	Acceptance Sampling by Attributes, where n items are sampled and each is 	classified as either defective or not defective.  Every item is inspected, and replaced if it is defective.

•	Acceptance Sampling by Variables, where n items are sampled, and a 	measurement is made on each one.  If the sample mean is closer than a distance, k, to a specification limit, the entire lot is rejected.

Both analyses work the same way: First a sample of size n is taken from a lot of size N, and each item is inspected, or in the case of sampling by variables, measured.  Then, based on the sample, the entire lot is either:

•	Accepted as is.

•	Rejected.  If the lot is rejected, you can return the rejected lots to the vendor or you can subject the lot to 100 percent inspection, where every item is inspected and replaced if it is defective.


Using the Acceptance Sampling by Variables Analysis
Using Acceptance Sampling by Variables Analysis

Acceptance sampling by variables has a primary advantage in that you can obtain the same operating-characteristic curve using a smaller sample size than you would using an attributes sampling plan.  Therefore, a variables acceptance-sampling plan requires fewer samples.  Another advantage is that measurement data usually provide more information about the manufacturing process.  And, when acceptable quality levels are small, the required sample sizes are usually very large.

MIL STD 414 is a lot-by-lot acceptance sampling-sampling plan for variables introduced in 1957.  The primary focus of this standard is the acceptable quality level (AQL).  Again, Montgomery (1997) provides an informative and in-depth discussion.

To Create an Acceptance Sampling - Variables Analysis

1.	Choose SPECIAL... QUALITY CONTROL... ACCEPTANCE SAMPLING... VARIABLES... from the Menu bar to display the Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and the OC Curve in the Analysis window.


Using the ARIMA Analysis
Using ARIMA Analysis

Auto-Regressive Integrated Moving Average (ARIMA) models are a complex set of statistical techniques for time-series analysis that combines autoregressive analysis procedures with those of moving averages.  A researcher using ARIMA models is able to construct a trend line that accounts for both systematic error (autocorrelation) and nonsystematic (random) error.

Over the years, ARIMA models have been studied extensively.  Yule first introduced Autoregressive (AR) models in 1926, Walker generalized them in 1931, and Slutzky used moving average (MA) models in 1937.  Wold, however, provided the theoretical foundations of the combined ARMA processes in 1938.  Building on Wold’s work, ARMA models developed in three directions:

•	identification and estimation procedures (for AR, MA, and mixed ARMA processes)

•	seasonal time series

•	nonstationary processes (ARIMA) (Makridakis, Wheelwright, and McGee, 1983).

Box and Jenkins (1976) put together the much-needed information that was necessary to understand and use univariate time-series ARIMA models.  Their approach consisted of three phases: identification, estimation and testing, and application.

Many researchers, including Montgomery (1997), point out the problem of conventional control charts not working well when  “. . . quality characteristics contain even low levels of correlation over time” . . . “because these control charts will give misleading results in the form of too many false alarms if the data are correlated.”

Montgomery further says that an approach useful in dealing with autocorrelated data is to “directly model the correlative structure with an appropriate time-series model, use that model to remove the autocorrelation from the data, and apply control charts to the residuals.”

The ARIMA and ARIMA Individuals charts analyses in STATGRAPHICS Plus, use Montgomery’s approach.  The analyses are designed to handle serially correlated subgroup or individuals data.  They also provide complete ARIMA modeling without limits on the order of autoregressive or moving-average processes.

To Create an ARIMA Chart Analysis

1.	Choose SPECIAL... QUALITY CONTROL... SPECIAL PURPOSE CONTROL CHARTS... ARIMA CHART... to display the Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and the ARIMA Chart in the Analysis window.


Using the ARIMA Individuals Chart Analysis
Using ARIMA Individuals Chart Analysis

Auto-Regressive Integrated Moving Average (ARIMA) models are a complex set of statistical techniques for time-series analysis that combines autoregressive analysis procedures with those of moving averages.  A researcher, in using ARIMA models, is able to construct a trend line that accounts for both systematic error (autocorrelation) and nonsystematic (random) error.

Over the years, ARIMA models have been studied extensively.  Yule first introduced Autoregressive (AR) models in 1926, Walker generalized them in 1931, and Slutzky used moving average (MA) models in 1937.  Wold, however, provided the theoretical foundations of the combined ARMA processes in 1938.  Building on Wold’s work, ARMA models developed in three directions:

•	identification and estimation procedures (for AR, MA, and mixed ARMA 	processes)

•	seasonal time series

•	nonstationary processes (ARIMA) (Makridakis, Wheelwright, and McGee, 1983).

Box and Jenkins (1976) put together the much-needed information that was necessary to understand and use univariate time series ARIMA models.  Their approach consisted of three phases: identification, estimation and testing, and application.

Many researchers, including Montgomery (1997), point out the problem of conventional control charts not working well when  “. . . quality characteristics contain even low levels of correlation over time” . . . “because these control charts will give misleading results in the form of too many false alarms if the data are correlated.”

Montgomery further says that an approach useful in dealing with autocorrelated data is to “directly model the correlative structure with an appropriate time-series model, use that model to remove the autocorrelation from the data, and apply control charts to the residuals.”

The ARIMA and ARIMA Individuals charts analyses in STATGRAPHICS Plus, use Montgomery’s approach.  The analyses are designed to handle serially correlaed subgroup or individuals data.  They also provide complete ARIMA modeling without limits on the order of autogressive or moving-average processes.

The functionality in the ARIMA Individuals Chart Analysis is identical to that in the ARIMA Chart Analysis, except you use for observations instead of subgroups.

To Create an ARIMA Individuals Chart Analysis

1.	Choose SPECIAL... QUALITY CONTROL... SPECIAL PURPOSE CONTROL CHARTS... ARIMA INDIVIDUALS CHART... to display the Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and the ARIMA Chart in the Analysis window.


Using the Toolwear Chart Analysis
Using Toolwear Chart Analysis

Over the years, useful process-control techniques other than standard control charts have been developed.  One production process in particular — tool wear — has been studied, probably because so many production processes are subjected to tool wear.

In 1990, Grant and Leavenworth found that tool wear occurred at a uniform rate over the lifetime of a tool.  This type of tool wear adversely affected the average value of some dimension of the product being manufactured, therefore causing a trend.  They discovered that the spread of the upper and lower specification limits was much higher than the range of the natural tolerance, which provided an adequate safety margin against producing nonconforming product as long as the machine setting held the average value somewhere near a point midway between the specification limits.  However, the tendency of the value to shift rapidly due to tool wear, required many new machine setups to restore the value to the preferred position.  Each new setup involved substantial costs in both idle machine time, setup expense, and possible tool replacement.

Montgomery (1997) reports research by others who confirm that adapting control charts for the tool-wear problem is a good approach.  This concept calls for an initial tool setting at some multiple of sigma above the lower specification limit, while the maximum permissable process average is at the same multiple of sigma, below the upper specification limit.  If the rate of wear is known or can be estimated from the data, a set of slanting control limits about the tool-wear trend can be constructed.  If the sample values of X-bar fall within these limits, the tool wear is in control.  When the trend line exceeds the maximum permissible process average, the process should be reset or the tool replaced.

To Create a Toolwear Chart Analysis

1.	Choose SPECIAL... QUALITY CONTROL... SPECIAL PURPOSE CONTROL CHARTS... TOOLWEAR CHART... to display the Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and the Toolwear Chart in the Analysis window.


Using the Toolwear Individuals Analysis
Using Toolwear Individuals Analysis

Over the years, useful process-control techniques other than standard control charts have been developed.  One production process in particular — tool wear — has been studied, probably because so many production processes are subjected to tool wear.

In 1990, Grant and Leavenworth found that tool wear occurred at a uniform rate over the lifetime of a tool.  This type of tool wear adversely affected the average value of some dimension of the product being manufactured, therefore causing a trend.  They discovered that the spread of the upper and lower specification limits was much higher than the range of the natural tolerance, which provided an adequate safety margin against producing nonconforming product as long as the machine setting held the average value somewhere near a point midway between the specification limits.  However, the tendency of the value to shift rapidly due to tool wear, required many new machine setups to restore the value to the preferred position.  Each new setup involved substantial costs in both idle machine time, setup expense, and possible tool replacement.

Montgomery (1997) reports research by others who confirm that adapting control charts for the tool-wear problem is a good approach.  This concept calls for an initial tool setting at some multiple of sigma above the lower specification limit, while the maximum permissible process average is at the same multiple of sigma, below the upper specification limit.  If the rate of wear is known or can be estimated from the data, a set of slanting control limits about the tool-wear trend can be constructed.  If the sample values of X-bar fall within these limits, the tool wear is in control.  When the trend line exceeds the maximum permissible process average, the process should be reset or the tool replaced.

The functionality in the Toolwear Individuals Chart Analysis is identical to that in the Toolwear Chart Analysis, except that you use observations instead of subgroups.

To Create a Toolwear Individuals Chart Analysis

1.	Choose SPECIAL... QUALITY CONTROL... SPECIAL PURPOSE CONTROL CHARTS... TOOLWEAR INDIVIDUALS CHART... to display the Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and the Toolwear Chart in the Analysis window.


Using the Acceptance Chart Analysis
Using Acceptance Chart Analysis

Acceptance charts are one of two methods used for relaxing the level of surveillance provided by a standard control chart (Montgomery, 1997).  The purpose of the analysis is to monitor processes that tend to operate well within process specifications (with high Cp).  Rather than place the control limits at +/- 3 sigma from the centerline, STATGRAPHICS Plus places them relative to the specification limits.  This allows the process to drift around the centerline, while still ensuring that little if any product is out of specification.

The basis of the Acceptance Chart is controlling both the risk of rejecting a satisfactory process (α-risk), and the risk of accepting an unsatisfactory process (β-risk).

To Create an Acceptance Control Chart Analysis

1.	Choose SPECIAL... QUALITY CONTROL... SPECIAL PURPOSE CONTROL CHARTS... ACCEPTANCE CHART... to display the Acceptance Chart Analysis dialog box.

2.	Complete the dialog box and click OK to display the Specification Limits dialog box.

3.	Complete the dialog box and click OK to display the Analysis Summary and Acceptance Chart in the Analysis window.


Using the Acceptance Individuals Control Chart Analysis
Using Acceptance Individuals Control Chart Analysis

Acceptance charts are one of two methods used for relaxing the level of surveillance provided by a standard control chart (Montgomery, 1997).  The purpose of the analysis is to monitor processes that tend to operate well within process specifications (with high Cp).  Rather than place the control limits at +/- 3 sigma from the centerline, STATGRAPHICS Plus places them relative to the specification limits.  This allows the process to drift around the centerline, while still ensuring that little if any product is out of specification.

The basis of the Acceptance Chart is controlling both the risk of rejecting a satisfactory process (α-risk), and the risk of accepting an unsatisfactory process (β-risk).

The functionality in the Acceptance Individuals Chart Analysis is identical to that in the Acceptance Chart Analysis, except that you use individual observations instead of subgroups.

To Create an Acceptance Individuals Control Chart Analysis

1.	Choose SPECIAL... QUALITY CONTROL... SPECIAL PURPOSE CONTROL CHARTS... ACCEPTANCE INDIVIDUALS CONTROL CHART... to display the Acceptance Individuals Chart Analysis dialog box.

2.	Complete the dialog box and click OK to display the Specification Limits dialog box.

3.	Enter values for the Upper and Lower specifications in the text boxes, then click OK to display the Analysis Summary and the Acceptance Chart in the Analysis window.


Overview of Quality Control

Consumers consider the quality of products as a major factor in their purchasing decisions.  Consequently, quality control is a major concern to most corporations.  The quality of a product is determined by how a product meets the needs of consumers and if the product is free from manufacturing defects.

Since World War II, manufacturers have realized that applying statistical quality control methods to manufacturing and production processes results in better quality products that cost less to produce.  Statistical quality control is broadly defined by Montgomery and Runger (1994) as “those statistical methods that are used in measuring, controlling, and improving quality.”

Quality control methods measure the variation of the output of a process.  Studying the variation in data helps to analyze the process, evaluate its effectiveness in producing high-quality, low-cost output; and adjust and improve the process to achieve better results.

See also

Identifying Defects


Using Attributes Control Charts

STATGRAPHICS Plus offers four attributes control charts: p Chart, np chart, u Chart, and c Chart.  The type of chart you use depends on the way you count the defectives.

For each type of chart you can include warning limits or moving averages.  When you run an Initial Study you can exclude subgroups without altering the data.  When you run a Control-to-Standard study, you can specify the value for the parameter or control limits to test to see if the process meets the standard.

See also

Using p Charts

Using np Charts

Using u Charts

Using c Charts


Using  Analyses for Experimental Design

The topics in the first list below provide background information about experimental designs in general.  The last list provides information about specific designs in STATGRAPHICS Plus.

Using Experimental Designs

Basic Principles of Experimental Design

Understanding Design Classes

Creating Designs

Choosing Tabular Options for a Design Class

Choosing Graphical Options for Design Classes

Modifying Designs

Optimizing Designs

Analyzing Designs

Augmenting Designs

Using Augment Design Actions

Saving Designs

Using Screening Designs

Creating Screening Designs

Choosing a Screening Design

Using Response Surface Designs

Creating a Response Surface Design

Choosing a Response Surface Design

Using Mixture Designs

Creating a Mixture Design

Choosing a Mixture Design

Using Multilevel Factorial Designs

Creating a Multilevel Factorial Design

Using Inner/Outer Arrays Designs

Creating An Inner/Outer Arrays Design

Using Single Factor Categorical Designs

Creating a Single Factor Categorical Design

Choosing a Single Factor Categorical Design

Using Multi-Factor Categorical Designs

Creating a Multi-Factor Categorical Design

Using Variance Components (Hierarchical) Designs

Creating a Variance Components (Hierarchical) Design

Using Multiple Response Optimization

Createing a Multiple Response Optimization

To Further Refine An Optimization

To Create Plots for the Optimization


Understanding Experimental Design Techniques
Understanding Experimental Design Techniques don’t use; use Using Experimental Designs

Experimental design is a scientific approach that allows an experimenter to better understand a process and how the inputs affect the output.  Process, in this case, is defined as some combination of materials, methods, people, environment, and measurement, which used together form a service, produce a product, or complete a task (Schmidt and Launsby, 1989).

In any experiment, the results and conclusions depend to a large extent on the manner in which you collect the data.  One of the primary reasons for using any designed experiment is to use data that can provide answers to well thought out questions.

Many disciplines use experimental design methods where experimentation is viewed as part of a scientific process where opinions are formed about a process, experiments are performed to generate data from a process, information gained from an experiment is used to establish new opinions, which lead to new experiments, and so on (Montgomery 1991).

In the engineering world, experimental design methods are a critical tool that can improve the performance of a manufacturing process, which leads to:

•	improvement in process yields

•	reduction in variability and closer conformance to nominal or target requirements.

•	reduction in development time

•	reduction in overall costs.

In engineering design activities, where new products are developed and existing ones improved, experimental design methods provide tools to:

•	evaluate and compare basic design configurations

•	evaluate alternative materials

•	select design parameters so a product will work well under a wide variety of field conditions

•	determine key product design parameters that impact a product’s performance.

In summary, experimental design methods play an important role in developing and troubleshooting processes that improve performance.  These methods are important because they improve performance characteristics, reduce costs, and shorten product development and production time.


Understanding Design Classes

One experimental design will often lead to greater efficiency than other designs in testing hypotheses and making estimates.  STATGRAPHICS Plus helps you choose the right design and includes designs for these design classes: Screening, Response Surface, Mixture, Multilevel Factorial, Inner/Outer Arrays, Single Factor Categorical, Multi-Factor Categorical, and Variance Component (Hierarchical).

Screening

A Screening design determines the amount of change that occurs in the response variable (defects per unit) when each factor is changed, and if changing the factors together produces results different from changing the factors individually.

Response Surface

Response surface methodology is a process for locating an optimal value in a higher-order model.  It utilizes regression, contour plots, and/or a method of steepest ascent/descent.

Mixture

Mixture designs involve experiments where a product is comprised of two or more ingredients or components.

Multilevel Factorial

Multilevel Factorial designs consist of combinations of specific levels of two or more factors, where the user sets the number of levels.  This design class is intended for quantitative factors only and is analyzed as a Response Surface design.

Inner/Outer Arrays Designs

Inner/Outer Arrays designs are a variation on an implementation of Taguchi (Robust) designs.  The designs in STATGRAPHICS Plus consist of both controllable and uncontrollable noise factors.  This design class is intended to determine the combination of factors that reduce the sensitivity to uncontrollable sources of variability.

Single Factor Categorical

Single Factor Categorical designs compare levels of a single nonquantitative variable, with or without blocking factors.

Multi-Factor Categorical

Multi-Factor Categorical designs consist of all combinations of specified levels of two or more factors, where the user sets the number.  The design is intended for nonquantitative factors and is analyzed using ANOVA.

Variance Components (Hierarchical)

Variance Components designs quantify the effects of various factors on the variability of a response.  The design consists of nested factors.


Modifying Designs

If you need to select a different design, redefine the factors or response variables, or make any other changes, you can quickly modify the experimental design without starting over.

Note:  Once you enter response data into the DataSheet, the modifications you can make are limited to that particular experimental design.

To Modify An Existing Design

1.	Click the right mouse button in the Design Summary pane, then choose Analysis Options… to display the Design Options dialog box.

2.	Click the Back... button to redisplay the Design Selection dialog box.  You can then select a different design from the list.

3.	Continue clicking Back... until you reach the Create Design Options dialog box where you can either create a completely new design or modify the design you are currently working on.

A quick way to return to the Create Design Options dialog box is to click the Return to Input Dialog Box button (the first button on the Attributes window toolbar).


Creating Designs

This topic summarizes the preliminary steps you perform to create a design. The explanations that follow are generic; that is, the process is the same regardless of the design class you are using.  For detailed instructions about creating a certain design, refer to the specific section that explains it.

To Create An Experimental Design

1.	Choose SPECIAL... EXPERIMENTAL DESIGN... CREATE DESIGN... from the Menu bar to display the Create Design Options dialog box.

2.	Complete the dialog box.  You will select a design class and either accept the defaults or enter specific parameters for each of the options on the dialog box.

3.	Click OK to display additional Options dialog boxes specific to the design class you are creating.

4.	Complete all the applicable dialog boxes, then click OK to display a 	Design Summary in the Design Attributes window.  Before you click OK, you can modify the design you created.


Using Screening Designs

Screening designs let you set up and analyze the following types of designs:

•	two-level and fractional factorial

•	mixed-level fractional

•	irregular fractional

•	Plackett-Burman

•	user-specified.

These designs provide a means for reducing experimental time and cost.  They are appropriate when some of the variables may have negligible main effects and interactions, or when higher-order interactions are insignificant.  In these designs, the number of experimental runs or trials can be reduced by intentionally confounding some of the experimental effects.

A screening design determines:

•	the amount of change that occurs in the response variable when the level of a factor is changed

•	if changing the factors together produces results different from changing the factors individually.


Creating a Response Surface Design

Follow these steps to create a Response Surface Design:

To Create A Response Surface Design

1.	Choose SPECIAL... EXPERIMENTAL DESIGN... CREATE DESIGN... from the Menu bar to display the Create Design Options dialog box.

2.	Complete the dialog box by choosing the Response Surface design option, entering a number for the response variable(s) and number of experimental factors, and optionally, entering a descriptive comment that will identify the design.

3.	Click OK to display the Factor Definition Options dialog box.

4.	Complete the dialog box by either accepting the defaults or choosing a factor and entering a name for it, as well as for the lowest and highest values for the factor, and, if applicable, entering a value for the units of measure.

Clicking the Back... button redisplays the previous dialog box.

5.	Click OK to display the Response Definition Options dialog box.

6.	Complete the dialog box by either accepting the defaults or choosing a response variable and defining it by entering a name for it and, if applicable, entering a value for the units of measure.

Clicking the Back... button redisplays the previous dialog box.

7.	Click OK to display the Response Surface Design Selection dialog box.

8.	Indicate if you want the list to include blocked designs by either selecting or deselecting Display Blocked Designs, then choose a design from the list of designs.  Displaying Blocked Designs is the default.

Clicking the Back... button redisplays the previous dialog box.

9.	Click OK to display one of three Design Options dialog boxes: Three-Level, Composite, or a Blocked Composite. The dialog box that displays depends on the design choice.

10.	Complete the dialog box you are using by either accepting the defaults or by entering the design characteristics, the number of centerpoints and where they will be placed; indicating if the design will be replicated, and if so, entering the number of times; and indicating if the runs will be created in random order.

If you click OK now, the experimental runs are placed in the Worksheet and the Design Summary displays in the Design Summary window.


Creating a Mixture Design

Follow these steps to create a Mixture Design.

1.	Choose SPECIAL... EXPERIMENTAL DESIGN... CREATE DESIGN... from the Menu bar to display the Create Design Options dialog box.

2.	Complete the dialog box by choosing the Mixture design option, entering a number for the number of response variable(s) and number of components, then optionally, entering a descriptive comment that will identify the design.

3.	Click OK to display the Component Definition Options dialog box.

4.	Complete the dialog box by either accepting the defaults or choosing a component and entering a name for it, as well as for the lowest and highest values, and if applicable, entering a value for the mixture total, and the number for the units of measure.

Clicking the Back... button redisplays the previous dialog box.

5.	Click OK to display the Response Definition Options dialog box.

6.	Complete the dialog box by either accepting the defaults or choosing a response variable and defining it by entering a name for it, as well as, and if applicable, entering a value for the units of measure.

Clicking the Back... button redisplays the previous dialog box.

7.	Click OK to display the Mixture Design Selection dialog box.

8.	Complete the dialog box by either accepting the defaults or choosing a design from the list of design types, entering a value for it and, if applicable, entering a value for the units of measure.

Clicking the Back... button redisplays the previous dialog box.

9.	Click OK to display the Mixture Design Options dialog box.

10.	Complete the dialog box.  Notice that the dialog box displays the name of the chosen design and indicates the total number of runs.  Choose the type of model you want to analyze when you complete the experimental runs.  Enter a value for the number of replicate points, then indicate if the design should be augmented and if the experimental runs should be created in random order by 	selecting or deselecting the Randomize check box.

If you click OK now, the experimental runs are placed in the DataSheet and the Design Summary displays in the Mixture Design window.


Analyzing Designs

A primary advantage in using statistical methods to analyze experimental responses is to add objectivity to the decision-making process, which ensures that the results and conclusions will be objective rather than judgmental.

Statistical methodologies allow you to measure the likelihood of error in a conclusion or to attach a level of credibility to a statement.

STATGRAPHICS Plus contains important statistical methodologies for proving reliability and validity in tabular results.  Its graphical capabilities are useful for visualizing the results and presenting them to others.

Before you can analyze a design, you must open the design file.

To Open a Design File

1.	Choose SPECIAL... EXPERIMENTAL DESIGN... OPEN DESIGN... from the Menu bar to display the Open Design dialog box.

2.	Choose the design file you want to open, then click Open.

Note:  If you created design files in DOS, before you can use them, you must rename them using the file extension .sfx, then bring them into STATGRAPHICS Plus for Windows.

To Analyze an Experimental Design

1.	Choose SPECIAL... EXPERIMENTAL DESIGN... ANALYZE DESIGN... from the Menu bar to display the Analyze Design dialog box.

2.	Complete the dialog box by entering the name of the variable that contains the experiment results you want to analyze.

When you click OK, the first tabular option, Analysis Summary, and the first graphical option, which will vary depending on the design, will display in the Analysis window.  You can interpret the results, then select other tabular and graphical options.

Because the options are so numerous, depending on the design class and its parameters, it is impossible to document them here.


Analyzing Screening Designs
Analyzing Screening Designs – no longer used

Follow the steps below to analyze a Screening Design.

1.	Open the application.

2.	Select SPECIAL… EXPERIMENTAL DESIGN… OPEN DESIGN from the Menu bar to display the Open Experiment Files dialog box displays.

3.	Double-click on the name of the file that contains the Screening Design you want to analyze (or type the name of the file in the File Name text box), then click the OK button.  The program opens the Screening Design file and displays the icons for the design file and the design attributes.

4.	Select SPECIAL… EXPERIMENTAL DESIGN… ANALYZE DESIGN from the Menu bar; the Analyze Design dialog box displays.

5.	Complete the dialog box and click the OK button; the Analysis Summary displays for the response variable.

6.	Select the tabular options you want to use to analyze the design, then click the OK button; the options you selected display in the text panes of the window .

The tabular options available for analyzing a Screening Design are: Analysis Summary, ANOVA Table, Regression Coefficients, Correlation Matrix, Predictions, Path of Steepest Ascent, and Influential Points.

The graphical options available for analyzing a Screening Design are: Pareto Charts, Main Effects Plots, Interaction Plots, Normal Probability Plots of Effects, Response Plots, and Diagnostic Plots.


Analyzing Response Surface Designs
Analyzing Response Surface Designs – no longer used

Follow the steps below to analyze a Response Surface Design.


Analyzing Mixture Designs
Analyzing Mixture Designs – no longer used

Follow the steps below to analyze a Mixture Design.


Using Experimental Designs

The role of experimental design is to estimate the effects of several variables simultaneously.  The experimental design then contains a group of experimental runs (Box, Hunter, and Hunter, 1978).  Said another way, experimental design is a scientific approach that allows an experimenter to make intentional changes to the inputs of a process or system to identify and observe the reasons for the changes that occur to the response.

Process is defined as some combination of materials, methods, people, environment, and measurement, which used together form a service, produce a product, or complete a task (Schmidt and Launsby, 1989).

In any experiment, the results and conclusions depend to a large extent on the manner in which the data are collected.  The primary reason for using any designed experiment is to use data that can provide answers to well thought out questions.

Montgomery (1991) outlines the many disciplines that use experimental design methods.  Experimentation is viewed as part of the scientific process where opinions are formed about a process and experiments are performed to generate data from the process.  Information from the experiment is then used to establish new opinions, which lead to new experiments, and so on.

In the engineering world, experimental design methods are critical tools that improve the performance of a manufacturing process, which results in:

•	improvements in process yields

•	reductions in variability and closer conformance to nominal or target requirements

•	reductions in development time

•	reductions in overall costs.

In engineering design activities, where new products are developed and existing ones improved, experimental design methods provide tools for:

•	evaluating and comparing basic design configurations

•	evaluating alternative materials

•	selecting design parameters so a product will work well under a wide variety of field conditions

•	determining key product design parameters that impact a product's performance.

The role of experimental design is to estimate the effects of several variables simultaneously.  The experimental design then contains a group of experimental runs (Box, Hunter, and Hunter, 1978).  Said another way, experimental design is a scientific approach that allows an experimenter to make intentional changes to the inputs of a process or system to identify and observe the reasons for the changes that occur to the response.

Process is defined as some combination of materials, methods, people, environment, and measurement, which used together form a service, produce a product, or complete a task (Schmidt and Launsby, 1989).

In any experiment, the results and conclusions depend to a large extent on the manner in which the data are collected.  The primary reason for using any designed experiment is to use data that can provide answers to well thought out questions.

Montgomery (1991) outlines the many disciplines that use experimental design methods.  Experimentation is viewed as part of the scientific process where opinions are formed about a process and experiments are performed to generate data from the process.  Information from the experiment is then used to establish new opinions, which lead to new experiments, and so on.

In the engineering world, experimental design methods are critical tools that improve the performance of a manufacturing process, which results in:

•	improvements in process yields

•	reductions in variability and closer conformance to nominal or target requirements

•	reductions in development time

•	reductions in overall costs.

In engineering design activities, where new products are developed and existing ones improved, experimental design methods provide tools for:

•	evaluating and comparing basic design configurations

•	evaluating alternative materials

•	selecting design parameters so a product will work well under a wide variety of field conditions

•	determining key product design parameters that impact a product's performance.


Optimizing Designs

STATGRAPHICS Plus provides a capability to optimize an experiment.  Typically, this involves creating a design, then selecting Optimize Design from the Menu bar to determine if there are runs that could be removed from the design before you run the experiment.

Optimize Design is an automated feature that is activated after you create or open a design, with logic to estimate a minimum number of runs (candidate runs) for a design.  You then use the candidate runs when you analyze the design.

The Optimize Experiment window that displays after you open the design displays the algorithm used to select the subset of original runs used to reach D-optimality.  D-optimality is a criterion that measures the variability of the estimated parameters.

Because D-optimal designs are often used with mixture experiments, the remainder of this topic uses a Simplex-Centroid design.

When you optimize designs, several tabular options are available for the various design classes.

To Optimize a Mixture Design

1.	Choose SPECIAL... EXPERIMENTAL DESIGN... CREATE DESIGN... from the Menu bar to display the Create Design Options dialog box.

2.	Choose the Mixture option, accept 1 (the default) for the No. text box, accept 3 (the default) for the number of components, then enter a comment about the design into the Comment text box.

3.	Click OK to display the Component Definition Options dialog box.

4.	Accept the defaults by clicking OK; the Response Definition Options dialog box displays.

5.	Accept the defaults by clicking OK to display the Mixture Design Selection dialog box.

6.	Choose the Simplex Centroid design by clicking on it.  The 7s that appear for Linear, Quadratic, and Special Cubic are the number of runs for each design.

7.	Click OK to display the Mixture Design Options dialog box. The number of runs (7) also appears on this dialog box.

8.	Complete the dialog box by clicking OK to accept the defaults and to display the Design Summary in the Mixture Design Attributes window. The summary contains information about the design you created.

9.	Choose SPECIAL... EXPERIMENTAL DESIGN... OPTIMIZE DESIGN... from the Menu bar to optimize the design and display the Optimize Experiment window.

Notice that the optimize algorithm selected a subset of three of the original runs to reach D-Optimality.  You can continue with further optimization or choose another model.

To continue with the optimization:

10.	Click the right mouse button, then select Analysis Options... from the pop-up menu to display the Optimize Design Options dialog box.

11.	Choose another model, enter the number of runs, and click OK to display the Optimize Experiment window that contains the Optimization report.

When you are satisfied with the optimization, you can use the tabular options to print the worksheet.

12.	Click the Tabular Options button on the Analysis toolbar to display the Tabular Options dialog box, select the Worksheet option, then click OK to display the Worksheet.

Note:  Existing runs will not be discarded.  For example, if you open the sample experiment file, CHEMICAL.SFX, and select Optimize Design, the existing runs will not be discarded even though there are more runs than would be required if you started the design from the create stage then optimized it.


Choosing a Screening Design
Choosing a Screening Design – Duplicate Don’t Use

STATGRAPHICS Plus allows you to set up and analyze highly structured designs and includes predefined designs.  You can generate both blocked and unblocked designs.  You can also create and analyze your own designs.


Choosing Tabular Options for a Design Class

Several report options provide additional information about the design you select.  However, not all of the options are available for every design class.  For example, in Screening Designs, the available tabular options are Design Summary, Worksheet, Alias Structure, and Correlation Matrix; while for other design classes, the available tabular options are Design Summary and Worksheet.  Also, a Power Curve graphical option is available for Screening Designs.  The four possible tabular options and the graphical option are described next.  The descriptions of the options are the same, regardless of the design class you use.

Design Summary

The Design Summary option displays a summary of the design you choose.  The summary information includes the design class, design name, and file name.  Other information about the base design includes the number of experimental factors, blocks, responses, runs, error degrees of freedom, and indicates if the factors were randomized.  A table shows the lowest and highest values for each of the factors, and indicates if the factors are Continuous.  The name of the response variable is shown.

Worksheet

The Worksheet option displays a Worksheet that contains the experimental runs that will be performed, as well as the order in which you should run them.

Print the Worksheet to record the information, then record the values for the responses in the blank spaces provided.  Restore the DataSheet and enter the values into the appropriate column(s) of the DataSheet, then analyze the design.

Alias Structure

The Alias Structure option displays the alias pattern for the design, which shows the main effects, interactions, and any confounding that involves them.  If the main effects and interactions are clear of confounding, an appropriate message displays.  Confounded effects are joined by a plus sign; for example, A + BC indicates that the main effect, A, is confounded with the two-factor interaction, BC.

Correlation Matrix

The Correlation Matrix option displays a correlation matrix for all the factor and interaction effects, based on the actual design matrix.


Choosing Graphical Options for Design Classes

Power Curve

The Power Curve option displays a plot that determines whether or not an experiment can detect effects of the magnitude you expect.


Basic Principles of Experimental Design

Experimental design is based on these basic principles:

Replication

Replication is a repetition of a basic experimental run.  It has two important properties.  First, you obtain an estimate of the experimental error that becomes a basic unit of measurement used to determine if observed differences in the data are really statistically different.  Second, you use the sample mean to estimate the effect of a factor.

Randomization

Randomization is the basis underlying the use of statistical methods in experimental design.  Randomization means that you randomly determine how the experimental material is allocated, and the order in which the individual runs or trials of the experiment will be performed.

Blocking

Blocking is a technique that increases the precision of an experiment.  A block is a portion of experimental material that should be more homogeneous than the entire set of material.  Blocking involves making comparisons in each block among common conditions in the experiment.  Blocking is often necessary to remove the effects of different batches of material, different experimenters, or experiments run on different days.

In some production processes, units are produced in natural “chunks” or blocks.  You want to make sure that these blocks do not bias your estimates of main effects.

Confounding

Confounding is a design technique for arranging a complete factorial experiment in blocks, where the block size is smaller than the number of treatment combinations in one replicate.

See also

Using Experimental Designs

Understanding Design Classes


Saving Designs

After you create a design, you must name and save it permanently to the hard disk or to a diskette.  STATGRAPHICS Plus saves experimental design files as *.sfx files.

To Save Experimental Designs

1.	Choose FILE... SAVE AS... SAVE DESIGN FILE AS... from the Menu bar to display the Save Design As dialog box.

2.	Type the name for the title of the experimental design and click OK.  The program adds the *.sfx extension, saves the file, and displays the Data icon in a Taskbar at the bottom of the window.

After the file is saved, the design remains open so you can continue working; the new file name appears on the title bar.


Using Response Surface Designs

“Response surface methodology consists of a group of techniques used in the empirical study of relationships between one or more measured responses such as yield, color index, and viscosity, on one hand, and a number of input variables such as time, temperature, pressure, and concentration, on the other” (Box, Hunter, and Hunter, 1978).

Montgomery (1997) states that response surface methodology (RSM) is a collection of mathematical and statistical techniques useful for modeling and analysis in applications where a response is influenced by several variables and the objective is to optimize the response.

Montgomery also notes that another objective of RSM is to find a region of the factor space that satisfies the operating specifications.  He states that “optimum” is used in a special way because the initial estimate of the optimum operating conditions will be far away from the “actual optimum.”  In cases such as this, the object is to quickly move to the general area of the optimum.

The path of steepest ascent is a technique for moving consecutively along a path of steepest ascent or descent, depending on whether the direction is to be maximized or minimized.   The path of steepest ascent is usually a line through the center of the regions.

Experiments conducted along a path of steepest ascent continue until no further increase is observed or until the desired response region is reached.  Then a new first-order model can be fitted, a new direction of steepest ascent determined, and if necessary, further experiments conducted in that direction until the process is near the optimum.


Using Mixture Designs

Mixture designs are usually a special form of response surface designs where two or more formulations, blends, combinations, or components make up a product.

Mixture designs are used in industrial situations that involve mixtures that are measured in some type of units, such as volume or weight, that add up to a whole.  In addition, mixture designs are usually constructed to estimate linear interactions.


Using Multilevel Factorial Designs

The Multilevel Factor design class allows you to create a design that consists of all combinations of specific levels of two or more factors; for example, a two- or three-level factorial design.  This design class is intended for quantitative factors only and is analyzed as a response surface design.


Using Inner/Outer Arrays Designs

The Inner/Outer Arrays Designs Analysis in STATGRAPHICS Plus is a variation on an implementation of Taguchi (Robust) designs.  The designs in STATGRAPHICS Plus consist of both controllable and uncontrollable noise factors.  A typical use is to determine the combination of factors that reduce the sensitivity to uncontrollable sources of variability.

Uncontrollable factors, or noise factors, can be external or internal.  External sources or outer noise, are variations in environmental conditions such as temperature, humidity, vibrations, dust, or human variations in operating a product.  Internal sources of noise or inner noise, are deviations of the actual characteristics of a product from its nominal settings.  These can result from imperfections in a manufacturing process, or from deterioration over time of internal elements and components.

To minimize the effects of noise sources, STATGRAPHICS Plus uses a technique of combined arrays design, which incorporates both controllable and uncontrollable noise factors.  The combined arrays design must be used with a resolution high enough to estimate all the interactions (usually resolution IV or higher).  Montgomery (1997) says “this approach will almost always lead to a dramatic reduction in the size of the experiment” . . . and at the same time produces “information that is more likely to improve process understanding.”

Montgomery (1997) finds Taguchi’s theory of “robust design” to be sound, and says it “ . . . should be included in the quality improvement process of any organization”.  In this type of robust design, most American and European engineers focus on system and tolerance design to achieve performance.

It is common in product and process design to base an initial prototype on system design, then use reliability and stability against noise factors, and correct any problems using tolerance design and skip parameter design altogether (Cullen and Hollingum, 1987; Phadke, 1989).

An eight-step process is suggested for conducting a robust design:

1.	Identify the main function.

2.	Identify the noise factors and testing conditions.

3.	Identify the quality characteristics to be observed and the function to be optimized.

4.	Identify the control factors and their alternative levels.

5.	Design the matrix experiment and define the data analysis procedure.

6.	Conduct the matrix experiment.

7.	Analyze the data and determine near optimum levels for the control factors.

8.	Predict the performance at these levels (Phadke, 1989).

Overall, robust design is a powerful tool that offers simultaneous improvements in quality, cost, and engineering productivity.


Using Single Factor Categorical Designs

Single factor categorical designs compare levels of a single nonquantitative variable, with or without blocking factors.  This type of experiment is the simplest type of experiment because it contains only a single factor of interest.  You can analyze these designs as either a multifactor or one-way ANOVA.

In STATGRAPHICS Plus you can create seven different types of single factor categorical designs:

•	completely randomized with no blocking

•	randomized block with one blocking factor

• 	combinatoric BIB with one blocking factor

•	small BIB with one blocking factor

•	Latin square with two blocking factors

•	Graeco-Latin square with three blocking factors

•	hyper-Graeco-Latin square with four blocking factors.


Using Multi-Factor Categorical Designs

Multi-factor categorical designs consist of all combinations of levels for two or more factors, where you set the number of levels.  The analysis is intended for nonquantitative factors and is analyzed using ANOVA.


Using Variance Components (Hierarchical) Designs

Variance Components (Hierarchical) designs consist of nested factors.  The analysis is intended for quantifying the effects of various factors on the variability of the response variable(s).  It is analyzed as a Variance Components analysis.


Using Multiple Response Optimization

Multiple Response Optimization is a function that determines the combination of experimental factors that simultaneously optimize several response variables.

The goal of the function is to maximize a desirability function.  The function can be used after you analyze two or more design components.  Several of the Analyze Design windows must be open to use the function.  If an Analyze Design window is minimized to a Taskbar, the program will not recognize the analysis.


Choosing a Screening Design

STATGRAPHICS Plus allows you to set up and analyze highly structured designs and includes predefined designs.  You can generate both blocked and unblocked designs.  You can also create and analyze your own designs.

Your entries on two dialog boxes determine which designs will display: Create Design and Screening Design Selection.  On the first, enter parameters that fit the data you are using; on the latter ensure that the check box for Display Blocked Designs is either checked or unchecked, then click the Down Arrow to the right of the list on the dialog box, and choose a design.

A brief description of the available designs follows; the description also indicates if the design is blocked or unblocked.

Two-Level and Fractional Factorial

Factorial designs include all combinations of the factor level.  Fractional Factorial designs are regular fractions such as 1/2, 1/4, 1/8, and so on or an irregular unbalanced fraction of a complete factorial design.

Mixed-Level Factorial

Use to study factorial designs based on one or more blocked or unblocked factors that are fixed and where one or more are random.

Irregular Saturated Half Fraction

Designs of an orthogonal property used to study factorial designs based on half of all combinations of blocked or unblocked factors.  Creates a design of resolution III by inundating all the interactions of a full factorial design with additional factors.

Plackett-Burman

Designs that can be generated in steps of 4 runs, from 4 to 100 runs.  The designs have the same number of runs as an equivalent fractional factorial; they are identical to fractional factorials with rows and columns reordered.  Those designs of intermediate size are orthogonal.

User-Specified Design

Designs created by the user that can be blocked or unblocked.


Choosing a Mixture Design

The Mixture Design Selection dialog box lists the available designs.  You can also design and create designs of your own choosing.  To display a list of available designs, click the Down Arrow to the right of the list.  If a simplex design is not available due to the specified constraint, Extreme Vertices and User-Specified Design displays.

Simplex-Lattice

A design determined by the number of components, q, and the degree, m, of the polynomial model.  The design includes all combinations of the components in which the proportions are defined by:

xi = 0, 1/m, 2/m, ..., 1

For example, a quadratic, three-component, standard unit design includes the following blends:  (1,0,0), (0,1,0), (0,0,1), (1/2, 1/2, 0), (1/2, p, 1/2), (0, 1/2, 1/2).

Simplex-Centroid

Includes every subset of the components, q, where the proportions are equal for 	each included component.  These subsets consist of pure blends, binary blends, 	tertiary blends . . . , and the overall centroid.

For example, a three-component, standard unit design includes the following blends:  (1,0,0), (0,1,0), (0,0,1), (1/2, 1/2, 0), (1/2, 0, 1/2), (0, 1/2, 1/2), and the centroid (1/3, 1/3, 1/3).

Extreme Vertices

A computer-aided design that includes the vertices in a constrained region that 	does not form a simplex.  In a simplex region, the extreme vertices are identical to the vertices found in the simplex-lattice and simplex-centroid designs.

User-Specified Design

Designs created by the user from data already in a DataSheet.


Creating Screening Designs

To Create A Screening Design

1.	Choose SPECIAL... EXPERIMENTAL DESIGN... CREATE DESIGN... from the Menu bar to display the Create Design Options dialog box.

2.	Complete the dialog box by choosing the Screening design option, entering a number for the response variable(s) and number of experimental factors, then, optionally, entering a descriptive comment that will identify the design.

3.	Click OK to display the Factor Definition Options dialog box.

4.	Complete the dialog box by either accepting the defaults or choosing a factor and entering a name for it, as well as entering the lowest and highest values for the factor in the Low and High text boxes, and, if applicable, entering a value for the units of measure.  Then indicate if you want the factor to be Continuous (Quantitative) or Categorical (Qualitative).  The default is Continuous (check box marked).

Clicking the Back... button redisplays the previous dialog box.

5.	Click OK to display the Response Definition Options dialog box.

6.	Complete the dialog box by either accepting the defaults or choosing a response variable and defining it by entering a name for it, as well as, if applicable, entering a value for the units of measure.

Clicking the Back... button redisplays the previous dialog box.

7.	Click OK to display the Screening Design Selection dialog box.

8.	Indicate if you want the list to include blocked designs by either choosing or not choosing Display Blocked Designs, then choose a design from the list of designs.  Displaying Blocked Designs is the default.

Clicking the Back... button redisplays the previous dialog box.

9.	Click OK to display the Screening Design Options dialog box.

10.	Complete the dialog box.  Notice that the dialog box displays the name of the base design, indicates the total number of experimental runs, and the degrees of freedom available for the error.  Choose the number of centerpoints that will be used and where they will be placed in the design.  If the design will be replicated, enter the number of times, then indicate if the runs should be created in random order by choosing or not choosing the Randomize check box.

If you click OK now, the experimental runs will be placed in the DataSheet and the Design Summary will display in the Design Summary window.

For some design classes, you may be able to use the Generators... command and display the Design Generators dialog box, which lists the design generators used to create the last column(s) of the design matrix.  When you click OK, the Screening Design Options dialog box redisplays.


Choosing a Response Surface Design

STATGRAPHICS Plus allows you to set up and analyze highly structured designs and includes predefined designs.  You can generate both blocked and unblocked designs.  You can also create and analyze your own designs.

Your entries on two dialog boxes determine which designs will display: Create Design and Response Surface Design Selection.  On the first, enter parameters that fit the data you are using; on the latter, ensure that the check box for Display Blocked Designs is either checked or unchecked, then click the Down Arrow to the right of the list on the dialog box, and select a design.

A brief description of the available designs follows; the description also indicates if the design is blocked or unblocked.

Three-Level Factorial

A design that consists of all combinations of all factor levels.  The design is capable of estimating all factors and their interactions.  For example, a complete factorial design of three factors, each at three levels, would consist of 3 x 3 x 3 =  27 runs.

Central Composite Designs

Designs that span a set of quantitative factors with fewer points than a standard factorial multilevel design, without a large loss in efficiency.  This major class of designs has two parts: a cube and a 	star.  The cube portion corresponds to a factorial screening design.  For example, in a three-factor study, eight points in a central composite design form a cube that corresponds to a 2^3 factorial.  The star portion of the design consists of an additional set of points arranged at equal distances from the center of the cube on radii that pass through the centerpoint on each face of the cube.  The distance from the center of the cube to one of these points is called the axial distance of the star.

Central composite designs are desirable because of two attributes: orthogonality and rotatability.  Orthogonality allows you to measure the desired effects independently of each other.  Nonorthogonal designs result in a dependency of effects that is particularly undesirable; that is, some of the factors are correlated.  Rotatability implies that you can estimate the response with equal variance regardless of the direction from the center of the design.

Box-Behnken Design

Uses a selection of corner, face, and central points to span an experimental space with fewer points than a Complete Factorial Design.  It is similar in intent to a Central Composite Design, but differs in that no corner or extreme points are used.  It has no extended axial points, so it uses only three-level factors.  It can be a blocked or unblocked design.

Draper-Lin

A small central composite design.  Rather than a full factorial, the design uses a fractional factorial.

User-Specified Design

Designs created by the user that can be blocked or unblocked.


Creating a Multilevel Factorial Design

To Create a Multilevel Factorial Design

1.	Choose SPECIAL... EXPERIMENTAL DESIGN... CREATE DESIGN... from the Menu bar to display the Create Design Options dialog box.

2.	Complete the dialog box by choosing the Multilevel Factorial design class option, entering a number for the number of response variable(s) and number of experimental factors, then, optionally, entering a descriptive comment that will identify the design.

3.	Click OK to display the Factor Definition Options dialog box.

4.	Complete the dialog box by either accepting the defaults or choosing a factor and entering a name for it as well as for values for the lowest and highest factor, and, if applicable, entering a value for the units of measure.

Clicking the Back... button redisplays the previous dialog box.

5.	Click OK to display the Response Definition Options dialog box.

6.	Complete the dialog box by choosing a response variable and defining it by entering a name for it, and, if applicable, entering a value for the units of measure.

Clicking the Back... button redisplays the previous dialog box.

7.	Click OK to display the Multilevel Factorial Design Options dialog box.

8.	Complete the dialog box by either accepting the defaults or changing the number of times the design will be replicated.  The number you enter will determine the number of experimental runs and the degrees of freedom 	for the design.  Selecting or deselecting the check box indicates if the runs will be randomized.

Clicking the Back... button redisplays the previous dialog box.

If you click OK now, the experimental runs will be placed in the DataSheet and the Design Summary will display in the Design Attributes window.


Choosing a Multilevel Factorial Design
Choosing a Multilevel Factorial Design – don’t use – not needed


Creating An Inner/Outer Arrays Design

To Create an Inner/Outer Arrays Design

1.	Choose SPECIAL... EXPERIMENTAL DESIGN... CREATE DESIGN... from the Menu bar to display the Create Design Options dialog box.

2.	Complete the dialog box by choosing the Inner/Outer Arrays option, entering a number for the number of response variable(s), number of control factors, number of noise factors, and, optionally, entering a descriptive comment that will identify the design.

3.	Click OK to display the Response Definition Options dialog box.

4.	Complete the dialog box by either accepting the defaults or choosing a 	response variable and defining it by entering a name for it, and, if applicable, entering a value for the units of measure.

Clicking the Back... button redisplays the previous dialog box.

5.	Click OK to display the Inner/Outer Arrays Options dialog box.

6.	Complete the dialog box.  Depending on your earlier choices, you can choose an Inner Array, or if you entered a value for the noise factors, you can also choose an Outer Arrray.  There are 18 available options under each array.  Click the Randomize check box if you want the runs randomized.

Clicking the Back... button redisplays the previous dialog box.

7.	Click OK to display the Column Assignments dialog box.

8.	Complete the dialog box by entering a number for each factor in the Inner Array.

9.	Click OK to display the Control/Noise Factor Definition Options dialog box.

10.	Complete the dialog box by choosing a factor, entering a name for it, and, optionally, entering a value for the units of measure.

Clicking the Labels... button displays the Factor Levels dialog box, which lets you enter labels for each of the factor levels.

If you click OK now, the experimental runs will be placed in the DataSheet and the Design Summary will display in the Design Attributes window.


Creating a Single Factor Categorical Design

To Create a Single Factor Categorical Design

1.	Choose SPECIAL... EXPERIMENTAL DESIGNS... CREATE DESIGN... from the Menu bar to display the Create Design Options dialog box.

2.	Complete the dialog box by choosing the Single Factor Categorical design option, entering a number for the response variable(s), then, optionally, entering a descriptive comment that will identify the design.

3.	Click OK to display the Factor Definition Options dialog box.

4.	Complete the dialog box by either accepting the defaults or entering a name for the factor, as well a value for the number of levels, and, if applicable, the units of measure.

Clicking the Labels... button displays the Factor Levels dialog box, which you use to enter labels for each of the factor levels.

Clicking the Back... button redisplays the previous dialog box.

5.	Click OK to display the Response Definition Options dialog box.

6.	Complete the dialog box by either accepting the defaults or choosing a response variable and defining it by entering a name for it, and if applicable, entering a value for the units of measure.

Clicking the Back... button redisplays the previous dialog box.

7.	Click OK to display the Single Factor Categorical Design Options dialog box.

8.	Complete the dialog box by either accepting the defaults or choosing a design from the list of design types, entering a value for the number of times the 	design will be replicated, and indicating if the design will be randomized.  If you are using a blocked design, enter the number and size of the block.

Notice that the dialog box displays the number of runs and blocks in the experiment, as well as the error degrees of freedom.

Clicking the Back... button redisplays the previous dialog box.

If you click OK now, the experimental runs will be placed in the DataSheet and the Design Summary will display in the Design Attributes window.


Creating Single Factor Categorical Designs

To Create a Single Factor Categorical Design

1.	Choose SPECIAL... EXPERIMENTAL DESIGNS... CREATE DESIGN... from the Menu bar to display the Create Design Options dialog box.

2.	Complete the dialog box by choosing the Single Factor Categorical design option, entering a number for the response variable(s), then, optionally, entering a descriptive comment that will identify the design.

3.	Click OK to display the Factor Definition Options dialog box.

4.	Complete the dialog box by either accepting the defaults or entering a name for the factor, as well a value for the number of levels, and, if applicable, the units of measure.

Clicking the Labels... button displays the Factor Levels dialog box, which you use to enter labels for each of the factor levels.

Clicking the Back... button redisplays the previous dialog box.

5.	Click OK to display the Response Definition Options dialog box.

6.	Complete the dialog box by either accepting the defaults or choosing a response variable and defining it by entering a name for it, and if applicable, entering a value for the units of measure.

Clicking the Back... button redisplays the previous dialog box.

7.	Click OK to display the Single Factor Categorical Design Options dialog box.

8.	Complete the dialog box by either accepting the defaults or choosing a design from the list of design types, entering a value for the number of times the 	design will be replicated, and indicating if the design will be randomized.  If you are using a blocked design, enter the number and size of the block.  For a list of the available designs, see the section, “Selecting a Single-Factor Categorical Design,” below.

Notice that the dialog box displays the number of runs and blocks in the experiment, as well as the error degrees of freedom.

Clicking the Back... button redisplays the previous dialog box.

If you click OK now, the experimental runs will be placed in the DataSheet and the Design Summary will display in the Design Attributes window.


Choosing a Single Factor Categorical Design

The Single Factor Categorical Design Options dialog box provides details about the base design by displaying the number of runs, the number of blocks, error degrees of freedom; and indicating the number of times the design will be replicated, and whether or not the design will be randomized.

The list of designs shown for the Design Type options are briefly described below.

Completely Randomized (No Blocking)

An experiment in which all treatments are present and all runs are randomly ordered.

Randomized Block (One Blocking Factor)

A design in which you randomly assign the treatments to be compared with positions in each of several blocks of replications.  In a complete block experiment, each block contains all treatments.

Combinatoric BIB (One Blocking Factor)

This type of design is used when it is not possible to include all factor combinations in every block.  However, every factor-level combination occurs an equal number of times and each pair of factors occurs together in an equal number of blocks.

Small BIB (One Blocking Factor)

A small, balanced, incomplete block (BIB) design that reduces the 	number of runs required by combinatoric BIB designs.

Latin Square (Two Blocking Factors)

A Latin square design is an arrangement of the first n integers in an n by n array so every integer appears exactly once in every row and exactly once in every column.  In this particular case it is used with two blocking factors.  This type of design is useful for reducing two sources of variability.

Graeco-Latin Square (Three Blocking Factors)

A Graeco-Latin square design is an arrangement of a k x k pattern that permits the study of k treatments simultaneously with three different blocking variables.  This type of design is useful for reducing more than two sources of variability.

Hyper-Graeco-Latin Square (Four Blocking Factors)

A hyper-Graeco-Latin square design is an arrangement that allows the study of k treatments with more than three blocking variables.  This type of design is useful for reducing more than two sources of variability.

For an example that uses these types of designs, see Box, Hunter, and Hunter (1978).


Creating a Multi-Factor Categorical Design

To Create a Multi-Factor Categorical Design

1.	Choose SPECIAL... EXPERIMENTAL DESIGNS... CREATE DESIGN... from the Menu bar to display the Create Design Options dialog box.

2.	Complete the dialog box by choosing the Multi-Factor Categorical design class option, entering a number for the number of response variable(s) and number of experimental factors, then, optionally, entering a descriptive comment that will identify the design.

3.	Click OK to display the Factor Definition Options dialog box.

4.	Complete the dialog box by either accepting the defaults or choosing a factor and entering a name for it, as well as a value for the number of levels, and, if applicable, the number of units of measure.

Clicking the Labels... button displays the Factor Levels dialog box which you use to enter labels for each of the factor levels.

Clicking the Back... button redisplays the previous dialog box.

5.	Click OK to display the Response Definition Options dialog box.

6.	Complete the dialog box by either accepting the defaults or choosing a response variable, and defining it by entering a name for it, and, if 	applicable, entering a value for the units of measure.

Clicking the Back... button redisplays the previous dialog box.

7.	Click OK to display the Multi-Factor Categorical Design Options dialog box.

8.	Complete the dialog box by either accepting the defaults or changing  the number of times the design will be replicated.  The number you enter will determine the number of experimental runs and the degrees of freedom for the design.  You can select or deselect the check box to indicate if the runs will be randomized.

Clicking the Back... button redisplays the previous dialog box.

If you click OK now, the experimental runs will be placed in the DataSheet and the Design Summary will display in the Design Attributes window.


Creating a Variance Components (Hierarchical) Design

To Create a Variance Components (Hierarchical) Design

1.	Choose SPECIAL... EXPERIMENTAL DESIGNS... CREATE DESIGN... from the Menu bar to display the Create Design Options dialog box.

2.	Complete the dialog box by choosing the Variance Components (Hierarchical) design option, entering a number for the response variable(s) and number of experimental factors, then, optionally, entering a descriptive comment that will identify the design.

3.	Click OK to display the Factor Definition Options dialog box.

4.	Complete the dialog box by either accepting the defaults or choosing a factor and entering a name for it, as well as a value for the number of levels, and, if applicable, a value for the number of units.

Clicking the Labels... button displays the Factor Levels dialog box, which you use to enter labels for each factor level.

Clicking the Back... button redisplays the previous dialog box.

5.	Click OK to display the Response Definition Options dialog box.

6.	Complete the dialog box by either accepting the defaults or choosing a response variable and defining it by entering a name for it, and, if applicable, entering a value for the units of measure.

Clicking the Back... button redisplays the previous dialog box.

7.	Click OK to display the Variance Components Design Options dialog box.

8.	Complete the dialog box by either accepting the defaults or changing the number of times the design will be replicated.  The number you enter will determine the number of experimental runs and the degrees of freedom for the design.  You can select or deselect the check box to indicate if the runs will be	 randomized.

Clicking the Back... button redisplays the previous dialog box.

If you click OK now, the experimental runs will be placed in the DataSheet and the Design Summary will display in the Design Attributes window.


Creating a Multiple Response Optimization

To Create the Multiple Surface Designs

1.	Choose SPECIAL... EXPERIMENTAL DESIGN... CREATE DESIGN... from 	the Menu bar to display the Create Design Options dialog box.

2.	Complete the dialog box by choosing the Response Surface design option, entering 2 for the number of response variables, accepting the default in the No. of Experimental Factors dialog box, and, optionally, entering a comment about the design in the Comments text box.

3.	Click OK to display the Factor Definition Options dialog box.

4.	Complete the dialog box by accepting all the defaults.

5.	Click OK to display the Response Definition Options dialog box.

6.	Complete the dialog box by accepting all the defaults.

7.	Click OK to display the Response Surface Design Selection dialog box.

8.	Click the arrow on the right side of the design options and choose the 3-Level Factorial Design (3^3), and accepting the other default.

9.	Click OK to display the Three-Level Design Options dialog box.

10.	Complete the dialog box by accepting all the defaults.  Notice that the dialog box provides information about the design you chose.

11.	Click OK to place the experimental runs in the DataSheet and the Design Summary in the Design Attributes window shown.

12.	Click the Tabular Options button on the Analysis toolbar to display the 	Tabular Options dialog box, then select the Worksheet option and click OK to display the Worksheet in the second text pane of the Design window.

13.	Maximize the Worksheet, print it, and enter the values for Var_1 into the blank spaces provided.

14.	Restore the DataSheet, enter the values for Var_1 into the appropriate column of the DataSheet.

15.	Choose SPECIAL... EXPERIMENTAL DESIGN... ANALYZE DESIGN... from the Menu bar to display the Analyze Design dialog box.

Enter Var_1 into the Data text box, then click OK to display the Analysis Summary and the Pareto Chart in the Analysis window.

17.	Enter the values for Var_2 into the blank spaces on the Worksheet you printed.

18.	Repeat Steps 14, 15, and 16, using Var_2.  Leave both of the Analysis windows open.


Using the Multiple Response Optimization Function

To Use the Multliple Response Optimization Function

1.	Choose SPECIAL… EXPERIMENTAL DESIGN… MULTIPLE RESPONSE OPTIMIZATION… from the Menu bar to display the Multiple Response Optimization dialog box.

2.	Enter Var_1 and Var_2 into the Response text box.

3.	Click OK to display the Multiple Response Optimization window.

4.	Click the Tabular Options button on the Analysis toolbar to display the Tabular Options dialog box, which contains two pains: Analysis Summary and Optimize Desirability.

5.	Choose the latter option, click OK then maximize and second the second pane.


To Further Refine the Optimization

1.	Place the mouse pointer on the Optimize Desirability pane, click the right button, then the left on Analysis Options... to display the Multiple Response Optimization Options dialog box.  This dialog box lets you further refine the optimization.

2.	Click OK, then place the mouse pointer on the Optimize Desirability pane, click the right button, then the left on Pane Options... to display the Optimize Response Options dialog box.

This dialog box lets you choose the type of optimization, and set additional starting points for the optimization process.


Augmenting Designs

In experimental design, it is usually most effective to estimate the effects of several variables simultaneously when each design contains a certain set of experimental runs.  You will not necessarily use a new design for each iteration of experimentation.

Problems arise when it is not clear how you should change an unsatisfactory hypothesis, or when a hypothesis appears satisfactory, but you feel you need further confirmation.  Many times the solution is to add more data.  To do this, you choose a new experimental design or attach additional experimental runs through augmentation.

The design you choose depends on the hypothesis you are currently using.  The design should allow you to explore areas for which you lack information, and should add greater significance to the study.  For example, you may want to augment a design to:

•	clear main effects so the effects of certain interactions are not confounded

•	obtain results that are more conclusive

•	remove (collapse) a factor that does not have a significant effect on the response

•	add star points to a design to create a central composite design for estimating 	quadratic terms.

STATGRAPHICS Plus provides capabilities that allow you to add experimental runs to an existing design.  The program adds the runs to the original design (the base set of runs), and typically places the added runs in a new block.

Before you begin the augmentation, open STATGRAPHICS Plus, then open a design file.

To Open a Design File

1.	Choose SPECIAL... EXPERIMENTAL DESIGN... OPEN DESIGN... from the Menu bar to display the Open Experiment Files dialog box.

2.	Enter the name of the design file into the File Name text box to load the data.


To Create Plots for the Optimization

To Create Plots for the Optimization

1.	Click the Graphical Options button on the Analysis toolbar to display the 	Graphical Options dialog box.  The options include two Response plotsts so you can display both a Response Surface Plot and a Contour Plot simultaneously, s well as Overlaid Contour plots.

2.	Use Pane... options for the Response plots to display the Response Plot Options dialog box.  Use Pane... options for the Overlaid Contour Plots to display the Response Plot Factors dialog box.


Using Augment Design Actions

This topic explains each of the augment actions and takes you through the steps required for augmenting a design.

Depending on the action you choose and the design you are using, the program may display options dialog boxes for you to complete.  For example, when you choose the Replicate Design action and click OK, the Replicate Design dialog box displays, which you use to enter the number of complete replicates you want to add to the original design.

If the action does not require you to complete more dialog boxes, the design is augmented and the results displayed in the Design Attributes window.

The following actions are available from the Augment Design menu: Replicate Design, Add a Fraction, Collapse Design, Clear Main Effects, Clear a Factor, and Add Star Points.  The type of design you are using determines the action you use.

Replicate Design

This action replicates an entire design, including its centerpoints and block structure.  When you replicate a design, each replicate is placed in its own block.  If you are using a User-Specified design, all the runs in the design will be replicated.

To Replicate a Design

1.	Choose SPECIAL... EXPERIMENTAL DESIGN... AUGMENT DESIGN... from the Menu bar to display the Augment Design dialog box.

2.	Choose the Replicate Design option, then click OK to display the Replicate Design dialog box.

3.	Enter a positive integer into the Number of Replicates text box to indicate the 	number of times the design will be replicated.

4.	Click OK to display the Design Summary in the Design Attributes window.

Add a Fraction

This action adds a fraction to the design, which removes all confounding of main effects from second-order interactions in a resolution III design.  The new runs are added to the design in a way that clears the main effects from confounding and produces a resolution IV design.

To Add a Fraction to a Design

1.	Choose SPECIAL... EXPERIMENTAL DESIGN... AUGMENT DESIGN... from the Menu bar to display the Augment Design dialog box.

2.	Choose the Add a Fraction option, then click OK to perform the augmentation and display the results in the Design Summary in the Design Attributes window.

Collapse Design

This action removes a single factor from a factorial design.  The design that results is less fractioned, and may be a replicate of the original design.

To Collapse a Design

1.	Choose SPECIAL... EXPERIMENTAL DESIGN... AUGMENT DESIGN... from the Menu bar to display the Augment Design dialog box.

2.	Choose the Collapse Design option, then click OK to display the Collapse Design dialog box.

3.	Complete the dialog box by choosing one of the listed factors.

4.	Click OK to remove the factor from the design and display the results in the Design Summary in the Design Attributes window.

Clear Main Effects

This action is similar to the Foldover Design action in that it removes confounding of all main effects from second-order interactions in a resolution III design.  The difference is that this action always produces a resolution IV design.

The Clear Main Effects action does not allow you to add a new factor.  If the original design was unblocked, the additional runs are added in a new block.  If the original design was a blocked design, the additional runs follow the same block structure, which doubles the number of blocks.

To Clear Main Effects

1.	Choose SPECIAL... EXPERIMENTAL DESIGN... AUGMENT DESIGN... from the Menu bar to display the Augment Design dialog box.

2.	Choose the Clear Main Effects option, then click OK to add the additional run in a new block and display results in the Design Summary in the Design Attributes window.

Clear a Factor

This action clears all confounding of a factor with other effects; that is, all the interactions that include that factor.  When you clear a factor, the main effect and its interactions appear without confounding.  The program adds runs that contain reversed factor levels (for the factor you select), and unchanged factor levels for all the other factors, which doubles the number of runs in the design.

To Clear a Factor

1.	Choose SPECIAL... EXPERIMENTAL DESIGN... AUGMENT DESIGN... from the Menu bar to display the Augment Design dialog box.

2.	Choose the Clear a Factor option, then click OK to display the dialog box shown in Figure 12-4.

3.	Complete the dialog box by choosing one of the listed factors.

4.	Click OK to add the additional runs to the design, clear the factor from the esign, and display the results in the Design Summary in the Design Attributes window.

Add Star Points

This action adds star points to a Screening design to create a central composite design.  The program calculates the axial distance, based on the number of star points and the number of base points in the base design, and creates a design that is orthogonally blocked.

To Add Star Points

1.	Choose SPECIAL... EXPERIMENTAL DESIGN... AUGMENT DESIGN... from the Menu bar to display the Augment Design dialog box.

2.	Choose the Add Star Points option, then click OK to add the runs to the design and display the results in the Design Summary in the Design Attributes window.


Using Analyses for Time-Series

Much of the data in statistics represent observations in a sequence.  When these observations occur sequentially in time at uniformly spaced intervals, they make up a time series.

Overview of Time Series Analysis

Using the Descriptive Methods Analysis

Using the Smoothing Analysis

Using the Seasonal Decomposition Analysis

Using the Forecasting Analysis


Overview of Time Series Analysis
Overview of Time-Series Analysis

The statistical techniques for analyzing time-series data range from straightforward to very complex, but the first step in any analysis is to identify the characteristics of the data.  Identifying the characteristics, such as stationarity or seasonality, gives a clear picture of the data and helps to determine any seasonal effects, cyclic changes, trends, errors, outliers, or turning points.  These in turn help in the selection of appropriate smoothing and forecasting methods.

This module for STATGRAPHICS Plus contains four analyses for time-series data:  Descriptive Methods, Smoothing, Seasonal Decomposition, and Forecasting.

Descriptive Methods

This analysis helps in visualizing the shape, trend, and patterns of data and in describing the history of the time period.

Smoothing

This analysis estimates a function or prepares data for other statistical procedures.

Seasonal Decomposition

This analysis separates the time-series pattern into the three components of trend, cycle, and seasonal factors.

Forecasting

This analysis assists in examining the three components and in comparing the models that predict future values for the series.


Using the Descriptive Methods Analysis

This analysis provides various techniques you can use to adjust or transform data to improve the results.  It allows you to:

•	perform statistical calculations that reveal correlations in the data

•	test for nonrandomness of the data

•	produce various plots that reveal trends and cycles as well as data errors and outliers.

You can use any of the following tools to analyze time-series data.

Horizontal Time Sequence Plots

These are connected lineplots of the time-series variable against time.  The plots show important features such as trend, seasonality, discontinuity, and outliers.  When a trend exists in the data it means that successive values will be positively correlated.  Seasonality is a pattern that repeats itself over fixed intervals of time.  Discontinuity is an abrupt change or shift in a pattern.  Outliers are extreme values in the data.

Autocorrelations

Autocorrelations help to determine if the data are random or have a pattern.  The program calculates the correlation coefficients between the values in the time-series variable and the values for earlier time periods.  You can display a table of estimated autocorrelations, standard errors, or upper and lower probability limits for each lag.  For a single time series, it is very useful to compare the observation at one time period with the observation at another time period; similarly it is possible to compare the series with itself, lagged two periods . . . three periods . . . and so on.  You can also display the autocorrelation as a graph, which makes it easier to determine if there is a pattern in the data.  The amount of correlation is shown as the height of the bars.

Periodograms and Periodogram Tables

A periodogram is a plot of frequency and ordinate pairs for a specific time period used to construct a frequency spectrum.  A periodogram can be helpful in identifying randomness and seasonality in time-series data, and in recognizing the predominance of negative or positive autocorrelation — help you often need to identify an appropriate model for forecasting a given time series.  If the periodogram contains one spike, the data may not be random and you need to use a periodogram table to determine the seasonality.  The table includes a column of ordinates and a column of periods.  It also shows the cumulative sum and integrated periodograms for each period.

Tests for Randomness

Tests for randomness confirm that data are random or nonrandom.  Two runs tests and a Box-Pierce test is run on the data.  The Runs Above and Below the Median test counts the number of runs that are completely above or below the median and ignores the values that are equal to the median.  If the test statistic is large (corresponds to a p-value less than .05), you can conclude that the values occur in a nonrandom order.  The Runs Up and Down test counts the numbe of times a sequence rises or falls.  This test is sensitive to long-term cycles.  If the test statistic is small (corresponds to a p-value greater than .05), you can conclude that the values occur in a random order.  The Box-Pierce test verifies if the autocorrelation is equal to 0.  If the test statistic is large (corresponds to a p-value less than .05), the autocorrelation is not equal to 0.

To Create a Descriptive Methods Analysis

1.	Choose SPECIAL… TIME-SERIES ANALYSIS… DESCRIPTIVE METHODS… from the Menu bar to display the Descriptive Methods Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Horizontal Time Sequence Plot in the Analysis window.


Using the Smoothing Analysis

If time-series data involve a trend (an upward or downward direction) or a seasonal effect (for example, strong sales of disposable tissues in winter months), or both a trend and a seasonal effect, you need to apply a smoothing method to the data.  Smoothing methods move through the known data period by period, as opposed to using all the past data in one model-fitting exercise.

When you smooth data you combine observations, which tends to reduce randomness by allowing the positive and negative effects to partially offset each other.  For example, when you analyze and plot time-series data, the values do not always follow a straight line.  Often, the scatterplot you produce will have points that are scattered more or less randomly, which makes it difficult to see cycles and trends.  To eliminate the randomness in the pattern, you can combine two or more observations from periods during which the causal factors were in effect to achieve a smoothed value.  The plot you create after you smooth the data will have a curve that more clearly shows the general pattern.

The Smoothing Analysis in STATGRAPHICS Plus allows you to apply up to two consecutive smoothing methods to a time-series variable.  After you apply smoothing methods to the data, the program plots the data to reveal trends and cycles as well as errors and outliers.  It also plots residuals.  The analysis also provides several methods you can use to adjust or transform data to make it more appropriate for the evaluation.

To Create a Smoothing Analysis

1.	Choose SPECIAL… TIME-SERIES ANALYSIS… SMOOTHING… from the Menu bar to display the Smoothing Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Time Sequence Plot.


Using the Seasonal Decomposition Analysis

The time-series decomposition approach to forecasting is based on the principle of “breaking down” a time series into each of its components — and then forecasting by predicting each component separatately, except randomness, which you cannot predict (Makridakis et al., 1983).

The Seasonal Decomposition Analysis in STATGRAPHICS Plus allows you to perform a classical decomposition of the data.  Classical decomposition breaks the time-series data into four components: trend, seasonality, cycle, and irregular movement.

Trend

Trend is the long-term behavior of the data.

Seasonality

Seasonality is the periodic fluctuation of constant lengths that usually repeats itself at fixed intervals.

Cycle

Cycle is the wave-like patterns of ups and downs that are similar to seasonality.  Cycles can take place over a long time period such as several years.  The length of time between peaks is not fixed as it is with seasonal movement.

Irregular Movement

Irregular movement is movement in the data that you cannot attribute to trend, seasonality, or cycle.  This component is often known as noise.

The Seasonal Decomposition Analysis allows you to perform a classical decomposition of time-series data using a multiplicative or additive model.  The analysis provides several methods you can use to adjust or transform the data to make it more appropriate for the analysis you are performing.

To Create a Seasonal Decomposition Analysis

1.	Choose SPECIAL… TIME-SERIES ANALYSIS… SEASONAL DECOMPOSITION… from the Menu bar to display the Seasonal Decomposition Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Trend-Cycle Plot in the Analysis window.


Using the Forecasting Analysis

There is frequently a delay between the time you become aware of an upcoming event or need and when that event or need actually occurs.  This delay is the primary reason for planning and forecasting.

Forecasting is based on fitting a model to past observations in a given time series.  The model you choose depends on how you will use the forecast, the degree of accuracy you require from the forecast, the amount of time and capital available to you, the amount and type of data available to you, and how far ahead you must forecast.

STATGRAPHICS Plus includes 13 forecasting models you can modify by changing the parameters.  You can choose up to five models.  With each model you can transform the data or apply a constant rate of inflation.  Depending on the model you choose, the program also allows you to optimize the parameters or include a constant term.  If the data are seasonal, you can apply differencing and choose a seasonal adjustment.  The forecasting models follow.

Random Walk

This model randomly forecasts the next observation based on the current observation and ghe mean and standard deviation for the difference of the values.

Mean

This model forecasts by adding together the values of the items and dividing them by the number of ters; more simply, by using the average.

Linear Trend

This model fits a straight line through the data and into the forecasting periods.

Quadratic Trend

This model fits a quadratic curve through the data and into the forecasting periods.

Exponential Trend

This model fits an exponential curve through the data and into the forecasting periods.

S-Curve

This model fits an S-shaped curve through the data and into the forecasting periods.

Moving Average

This model uses the moving average to smooth the data and to predict future values.

Simple Exponential Smoothing

This model smoothes the data and predicts the future values by exponentially weighting the values in the time series.

Brown’s Linear Exponential Smoothing

This model smoothes the data and predicts future values by applying a double-smoothing formula to the data using one parameter, alpha.

Holt’s Linear Exponential Smoothing

This model applies a double-smoothing formula to the data using two smoothing parameters:  alpha and beta.

Quadratic Exponential Smoothing

This model assumes that the data follow a trend characterized as a second-order polynomial.

Winter’s Exponential Smoothing

This model applies three separate smoothing parameters to the data:  alpha, beta, and gamma.  It estimates the level of the series (the stationarity), the linear trend, and the seasonality.

ARIMA Model

This model estimates and forecasts using the methods prescribed by Box and Jenkins (1976).

To Create a Forecasting Analysis

1.	Choose SPECIAL… TIME-SERIES ANALYSIS… FORECASTING… from the Menu bar to display the Forecasting Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Time Sequence Plot in the Analysis window.


Using Analyses for Multivariate Methods

Multivariate methods are important statistical techniques whose usage is particularly widespread in the physical, social, and medical sciences.  In many of these areas there is a need to understand the relationship between many variables, which requires a simultaneous examination of two or more measurements on many variables.

Overview of Multivariate Methods

Using the Cluster Analysis

Using the Factor Analysis

Using the Principal Components Analysis

Using the Discriminant Analysis

Using the Canonical Correlations Analysis

Creating and Saving Matrix Data


Overview of Multivariate Methods

Multivariate methods are important statistical techniques whose usage is particularly widespread in the physical, social, and medical sciences.  In many of these scientific studies there is a need to understand the relationships between many variables, which requires that you simultaneously examine two or more measurements on many variables.

Multivariate analysis can also be complex because it is hard to identify techniques that are designed to study both dependent and interdependent relationships, and techniques that study the number of sets of variables or the number of observations.

Multivariate methods lend themselves to:

•	reducing or simplifying data

•	0sorting or grouping data

•	investigating the dependence among variables

•	predicting relationships between variables

•	constructing and testing hypotheses.

The Multivariate Methods analyses in STATGRAPHICS Plus are:  Cluster, Factor, Principal Components, Discriminant, and Canonical Correlations.  It is important that you:

•	understand the strengths and shortcomings of each of these analyzes

•	choose and use the appropriate analysis

•	properly interpret the results.

Cluster Analysis

Identifies hierarchical clusters of observations in a dataset by using one of six methods or algorithms.

In hierarchical methods each observation begins in its own cluster.  Two clusters are then merged to form a new cluster that replaces the two ol clusters.  This process repeats until only one cluster is left.  The algorithms the program uses differ in how they compute the distance between the two clusters.

In the K-Means method, clusters are formed beginning with an initial partition.  A search algorithm is then used to test other partitions to identify the one with the least error.

Factor Analysis

Performs classical and principal components factoring with rotations.  You can analyze raw standardized data, a correlation matrix, or a covariance matrix.  After factoring a matrix, three different rotation methods are available as an aid to interpretation.  You can also use factor analysis to rotate coefficients you produce using other analyses.

The purpose of the analysis is to:

•	identify a set of dimensions that cannot be easily seen in a larger set of variables

•	devise a method for combining or condensing large numbers of observations into distinctly different grioups

•	reduce the number of variables fom a larger set that can be used in different analyses

•	create an entirely new set of a smaller number of variables to partially or completely replace the original set of variables.

Principal Components Analysis

Determines the relationships among several quantitative variables.  You use the analysis to summarize data and to detect linear relationships.  It is a helpful tool when you need to reduce the number of variables in regression or clustering analyses.

The analysis determines a small number of linear combinations in a set of variables, keeping as much of the information from the original variables as possible.  You can use the resulting variables in place of the original variables for regression, clustering, and so on.

Discriminant Analysis

Develops a discriminant model that is then used to classify each observation into one of the groups previously identified in the study.  Also known as classification criterion, the discriminant model is determined by a measure of generalized squared distance.  It is based on either the individual within-group covariances matrices or the pooled covariance matrixs or the pooled covariance matrix and accounts for probabilities in previous groups.

Canonical Correlations Analysis

Explains or summarizes the relationship between two sets of variables by finding a small number of linear combinations from each set of variables.  The linear combinations are those that contain the highest correlations possible between the sets.


Using the Cluster Analysis

Cluster analysis is the name of a multivariate techinque you can use to identify similar characteristics in a group of observations.  In cluster analysis, you also identify and classify observations or variables so that each observation or variable in a cluster is most like others in the same cluster.  If your classification is correct, the observations or variables within the clusters will be “close”; objects in different clusters will be “far” apart.

Cluster analysis is useful in many different disciplines such as business, biology, psychology, and sociology.  Also referred to as Q-analysis, classification analysis and numerical taxonomy, the name varies from discipline to discipline.

There is, however, one commonality: classification by natural relationship, which suggests that the value of cluster analysis lies in preclassifying data.  For example, you might classify large amounts of otherwise meaningless data into manageable groups; you might reduce the data into specific smaller subgroups; or you might develop hypotheses about the nature of the data.  Whatever the situation, using cluster analysis becomes increasingly complex when you add more variables or include mixed datasets.

Cluster analysis involves using three stages of techinques: partition, interpret, and profile.

Partition

During this stage, decisions are made about how to measure the data, which algorithms are best suited to classify the data, and the number of clusters that will be formed.

Interpret

In this stage, the statements used to develop the clusters are examined and assigned a name or label that accurately describes the characteristics of each cluster.

Profile

In this stage, the characteristics of each cluster are described, providing an explanation of how each cluster differs on relevant dimensions.

The most commonly used algorithms are hierarchical and nonhierarchical.  Hierarchical methods construct tree-like structures, either agglomerative or divisive.  In the agglomerative method, each observation begins as its own cluster and in subsequent steps clusters are combined into new aggregate clusters, which reduces the number of clusters in each step.

When the clustering process goes in the opposite direction, it is known as a divisive or K-Means method.  Nonhierarchical algorithms do not involve tree-like sructures.

Determining how to choose the number of clusters is not a definitive process.  Generally, the distances between clusters at sequential steps provide a guideline.  Usually, it is best to try several solutions for different clusters and then decide among the solutions.

The six hierarchical clustering methods are defined next.

Nearest Neighbor

This method finds the two observations that have the shortest distance and places them in the first cluster.  Then it finds the next shortest distance and either joins a third observation to the first two to form a cluster or forms a new two-observation cluster.  This process continues until all the observations are in one cluster.  This method is also known as Single Linkage.

Furthest Neighbor

This method uses the maximum distance between any two observations in a cluster.  All the observations in a cluster are linked to each other at some maximum distance or by some minimum similarity.  This method is also known as Complete Linkage.

Centroid

In this method, the distance between the means of two clusters is the measurement.  Each time you group observations, you form new centroids.  The cluster centroids move when a new observation or group of observations is added to an existing cluster.  Centroid methods require that you use metric data; other methods do not.

Median

This method uses the median distance from observations in one cluster to observations in another as the measurement.  This approach tends to combine clusters that have small variances and may produce clusters that have the same variance.

Group Average

In this method, the distance between clusters is calculated as the average distance between all the observations in one cluster and the average distance between all the observations in another cluster.

Ward’s

In Ward’s method, the distance between two clusters is the sum of squares between two clusters summed over all the variables.  This method combines clusters that have a small number of observations, and tends to produce clusters that have approximately the same number of observations.

To Create a Cluster Analysis

1.	Choose SPECIAL… MULTIVARIATE MTHODS… CLUSTER ANALYSIS… from the Menu bar to display the Cluster Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Dendrogram in the Analysis window.


Using the Factor Analysis

Factor analysis is a technique useful for reducing information in a large number of variables into a smaller set, while losing only a small amount of information.  Variables in a factor analysis model represent a linear function of a small number of common factor variables and a single specific variable.  The common factors create covariances among the responses, while the specific variable adds only to the variances of specific responses.

The general purposes of factor analysis are to:

•	identify a set of dimensions you cannot easily observe in a large set of variables

•	devise a means for combining or condensing large numbers of observations into distinctly different groups within a larger population

•	create an entirely new set of a smaller number of variables to partially or to completely replace the original set of variables you can then use in regression, correlation, cluster, or discriminant analysis.

There are a number of general steps you must consider when you are deciding which factor-analysis technique to use:

•	the problem

•	the correlation matrix

•	the type of model

•	how you will extract the factors

•	the number of factors you will extract

•	whether or not you will rotate the factors

•	how you will rotate the factors

•	how you will interpret the rotated factors and their scores.

Generally, you would not use factor analysis if the data contain fewer than 50 observations but, preferably, 100 or more.

Althouigh there are several kinds of general factor models, the two that analysts use most are principal component analysis and common factor analysis.

Principal Component Analysis

Principal component analysis is the amount of variance in a variable that is shared by all the variables.  Principal component analysis summarizes nearly all of the original information into a smaller number of factors that can then be used for estimation purposes.

Common Factor Analysis

Common factor analysis is the amount of variance that can be related only to a specific variable.  Common factor analysis identifies conditions or proportions that are not easily recognizable.

Besides determining the type of factor analysis that will be used, you must also determine if  the factors should be orthogonally extracted.  Mathematically, orthogonal solutions are simpler; they extract factors so the axes remain at 90 degrees, and each factor remains indepndent of the others.

Factor rotation is another important concept in factor analysis.  Rotation means that the factors are turned until they reach another position.  The primary reason for rotating factors is to attain a simpler and more meaningful solution.  Rotation is generally desirable because it simplifies the rows and/or columns of the matrix.  STATGRAPHICS Plus contains three primary approaches for rotation: Quartimax, Varimax, and Equimax.

Quartimax

This approach simplifies the rows of the factor matrix.

Varimax

This approach simplifies the columns of the factor matrix.

Equimax

This approach simplifies the rows or the columns by combining aspects of each of the above two approaches.

STATGRAPHICS Plus also contains two methods you can use to determine the number of factors to extract from an analysis: minimum eigenvalues or the number of factors.

To Create a Factor Analysis

1.	Choose MULTIVARIATE METHODS… FACTOR ANALYSIS… from the Menu bar to display the Factor Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Scree Plot in the Analysis window.


Using the Principal Components Analysis

Principal components analysis differs from factor analysis in that you use it whenever you want uncorrelated linear combinations of variables.  That is, principal components analysis is a factor analysis technique that reduces the dimensions of a set of variables by reconstructing them into uncorrelated combinations.

The analysis combines the variables that account for the largest amount of variance to form the first principal component.  The second principal component accounts for the next largest amount of variance, and so on, until the total sample variance is combined into component groups.  Each successive component explains progressively smaller portions of the variance in the total sample.  All of the components are uncorrelated.

Often a few components will account for 75 to 90 percent of the variance in an analysis.  These components are the ones you use to plot the data.  Other uses for principal components analysis include various forms of regression analysis and classification and discrimination problems.

To Create a Principal Components Analyisis

1.	Choose SPECIAL… MULTIVARIATE METHODS… PRINCIPAL COMPONENTS… from the Menu bar to display the Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary.


Using the Discriminant Analysis

Complex problems and the results of bad decisions frequently force researchers to look for more objective ways to predict outcomes.  A classic example often cited in statistical literature is creditworthiness where, based on a collection of variables, potential borrowers are identified as either good or bad credit risks.

Discriminant analysis is the statistical technique that is most commonly used to solve these types of problems.  Its use is appropriate when you can classify data into two or more groups, and when you want to find one or more functions of quantitative measurements that can help you discriminate among the known groups.  The objective of the analysis is to provide a method for predicting which group a new case is most likely to fall into, or to obtain a small number of useful predictor variables.

Discriminant analysis is capable to handling either two groups or multiple groups (three or more).  When two classifications are involved, it is known as two-group discriminant analysis.  When three or more classifications are identified, it is known as multiple discriminant analysis.  The concept of discriminant analysis involves forming linear combinations of independent (predictor) variables, which become the basis for group classifications.

Discriminant analysis is appropriate for testing the hypothesis that the group means for two or more groups are equal.  Each independent variable is multiplied by its corresponding weight, then the products are added together, which results in a single composite discriminant score for each individual in the analysis.

Averaging the scores derives a group centroid.  If the analysis involves two groups there are two centroids; in three groups there are three centroids; and so on.  Comparing the centroids shows the distance of the groups along the dimension you are testing.

Applying and interpreting discriminant analysis is similar to regression analysis, where a linear combination of measurements for two or more independent variables describes or predicts the behavior of a single dependent variable.  The most significant difference is that you use discriminant analysis for problems where the dependent variable is categorical versus regression where the dependent variable is metric.

The objectives for applying discriminant analysis include:

•	determining if there are statistically significant differences among two or more groups

•	establishing procedures for classifying units into groups

•	determining which independent variables account for most of the difference in two or more groups.

Discriminant analysis involves three steps: Derivation, validation, and interpretation.

Derivation

In this first step, you must first choose the variables, test the validity of the discriminant function, determine a computational method, and assess the level of significance.

Validation

This step involves determining the reason for developing classification matrices, deciding how well the groups are classified into statistical groups, determining the criterion against which each individual score is judged, constructing the classification matrices, and interpreting the discriminant functions to determine the accuracy of their classification.

Interpretation

This step involves examining the discriminant functions to determine the importance of each independent variable in discriminating between the groups, then examining the group means for each important variable to outline the differences between the groups.

The Discriminant analysis in STATGRAPHICS Plus allows you to generate discriminant functions from the variables in a dataset, and return values for the discriminant functions in each case.  The analysis assumes that the variables are drawn from populations that have multivariate normal distributions and that the variables have equal variances.

To Create a Discriminant Analysis

1.	Choose SPECIAL… MULTIVARIATE METHODS… DISCRIMINANT ANALYSIS… from the Menu bar to display the Discriminant Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and 2D Scatterplot in the Analysis window.


Using the Canonical Correlations Analysis

Developed by Hotelling in 1936, canonical correlations analysis is a technique you can use to study the relationship between two sets of variables, each of which might contain several variables.  Its purpose is to summarize or explain the relationship between the sets of variables by finding a small number of linear combinations from each set that have the highest correlation possible between the sets.  This is known as first canonical correlation.  The coefficients of these combinations are canonical coefficients or canonical weights.  Usually the canonical variables are normalized so each canonical variable has a variance of 1.

A second set of canonical variables is found, which produces the second correlation coefficient.  This process continues until the number of pairs equals the number of variables in the smallest group in the study.

Canonical correlation analysis is helpful in many disciplines.  For example, in an educational study, the first set of variables could be measures of word attack skills (sounding-out words); the second might be measure of comprehension.  In market research, the first set of variables could be measures of product characteristics (number of rolls in a package, size of each roll, price of the package, price of each roll); the second might be measures of customer reaction or buying trends.

In STATGRAPHICS Plus, the analysis assumes that the data are drawn from a population that is multivariate normal.  You can test this assumption for pairs of variables by producing an X-Y plot to verify that each pair of variables is roughly elliptical and that their points are widely scattered.  Or you can produce an X-Y-Z plot to test this assumption for sets of three variables.  However, even if sets of two and three variables satisfy the multivariate normal assumptions, a full set of data may not.  If that is the case, you may want to try using square root, logarithmic, or some other transformation.

To Create a Canonical Correlations Analysis

1.	Choose SPECIAL… MULTIVARIATE METHODS… CANONICAL CORRELATIONS… from the Menu bar to display the Canonical Correlations Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Canonical Variables Plot in the Analysis window.


Creating and Saving Matrix Data

STATGRAPHICS Plus allows you to create and save correlation and covariance matrices.  You can use matrix data in the Multivariate Methods module by entering them into any of these analyses: Principal Components, Factor Analysis, and Cluster Analysis.

To Create and Save Matrix Data

1.	Open the data file.

2.	Choose DESCRIBE… NUMERIC DATA… MULTIPLE-VARIABLE ANALYSIS… from the Menu bar to display the Multiple-Variable Analysis dialog box.

3.	Enter the names of the variables into the Data text box.

4.	Enter an expression into the Select text box to choose the number of observations you want to include in the set.

5.	Click OK to display the Analysis Summary.

6.	Click the Save Results  button on the Analysis toolbar.

7.	Choose the type of results you want to save by clicking the check box.

8.	Click OK to save the correlation matrix as a set of variables and redisplay the Analysis Summary.

After you save the matrix, the program places the names in the variable list box.


Using Analyses for Advanced Regression

The Advanced Regression module in STATGRAPHICS Plus consists of seven analyses:  General Linear Models (GLM), Calibration Models, Comparison of Regression Lines, Regression Model Selection, Nonlinear Regression, Ridge Regression, and Logistic Regression.

Overview of Advanced Regression

Overview of the Model-Building Process

Validating a Model

Validating Data

Specifying Effects

Using the General Linear Regression Models Analysis (GLM)

Using the Comparison of Regression Lines Analysis

Using the Calibration Models Analysis

Using the Regression Model Selection Analysis

Using the Nonlinear Regression Analysis

Using the Ridge Regression Analysis

Using the Logistic Regression Analysis


Overview of Advanced Regression

The Advanced Regression analyses in STATGRAPHICS Plus are the following: General Linear Models, Calibration Models, Comparison of Regression Lines, Regression Model Selection, Nonlinear Regression, Ridge Regression, and Logistic Regression.  A brief overview of each analysis follows.

General Linear Models

Analyzes one or more continuous dependent variables and one or more independent variables, whether they are categorical or quantitative.  The relationship between a dependent variable and an independent variable is expressed as an equation that contains a term for the weighted sums of the values for the independent variable, plus a term for all the unknowns; that is, for the error term.

Comparison of Regression Lines

Fits a simple regression model of the form Y = a + bX with an additional categorical variable.  Separate lines are fit for each level of the categorical variable.  You can then test to see if the intercepts and/or slopes differ among the levels of that variable.

Calibration Models

Uses the regression model Y = aX + b to predict values for X as well as for Y.  You first determine the calibration line by running an experiment, taking several samples where the true quantity is known (X), measuring those samples with the instrument or process being calibrated (Y), and plotting the pairs on the XY plane.  You can then use the calibration line to translate measurements from the scale of a measuring device or a process to an interval estimate for a true quantity.

Regression Model Selection

Fits multiple regression models that contain all or chosen combinations of the independent variables.  It shows those that maximize the Adjusted R-Squared statistics or minimize the Mallows' Cp statistic.

Nonlinear Regression

Fits multiple regression models that are nonlinear in the parameters.  You can supply a starting value for each parameter that will be estimated and choose from three different estimation methods.

Ridge Regression

Remedies multicollinearity problems by modifying the method of least squares to allow biased estimators for the regression coefficients.  Tables and plots of natural and standardized coefficients and variance inflation factors help you to choose the best ridge parameter.

Logistic Regression

Estimates multiple regression models where the response variable is binary.  You can enter either individual observations (0,1) or proportions with group sizes.  The independent variables can be categorical and/or quantitative.


Overview of the Model-Building Process

Each of the analyses uses the concept of model-building.  The concept is generally covered in these phases:

1.	Collect and prepare the data.

2.	Reduce the number of explanatory variables, if possible (in exploratory observational studies).

3.	Refine and choose a model.

4.	Verify the conformance to the assumptions; that is, detect problems with multicollinearity, autocorrelations, or ill-conditioned data.

5.	Validate the model.

Collecting data for building a regression model varies depending on the type of analysis you are conducting.  Statistics textbooks such as Neter et al. (1996) define these studies, explain how to prepare the data prior to beginning the investigation, describe how to reduce the number of explanatory variables for each type of study, and how to refine, verify, and choose models.


Validating Data
Validating a Model

Model validation is a useful and necessary part of the model-building process.  Before you use a regression model to make predictions for new observations, it is good practice to test the model on known cases.

Neter et al. (1996) suggest you partition the available cases into two groups: A “holdout” sample and a “model-building” (estimation) sample.  Reserve the holdout sample to validate the model after you use the model-building sample to estimate model parameters.  If the model is appropriate for predicting future cases, the values of the error statistics for the estimation sample should not drastically deteriorate when you compute the statistics for the holdout sample.

Two methods you can use to create validation and estimation statistics are discussed here:  using a random holdout sample for estimation, and using newer data as the validation set.

Note:  All the advanced regression analyses feature the validation capability except Regression Model Selection.

1.	Generally, to use a holdout sample for model validation, choose the observations using the Select text box.  The program uses the remaining complete observations (those you do not choose) to validate the model.  The validation and estimation results appear in the Residual Analysis in the Residual Table after the Analysis Summary.

Or you can use the RANDOM operator in the DataSheet to create random holdout samples to produce and save selection variables, then use the variables in the Select text box; that is, if you enter Random(100) into the Select text box, the program randomly divides the data into samples — 100 observations for estimation; the remaining 80 for validation.  Each time you re-run the analysis, the program partitions the samples differently.

2. 	To validate a model using newer data, enter or sort the file so the newer data are at the bottom, then choose the observations you want to use to estimate the parameters in the model.  For example, if there are 180 observations and you enter First (100) into the Select text box, the program uses the first 100 to estimate the model parameters and the last 80 to create and display error statistics in the Validation column of the Residual Analysis table that appears after the Analysis Summary.

When deciding the number of observations you can give up for validation, Neter et al. (1996) says that “the number of cases should be at least six to 10 times the number of variables in the pool of explanatory variables . . . when 10 variables are in the pool, the dataset should contain at least 60 to 100 cases.”

If you want to choose observations, but you do not want to create validation statistics, use the SELECT operator in the Dependent or Independent Variables text boxes on the Analysis dialog box and leave the Select text box blank.  For example, to use the SELECT operator, you might enter Select(mpg,origin=1) in the Dependent or Independent text boxes.


Using General Linear Regression Models (GLM)
Using the General Linear Regression Models Analysis  (GLM)

The following information is provided only for background information; except as noted, it does not necessarily apply to features in STATGRAPHICS Plus.

MANOVA, ANOVA, ANCOVA, and Multiple Regression models belong to a family of models known as Generalized Linear Models (GLM), which were first introduced by Nelder and Wedderburn (1972).  General linear models are a common set of statistical assumptions upon which regression, correlation, and analysis of variance are based; that is, the full range of methods analysts use to study one or more continuous dependent variables and one or more independent variables, whether they are continuous or categorical.

The basic concept of GLM is that the relationship between the dependent variables and the independent variables is expressed as an equation that contains a term for the weighted sum of the values of the independent variables, plus an error term for unexplained effects.

The General Linear Models Analysis in STATGRAPHICS Plus allows you to estimate linear statistical models that relate one or more dependent variables to one or more independent variables.  You can use it for regression, analysis of variance, multifactor ANOVA, or for an analysis of covariance.

The independent variables you use can be continuous or categorical; categorical variables can be crossed or nested.  While STATGRAPHICS Plus contains other analyses such as Multiple Regression and Multifactor ANOVA, which can fit certain types of linear models, the General Linear Models analysis is more flexible, particularly for models that involve both continuous and categorical factors.

The General Linear Models analysis in STATGRAPHICS Plus contains many features, including the following.

•	The program allows you to specify more than one dependent variable.  It fits the model you choose to each of the dependent variables.  You can also perform a MANOVA.

•	The program allows for crossed and nested effects.

•	The program can create tables that contain the predicted and the residual values from the analysis.

•	The program allows you to choose the error term that is associated with each effect in the model.

You use the General Linear Models analysis when:

•	you have both crossed and nested factors, such as in split plot and repeated measures designs

•	you want to enter your own contrasts in an analysis of variance

•	you want to obtain MANOVA statistics for multiple dependent variables.

To Create a General Linear Regression Models (GLM) Analysis

1.	Choose SPECIAL... ADVANCED REGRESSION... GENERAL LINEAR MODELS… from the Menu bar to display the Analysis dialog box.

2.	Complete the dialog box and click OK to display the GLM Model Specification dialog box.

3.	Complete the dialog box and click OK to display the Analysis Summary and Scatterplot in the Analysis window.


Specifying Effects

General linear models are made up of terms you define using special annotations that represent the names of variables and operators.  In the General Linear Models Analysis, STATGRAPHICS Plus uses two types of independent variables: Categorical and quantitative, and two operators, * (Cross) and (  ) (Nest).

How you use the operators depends on whether the factors are categorical or quantitative.  For example, if the model contains three categorical factors — C1, C2, and C3 — and three quantitative factors — Q1, Q2, and Q3 — the factors are named A, B, C, D, E, and F according to the order you enter them into the General Linear Models Analysis dialog box.

The Factors list box on the GLM Model Specification dialog box displays the names of the factors and their assigned letters; the Effects list box, by default, contains the letters for all the main effects.

You can delete a main effect and you can add additional terms to a model by typing them into the Effects list box.  You also can create many different types of models by using a variety of effects.  For example, for these four rows of effects: A, B, A*B, and C(A), the model looks like this:

A + B + A*B + C(A)

By default, the program adds a constant term to the model.  To remove the constant, use the GLM Model Specification dialog box.  You can specify up to 26 factors and 256 effects.

The seven types of effects you can use with the factors are:

1.	regressor effects that involve a single quantitative factor, such as D or E

2.	polynomial effects that are products of two or more quantitative factors, such as D*E or E*E

3.	main effects that involve a single categorical factor, such as A

4.	crossed effects that involve two or more categorical factors, such as A*C or A*B*C

5.	a quantitative variable that is crossed with a categorical variable, such as A*D

6.	nested categorical effects, such as C(B) or C(B A)

7.	quantitative variables, nested within categorical variables, such as F(B).


Using Calibration Models
Using the Calibration Models Analysis

The following information is provided only for background information; except as noted, it does not necessarily apply to features in STATGRAPHICS Plus.

With quality improvement increasingly becoming a major business strategy, ensuring that parts and processes conform to product specifications, one important concept of quality improvement, means that companies must continuously analyze data and feed it back into the manufacturing process to prevent production problems.  Quantifying this type of data involves defining standard units, calibrating instruments to meet the standard units, and using the instruments to quantify the parts and processes (DataMyte Handbook, 1987).

Today companies involved in international commerce use several systems of international units of measure: English, metric, and the Systeme International d'Unities (SI); the preferred system is the SI.  All industrialized countries maintain primary reference standards through an institute or bureau whose purpose is to construct and maintain the standards, which are then used as a basis for calibrating equipment.  Because it is impossible and impractical for these institutes or bureaus to calibrate every piece of equipment, second- and third-order standards were developed for calibrating instruments that are used in general laboratories and manufacturing areas.

Technicians and inspectors calibrate their equipment against a set of working standards, which are directly tied to the primary standards through the use of transfer standards.  Transferring from one standard to a higher, more accurate standard, is known as calibration.  When a piece of equipment is calibrated and transferred back to a primary standard through transfer standards, the process is known as traceability.  Quality standards such as ISO 9000 and ASQC, often require that equipment be calibrated against a set of working standards that are referred back to primary standards; perhaps even all the way back to the standards maintained by an agency such as the National Institute of Standards and Technology in the United States.

Regression analysis is a mathematical tool that quantifies the relationship between two methods of measurement and provides information that helps researchers determine if a less accurate tool might still be adequate for its intended purpose.  At times, a regression model of Y is used to make a prediction for X, given a new observation Y.  This is known as an inverse prediction problem or a calibration problem.

Calibration problems often occur when the following takes place: A researcher finds that there are two ways to measure the same quantity.  One is extremely accurate, very time-consuming, and possibly expensive — the “gold” standard.  The other is more alterable, easier to obtain, and usually less expensive.  One may be a direct measurement; the other an indirect measurement.

When you can use the regression model Y = aX + b to predict values for X rather than for Y, it is known as a calibration problem; that is, you cannot take the prediction intervals directly from the intervals that you would use for predicting Y values.  For example, analytical chemists and engineers use the calibration line to translate measurements from the scale of a measuring device or process to an interval estimate for a true quantity.  They determine the calibration line by running an experiment, taking several samples where the true quantity is known (X), measuring those samples with the instrument or process being calibrated at (Y), and plotting the pairs on the XY plane.  The equation of the line that best fits through these points is the calibration line; the mathematical tool that provides the equation of that line is least squares regression.

The Calibration Models Analysis in STATGRAPHICS Plus allows you to find a calibration line that fits the data, letting you choose from several ransformations when the points do not follow a straight line.  You can choose to eliminate the constant from the model, which forces the line through the point (0,0).  You also can associate a weight with each observation to perform a weighted regression.  If the calibration experiment includes replicate observations for any of the X values, you can use a lack-of-fit test in the ANOVA table.  The tables and graphs in the analysis help you to determine the validity of the calibration line by completely testing the hypotheses, model diagnostics, and residuals.

Once you are completely satisfied with the calibration line, the program can add values to the equation for either Y or X to calculate estimates with intervals for the opposite variable.  Corresponding values for the measurement and the converted quantity with intervals are shown in tables or directly on an XY plot.  In addition, you can save a calibration line for later use when you convert additional measurements into interval estimates.  Finally, if you have two sets of experimental data, you can compare the two calibration lines with each other using a hypothesis test to see if the results are consistent.

To Create a Calibration Models Analysis

1.	Choose SPECIAL... ADVANCED REGRESSION... CALIBRATION MODELS… from the Menu bar to display the Calibration Models Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Plot of Fitted Model in the Analysis window.


Using the Comparison of Regression Lines Analysis

The following information is provided only for background information; except as noted, it does not necessarily apply to features in STATGRAPHICS Plus.

An important technique in regression analysis involves the use of indicator variables as well as the usual quantitative variables.  Consider an example given in Myers (1990): A chemical engineer is modeling yield of a reaction y as a function of temperature (x1) and pressure (x2); the goal is a model that accounts for the fact that two different catalysts are used.  Catalyst would qualify as a categorical variable; an indicator variable could be used to help understand its role in the relationship between the y and x variables.

A convenient way to study the effect of a qualitative variable is to use indicator or “dummy” variables that take on the values of 0 and 1; that is, a variable usually coded 1 to indicate the presence of an attribute and 0 to indicate its absence.  The indicator or dummy variables may sometimes appear as unplanned nuisance variables; at other times they may be planned as part of the research.

Neter et al. (1996) suggest examples of qualitative explanatory variables as gender (male, female), purchase status (purchase, no purchase), and disability status (not disabled, partly disabled, fully disabled).

Researchers in business, economics, and the social and biological sciences use many indicator variables to compare regression models across groups because they want to simplify a model by determining that grouping is not significant, or they want to improve the prediction capability of a model by using groups.

The Comparison of Regression Lines Analysis in STATGRAPHICS Plus automatically constructs the necessary indicator variables to allow you to compare two or more simple regression models, usually to test whether you can use a single model across groups.  You first enter a model of the form Y = a + bX and a grouping variable, and STATGRAPHICS Plus adds the indicator variables to the model.  In effect, this fits separate lines for each level of the categorical variable and allows you to determine if the intercepts and/or the slopes differ among the levels of that variable.

The tables and graphs in the program are designed specifically for comparing slopes and intercepts.  The tabular and graphical options are helpful when either the slopes or intercepts do not differ significantly and you want to force them to be equal to simplify the model.  The final step in the model-building process is to validate the model.

To Create a Comparison of Regression Lines Analysis

1.	Choose SPECIAL... ADVANCED REGRESSION... COMPARISON OF REGRESSION LINES… from the Menu bar to display the Comparison of Regression Lines Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Plot of Fitted Model in the Analysis window.


Using the Regression Model Selection Analysis

The following information is provided only for background information; except as noted, it does not necessarily apply to features in STATGRAPHICS Plus.

Multiple regression analysis involves fitting a random variable to a set of explanatory variables to provide regression coefficients for a linear model.  The resulting model yields many different statistics you can use to determine how well the model fits the data; that is, to determine the “best” model.  How well the model describes the data determines the degree to which the conclusions are believed reliable.  However, it is important to note that a model accepted for one scenario will not necessarily provide an acceptable solution for another.

Frequently a problem arises when you are faced with determining which of several candidate variables to include in the model.  Further complications occur when multicollinearity exists, when the quality of the data is suspect, or when outside factors such as budget or security issues arise during data collection.

Myers (1990), notes that prior to beginning the analysis it is a good idea to learn something about the nature of the data; for example, can you expect a positive or negative sign for a particular coefficient, or can you determine which regressor variables are important and which are not.  Most importantly, your goal should be to create an uncomplicated model.

Neter et al. (1996) also notes that it is important to remember that linear models are experimental approximations and that with many sets of data you can fit different models that are nearly equal in effectiveness.  The problem is to choose the one “best” model from a pool of candidate models.

The Regression Model Selection Analysis in STATGRAPHICS Plus ranks the best subsets of the explanatory variables, based on the criterion you enter in the Regression Model Selection Analysis dialog box, calculates the statistics for all possible linear regression models, and sorts the values so you can choose the “best” model.  After you decide upon and thoroughly check the final regression model, you should validate it using the Multiple Regression Analysis to examine the relationship between the dependent variable and the final set of independent variables.

Note:  While the Regression Model Selection Analysis is a useful tool for exploratory model-building, you cannot rely on any one statistical test to identify a “true” model.  Remember that using the values of the Cp and R-Squared statistics to choose variables has long been a subject of controversy in statistical literature.

To Create a Regression Model Selection Analysis

1.	Choose SPECIAL... ADVANCED REGRESSION... REGRESSION MODEL SELECTION… from the Menu bar to display the Regression Model Selection Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Adjusted R-Squared Plot in the Analysis window.


Using the Nonlinear Regression Analysis

The following information is provided only for background information; except as noted, it does not necessarily apply to features in STATGRAPHICS Plus.

The goal of nonlinear regression is to find a least squares solution for a nonlinear model, which cannot be done using matrix algebra as it is in linear regression.  In linear regression, the parameters enter the model in a linear fashion and least squares estimates are calculated using matrix algebra.  A least squares solution has an additional property of being the unbiased and minimum variance estimator.  A regression function that is not a straight line can be linear in the parameters, such as polynomial functions and models that can be linearized by transforming the variables.

Often the form of a function that is known to be nonlinear in the parameters cannot be algebraically linearized or, if it can be, the error term is distorted while it should be normally distributed with constant variance.  Neter et al. (1996) and Myers (1990) list several types of nonlinear models that regularly occur in various scientific and other applications.

Unlike linear regression, it is usually possible to find analytical expressions for the least squares by using numerical search procedures (iterations).  In an iterative search, the program starts with an initial estimated value for each parameter in the equation.  It calculates the sum of squares (the sum of the squares of the vertical distances of the points from the curve), then adjusts the parameters to make the curve come closer to the points.  It then adjusts the parameters again so the curve comes even closer to the points.  The program keeps adjusting the parameters until the adjustments virtually make no difference, then it reports the best-fit results.  The preciseness of the values depends in part on the initial values you choose and the stopping criteria.  This means that if you repeat the analysis on the same data you will not always get the same exact information.  It is important to begin the search using reasonable values for each parameter.

In STATGRAPHICS Plus, you first define the function that the program will use to fit the data.  Then you choose an iterative search algorithm to determine the estimates that minimize the residual sum of squares.  The methods are: Marquardt, Gauss-Newton, and Steepest Descent.  All three require you to supply initial values for the estimates of the parameters; see Draper and Smith (1981), Neter et al. (1996), and Myers (1990).  Because the method you use depends on these initial parameters, you should take time to develop reasonable initial estimates.

One caution regarding the initial estimates is that the model may converge to a local minimum instead of a global minimum.  To partially guard against this situation, you can perform the analysis several times using widely differing initial estimates.  Sometimes you can obtain initial estimates from estimates for a linearized form of the regression equation, or by using your own observations.  Either way, remember that different starting values can result in very different estimates for the parameters.

Estimation also sometimes fails to converge due to misplaced parentheses or other errors in the functions.  At other times, adjusting the convergence control details will help, however, there will be cases when function estimation fails because the search algorithm simply does not converge on a solution because it is not completely foolproof.

To Create a Nonlinear Regression Analysis

1.	Choose SPECIAL... ADVANCED REGRESSION... NONLINEAR REGRESSION… from the Menu bar to display the Nonlinear Regression Analysis dialog box.

2.	Complete the dialog box and click OK to display the Initial Parameter Estimates dialog box.

3.	Complete the dialog box and click OK to display the Analysis Summary and Plot of Fitted Model in the Analysis window.


Using the Ridge Regression Analysis

The following information is provided only for background information; except as noted, it does not necessarily apply to features in STATGRAPHICS Plus.

Neter et al. (1996) define ridge regression as one of several methods that have been proposed to remedy multicollinearity problems by modifying the method of least squares to allow biased estimators of the regression coefficients.  In Multiple Regression Analysis, multicollinearity exists when two or more independent variables are highly correlated, which makes it difficult, if not impossible, to determine their separate effects on the dependent variable.

This method falls into the category of biased estimation techniques; that is, though ordinary least squares give unbiased and minimum variance regression estimates, there is no upper bound on the variance of the estimators, and when multicollinearity occurs it may produce large variances.  When the variance is reduced using biased estimation, a noticeable increase in stability occurs in the regression coefficients.  Reducing variance may provide benefits that offset any loss suffered due to using biased estimates.  An estimator that has only a small bias, and that is substantially more precise, is the preferred estimator because it more likely will be closest to the true value of the parameter (Myers, 1990).

Small changes in the data used for fitting the regression usually do not affect the ridge regression estimates, which tend to be quite stable.  However, under the same conditions, and when the predictor variables are highly multicollinear, the least squares estimates may be very unstable.  Neter et al. (1996) notes that predictions of new observations made from ridge-estimated regression functions tend to be more precise than predictions made from ordinary least squares regression functions when the explanatory variables are correlated and the new observations follow the same multicollinearity pattern.  The advantage in making predictions using ridge regression becomes even greater when intercorrelations among the explanatory variables are high.

Analyzing the ridge trace is helpful when you need to reduce the number of potential explanatory variables in exploratory observational studies.  When the ridge trace is unstable, variables whose coefficients tend toward the value of zero are dropped from the study as are variables whose ridge trace is stable but at a very small value.  Variables that have unstable ridge traces that do not tend toward zero are also likely candidates for dropping.

The Ridge Regression Analysis in STATGRAPHICS Plus allows you to modify the least squares method to estimate the multiple regression model using slightly modified normal equations (see Appendix B, Calculations in the Advanced Regression User Manual).  The estimates that result are often more precise than those that result when you use ordinary least squares and, in the case of correlated independent variables, may be closer to the “true value” of the parameter.

The analysis provides tools for choosing a value for theta (the ridge parameter), which controls the extent of the bias that is introduced.  When theta equals zero, the estimates that result are the same as those for least squares.  As theta increases, but usually remains less than one, bias increases; however, the coefficients usually become more precise.  Ordinarily, an appropriate value for theta is the smallest value that occurs before the estimates begin to slowly change.

To Create a Ridge Regression Analysis

1.	Choose SPECIAL... ADVANCED REGRESSION... RIDGE REGRESSION… from the Menu bar to display the Ridge Regression Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Ridge Trace in the Analysis window.


Using the Logistic Regression Analysis

The following information is provided only for background information; except as noted, it does not necessarily apply to features in STATGRAPHICS Plus.

Logistic regression analysis allows analysts to estimate multiple regression models when the response being modeled is dichotomous and can be scored 0,1; that is, the outcome must be one of two choices.  Analysts use logistic regression when they want to model something that can be expressed as Event/Nonevent or something that has two possible outcomes.  For example, those given by Neter et al. (1996) as financial status of a firm (sound status, headed toward insolvency) or blood pressure status (high blood pressure, not high blood pressure).

The logistic transformation in Appendix B, Calculations, in the Advanced Regression User Manual provides the basis for the linear logistic model.  It is ideal in that it restricts predictions to the interval (0,1),  which is suitable for proportions and can be easily transformed into a linear form.  The function takes on a monotonically increasing or decreasing S shape that frequently occurs in Dose/Response and other survival rate studies.  It is an increasingly popular alternative to discriminant analysis because it relaxes some of the assumptions.

STATGRAPHICS Plus allows you to enter dichotomous response data in either of two forms.

1.	The dependent variable can consist of individual observations of either a 0 or a 1, representing the actual outcome for each individual case.

2.	The dependent variable can contain probabilities between 0 and 1 that are the proportions of successes for groups of observations, whose sizes can vary.

The independent or explanatory variables can be either categorical or continuous.  The program creates indicator variables for categorical factors that can simplify the use of the model when making predictions for future cases.  There are several statistics and graphs that help to assess the accuracy and usefulness of the model.

To Create a Logistic Regression Analysis

1.	Choose SPECIAL... ADVANCED REGRESSION... LOGISTIC REGRESSION… from the Menu bar to display the Logistic Regression Analysis dialog box.

2.	Complete the dialog box and click OK to display the Analysis Summary and Plot of Fitted Model in the Analysis window.


Adjusted R-Squared Statistic

A statistic suitable for comparing models that have different numbers of independent variables; indicates the percentage of variability for which the model accounts.


Alternative Hypothesis

A hypothesis, HA, against which an assumption or null hypothesis is tested.


ANOVA

Analysis of variance.


Autocorrelation Function Plot

A plot of the autocorrelation estimates for the residuals.


Backward Selection

Selects variables by performing a backward stepwise regression, which begins with all the variables in a model and removes them one at a time.


Biased Estimates

The over-estimation or under-estimation of an expected value of a sample statistic.


Bonferroni

A way of estimating the probability of making at least one Type I Error when conducting a series of t tests on the means of three or more groups.

In STATGRAPHICS Plus, an option, when the F-ratio is not significant, which allows you to make a small number of planned comparisons.


Calibration Line

The equation of a line that best fits through the calibration points.


Calibration Problem

The process of using a regression equation to predict in reverse; for example, predict X given Y.


Categorical Variables

Variables that contain the level codes.  When an independent variable is entered as a categorical variable, sets up indicator variables for each level except the first one.


Comparison of Regression Lines

Using hypothesis tests to compare two or more regression lines for significantly different slopes and/or intercepts.


Conditional Sums of Squares

Tests the statistical significance of the terms in a linear model.


Confidence Intervals

Shows the precision of the estimated coefficients given the amount of available data and noise in the model.


Confidence Limits for Forecast Means

The end points for the confidence interval for the means of each estimated value.


Confidence Limits for Individual Forecasts

The end points for the prediction interval for the individual estimated values.


Constants

(a) A measure or value that is the same for all units of analysis.  (b) A quantity that does not change value in a particular context.  (c) In a regression equation, another name for the intercept.


Contour Plot

A two-dimensional plot that traces the contours of the estimated dependent variable as a function of the other variables.


Cook's Distance

A statistic that measures the distance between the estimated coefficients with and without each observation.


Collinear

Having a common line.


Correlation Matrix

A table of correlation coefficients that shows all the pairs of correlations for a set of variables.


Cross Operator

An operator that multiplies two factors together to form a crossed effect.


Cube Plot

A plot of the estimated effects for the high and low settings of three factors.


Dependent Variable

The presumed response in a study; known as dependent because it “depends” on other variables; a variable whose values are characterized by the independent variable(s), whether or not a causal relationship.


DFITS

A statistic that measures the amount of change for each estimated coefficient if the observation is removed from the data.


Double Reciprocal Model

A model that fits the reciprocal of the dependent variable and the reciprocal of the independent variable; defined by the equation Y = 1/(a + b/X).


Dummy Variable

A dichotomous variable, usually coded 1 to indicate the presence of an attribute and 0 to indicate its absence.


Duncan Test

A test used after an ANOVA to determine which sample means differ significantly from one other, which allows you to protect the results from Type I errors for a small number of comparisons.


Dunnett

An option in the General Linear Models Analysis allowding you to use a control treatment as a benchmark for making comparisons.


Durbin-Watson Statistic

A test for autocorrelation or serial correlation in the residuals of a least squares regression analysis.  As the autocorrelation increases, the Durbin-Watson goes down.  The larger the autocorrelation, the less reliable the results of the regression analysis.


Error Term

The part of an equation that indicates what is unexplained by the independent variables.  In STATGRAPHICS Plus, a list box that allows you to select the name of the mean square that will be used as the denominator when the F-ratio is calculated for the selected factor(s).


Estimator

A sample statistic used to determine a probable value for a population parameter.


Exclude... Command

A command in STATGRAPHICS Plus that allows you to select terms that will be excluded from a model.


Exponential Model

A model that is equivalent to taking the natural log of Y defined by the equation Y = exp(a + bX).


Factors

In analysis of variance, an independent variable; that is, a variable presumed to affect the value of another variable.


Forecast

A prediction generated by calculating the value of a function given a new set of values.


Forward Selection

In STATGRAPHICS Plus, an option for selecting variables for a multiple regression, which begins with no variables in the model and adds them one at a time.


Gauss-Newton Method

A method of estimation for nonlinear regression that uses a Taylor series expansion to approximate a model with linear terms and then uses ordinary least squares to estimate the parameters.


General Linear Model (GLM)

A common set of statistical assumptions upon which are based a full range of methods used to study one or more continuous dependent variables and one or more independent variables, whether they are continuous or categorical.

The basic concept of GLM is that the relationship between the dependent variable and the independent variables is expressed as an equation that contains a term for the weighted sum of the values of the independent variables, plus a term for everything that is unknown (an error term). The least-squares criteria determine the weight for each independent variable.


Goodness-of-Fit

How well observed data match expected values under a specific assumption.


Hold... Command

A command that allows you to set the level of the quantitative factors when you are plotting a fitted model.


Independent Variable

A variable that can explain or predict the values of another variable.


Interaction

A multiplicative effect.


Intercept

The point at which a regression line crosses the vertical (Y) axis; that is, when the value on the horizontal (X) axis is zero.


Lag

In STATGRAPHICS Plus, a user-entered integer value used to estimate the autocorrelation values.


Least Squares Regression

A method that fits a regression by finding the coefficients that minimize the sum of the squared effects.


Leverage

A statistic that measures the amount each estimated coefficient would change if each observation was removed from the data.


Linear Regression Model

A model that fits a dependent variable Y to a linear function of an independent variable X.


Log Probit Model

A model that fits a response of observed proportions or probabilities at each level of an independent variable; defined by the equation Y = normal (a + b(LogX)).  The model is appropriate when the response variable tends to follow a cumulative normal distribution.


Logarithmic-X Model

A calibration model defined by the equation Y = a + b(LogX).


Logistic Model

A model that fits a response of observed proportions or probabilities at each level of an independent variable; defined by the equation Y = exp(a + bX )/(1 + exp(a + bX )).  The response function is a nonlinear S-shaped curve with asymptotes at 0 and 1.  The dependent variable must have values greater than 0 and less than 1.


Lower Bound Interval

An option in STATGRAPHICS Plus that calculates the one-sided, lower confidence limit for each coefficient.


LSD (Least Significant Differences)

A method for testing the statistically significant differences between means when the F-ratio is significant and comparisons are planned


MAE (Mean Absolute Error)

The average of the absolute values of the residuals; appropriate for linear and symmetric data.  If the result is a small value, you can predict performance more precisely; if the result is a large value, you may want to use a different model.


Mallows' Cp

A measure of the bias in a model based on a comparison of total Mean Squared Error to the true error variance.  Unbiased models have an expected Cp value of approximately p, where p is the number of coefficients in the fitted model. Cp is based on the assumption that the model that contains all the candidate variables is unbiased; therefore, the full model will always have Cp = p.  Look for models that have Cp values close to p.


MANOVA

Multivariate analysis of variance.


MAPE (Mean Absolute Percentage Error)

The mean or average of the sum of all the percentage errors for a given set of data without regard to sign (that is, their absolute values are summed and the average is computed).


Marquardt Algorithm

An algorithm that uses the best features of the Gauss-Newton method and the method of steepest descent, which results in a middle ground between the two methods.


Maximum Likelihood

A method used to calculate an estimation.  It first calculates the probability that the sample statistic (observed value) would occur if it were the true value of the parameter; then chooses the parameter that has the greatest probability of being the actual observation.


ME (Mean Error)

The average of the residuals.  The closer the ME is to 0, the less biased, or more accurate, the prediction.


Means Plot

A plot of the mean for a dependent variable for each level of an independent categorical variable, if there is one. The plot displays the confidence intervals for each of the means separately.


MPE (Mean Percentage Error)

The average of the absolute values of the residuals divided by the corresponding estimates.


MSE (Mean Square Error)

A measure of accuracy computed by squaring the individual error for each item in the set of data, then finding the average or mean value for the sum of those squares.


Multicollinearity

Exists in multiple regression analysis when two or more independent variables are highly correlated, which makes it difficult if not impossible to determine their separate effects on the dependent variable.


Multiplicative Model

This calibration model is equivalent to taking the natural logs of Y and X; defined by the equation Y = aX^b.


Multivariate t

A multiple range test that tests only a few comparisons (those of most importance).


Nest Operator

An operator that adds the left (first) and right (second) parentheses to an expression, which instructs the program to create a nested effect.


Newman-Keuls

An option in STATGRAPHICS Plus, that when the F-ratio is significant, allows you to test multiple hypotheses. The Type I error rate is smaller when you use this method than it is when you use the Duncan method.


Nonlinear Regression

Regression analysis that finds a least squares solution for a nonlinear model, which cannot be done using matrix algebra as it is in linear regression.  Often the form of a function that is known to be nonlinear in the parameters cannot be algebraically linearized or, if it can be, the error term is distorted while it should be normally distributed with constant variance.


Normal Probability Plot

A plot that displays the residuals to determine if the errors follow a normal distribution.  The plot consists of an arithmetic (interval) horizontal axis scaled for the data and a vertical axis scaled so the cumulative distribution function of a normal distribution plots as a straight line. The closer the data are to the reference line, the more likely they follow a normal distribution.


Observed versus Predicted Plot

A plot of the observed values of Y versus the values predicted by the predicted model.


p-Value

A component of the ANOVA table that serves as a measure of significance.  When the p-value is less than 0.01, there is a statistically significant relationship between two variables at the 99 percent confidence level.


Pairwise Means Comparison

A comparison of the difference between two treatment group means.


Plot of Fitted Model

A plot of the curve or fitted line that includes the confidence limits for the means and the prediction limits.


Prediction Capability Plot

A plot that summarizes the prediction capability of a fitted logistic model:  The percentages of correct values versus the cutoff values for a dependent variable that was Total, True, or False.


Prediction Histogram

A plot that demonstrates the ability of a fitted logistic model to distinguish between cases when a dependent variable is True or False.  The plot shows the frequency distribution of the True and False cases in the data versus the probability predicted by the fitted model.


Quantitative Variables

Numeric variables that contain continuous data.


Quartiles

Divisions of the total cases or observations in a study  into four groups of equal size.


Reciprocal-X Model

A calibration model that is defined by the equation Y = a + b/X.


Reciprocal-Y Model

A calibration model that is defined by the equation Y = 1/(a + bX ).


Regression Analysis

A mathematical tool that can quantify the relationship between a dependent variable and one or more independent variables.


Regression Coefficient

A parameter or its estimate, for a regression model; often denoted by the Greek letter beta.


Residuals

The difference between the observed value and the fitted values.


Residuals versus Level Codes Plot

A plot that displays the residuals or the studentized residuals versus the level codes.


Residuals versus Predicted Plot

A plot of the residuals versus the predicted values.  The plot is helpful in showing heteroscedasticity; an indication of the variability of the changes in the residuals as the values of the dependent variable change.


Residuals versus Row Number Plot

A plot that displays the residuals or the studentized residuals versus the row number.  The plot is helpful in determining sequential correlations among the residuals.


Residuals versus X Plot

A plot of the residuals versus the independent variable (X), where X equals the name of each independent variable you select.


Ridge Parameter

A parameter that controls the extent of the bias that is introduced in ridge regression.  A good value for the ridge parameter is the smallest value that occurs before the estimates slowly change.


Ridge Regression

One of several methods proposed to remedy multicollinearity problems by modifying the method of least squares to allow biased estimators of the regression coefficients.


Ridge Trace Plot

A plot of the values for the standardized or unstandardized coefficients versus the values for the ridge parameter.  As the ridge parameter increases from 0.0, the coefficients at first change dramatically, then become relatively stable.


R-Squared Statistic

A statistic that measures the proportion of variability in a model for the dependent variable.


S-Curve Model

A model that takes the natural log of Y and the reciprocal of X; defined by the equation Y = exp(a + b/X).


Scatterplot

A plot of the values as point symbols along a single horizontal axis.


Scheffe

A test of statistical significance used for post-hoc multiple comparisons after a regression analysis or an analysis of variance.  In STATGRAPHICS Plus, an option, when the F-ratio is significant, that allows you to make unplanned comparisons between pairs of means.  Scheffe is the most controversial method because the Type I error is the smallest.


Second Factor Plot

A plot of the dependent variable on the X-axis using the second factor in the interaction.  A line is drawn for each level of the first factor.


Slope

The rate at which a line or curve rises or falls when covering a given horizontal distance.  The most common reference is to the steepness or angle of a regression line.


Square Plot

A plot of the predicted values of the dependent variable versus the high and low values of a factor.


Square Root-X Model

A calibration model defined by the equation Y = a + b sqrt(X).  The reciprocal-X, logarithmic-X, and square root-X transformations linearize a nonlinear relationship between the dependent and independent variables.  The transformations are suitable when the error terms are normal and have constant variance.


Square Root-Y Model

A calibration model defined by the equation Y = (a + bX)^2.  The exponential, reciprocal-Y, and square root-Y transformations can help remedy error terms that are not normal and that do not have constant variance.


Standard Error of the Estimate Statistic

This statistic explains the value for the standard deviation of the residuals.  You can use this value to construct prediction limits for new observations.


Standard Errors for Forecasts Statistic

This statistic includes the standard deviation for the distribution of the estimated values in a report.


Standard Regression Coefficient

A statistic that provides a way to compare the relative importance of different variables in a multiple regression analysis.


Steepest Descent

A method of nonlinear regression analysis that  searches for the minimum least squares criterion measure by iteratively determining the direction in which the regression coefficients should be changed.  This method is particularly effective when the initial values are not "good"; that is, they are far from the final values.


Stopping Criterion

A number used to stop the estimation process; that is, the estimation stops when this value is less than the estimated values (as a proportion) for all the unknown parameters.


Studentized Residuals

The residuals scaled by an estimate of the variance from the data with the observation removed.


Surface Plot

A three-dimensional plot of the relationship between the estimated dependent variable and two selected variables.


Tukey HSD (Honestly Significant Differences)

A test that determines the means that are significantly different after an analysis of variance of the differences in group means is performed.

In STATGRAPHICS Plus, an option that allows you to make many comparisons.  The test is based on the studentized range distribution.  The Type I error is smaller than the LSD, Newman-Keuls, and Duncan methods.


Two-Sided Interval

An option that calculates the upper and lower confidence limits for each coefficient.


Type I Sums of Squares

An option that computes the sums of squares for each factor in the order you enter the factors into the Effects list box on the GLM Model Specification dialog box.  The program measures the effect of each factor as you enter it.


Type III Sums of Squares

An option in STATGRAPHICS Plus that computes additional sums of squares for each factor as though that factor was the last one added to the model.


Unbalanced Design

Factorial designs that contain unequal numbers of observations for different factor levels or combinations, or cells that contain unequal numbers of subjects.


Upper Bound Interval

In STATGRAPHICS Plus, an option that calculates the one-sided, upper confidence limit for each coefficient.


User-Specified Comparison

In STATGRAPHICS Plus, an option you use to select contrasts for multiple range tests in the General Linear Models Analysis.


Variance Inflation Factors (VIFs)

Factors that measure the extent to which explanatory variables are correlated among themselves. VIF values above 10 usually indicate serious multicollinearity, which greatly increases the estimation error of the model coefficients when compared with an orthogonal sample.


Weights

The values applied to residuals when the program estimates the model coefficients in a weighted least squares regression.


General Linear Models Analysis Dialog Box

The General Linear Models analysis estimates linear statistical models that relate one or more dependent variables to one or more independent variables.  You can use it for regression, analysis of variance, multifactor ANOVA, or for an analysis of covariance.

The independent variables can be continuous or categorical; categorical variables can be crossed or nested and declared to correspond to either fixed or random effects.

For more information about this analysis, see these sections in the User Manual:  “Background Information,” “General Linear Models in STATGRAPHICS,” “Specifying Effects,” and “Treating Missing Values.”

Dependent Variables

Categorical Factors

Quantitative Factors

Weights

Select

Sort

Delete...

Transform...

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on the text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the General Linear Models Analysis

General Linear Models Options

Residual Plots


Dependent Variables

Enter the names of from one to 10 dependent variables.  You must enter numeric variables.


Categorical Factors

Enter the names of either numeric or character variables that contain the categorical factors. Use at least one categorical factor in the model to create multiple range tests.

The total number of categorical and quantitative factors cannot exceed 26.  You must enter at least one variable in either this or the Quantitative Factors text box.


Quantitative Factors

Enter the names of the numeric variables that contain the quantitative factors or covariates.  The total number of categorical and quantitative factors cannot exceed 26.


Weights

Enter the name of a variable that contains the values for the weights that will be applied to the squared residuals when the model statistics are estimated.

Enter a numeric variable, which will result in a weighted least squares estimation.


Select

Select a subset of observations.  For example, to analyze the first 50 values in each variable, enter first (50) in this text box.  Or you can select the observations that will be used to estimate the model.  The remaining complete observations (those you do not select) are used to validate the model.

The validation and estimation results appear in the Residual Analysis table at the end of the Analysis Summary.


Sort

Indicate if the variables should be sorted alphabetically.  The default is sorted.


GLM Model Specification Dialog Box

General linear models are made up of terms you define using special annotations that represent the names of variables and operators.  In the General Linear Models analysis, STATGRAPHICS Plus uses two types of independent variables: categorical and quantitative, and two operators, * (Cross) and (  ) (Nest).

How you use the operators depends on whether the factors are categorical or quantitative.  For example, if the model contains three categorical factors —   C1, C2, and C3 —    and three quantitative factors —   Q1, Q2, and Q3 —   the factors are named A, B, C, D, E, and F according to the order you enter them into the General Linear Models Analysis dialog box.  The Factors list box on the GLM Model Specification dialog box displays the names of the factors and their assigned letters; the Effects list box, by default, contains the letters for all the main effects.

You can delete a main effect and you can add additional terms to a model by typing them into the Effects list box.  You also can create many different types of models by using a variety of effects.  For example, for these four rows of effects:  A, B, A*B, and C(A), the model looks like this:

A + B + A*B + C(A)

By default, a constant term is added to the model.  To remove the constant, use the GLM Model Specification dialog box.  You can specify up to 26 factors and 256 effects.

The seven types of effects you can use with the factors are:

1.	regressor effects that involve a single quantitative factor, such as D or E

2.	polynomial effects that are products of two or more quantitative factors, such as D*E or E*E

3.	main effects that involve a single categorical factor, such as A

4.	crossed effects that involve two or more categorical factors, such as A*C or A*B*C

5.	a quantitative variable that is crossed with a categorical variable, such as A*D

6.	nested categorical effects, such as C(B) or C(B A)

7.	quantitative variables crossed witrh nested categorical variables, such as F*B(A)

Categorical variables may also be declared to have random rather than fixed effects by checking the Random Factors box.

Factors

* Cross Operator

( Nest Operator

) Nest Operator

Effects

Enter Command

Delete Command


Factors

Displays the names of the factors and their assigned letters.


* Cross Operator

Multiplies two factors together to form a crossed effect.  For example, if you enter A*B, the AB interaction term is added to the design.


( Nest Operator

Adds the left (first) parenthesis to an expression to create a nested effect.  For example, B(A) indicates that factor B is nested within factor A.  C(A B) indicates that C is nested within combinations of A and B.


) Nest Operator

Adds the right (last) parenthesis to an expression to indicate nested effects.  For an example, see the ( Nest Operator.


Effects

Adds one or more effects to create the model.  You can either type the model terms directly into the expression, or you can highlight a factor by clicking it, click the arrow button to the left of the Effects list box to enter the factor, then, if applicable, use the operators * (Cross) and ( ) (Nest), or the Enter or Delete commands to complete the expression.


Enter... Command

Enter another term on the next line.

Note:  The mouse pointer does not appear on the line.


Delete... Command

Deletes highlighted text.


General Linear Models Tabular Options Dialog Box

Allows you to select tabular options for the General Linear Models analysis.

Analysis Summary (General Linear Models)

Model Coefficients (General Linear Models)

Table of Means (General Linear Models)

Multiple Range Tests (General Linear Models)

Reports (General Linear Models)

Unusual Residuals (General Linear Models)

Influential Points (General Linear Models)


Analysis Summary (General Linear Models)

The Analysis Summary tabular option displays the results of fitting the general linear statistical model.  If the p-value in the first ANOVA table is less than 0.05, there is a statistically significant relationship between the variables at the 5% signficiance level.

The second ANOVA table tests the statistical significance for each of the factors.  If any p-value in this ANOVA table is greater than or equal to 0.05, that term is not statistically significant at the 95 percent or higher confidence level and you should consider removing it from the model.

The Expected Mean Squares Table shows the expected value of the sums of squares.  Each source of variation is numbered from the top as (1), (2), and so on.  A term such as Q1 represents a quadratic form related to the factor on the line where it appears.  These expected mean squares are used to determine the proper F-tests for each factor.

The F-Test Denominators show the error term used to test the significance of each factor in the model.  The terms (1), (2), and so on correspond to the estimated mean squares for each of the factors in the Expected Mean Squares table.

The Varaince Components table lists the estimated variance components for all random effects in the model.

Other statistics include:

1.	The R-Squared Statistic.  This statistic indicates the percentage of variability in the dependent variable for which the model accounts.

2.	The Adjusted R-Squared Statistic.  This statistic is more suitable for comparing models that have different numbers of independent variables and indicates the percentage of variability represented by the model.

3.	The Standard Error of the Estimate Statistic.  This statistic estimates the standard deviation of the residuals.  You can use this value to construct prediction limits by selecting the Reports tabular option.

4.	The Mean Absolute Error (MAE) Statistic.  This statistic is the average absolute value of the residuals.

5.	The Durbin-Watson Statistic.  This statistic tests the residuals to determine if there is significant serial correlation based on the order in which the values fall in the file

If you used the optional Select text box on the General Linear Models Analysis dialog box, the cases not selected will be used to validate the model.

If you decide to validate the model, see the Advanced Regression User Manual and use one of the methods discussed in the section, “Understanding Advanced Regression” in Chapter 1, Getting Started.

The Residuals Table includes values for the following statistics for the validation and estimation data:

1.	n —   the number of observations.

2.	MSE (Mean Square Error) — a measure of precision computed by squaring the residual for each item in the set of data, then finding the average or mean value for those squares.  If the result is a small value, you can predict performance more precisely; if the result is a large value, you may want to use a different model.

3.	MAE (Mean Absolute Error) — the average of the absolute values of the residuals.  If the result is a small value, you can predict performance more precisely; if the result is a large value, you may want to use a different model.

4.	MAPE (Mean Absolute Percentage Error) — the mean or average of the sum of all the percentage errors for a given set of data without regard to sign (that is, their absolute values are summed and the average is computed).  Unlike the ME, MSE, and MAE, the size of the MAPE is independent of scale.

5.	ME (Mean Error) — the average of the residuals.  The closer the ME is to 0, the less biased, or more accurate, the prediction

6.	MPE (Mean Percentage Error) — the average of the residuals divided by the corresponding value of the dependent variable.  Like MAPE, it is independent of scale

Each of these statistics is based on the residuals.  The first three statistics measure the magnitude of the errors; better models have smaller values.  The last two statistics measure the bias; better models have a value close to 0.0.


General Linear Models Options Dialog Box

Allows you to:

•	indicate the type of sums of squares the program will use. Type I sums of squares measure the sequential reduction in the error sum of squares as each term is entered into the model.  Type III sums of squares, the default, estimates the contribution of each term given that all other terms have been accounted for.

•	select the primary dependent variable which will be displayed in the analysis panes.

•	indicate if a constant  should be included in the model.

•	if more than one dependent variable has been specified, you may request a multivariate analysis of variance (MANOVA).

•	specify the type of Box-Cox transformation desired, if any. The transformation is specified by a power to which the values of the dependent variable will be raised, and by an addend which is first added to each value.  You may also request that the program find the optimal values of the power and addend (this requires a search and may be quite time-consuming).  A power of 1.0 and an addend of 0.0, the default, implies no transformation of the data.

•	select the error terms used in the F-tests for each of the factors in the model. Unless you wish to perform some special analysis, the Error terms should be set to Automatic, which instructs the program to determine the proper error terms.

•

Sums of Squares

Factor

Display

Constant in Model

Include MANOVA

Error Term

Selections

Box-Cox Transformation Power

Box-Cox Transformation Shift

Optimize


Sums of Squares

Select the method that will be used to calculate the sums of squares for each factor: Type I or Type III.

Type I

Computes the sums of squares for each factor in the order you enter the factors into the Effects list box.

Type III

Computes additional sums of squares for each factor as though that factor was the last one you added to the model.  Generally, you should use Type III; however, you can use either Type I or Type III sums of squares for unbalanced designs.  Type III sums of squares is the default.


Factor

Highlight the factor for which you want to select an error term.  Click the name of the factor to select it.


Display

Displays the name(s) of the dependent variable(s) you selected on the General Linear Models Analysis dialog box.  Click the name of the dependent variable for which you want to display plots.


Constant in Model

Indicates that a constant should be included in the model.  The default is for a constants included.

For more information about constants, see the entry for the Multiple Range Test Options Dialog Box.


Include MANOVA

Indicates that you want to include MANOVA values in the analysis.  The MANOVA statistics appear at the end of the Analysis Summary; the program simultaneously analyzes all the dependent variables.


Error Term

Select the name of the mean square that will be used as the denominator when the F-ratio is calculated for the selected factor.

Automatic

The program will determine the proper error mean squares based on the model specified.

None

An F-Ratio for the selected term will not be calculated.

Residual

Uses the residual mean square as the denominator for the selected term.

Term

Uses the mean square of the selected term as the denominator.


Selections

Displays the selected error term(s).


Type I

Computes the sums of squares for each factor in the order you enter the factors into the Effects list box on the GLM Model Specification dialog box.


Type III

Computes additional sums of squares for each factor as though that factor was the last one you added to the model.  Generally, you should use Type III; however, you can use either Type I or Type III sums of squares for balanced designs.

The default is computed Type III sums of squares.


None

Instructs the program not to calculate an F-ratio for the selected term.


Residual

Uses the residual mean square as the denominator for the selected term.


Term

Uses the mean square of the selected term as the denominator.


Model Coefficients (General Linear Models)

The Model Coefficients tabular option displays the coefficients in the model, including the confidence intervals.  The confidence intervals show the preciseness of the estimated coefficients given the amount of available data and noise in the model.

The table also includes the Variance Inflation Factors (VIFs), which you can use to measure the extent to which the explanatory variables are correlated among themselves.  VIF values above 10 usually indicate serious multicollinearity, which greatly increases the estimation error of the model coefficients when you compare them with an orthogonal sample.


Model Coefficients Options Dialog Box

Select the type of interval that will be used, enter a value for the confidence level, and indicate if you want the report to show the correlations.

Type of Interval

Confidence Level (for Model Coefficients)

Show Correlations


Type of Interval

Select the type of interval that will be used.

Two-Sided

Calculates upper and lower confidence limits for each coefficient.  This option is the default.

Lower Bound

Calculates a lower confidence bound for each coefficient.

Upper Bound

Calculates an upper confidence bound for each coefficient.


Show Correlations

Indicate if the report should include the correlation matrix for the estimated coefficients.


Two-Sided

Calculates the upper and lower confidence limits for each coefficient.  This option is the default.


Lower Bound

Calculates a lower confidence bound for each coefficient.


Upper Bound

Calculates an upper confidence bound for each coefficient.


Table of Means (General Linear Models)

The Table of Means tabular option displays the least squares means for each level of the categorical factors as well as the standard error for each mean, which is a measure of its sampling variability.  The Lower Limit and Upper Limit columns display confidence intervals.

The table also displays the means of any quantitative factors in the model.


Confidence Intervals Options Dialog Box

Enter a value that will be used to calculate the confidence intervals.  The default is 95 percent; other common levels are 90 and 99 percent.


Multiple Range Tests (General Linear Models)

The Multiple Range Tests tabular option displays the means that are significantly different from others in the analysis.  A multiple comparison procedure that you select is used to calculate the limits.

The upper portion of the table identifies the homogenous groups as columns of Xs.  The levels within each column that contains an X, form a group of means within which there are no statistically significant differences.  The lower portion of the table shows the estimated difference between each pair of means.

Pairs for which the differences are statistically significant are marked with an asterisk.  The method is used to discriminate among the means is selected using Pane Options.


Multiple Comparisons Options Dialog Box

Select the options that will be used to perform the multiple range tests when the model includes at least one categorical factor.

Type (of Limits)

Factor

Method

Control Level

Confidence Level (for Model Coefficients)


Type (of Limits)

Select the type of limits that will be used to perform the comparison.

All Pairwise Means

Performs the comparison for all the pairwise means.  This option is the default.

Versus Control

Selects one level mean against which the other means will be compared.

User-Specified

Selects contrasts for the groups.  When you want to define your own contrasts, select this option, and click OK; the Hypothesis Matrix dialog box displays.  Use the matrix to enter the contrasts that will be used to compare the means among the groups (defined by the categorical variable you select).  Enter the contrasts one per row.  The sum of each row should equal zero.  When you click OK, the program recalculates the comparisons and displays an updated table.

The reason for using the Hypothesis Matrix is that you may not want to print all of the possible contrasts, especially if the categorical variable has more than three levels.  Or, you might want to calculate contrasts that involve more than two levels at one time; for example, you could enter 2, -1, -1 in one row of the matrix to compare the mean of level 1 against the average of the means of levels 2 and 3..


All Pairwise Means

Performs the comparison for all the pairwise means.  This option is the default.


Versus Control

Select one level mean against which the other means will be compared.


User-Specified

Select contrasts for the groups.  When you want to define your own contrasts, select this option, and click OK to display the Hypothesis Matrix.


Hypothesis Matrix Dialog Box

Use the Hypothesis Matrix dialog box to enter the contrasts that will be used to compare the means among the groups (defined by the categorical variable you select).  Enter the contrasts one per row.  The sum of each row should equal zero.  When you click OK, the program recalculates the comparisons and displays an updated table.

For example, in the Cardata file, the variable origin has three levels:  1, 2, and 3 (USA, Europe, and Japan, respectively).  If the independent variable is origin, and you enter it into the Categorical Factors text box on the General Linear Models Analysis dialog box, the Analysis Summary for the Multiple Range Tests option shows all the pairwise differences among the three regions.

The reason for using the Hypothesis Matrix is that you may not want to print all of the possible contrasts, especially if the categorical variable has more than three levels.  Or, you might want to calculate the contrasts that involve more than two levels at one time; for example, you could enter 2, -1, -1 in one row of the matrix to compare the mean of the U.S. cars against the average mean of the European and Japanese cars.


Factor

Select the factor that will be used for the comparisons.


Method

Select the method that will be used to discriminate among the means.

LSD (Least Significant Differences)

Compares any two means at the specified level of confidence.

Tukey HSD (Honestly Significant Differences)

Performs all pairwise comparions amongst means, controlling the experiment-wide error rate.  The test is based on the studentized range distribution.  The Type I error is smaller than the LSD, Newman-Keuls, and Duncan methods.

Scheffe

When the F-ratio is significant, allows you to make unplanned comparisons between pairs of means.  Scheffe is the most conservative method because the Type I error is the smallest.

Bonferroni

When the F-ratio is not significant, allows you to make a small number of planned comparisons.

Multivariate t

Allows you to test only a few comparisons (those of most importance).  You also might use it when the contrasts form a linearly independent set.  This option is available only for 90, 95, and 99 percent confidence levels.

Newman-Keuls

When the F-ratio is significant, allows you to test multiple hypotheses.  The Type I error rate is smaller when you use this method than it is when you use the Duncan method.

Duncan

Protects the results from Type I errors for a small number of comparisons.

Dunnett

Uses a control treatment as a benchmark for making comparisons.  This option is available only for 90, 95, and 99 percent confidence levels.


LSD (Least Significant Differences)

When the F-ratio is significant, allows you to make planned comparisons.


Tukey HSD (Honestly Significant Differences)

Allows you to make many comparisons.  The test is based on the studentized range distribution.  The Type I error is smaller than the LSD, Newman-Keuls, and Duncan methods.


Scheffe

When the F-ratio is significant, allows you to make unplanned comparisons between pairs of means.  Scheffe is the most controversial method because the Type I error is the smallest.


Bonferroni

When the F-ratio is not significant, allows you to make a small number of planned comparisons.


Multivariate t

Allows you to test only a few comparisons (those of most importance).  You also might use it when the contrasts form a linearly independent set.  This option is available only for 90, 95, and 99 percent confidence levels.


Newman-Keuls

When the F-ratio is significant, allows you to test multiple hypotheses.  The Type I error rate is smaller when you use this method than it is when you use the Duncan method.


Duncan

Protects the results from Type I errors for a small number of comparisons.


Dunnett

Uses a control treatment as a benchmark for making comparisons.  This option is available only for 90, 95, and 99 percent confidence levels.


Control Level

Enter the group level that will be used as a control in conjunction with the Versus Control type of comparison.


Reports (General Linear Models)

The Reports tabular option displays information about the results generated for the regression using the fitted model.  Depending upon your selections on the Reports Options dialog box, the table includes the predicted value for the dependent variable, the predicted value for the standard error, the 95 percent prediction limits for new observations, and the 95 percent confidence limits for the mean response.

Each item corresponds to the values of the independent variables in a specific row of the file.  To create forecasts (predictions) for additional combinations of the variables, add additional rows to the bottom of the file.  In each new row, enter values for the independent variables but leave the cell for the dependent variable empty.  The predicted values for the new rows are added to the table, but the model is left unchanged.  Use Analysis Options to select the dependent variable that will be used to create the report.


Reports Options Dialog Box

Select the values that will be included in the report.

Include


Include

Select the type of values that will display in the report.

Observed Y

Includes the observed values for Y in the report.

Fitted Y

Includes the fitted values for Y in the report.  If the data include missing values of Y, predictions are made for those values.  This option is one of the defaults.

Residuals

Includes the values for the residuals in the report.


Observed Y

Includes the observed values for Y in the report.


Fitted Y

Includes the fitted values for Y in the report.  If the data include missing values of Y, predictions are made for those values.  This option is one of the defaults.


Standard Errors for Forecasts

Includes the standard deviation for the distribution of the estimated values.  This option is one of the defaults.


Confidence Limits for Individual Forecasts

Includes the end points for the prediction interval for the individual estimated values.  This option is one of the defaults.


Confidence Limits for Forecast Means

Includes the end points for the confidence interval of the means for each estimated value.  This option is one of the defaults.


Unusual Residuals (General Linear Models)

The Unusual Residuals tabular option displays a table that lists all the observations that have studentized residuals with values greater than 2.0 in absolute value.

Studentized residuals measure the number of standard deviations that each observed value of the dependent variable deviates from the model that was fitted using all the data except that observation.


Influential Points (General Linear Models)

The Influential Points tabular option displays a table that lists the observations that have leverage values greater than three times that of an average point, or that have unusually large DFITS or Cook's distance values.

Leverage is a statistic that measures the amount each estimated coefficient would change if each observation were removed from the data.  The Cook's distance statistic measures the distance between the estimated coefficients with and without each observation.


General Linear Models Graphical Options Dialog Box

This dialog box allows you to select graphical options for the analysis.

Scatterplot (General Linear Models)

Means Plot (General Linear Models)

Interaction Plot (General Linear Models)

Surface Plot (General Linear Models)

Contour Plot (General Linear Models)

Observed versus Predicted Plot (General Linear Models)

Residual Plots


Scatterplot (General Linear Models)

The Scatterplot graphical option displays a scatterplot of one dependent variable versus one independent variable.  Select the dependent variable using the General Linear Model Options dialog box and the independent variable from the Scatterplot Options dialog box.


Scatterplot Options Dialog Box

Allows you to select the independent variable that will be used to create the plot.


Means Plot (General Linear Models)

The Means Plot graphical option displays a plot of the mean for a dependent variable for each level of an independent categorical variable, if there is one.  The plot displays the confidence intervals for each of the means separately.  Or, if you select a quantitative variable, the program displays a Plot of Fitted Model for the regression versus the quantitative variable you select.

Any other quantitative variables are held at the value you enter using the Hold... command.


 Means Plot Options Dialog Box

Allows you to select the type of interval and the factor that will be displayed on the plot.  You can also select a value for the confidence level.

Type (of Interval)

Factor

Confidence Level

Hold... Command


Interaction Plot (General Linear Models)

The Interaction Plot graphical option shows the two-factor interactions, if any, that were estimated in the analysis using the current model.


Interaction Plot Options Dialog Box

Select the type of interval that will be displayed, select an interaction for the plot, enter a value for the confidence level, and select the factor that will plot on the axis.

Interval

Interaction

Confidence Level

Plot on Axis


Surface Plot (General Linear Models)

The Surface Plot graphical option allows you to select one of four types of plots:  Surface, Contour, Square, or Cube.  To use this option, you must enter at least two quantitative independent variables in the model.


Response Plot Options Dialog Box

Allows you to:

•	select the type of plot

•	select settings for Contour and Surface plots

•	access the Plot of Fitted Model Options dialog box, which allows you to select another factor.

Type (of Response Plot - Nonlinear Regression)

Contours

Resolution

Surface

Factors... Command


Contour Plot (General Linear Models)

The Contour Plot graphical option displays a Contour Plot, which is a two-dimensional plot that traces the contours of the estimated dependent variable as a function of the other variables.

Each contour line represents combinations of the independent variables, which have a selected value for the estimated dependent variable.  You can predict the next value for the dependent variable by following the ridge of the contour.

When you select this option, the Contours and Resolution options portions of the dialog box become active, which allows you to customize the plot.

You can also access the Plot of Fitted Model Options dialog box by clicking the Factors... command button.

The Factors command allows you to select two quantitative variables to plot against, to change the limits for those variables, and to select a level at which to hold any other quantitative variables.


Observed versus Predicted Plot (General Linear Models)

The Observed versus Predicted Plot graphical option displays a plot of the observed values versus the values predicted by the fitted model.  The plot includes a line with slope equal to one.  Points close to the diagonal line are those best predicted by the model.

Use the plot to detect situations in which the error variance is not constant, which indicates that you should probably transform the values for the dependent variable.


Residual Plots Options Dialog Box

Allows you to select a residual plot and its options.

Plot (Residuals or Studentized Residuals)

Type (of Plot - General Linear Models)

Plot versus:

Direction (for Residuals)

Fitted Line

Number of Lags

Confidence Level (for Probability Limits)


Save Results Options Dialog Box (General Linear Models)

The Save Results Options dialog box allows you to select the results you want to save.  There are 13 selections:  Predicted Values, Standard Errors of Predictions, Lower Limits for Predictions, Upper Limits for Predictions, Standard Errors of Means, Lower Limits for Forecast Means, Upper Limits for Forecast Means, Residuals, Studentized Residuals, Leverages, DFITS Statistics, Mahalanobis Distances, and Coefficients.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Type (of Interval)

Select the type of interval that will be displayed on the Means Plot when you select a categorical factor.

Confidence Interval

Displays the confidence intervals on the plot.

LSD (Least Significant Differences) Interval

Displays the least significant differences intervals on the plot.  Use this option when the F-ratio is significant, and you want to make planned comparisons.  This option is the default.

Tukey HSD (Honestly Significant Difference) Interval

Displays the Tukey HSD intervals on the plot.  Use this option when you plan to make many comparisons.  This test is based on the studentized range distribution.  The Type I error is smaller than the LSD error.

Scheffe Interval

Displays the Scheffe intervals on the plot.  Use this option when the F-ratio is significant, and you want to make unplanned comparisons between the pairs of means.  This method is the most conservative because the Type I error rate is the smallest.

Bonferroni Interval

Displays the Bonferroni intervals on the plot.  Use this option when the F-ratio is not significant, but you still want to make a small number of planned comparisons.


Confidence Interval

Displays the confidence intervals on the plot.


LSD (Least Significant Differences) Interval

Displays the least significant differences intervals on the plot.  Use this option when the F-ratio is significant, and you want to make planned comparisons.

This option is the default.


Tukey HSD (Honestly Significant Difference) Interval
Tukey HSD (Honestly Significant Differences) Interval

Displays the Tukey HSD intervals on the plot.  Use this option when you plan to make many comparisons.  This test is based on the studentized range distribution.  The Type I error is smaller than the LSD error.


Scheffe Interval

Displays the Scheffe intervals on the plot.  Use this option when the F-ratio is significant, and you want to make unplanned comparisons between the pairs of means.

This method is the most conservative because the Type I error rate is the smallest.


Bonferroni Interval

Displays the Bonferroni intervals on the plot.  Use this option when the F-ratio is not significant, but you still want to make a small number of planned comparisons.


Factor

Choose the factor that will be used in the analysis.  Click the factor to select it.

If you select a categorical factor, a Means Plot will display.  Quantitative factors produce a Plot of Fitted Model.


Hold... Command

Allows you to set the level of the quantitative factors when you are plotting the fitted model; that is, the categorical factors for the plot are held at zero.


Interval

Select the type of interval the plot will display.

None

Displays no intervals on the plot.  This option is the default.

Confidence Interval

Displays the confidence intervals for the means at each level of a two-factor interaction.

LSD (Least Significant Differences) Interval

Displays the least significant differences intervals for two-factor interactions.  Use this option when the F-ratio is significant and you want to make planned comparisons.

Tukey HSD (Honestly Significant Differences) Interval

Displays the Tukey HSD intervals for the two-factor interactions.  Use this option when you plan to make many comparisons.  This test is based on the studentized range distribution.  The Type I error is smaller than LSD.

Scheffe Interval

Displays the Scheffe intervals for the two-factor interactions.  Use this method when the F-ratio is significant and you want t make unplanned comparisons between the pairs of means.  Scheffe is the most conservative method because the Type I error rate is the smallest.

Bonferroni Interval

Displays the Bonferroni intervals for the two-factor interactions.  Use this option when the F-ratio is not significant, but you still want to make a small number of comparisons.


None

No intervals are displayed on the plot.  This option is the default.


Confidence Interval (for Interaction Plot)

Displays the confidence intervals for the means at each level of the two-factor interaction.


LSD (Least Significant Differences) Interval

Displays the least significant difference intervals for the two-factor interactions.  Use this option when the F-ratio is significant and you want to make planned comparisons.


Tukey HSD (Honestly Significant Differences) Interval

Displays the Tukey HSD intervals for the two-factor interactions.  Use this option when you plan to make many comparisons.  This test is based on the studentized range distribution.  The Type I error is smaller than LSD.


Scheffe Interval

Displays the Scheffe intervals for the two-factor interactions.  Use this option when the F-ratio is significant and you want to make unplanned comparisons between the pairs of means.  Scheffe is the most conservative method because the Type I error rate is the smallest.


Bonferroni Interval

Displays the Bonferroni intervals for the two-factor interactions.  Use this option when the F-ratio is not significant, but you still want to make a small number of comparisons.


Interaction

Select the interaction that will display on the plot.  Click the interaction to select it.


Plot on Axis

Select the factor in the interaction that will be used for the X-axis. The levels of the other factor are plotted as separate lines on the graph.

First Factor

Plots the selected dependent variable with the first factor in the interaction.  A line is drawn for each level of the second factor.  This option is the default.

Second Factor

Plots the dependent variable on the X-axis with the second factor in the interaction.  A line is drawn for each level of the first factor.


Type (of Response Plot - Nonlinear Regression)

Select the type of plot you want to create and display:  Surface, Contour, Square, or Cube.

Surface

Displays a Surface Plot, which is a three-dimensional plot of the relationship between the estimated dependent variable and the other two selected variables.  The height of the surface represents the value of the estimated dependent variable.

When you select this option, the Resolution and Surface options portions of the Response Plot Options dialog box become active, which allows you to customize the plot.  You can also access the Plot of Fitted Model Options dialog box by clicking the Factors… command button.

The Factors command allows you to select two quantitative variables to plot against, to change the limits for those variables, and to select a level at which to hold any other quantitative variables.

You can view three-dimensional graphs from different horizontal and vertical angles by spinning the graph to alter the location of the viewpoint.  The Smooth/Rotate button on the Analysis toolbar allows you to spin (rotate) three-dimensional graphs.

See the section “To Use the Smooth/Rotate Button” in the Using Graphics portion of the Online Help.

Contour

Displays a Contour Plot, which is a two-dimensional plot that traces the contours of the estimated dependent variable as a function of the other variables.  Each contour line represents combinations of the independent variables, which have a selected value for the estimated dependent variable.  You can predict the next value for the dependent variable by following the ridge of he contour.

When you select this option, the Contours and Resolution options portions of the dialog box becomes active, which allows you to customize the plot.  You can also access the Plot of Fitted Model Options dialog box by clicking the Factors… command button.

The Factors… command allows you to select two quantitative variables to plot against, to change the limits for those variables, and to select a level at which to old any other quantitative variables.

Square

Displays a Square Plot for the observed values of the dependent variable versus the values predicted by the fitted model.  The dependent variable is plotted with all combinations of the high and low values for each independent variable you select.  Points close to the diagonal line are those that best predict the observed data.

You can also access the Plot of Fitted Model Options dialog box by clicking the Factors… command button.  The Factors command allows you to select quantitative variables to plot, to change the limits for those variables, and to select levels at which to hold any other quantitative variables.

Cube

Displays a Cube Plot of the estimated effects for three factors.  The response variables are plotted with all combinations of the high and low values for each factor you select.  Use the Factors… command to select the factors and to specify the high and low values.


Surface

Displays a Surface Plot, which is a three-dimensional plot of the relationship between the estimated dependent variable and the other two selected variables.  The height of the surface represents the value of the estimated dependent variable.

When you select this option, the Resolution and Surface options portions of the dialog box become active, which allows you to customize the plot.  You can also access the Plot of Fitted Model Options dialog box by clicking the Factors... command button.

The Factors command allows you to select two quantitative variables to plot against, to change the limits for those variables, and to select a level at which to hold any other quantitative variables.

To view the plot from a different angle, click the Rotate button on the Analysis toolbar.


Contour

Displays a Contour Plot, which is a two-dimensional plot that traces the contours of the estimated dependent variable as a function of the other variables.  Each contour line represents combinations of the independent variables, which have a selected value for the estimated dependent variable.  You can predict the next value for the dependent variable by following the ridge of the contour.

When you select this option, the Contours and Resolution options portions of the dialog box become active, which allows you to customize the plot.  You can also access the Plot of Fitted Model Options dialog box by clicking the Factors... command button.

The Factors command allows you to select two quantitative variables to plot against, to change the limits for those variables, and to select a level at which to hold any other quantitative variables.


Square

Displays a Square Plot for the observed values of the dependent variable versus the values predicted by the fitted model.  The dependent variables are plotted, including all combinations of the high and low values for each independent variable you select.  Points close to the diagonal line are those that best predict the observed data.

You can also access the Plot of Fitted Model Options dialog box by clicking the Factors... command button.  The Factors command allows you to select two quantitative variables to plot, to change the limits for those variables, and to select levels at which to hold any other quantitative variables.


Cube

Displays a Cube Plot of the estimated effects for three factors.  The response variables are plotted, including all combinations of the high and low values for each factor you select.

Use the Factors... command to select the factors and to specify the high and low values.


Contours

Select attributes for the contours on the Contour Plot or for contours you want to place below a Surface Plot.

From

Allows you to enter a number that will determine the first contour line.  Enter a number less than the number you enter in the To text box.

To

Allows you to enter a number that will determine the last contour line.  Enter a number greater than the number you enter in the From text box.

By

Allows you to enter a number that will space the contour lines.  This number, along with the numbers from the From and To text boxes determine the levels of the contours.

Lines

Indicate if you want lines that connect the points plotted along each contour.  Lines connecting the points are the default.

Painted Regions

Indicate if the regions of the contours should be painted (filled in).  Nonpainted regions are the default.


From

Allows you to enter a number that will be used for the first contour line.  Enter a number less than the number you enter in the To text box.


To

Enter a number that will be used for the last contour line.  Enter a number greater than the number you enter in the From text box.


By

Enter a number that will be used to space the contour lines.  This number, along with the numbers from the From and To text boxes, determines the levels of the contours.


Lines

Indicate if you want lines connecting the points along each contour.  Lines connecting points are the default.


Painted Regions

Indicate if you want painted (filled-in) regions of the contours.  Nonpainted regions are the default.


Resolution

Enter a value that designates the number of density values that will be calculated.  Enter a number between 1 and 100; the default is 21.


Surface

Select specific attributes for a Surface Plot.

Horizontal Division

Enter a value that indicates the number of horizontal lines that will be included on the plot.  Enter a positive integer.  The default is 10.

Vertical Division

Enter a value that indicates the number of vertical lines that will be included on the plot.  Enter a positive integer.  The default is 10.

Contours Below

Displays a Contour Plot below the Surface Plot.

Show Points

Indicate if you want values displayed for the points on the plot.  This choice is available only when you select a Wire Frame Surface Plot.

Wire Frame

Indicate if you want only horizontal and vertical lines plotted on the Surface Plot.

Solid

Indicate if you want to display a solid Surface Plot.

Contoured

Indicate if you want to display a topographical representation of a Surface Plot, with colors corresponding to the height of the surface.


Factors... Command

Displays the Plot of Fitted Model Options dialog box, which allows you to select the two quantitative variables that will be plotted, to change the limits for those variables, and to select a level at which to hold any other quantitative variables.


Residuals

Plots the differences between the observed and the fitted values.


Studentized Residuals

Plots the residuals, scaled by an estimate of the variance from the data, with the observation removed.  A large studentized residual value may indicate an outlier and an influential observation.  This option is the default.


Type (of Plot - General Linear Models)

Select the plot you want to display.

Scatterplot

Displays a Scatterplot of the residuals.  When you select this option, the Plot versus: list box becomes active, allowing you to select a specific Residual plot.  This option is the default.

Residuals versus Predicted

Displays the residuals or the studentized residuals versus the predicted values for the observed variable.  A nonrandom pattern indicates that the model you selected does not adequately describe the observed data.  The plot is helpful in showing heteroscedasticity; an indication that the variability in the residuals changes as the values of the dependent variable change.

Residuals versus Row Number

Displays the residuals or the studentized residuals versus the row number.  The residuals are plotted in the order the observations appear in the file.  The plot is helpful for determining sequential correlations among the residuals.  Any nonrandom pattern indicates serial correlation in the data, particularly if the row order corresponds to the order in which the data were collected.

Residuals versus X (where X indicates each independent variable)

Displays the residuals or the studentized residuals versus the independent variable (X).  Use this plot to detect any nonlinear relationship between the dependent and independent variables.  You can also use the plot to determine if the variance of the residuals is constant.  Any nonrandom pattern indicates that the model you selected does not adequately describe the data.  Any studentized residual values outside the range of -3 to +3 might be outliers.

Normal Probability Plot

Displays the residuals to determine if the errors follow a normal distribution.  A Normal Probability Plot consists of an arithmetic (interval) horizontal axis scaled for the data and a vertical axis scaled so the cumulative distribution function of a normal distribution plots as a straight line.  The closer the data are to the reference line, the more likely they follow a normal distribution.  When you select this option, the Direction and Fitted Line options become active.

Autocorrelation Function

Displays a graph of the autocorrelation estimates for the residuals.  The plot contains a pair of dotted lines and vertical bars that represent the coefficient for each lag.  The distance from the baseline is a multiple of the standard error at each lag.  Significant autocorrelations extend above or below the probability limits.  When you select this option, the Number of Lags and Confidence Level text boxes become active.


Scatterplot (General Linear Models)

The Scatterplot graphical option displays a Scatterplot of the residuals.  When you select this option, the Plot versus: list box becomes active, allowing you to select a specific Residual plot.

Residuals versus Predicted Plot

Residuals versus Row Number Plot

Residuals versus X Plot


Residuals versus Predicted Plot (General Linear Models)

The Residuals versus Predicted Plot option displays the residuals or the studentized residuals versus the predicted values for the observed variable.  A nonrandom pattern indicates that the model you selected does not adequately describe the observed data.

The plot is helpful in showing heteroscedasticity; an indication that the variability in the residuals changes as the values of the dependent variable change.


Residuals versus Row Number Plot (General Linear Models)

Displays the residuals or the studentized residuals versus the row number.  The residuals are plotted in the order that the observations appear in the file.

The plot is helpful for determining sequential correlations among the residuals.  Any nonrandom pattern indicates serial correlation in the data, particularly if the row order corresponds to the order in which the data were collected.


Residuals versus X Plot (General Linear Models)

Displays the residuals or the studentized residuals versus the independent variable (X).

Use this plot to detect any nonlinear relationship between the dependent and independent variables.  You can also use the plot to determine if the variance of the residuals is constant.

Any nonrandom pattern indicates that the model you selected does not adequately describe the data.  Any studentized residual values outside the range of -3 to +3 might be outliers.


Normal Probability Plot (General Linear Models)

The Normal Probability Plot graphical option consists of an arithmetic (interval) horizontal axis scaled for the data and a vertical axis scaled so the cumulative distribution function of a normal distribution plots as a straight line.  The closer the data are to the reference line, the more likely they follow a normal distribution.

When you select this option, the Direction and Fitted Line options become active.


Autocorrelation Function Plot (General Linear Models)

Displays a graph of the autocorrelation estimates for the residuals.  The plot contains a pair of dotted lines and vertical bars that represent the coefficient for each lag.  The distance from the baseline is a multiple of the standard error at each lag.

Significant autocorrelations extend above or below the probability limits.  When you select this option, the Number of Lags and Confidence Level text boxes become active.


Plot versus:

Select the Residual Plot you want to create.  This is available only for Scatterplots you select on the Residual Plots Options dialog box.


Horizontal

Scales the residuals on the Y-axis for the Normal Probability Plot.


Vertical

Scales the residuals on the X-axis for the Normal Probability Plot.


Fitted Line

Allows you to select how the line on the Normal Probability Plot will be drawn.

None

Appears without the fitted line.

Using Quartiles

The reference line on the Normal Probability Plot is drawn through the median at 0.5 with the slope determined by the quartiles.

Using Least Squares

The reference line on the Normal Probability Plot is fitted using least squares regression.


Number of Lags

Enter the maximum lag for which the autocorrelation values should be estimated.  Typically, the number of lags should not exceed the number of observations divided by 4.  Enter any integer.


Residual Plots (General Linear Models)

The Residual Plots graphical option includes the following:  Scatterplots (Residuals versus Predicted, Residuals versus Row Number, and Residuals versus X (where X indicates each independent variable); Normal Probability Plot; and Autocorrelation Function Plot.  Use the Residual Plots Options dialog box to select a plot and its options.


None

Intervals will not be displayed on the plot.  This option is the default.


Calibration Models Analysis Dialog Box
Calibration Models Dialog Box

The Calibration Models Analysis finds a calibration line that fits the data, letting you select from several transformations when the points do not follow a straight line.

You can choose to eliminate the constant from the model, which forces the line through the point (0,0).  You can also associate a weight with each observation to perform a weighted regression.  If the calibration experiment includes replicate observations for any of the X values, you can use a lack-of-fit test in the ANOVA table.

The tables and graphs in the analysis help to determine the validity of the calibration line by completely testing the hypotheses, model diagnostics, and residuals.

Once you are completely satisfied with the calibration line, values can be added to the equation for either Y or X to calculate estimates with intervals for the opposite variable.  Corresponding values for the measurement and the converted quantity with intervals are shown in tables or directly on an XY Plot.

In addition, you can save a calibration line for later use when you convert additional measurements into interval estimates.  Finally, if you have two sets of experimental data, you can compare the two calibration lines with each other using a hypothesis test to see if the results are consistent.

Note:  You should enter data for a calibration model in two columns of the DataSheet; one for X (the known or standard quantity), and one for Y (the measurement you obtained with the instrument or process you are calibrating).  You do not necessarily need to name the variables X or Y, but it does make a difference if you reverse the actual and measured variables when you enter them into the Calibration Models Analysis dialog box.

Y (Measured)

X (Actual)

Fitted Model Statistics

Weights

Select

Action

Sort

Delete...

Transform...

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Calibration Models Analysis

Calibration Model Options

Confidence Interval Options

Hypothesis Tests Options

Predictions Options

Plot of Fitted Model Options

Residual Plots Options


Y (Measured)

Enter the name of a measured or dependent numeric Y variable. If you are predicting X rather than fitting a new model, the average value of the measurements and the number of observations in the variable are used to predict one X value and interval from a previous model.


X (Actual)

Enter the name of the actual or X numeric variable. This text box is active only when you select the Fit New Model option.


Fitted Model Statistics

Enter the results that were saved from a previous model fitting.  The saved results must come from a Model Statistics variable you saved from an earlier use of STATGRAPHICS Plus.

An entry in this text box is optional if you are fitting a new model.  If you enter results saved from a previous model and you are fitting a new model, you can compare the slopes between the previous and the new models.


Weights

If you are fitting a new model, this optional text box allows you to enter the name of a numeric variable that contains the values that will be applied to the residuals when the model coefficients are estimated.  Enter the name of a numeric variable, which will result in a weighted least squares regression.


Select

Allows you to select a subset of observations.  For example, to analyze the first 50 values in each variable, enter first (50) in this text box.  Or you can use this text box to select the observations the program will use to estimate the model.  The remaining complete observations (those that you do not select) are used to validate the model.

The validation and estimation results appear in the Residual Analysis table at the end of the Analysis Summary.


Action

Select an action.  The tabular and graphical options will vary depending on the action you select

Fit New Model

Fits a new model.  You must enter data for both the measured (Y) and the actual (X) variables.

Predict X from Y

Uses a previously estimated model to predict a value and its interval for X, if you provide one or more new measurements in the Y variable text box.


Sort

Indicate if you want the variables sorted alphabetically.  The default is sorted variables.


Fit New Model

Fits a new model.  You must enter data for both the measured (Y) and the actual (X) variables.


Predict X from Y

Uses a previously estimated model to predict a value and its interval for X, if you provide one or more new measurements in the Y variable text box.


Calibration Models Tabular Options Dialog Box

If you select the Fit New Model action on the Calibration Models Analysis dialog box, the Tabular Options dialog box allows you to select from seven options: Analysis Summary, Confidence Intervals, Hypothesis Tests, Predictions, Comparison of Alternate Models, Unusual Residuals, and Influential Points.

If you select the Predict X from Y action on the Calibration Models Analysis dialog box, the tabular Options dialog box allows you to select from four options:  Analysis Summary, Confidence Intervals, Hypothesis Tests, and Predictions.

Note:  To access the Options dialog boxes, click the right mouse button on the text pane, then the left on either Pane Options or Analysis Options.

Analysis Summary (Calibration Models)

Confidence Intervals (Calibration Models)

Hypothesis Tests (Calibration Models)

Predictions (Calibration Models)

Comparison of Alternative Models (Calibration Models)

Unusual Residuals (Calibration Models)

Influential Points (Calibration Models)


Analysis Summary (Calibration Models)

The Analysis Summary tabular option shows the results of fitting a linear model to describe the relationship between the dependent (measured) and independent (actual) variables.  The StatAdvisor includes the equation for the fitted model.  If the data contain replicate values for X, a lack-of-fit test is also performed.

1.	If the p-value in the ANOVA table is less than 0.01, there is a statistically significant relationship between the two variables at the 99 percent confidence level.

2.	The R-Squared statistic explains the percentage of variability represented by the dependent variable as it was fitted in the full model.

3.	The correlation coefficients value explains the strength of the linear relationship between the variables.

4.	The Standard Error of the Estimate statistic shows the value for the standard deviation of the residuals.  You can use this value to construct prediction limits for new observations.

5.	The Durbin-Watson statistic tests for autocorrelation or serial correlation in the residuals of a least squares regression analysis.

6.	The Lag-1 autocorrelation is the first-order autocorrelation.

If you used the optional Select text box on the Calibration Models Analysis dialog box, the prediction error statistics are used to validate the accuracy of the models and to display the Residuals Table at the end of the Analysis Summary.

If you decide to validate the model, see the Advanced Regression User Manual and use one of the methods discussed in the section, “Understanding Advanced Regression,” in Chapter 1, Getting Started.

The Residuals Table includes values for the following statistics for the validation and estimation data:

1.	n — the number of observations.

2.	MSE (Mean Square Error) — a measure of accuracy computed by squaring the individual error for each item in the set of data, then finding the average or mean value for the sum of those squares.  If the result is a small value, you can predict performance more accurately; if the result is a large value, you may want to use a different model.

3.	MAE (Mean Absolute Error) — the average of the absolute values of the residuals; appropriate for linear and symmetric data.  If the result is a small value, you can predict performance more accurately; if the result is a large value, you may want to use a different model

4.	MAPE (Mean Absolute Percentage Error) — the mean or average of the sum of all the percentage errors for a given set of data without regard to sign (that is, their absolute values are summed and the average is computed).  Unlike the ME, MSE, and MAE, the size of the MAPE is independent of scale

5.	ME (Mean Error) — the average of the residuals.  The closer the ME is to 0, the less biased, or more accurate, the prediction

6.	MPE (Mean Percentage Error) — the average of the absolute values of the residuals divided by the corresponding estimates.  Like MAPE, it is independent of scale


Calibration Model Options Dialog Box

Select one of 12 types of models, and indicate if you want to include a constant in the model.

Type of Model

Include Constant


Type of Model

Allows you to select the type of model that will be used.

Linear

Fits a simple linear regression equation for Y in terms of X.  The data are fit to the linear model before you select a different model.  This option is the default.  The model is defined by the equation Y = a + bX.

Exponential

Fits an exponential model.  This model is equivalent to taking the natural log of Y and is defined by the equation Y = exp(a + bX).

Reciprocal-Y

Fits a reciprocal-Y model.  This model is defined by the equation

Y = 1/(a + bX ).

Reciprocal-X

Fits a reciprocal-X model.  This model is defined by the equation Y = a + b/X.

Double Reciprocal

Fits the reciprocal of the dependent variable and the reciprocal of the independent variable.  This model is defined by the equation Y = 1/(a + b/X).

Logarithmic-X

Fits a logarithmic-X model.  This model is defined by the equation Y = a + b(Log X).

Multiplicative

Fits a multiplicative model.  This model is equivalent to taking the natural logs of Y and X.  It is defined by the equation Y = aX^b.

Square Root-X

Fits a square root-X model.  The model is defined by the equation Y = a + b sqrt(X).  The reciprocal-X, logarithmic-X, and square root-X transformations linearize a nonlinear relationship between the dependent and independent variables.  The transformations are suitable when the error terms are normal and have constant variance.

Square Root-Y

Fits a square root-Y model.  The model is defined by the equation Y = (a + bX)^2.  The exponential, reciprocal-Y, and square root-Y transformations can help remedy error terms that are not normal and that do not have constant variance.

S-Curve

Takes the natural log of Y and the reciprocal of X.  The model is defined by the equation Y = exp(a + b/X).  The double reciprocal, multiplicative, and S-Curve models transform the independent variable, linearizing the nonlinear relationship between the independent and dependent variables.  This transformation of the dependent variable helps remedy error terms that are not normal and that do not have constant variance.

Logistic

Fits a response of observed proportions or probabilities at each level of an independent variable.  The response function is a nonlinear S-shaped curve with asymptotes at 0 and 1.  The dependent variable must have values greater than 0 and less than 1.  The model is defined by the equation Y = exp(a + bX )/(1 + exp(a + bX )).

Log Probit

Fits a response of observed proportions or probabilities at each level of an independent variable.  The model is appropriate when the response variable tends to follow a cumulative normal distribution.  The response function is a nonlinear S-shaped curve with asymptotes at 0 and 1.  The dependent variable must have values greater than 0 and less than 1.  The model is defined by the equation Y = normal (a + b(Log X)).


Include Constant

Indicate if you want a constant included in the model.  This option is the default.


Linear

Fits a simple linear regression equation for Y in terms of X.  The data are fit to the linear model before you select a different model.  The model is defined by the equation Y = a + bX.

This option is the default.


Exponential

Fits an exponential model, which is equivalent to taking the natural log of Y and is defined by the equation Y = exp(a + bX).


Reciprocal-Y

Fits a reciprocal-Y model defined by the equation Y = 1/(a + bX ).


Reciprocal-X

Fits a reciprocal-X model defined by the equation Y = a + b/X.


Double Reciprocal

Fits the reciprocal of the dependent variable and the reciprocal of the independent variable.  This model is defined by the equation Y = 1/(a + b/X).


Logarithmic-X

Fits a logarithmic-X model defined by the equation Y = a + b(Log X).


Multiplicative

Fits a multiplicative model, which is equivalent to taking the natural logs of Y and X.  It is defined by the equation Y = aX^b.


Square Root-X

Fits a square root-X model defined by the equation Y = a + b sqrt(X).  The reciprocal-X, logarithmic-X, and square root-X transformations linearize a nonlinear relationship between the dependent and independent variables.  The transformations are suitable when the error terms are normal and have constant variance.


Square Root-Y

Fits a square root-Y model defined by the equation Y = (a + bX)^2.  The exponential, reciprocal-Y, and square root-Y transformations can help remedy error terms that are not normal and that do not have constant variance.


S-Curve

Takes the natural log of Y and the reciprocal of X; it is defined by the equation Y = exp(a + b/X).  The double reciprocal, multiplicative, and S-Curve models transform the independent variable, linearizing the nonlinear relationship between the independent and dependent variables.  This transformation of the dependent variable helps remedy error terms that are not normal and that do not have constant variance.


Logistic

Fits a response of observed proportions or probabilities at each level of an independent variable.  The response function is a nonlinear S-shaped curve with asymptotes at 0 and 1.  The dependent variable must have values greater than 0 and less than 1.  The model is defined by the equation Y = exp(a + bX )/(1 + exp(a + bX )).


Log Probit

Fits a response of observed proportions or probabilities at each level of an independent variable.  The model is appropriate when the response variable tends to follow a cumulative normal distribution.  The response function is a nonlinear S-shaped curve with asymptotes at 0 and 1.  The dependent variable must have values greater than 0 and less than 1.  The model is defined by the equation Y = normal (a + b(Log X)).


Confidence Intervals (Calibration Models)

The Confidence Intervals tabular option calculates and displays the confidence intervals or bounds for the parameters of the fitted model.  In repeated sampling, 95 percent of these intervals will contain the true values for the parameters, provided the model has the proper form and the errors are distributed normally and independently.


Confidence Interval Options Dialog Box

Select the type of interval that will be used, and enter a value for the confidence level.

Type of Interval

Confidence Level (for Model Coefficients)


Type (of Interval)

Allows you to select the type of interval that will be used.

Two-Sided

Calculates the upper and lower confidence limits for each coefficient. This option is the default.

Lower Bound

Calculates the lower confidence limit for each coefficient.

Upper Bound

Calculates the upper confidence limit for each coefficient.


Hypothesis Tests (Calibration Models)

The Hypothesis Tests tabular option allows you to test hypotheses about the intercept, slope, or difference between the current slope.

You can do this if you selected a hypothesis from a previous model (if you selected the Fit New Model option and entered the saved model statistics on the Calibration Models Analysis dialog box).

The results of the two hypothesis tests are displayed for the parameters of the fitted calibration model.  The results of the first test contain information about the intercept.  If the p-value is greater than 0.10, you cannot reject the hypothesis that the intercept equals 0.0 at a 90 percent or higher confidence level.

The results of the second test contain information about the slope.  If the p-value is less than 0.01, reject the hypothesis that the slope equals 1.0 at the 99 percent confidence level.


Hypothesis Tests Options Dialog Box

Enter a value that will test the intercept and slope, enter a percentage for the alpha level, and select an alternative hypothesis HA.

Intercept

Slope

Alpha

Alternative Hypothesis


Intercept

Enter a value that will be used to test the intercept.  The default is 0.


Slope

Enter a value that will be used to test the slope.  The default is 1.


Alpha

Enter a value (as a percentage) that will be used for the confidence level.  Enter a number greater than or equal to 0 and less than 100; the default is 5.


Alternative Hypothesis

Allows you to select an alternative hypothesis, HA, for the difference between the slopes of the saved model and the newly estimated model.

Not Equal

Performs a two-sided test.

Less Than

Perform a one-sided test with a lower rejection region.

Greater Than

Performs a one-sided test with an upper rejection region.


Predictions (Calibration Models)

The Predictions tabular option allows you to predict the values for Y, given X; or the values for X, given Y .  The results display the values for the predictions using the fitted model.

The table shows the best predictions and (1) the 95 percent prediction intervals for new observations, and (2) the 95 percent confidence intervals for the mean of many observations.  The prediction and confidence intervals correspond to the inner and outer bounds on the Plot of Fitted Model.


Predictions Options Dialog Box

Select the variable you want to predict, enter values for the confidence level and prediction mean size, and enter the values for the opposite variable for the displayed predictions.

Predict

Predict At

Confidence Level (for Predictions and Confidence Limits)

Mean Size or Weight


Predict

If you selected the Fit New Model action on the Calibration Models Analysis dialog box, allows you to select the variable you want to predict:  Y, given X; or X, given Y.

If you selected the Predict X from Y action on the Calibration Models Analysis dialog box, these options allow you to predict X, given the observed data on Y.


Predict At

Enter the values for the variable that will be used to make the predictions.


Mean Size or Weight

Change the number of observations upon which the mean is based.  Increasing the number of observations narrows the limits.  The default is 1.


Comparison of Alternative Models (Calibration Models)

(Available for only Fit New Model action)

The Comparison of Alternative Models tabular option fits the curvilinear models to the data and displays the values for the correlations and the R-Squared statistics, arranging them by the highest value.  To select a different model, use the Calibration Model Options dialog box.


Unusual Residuals (Calibration Models)

(Available for only Fit New Model action)

The Unusual Residuals tabular option for the Calibration Models Analysis lists all of the observations that have unusually large studentized residuals — those greater than 2.0 in absolute value.  Studentized residuals measure the number of standard deviations each observed value deviates from the model fitting using all the data except that observation.


Influential Points (Calibration Models)

(Available for only Fit New Model action)

The Influential Points tabular option for the Calibration Models Analysis identifies all the observations that have leverage values greater than three times that of an average point, or that have unusually large DFITS or Cook's distance values.

The leverage statistic helps determine the coefficients of the estimated model by measuring the amount of influence that can be attributed to each observation.  The DFITS statistic measures the amount of change for each estimated coefficient if the observation is removed from the data.  The Cook's distance statistic measures the distance between the estimated coefficients with and without each observation.


Calibration Models Graphical Options Dialog Box

If you select the Fit New Model action on the Calibration Models Analysis dialog box, allows you to select from three options:  Plot of Fitted Model, Observed versus Predicted, and Residual Plots.

You can access the Calibration Model Options dialog box from all of these options as well as from all of the tabular options.  Other dialog boxes you can access from these options are:  Plot of Fitted Model Options (Plot of Fitted Model), and Residual Plots Options (Residual Plots).

If you select the Predict X from Y action on the Calibration Models Analysis dialog box, allows you to select one option:  Plot of Fitted Model.

Note:  To access the Options dialog boxes, click the right mouse button on the graphics pane, then click the left on either Pane Options or Analysis Options.

Plot of Fitted Model (Calibration Models)

Observed versus Predicted Plot (Calibration Models)

Residual Plots (Calibration Models)


Plot of Fitted Model (Calibration Models)

If you select the Fit New Model action on the Calibration Models Analysis dialog box, displays a plot of the fitted model with confidence and/or prediction limits.  You can also plot a single prediction.

If you select the Predict X from Y action on the Calibration Models Analysis dialog box, displays a plot of the fitted model with prediction limits for the mean of m observations, where m is the number of Y values you entered on the Calibration Models Analysis dialog box.


Plot of Fitted Model Options Dialog Box

If you select the Fit New Model action on the Calibration Models Analysis dialog box, allows you to:

•	select the limits the program will plot (Prediction or Confidence Limits)

•	indicate if you want to predict X or Y

•	enter the value that will be used to make the prediction.

You can also enter values for the confidence level and for the prediction mean size.

Include

Confidence Level (for Prediction Intervals)

Predict

At

Mean Size or Weight


Include

Allows you to select the limits that will be plotted:  Prediction Limits or Confidence Limits.


Predict

Select the variable you want to predict:  Y, given X; or X, given Y.


At

Enter the value for the variable that will be used to make the predictions.


Mean Size or Weight

Change the number of observations upon which the mean is based.  Increasing the number of observations narrows the limits.  The default is 1.


Observed versus Predicted Plot (Calibration Models)

(Available for only Fit New Model action)

The Observed versus Predicted graphical option for the Calibration Models Analysis displays the observed values of Y versus the values predicted by the predicted model.  The closer the points lie to the diagonal line, the better the model predicts the observed data.  Look for various anomalies, such as increases in variability around the line as the value of Y increases (heteroscedasticity), or points that lie far away from the line (outliers).


Residual Plots (Calibration Models)

The Residual Plots graphical option for the Calibration Models Analysis includes the following:  Scatterplots (Residuals versus Predicted, Residuals versus Row Number, and Residuals versus X where X indicates each independent variable); Normal Probability Plot, and Autocorrelation Function.  Use the Residual Plots Options dialog box to select a plot and its options.


Residual Plots Options Dialog Box

Select a residual plot and its options.

Plot (Residuals or Studentized Residuals)

Type (of Plot - Calibration Models)

Plot versus:

Direction (for Residuals)

Fitted Line

Number of Lags

Confidence Level (for Probability Limits)


Type (of Plot - Calibration Models)

Select the plot you want to display.

Scatterplot

Displays a Scatterplot of the residuals.  When you select this option, the Plot versus: list box becomes active, allowing you to select a specific Residual Plot from this list.  This option is the default.

Residuals versus Predicted

Displays the residuals or the studentized residuals versus the predicted values for the observed variable.  A nonrandom pattern indicates that the model you selected does not adequately describe the observed data.  The plot is helpful in showing heteroscedasticity; an indication that the variability in the residuals changes as the values of the dependent variable change.

Residuals versus Row Number

Displays the residuals or the studentized residuals versus the row number.  The residuals are plotted in the order that the observations appear in the file.  The plot is helpful for determining sequential correlations among the residuals.  Any nonrandom pattern indicates serial correlation in the data, particularly if the row order corresponds to the order in which the data were collected.

Residuals versus X (where X indicates each independent variable)

Displays the residuals or the studentized residuals versus the independent variable (X).  Use this plot to detect any nonlinear relationship between the dependent and independent variables.  You can also use the plot to determine if the variance of the residuals is constant.  Any nonrandom pattern indicates that the model you selected does not adequately describe the data.  Any studentized residual values outside the range of -3 to +3 might be outliers.

Normal Probability Plot

Displays the residuals to determine if the errors follow a normal distribution.  The plot consists of an arithmetic (interval) horizontal axis scaled for the data and a vertical axis scaled so the cumulative distribution function of a normal distribution plots as a straight line.  The closer the data are to the reference line, the more likely they follow a normal distribution.  When you select this option, the Direction and Fitted Line options become active.

Autocorrelation Function

Displays a graph of the autocorrelation estimates for the residuals.  The plot contains a pair of dotted lines and vertical bars that represent the coefficient for each lag.  The distance from the baseline is a multiple of the standard error at each lag.

Significant autocorrelations extend above or below the probability limits.  When you select this option, the Number of Lags and Confidence Level text boxes become active.


Scatterplot (Calibration Models)

Displays a Scatterplot of the residuals.  When you select this option, the Plot versus: list box becomes active, allowing you to select a specific residual plot.

Residuals versus Predicted (Calibration Models)

Residuals versus Row Number (Calibration Models)

Residuals versus X (Calibration Models)


Residuals versus Predicted (Calibration Models)

Displays the residuals or the studentized residuals versus the predicted values for the observed variable (Y).  A nonrandom pattern indicates that the model you selected does not adequately describe the observed data.

The plot is helpful in showing heteroscedasticity; an indication of the variability of the changes in the residuals as the values of the dependent variable change.


Residuals versus Row Number (Calibration Models)

Displays the residuals or the studentized residuals versus the row number.  The residuals are plotted in the order that the observations appear in the dependent variable.

The plot is helpful in determining sequential correlations among the residuals.  Any nonrandom pattern indicates serial correlation in the data, particularly if the row order corresponds to the order in which the data were collected.


Residuals versus X (Calibration Models)

Displays the residuals or studentized residuals versus the independent variable (X), where X equals the name of the independent variable you selected.

Use this plot to detect the nonlinear relationship between the dependent and independent variables.  You can also use the plot to determine if the variance of the residuals is constant.  Nonrandom patterns indicate that the model you selected does not adequately describe the data.  Any studentized residual values outside the range of -3 to +3 might be outliers.


Normal Probability Plot (Calibration Models)

Displays the residuals used to determine if the data follow a normal distribution.  A Normal Probability Plot consists of an arithmetic (interval) horizontal axis scaled for the data and a vertical axis scaled so the cumulative distribution function of a normal distribution plots as a straight line.  The closer the data are to the reference line, the more likely they follow a normal distribution.

When you select this option, the Direction and Fitted Line options become active, allowing you to select the direction of the plot and the type of values the program will use for the fitted line.


Autocorrelation Function Plot (Calibration Models)

Displays a plot of the autocorrelation estimates for the residuals.  The plot contains a pair of dotted lines and vertical bars that represent the coefficient for each lag.  The distance from the baseline is a multiple of the standard error at each lag.  Significant autocorrelations extend above or below the confidence limits.

When you select this option, the Number of Lags and Confidence Level text boxes are activated.


Plot versus:

Allows you to select the residual plot you want to generate.


Direction (for Residuals)

Allows you to select the direction of the Normal Probability Plot.

Horizontal

Displays the plot horizontally, and scales the residuals on the Y-axis.

Vertical

Displays the plot vertically and scales the residuals on the X-axis.


Fitted Line

Select the line that will be drawn on the Normal Probability Plot.

None

Plots the Normal Probability Plot without the fitted line.

Using Quartiles

Plots the Normal Probability Plot with the fitted line drawn through the median at 0.5 with the slope determined by the quartiles.  This option is the default.

Using Least Squares

Plots the Normal Probability Plot with the line fitted using least squares


Number of Lags

Enter a value for the maximum lag that will be used to estimate the autocorrelation values.  Typically, the number of lags should not exceed the number of observations divided by 4.  Enter any integer.


Save Results Options Dialog Box (Calibration Models)

The Save Results Options dialog box allows you to select the results you want to save.  There are 10 selections:  Model Statistics, Predicted Values, Lower Limits for Predictions, Upper Limits for Predictions, Lower Limits for Forecast Means, Upper Limits for Forecast Means, Residuals, Studentized Residuals, Leverages, and Coefficients.

Note:  When you select the Model Statistics choice, save the values but do not alter them.  You can use them later for predicting X from Y.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Comparison of Regression Lines Analysis Dialog Box

The Comparison of Regression Lines analysis automatically constructs the necessary indicator variables to allow you to compare two or more simple regression models, usually to test to see if you can use a single model across groups.

You first enter a model of the form Y = a + bX and a grouping variable, and STATGRAPHICS Plus adds the indicator variables to the model.  In effect, this fits separate lines for each level of the categorical variable and allows you to determine if the intercepts and/or the slopes differ among the levels of that variable.

The tables and graphs are designed specifically for comparing slopes and intercepts.  The tabular and graphical options are helpful when the slopes or intercepts do not differ significantly and you want to force them to be equal to simplify the model.  The final step in the model-building process is to validate the model.

For information about model validation, see the Advanced Regression User Manual and the section “Understanding Advanced Regression” in Chapter 1, Getting Started.  Also see the Online Help entry for the Analysis Summary for this analysis.

Dependent Variable

Independent Variable

Level Codes

Select

Sort

Delete...

Transform...

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Comparison of Regression Lines Analysis

Comparison of Regression Lines Options

Forecasts Options

Residual Plots Options


Dependent Variable

Enter the name of a numeric dependent variable (Y).


Independent Variable

Enter the name of a numeric independent variable (X).


Level Codes

Enter the name of the variable that defines the groups that will be used to compare the regression models.  You can enter either a character or a numeric variable; each resulting group should contain three or more observations.


Select

Select a subset of observations.  For example, to analyze the first 50 values in each variable, enter first (50) in this text box.  Or you can use this text box to select the observations the program will use to estimate the model.  The remaining complete observations (those that you do not select), are used to validate the model.  The validation and estimation results appear in the Residual Analysis table at the end of the Analysis Summary.


Sort

Indicate if you want the variables sorted alphabetically.  The default is sorted variables.


Comparison of Regression Lines Tabular Options Dialog Box

This dialog box allows you to select tabular options for the analysis.

Note:  To access the Options dialog boxes, click the right mouse button on the text pane, then click the left on either Pane Options or Analysis Options.

Analysis Summary (Comparison of Regression Lines)

Conditional Sums of Squares (Comparison of Regression Lines)

Confidence Intervals (Comparison of Regression Lines)

Forecasts (Comparison of Regression Lines)

Unusual Residuals (Comparison of Regression Lines)

Influential Points (Comparison of Regression Lines)


Analysis Summary (Comparison of Regression Lines)

The Analysis Summary tabular option shows the results of the multiple regression analysis.  If the display includes the explanation provided by the StatAdvisor, the equation of the fitted model and an explanation of the terms in the equation are shown.

By default, the model contains an intercept, a coefficient for the X variable, a coefficient for the indicator variable for each group except the first, and for products of the X variable with each group indicator.  The table then shows the results of the fit:

1.	If the p-value in the ANOVA table is less than 0.01, the results indicate that there is a statistically significant relationship among the variables at the 99 percent confidence level.

2.	The R-Squared statistic indicates the percentage of variability the dependent variable accounts for as it was fitted in the full model.

3.	The Adjusted R-Squared statistic, which is more suitable for comparing models that have different numbers of independent variables and indicates the percentage of variability represented by the model after accounting for the number of parameters that were estimated.

4.	The Standard Error of the Estimate shows the value for the standard deviation of the residuals.  You can use this value to construct prediction limits for new observations by selecting the Forecasts tabular option.

5.	The value for the Mean Absolute Error (MAE) is the average absolute value of the residuals.

6.	You can use the value for the Durbin-Watson statistic to test the residuals to determine if there is significant serial correlation, based on the order in which the values fall in the file.  The StatAdvisor contains recommendations for further tests and plots.

If you used the optional Select text box on the Comparison of Regression Lines Analysis dialog box, the prediction error statistics are used to validate the accuracy of the model and to display the Residuals Table at the end of the Analysis Summary.  If you decide to validate the model, see the Advanced Regression User Manual and use one of the methods discussed in the section, “Understanding Advanced Regression,” in Chapter 1, Getting Started.

The Residuals Table includes values for the following statistics for the validation and estimation data:

1.	n — the number of observations.

2.	MSE (Mean Square Error) — a measure of accuracy computed by squaring the individual error for each item in the set of data, then finding the average or mean value for the sum of those squares.  If the result is a small value, you can predict performance more accurately; if the result is a large value, you may want to use a different model.

3.	MAE (Mean Absolute Error) — the average of the absolute values of the residuals; appropriate for linear and symmetric data.  If the result is a small value, you can predict performance more accurately; if the result is a large value, you may want to use a different model.

4.	MAPE (Mean Absolute Percentage Error) — the mean or average of the sum of all the percentage errors for a given set of data without regard to sign (that is, their absolute values are summed and the average is computed).  Unlike the ME, MSE, and MAE, the size of the MAPE is independent of scale.

5.	ME (Mean Error) — the average of the residuals.  The closer the ME is to 0, the less biased, or more accurate, the prediction.

6.	MPE (Mean Percentage Error) — the average of the absolute values of the residuals divided by the corresponding estimates.  Like MAPE, it is independent of scale.


Comparison of Regression Lines Options Dialog Box

Forces equal slopes or intercepts for all the groups.

Assume Equal Intercepts

Assume Equal Slopes


Assume Equal Intercepts

Removes the linear terms of the indicator variables from the model, which forces all the Y-intercepts to be the same.  There is no default.


Assume Equal Slopes

Removes the interaction terms of the X variable that has indicator variables from the model, which forces all the slopes to be the same.  There is no default.


Conditional Sums of Squares (Comparison of Regression Lines)

The Conditional Sums of Squares tabular option allows you to test the statistical significance of the terms in the model.

The option produces an analysis of variance table that shows the values for additional sums of squares as the various terms are added to the model.

The sums of squares are grouped for the linear indicator variable terms, labeled as intercepts, and grouped together for the interaction terms of the X variable with the indicators (slopes).  The StatAdvisor provides a specific interpretation of your data and makes suggestions for further tests.


Confidence Intervals (Comparison of Regression Lines)

The Confidence Intervals tabular option displays the confidence intervals for the coefficients in the model.  You use confidence intervals to see the preciseness of the estimates for the coefficients, given the amount of available data and the amount of noise.


Confidence Intervals Options Dialog Box

Enter a value for the confidence level that will be used to calculate the confidence intervals for the difference between the estimates.  The default is 95 percent; other common levels are 90 and 99 percent.

The three Interval Types are: 2-Sided, Upper Bound, and Lower Bound.

The Include Bootstrap check box lets you include this feature, together with your choice of number of subsamples.


Forecasts (Comparison of Regression Lines)

The Forecasts tabular option generates and displays predictions for the variable using the fitted model.  The display includes predictions for the values of the Y variable at each level code and includes values for the prediction and confidence limits.  Default predictions are shown for the minimum and maximum values of the X variable.


Forecasts Options Dialog Box

Select a value for the confidence level and for the X variable.

Confidence Level (for Prediction Intervals)

Forecast at X


Forecast at X

Enter values for the variable X for which you want to predict values of Y.  Default values are shown in the text boxes when the dialog box displays.


Unusual Residuals (Comparison of Regression Lines)

The Unusual Residuals tabular option lists all the observations that have unusually large studentized residuals — greater than 2.0 in absolute value.  Studentized residuals measure the number of standard deviations each observed value deviates from the model fitting using all the data except that observation.


Influential Points (Comparison of Regression Lines)

The Influential Points tabular option identifies all the observations that have leverage values greater than three times that of an average point, or that have unusually large DFITS or Cook's distance values.

The leverage statistic helps determine the coefficients of the estimated model by measuring the amount of influence that can be attributed to each observation.  The DFITS statistic measures the amount of change for each estimated coefficient if the observation is removed from the data.  Cook's distance measures the distance between the estimated coefficients with and without each observation.


Comparison of Regression Lines Graphical Options Dialog Box

This dialog box allows you to select graphical options for the analysis.

Note:  To access the Options dialog boxes, click the right mouse button on the graphics pane, then click the left on either Pane Options or Analysis Options.

Plot of Fitted Model (Comparison of Regression Lines)

Observed versus Predicted Plot (Comparison of Regression Lines)

Residual Plots (Comparison of Regression Lines)


Plot of Fitted Model (Comparison of Regression Lines)

The Plot of Fitted Model graphical option displays a plot of the fitted model.  A separate line is shown for each level code.


Observed versus Predicted Plot (Comparison of Regression Lines)

The Observed versus Predicted Plot graphical option displays a plot of the observed values (Y) versus the values predicted by the fitted model.  The plot includes a line with slope equal to one.  The closer the points lie to the diagonal line, the better the model predicts the observed data.

Use the plot to determine cases in which the variance is not constant, which indicates that you should probably transform the values for the dependent variable.


Residual Plots (Comparison of Regression Lines)

The Residual Plots graphical option includes the following:  Scatterplots (Residuals versus Predicted, Residuals versus Row Number, Residuals versus X where X indicates each independent variable, and Residuals versus Level Codes); Normal Probability Plot; and Autocorrelation Function Plot.


Residual Plots Options Dialog Box

Select a residual plot and its options.

Plot (Residuals or Studentized Residuals)

Type (of Plot - Comparison of Regression Lines)

Plot versus:

Direction (for Residuals)

Fitted Line

Number of Lags

Confidence Level (for Prediction Intervals)


Type (of Plot - Comparison of Regression Lines)

Select the plot you want to display.

Scatterplot

Displays a Scatterplot of the residuals.  When you select this option, the Plot versus: list box becomes active, allowing you to select a specific residual plot.  This option is the default.

Residuals versus Predicted

Displays the residuals or the studentized residuals versus the predicted values for the observed variable (Y).  A nonrandom pattern indicates that the model does not adequately describe the observed data.  The plot is helpful in showing heteroscedasticity; an indication of the variability of the changes in the residuals as the values of the dependent variable change.

Residuals versus Row Number

Displays the residuals or the studentized residuals versus the row number.  The residuals are plotted in the order that the observations appear in the dependent variable.  The plot is helpful in determining sequential correlations among the residuals.  Any nonrandom pattern indicates serial correlation in the data, particularly if the row order corresponds to the order in which the data were collected.

Residuals versus X (where X indicates the name of each independent X variable)

Displays the residuals or studentized residuals versus the independent variable (X), where X equals the name of the independent variable you selected.  Use this plot to detect the nonlinear relationship between the dependent and independent variables.  You can also use the plot to determine if the variance of the residuals is constant.  Nonrandom patterns indicate that the model you selected does not adequately describe the data.  Any studentized residual values outside the range of -3 to +3 might be outliers.

Residuals versus Level Codes

Displays the residuals or the studentized residuals versus the level codes.  A nonrandom pattern indicates that the model you selected does not adequately describe the observed data.  Any values of studentized residuals outside the range of -3 to +3 might be outliers.

Normal Probability Plot

Displays the residuals used to determine if the data follow a normal distribution.  A Normal Probability Plot consists of an arithmetic (interval) horizontal axis scaled for the data and a vertical axis scaled so the cumulative distribution function of a normal distribution plots as a straight line.  The closer the data are to the reference line, the more likely they follow a normal distribution.  When you select this option, the Direction and Fitter Line options become active.

Autocorrelation Function

Displays a graph of the autocorrelation estimates for the residuals.  The plot contains a pair of dotted lines and vertical bars that represent the coefficient for each lag.  The distance from the baseline is a multiple of the standard error at each lag.  Significant autocorrelations extend above or below the confidence limits.  When you select this option, the Number of Lags and Confidence Level text boxes become active.


Scatterplot (Comparison of Regression Lines)

Displays a Scatterplot of the residuals.  When you select this option, the Plot versus: list box becomes active, allowing you to select a specific residual plot.

Residuals versus Predicted Plot (Comparison of Regression Lines)

Residuals versus Row Number Plot (Comparison of Regression Lines)

Residuals versus X Plot (Comparison of Regression Lines)

Residuals versus Level Codes Plot (Comparison of Regression Lines)


Residuals versus Predicted Plot (Comparison of Regression Lines)

Displays the residuals or the studentized residuals versus the predicted values for the observed variable (Y).  A nonrandom pattern indicates that the model you selected does not adequately describe the observed data.

The plot is helpful in showing heteroscedasticity; an indication of the variability of the changes in the residuals as the values of the dependent variable change.


Residuals versus Row Number Plot (Comparison of Regression Lines)

Displays the residuals or the studentized residuals versus the row number.  The residuals are plotted in the order that the observations appear in the dependent variable.

The plot is helpful in determining sequential correlations among the residuals.  Any nonrandom pattern indicates serial correlation in the data, particularly if the row order corresponds to the order in which the data were collected.


Residuals versus X Plot (Comparison of Regression Lines)

Displays the residuals or studentized residuals versus the independent variable (X), where X equals the name of the independent variable you selected.

Use this plot to detect the nonlinear relationship between the dependent and independent variables.  You can also use the plot to determine if the variance of the residuals is constant.  Nonrandom patterns indicate that the model you selected does not adequately describe the data.  Any studentized residual values outside the range of -3 to +3 might be outliers.


Normal Probability Plot (Comparison of Regression Lines)

Displays the residuals used to determine if the data follow a normal distribution.  A Normal Probability Plot consists of an arithmetic (interval) horizontal axis scaled for the data and a vertical axis scaled so the cumulative distribution function of a normal distribution plots as a straight line.

The closer the data are to the reference line, the more likely they follow a normal distribution.  When you select this option, the Direction and Fitted Line options become active.


Autocorrelation Function Plot (Comparison of Regression Lines)

Displays a graph of the autocorrelation estimates for the residuals.  The plot contains a pair of dotted lines and vertical bars that represent the coefficient for each lag.  The distance from the baseline is a multiple of the standard error at each lag.

Significant autocorrelations extend above or below the confidence limits.  When you select this option, the Number of Lags and Confidence Level text boxes become active.


Plot versus:

Select the residual plot you want to generate.


Fitted Line

Select how the fitted line will be drawn.

None

Appears without the fitted line.

Using Quartiles

The fitted line is drawn through the median at 0.5 with the slope determined by the quartiles.  This option is the default.

Using Least Squares

The line is fitted using least squares regression.


Number of Lags

Enter the maximum lag for which the autocorrelation values should be calculated.  Typically, the number of lags should not exceed the number of observations divided by 4.  Enter any integer.


Save Results Dialog Box for the Comparison of Regression Lines Analysis
Save Results Dialog Box (Comparison of Regression Lines)

The Save Results Options dialog box allows you to select the results you want to save.  There are 13 selections:  Predicted Values, Standard Errors of Predictions, Lower Limits for Predictions, Upper Limits for Predictions, Standard Errors of Means, Lower Limits for Forecast Means, Upper Limits for Forecast Means, Residuals, Studentized Residuals, Leverages, DFITS Statistics, Mahalanobis Distances, and Coefficients.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results Options button on the Analysis toolbar (the fourth button from the left).


Regression Model Selection Dialog Box

The Regression Model Selection analysis ranks the best subsets of the explanatory variables, based on the criterion you enter in the Regression Model Selection analysis dialog box, calculates the statistics for all possible linear regression models, and sorts the values so you can choose the “best” model.

After you decide upon and thoroughly check the final regression model, you should validate it using the Multiple Regression analysis to examine the relationship between the dependent variable and the final set of independent variables.

Note:  While the Regression Model Selection analysis is a useful tool for exploratory model-building, you cannot rely on any one statistical test to identify a “true” model.  Remember that using the values of the Cp and R-Squared statistics to select variables has long been a subject of controversy in statistical literature.

Dependent Variable

Independent Variables

Select

Weights

Sort

Delete...

Transform...

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Regression Model Selection Analysis

Regression Model Selection Options

Best Adjusted R-Squared Options

Best Cp Options

Adjusted R-Squared Plot Options

Mallows’ Cp Plot Options

MSE Plot Options

R-Squared Plot Options


Dependent Variable

Enter the name of the dependent or response variable (Y).  Enter a numeric variable.


Independent Variables

Enter the names of one or more numeric independent variables (X), whose subsets will be ranked according to the values of the Adjusted R-Squared and Cp statistics.


Select

Select a subset of the observations.  For example, to use the first 50 values in each variable, enter first (50) in this text box.


Weights

Enter the name of a variable that contains the values the program will apply to the residuals when it estimates the model statistics.  The type of variable you enter must be numeric, which will result in a least squares regression.


Sort

Indicate if you want the variables sorted alphabetically.  This option is the default.


Analysis Summary (Regression Model Selection)

The Analysis Summary tabular option displays statistics you can use to compare various multiple regression models with the dependent variable and the subsets of the independent (predictor) variables.

It also provides a key for the labels on all the tables and graphs; for example, A = Variable1, B = Variable2, and so on.  Statistics in the table include values for the Mean Squared Error (MSE), R-Squared, Adjusted R-Squared, Mallows' Cp, and a model identifier for each of the subsets of variables.

Better models have low MSE values, low Mallows' Cp values (close to p — the number of coefficients in the model, including the constant), and high Adjusted R-Squared values.  The models are sorted by the number of variables.  The Adjusted R-Squared statistic measures the proportion of variability in the independent variable for which the model is accountable.  This statistic is useful for comparing regression models that have different numbers of independent variables.


Regression Model Selection Options Dialog Box

Enter a number that will be used to limit the number of subsets that will be ranked.  You do this by placing restrictions on the number of independent variables in the smallest and largest models.

Number of Variables in Model


Number of Variables in Model

Limit the number of subsets that will be ranked by placing restrictions on the number of independent variables in the smallest and largest models.

Minimum

Enter a number that will be used as the minimum size for any subset; that is, it will list no models that have less than this number of variables.  For example, if there are 10 independent variables and you enter 3 in this text box, the program will not list any one- or two-variable models.  The number must be less than or equal to the number you enter in the Maximum text box.

Maximum

Enter a number that will be used as the maximum size for any subset; that is, no models will be listed that have more than this number of variables.

For example, if there are 15 independent variables and you enter 4, no five-, six-, seven, ..., fifteen-variable models will be listed.  The number you enter must be greater than or equal to the number you enter in the Minimum text box.


Best Adjusted R-Squared (Regression Model Selection)

The Best Adjusted R-Squared tabular option lists the models that give the largest Adjusted R-Squared values.  The table lists the models in order of decreasing value, which places the “best” models near the top of the list.

The Adjusted R-Squared statistic measures the proportion of variability in the dependent variable for which the model is accountable.  Larger values of the Adjusted R-Squared statistic correspond to smaller values of the Mean Squared Error (MSE).


Best Adjusted R-Squared Options Dialog Box

Allows you to enter a number that will determine the maximum number of models that will be listed for each subset size.

For example, if you enter the names of 10 independent variables, then enter 3, the three “best” models for each subset size will not be listed — three with nine variables, three with eight variables, and so on.


Best Cp (Regression Model Selection)

The Best Cp tabular option displays the models that have the smallest values of the Mallows' Cp statistic.  Cp is a measure of the bias in the model based on a comparison of total Mean Squared Error to the true error variance.

Unbiased models have an expected Cp value of approximately p, where p is the number of coefficients in the fitted model.  Cp is based on the assumption that the model that contains all the candidate variables is unbiased; therefore, the full model will always have Cp = p.  Look for models that have Cp values close to p.

The models are listed in order of increasing values, which places the best models near the top of the list.  For more information, see Mallows (1973, 1995).


Best Cp Options Dialog Box

Enter a number that will determine the maximum number of models that will be shown per subset size.


Regression Model Selection Graphical Options Dialog Box

The Regression Model Selection Graphical Options dialog box allows you to select graphical options for the analysis.

Note:  To access the Options dialog boxes, click the right mouse button on the graphic pane, then click the left on either Pane Options or Analysis Options.

Adjusted R-Squared Plot (Regression Model Selection)

Mallows' Cp Plot (Regression Model Selection)

MSE Plot (Regression Model Selection)

R-Squared Plot (Regression Model Selection)


Adjusted R-Squared Plot (Regression Model Selection)

The Adjusted R-Squared Plot graphical option displays a plot of the Adjusted R-Squared values for each model plotted against the value of p (the number of independent variables, plus one).  A line connects each number of coefficients with the models that have the highest values of the Adjusted R-Squared statistic.


Adjusted R-Squared Plot Options Dialog Box

Allows you to:

•	indicate if you want the points on the plot labeled with the names of the models according to the key in the Analysis Summary — A, AB, and so on

•	enter a number that determines the maximum number of models that will be shown per subset size.

Label Models

Indicate if you want the points on the plot labeled with the names of the models.  This option is the default.

Maximum Number per Subset

Enter a value that will be used to determine the maximum number of models that will be shown in each subset size.  The default is 5.


Mallows' Cp Plot (Regression Model Selection)

The Mallows' Cp Plot graphical option displays the Cp statistic for each model plotted with the number of coefficients in the model.

A reference line is drawn for Cp = p.  Cp is a measure of the bias in the model, based on a comparison of the total Mean Squared Error with the true error variance, and assumes that the full model is unbiased.

Unbiased models have an expected value of approximately p, where p is the number of coefficients in the fitted model.  Look for models that have Cp values close to p.  Unbiased models should be close to the line on the plot; the full model will always have Cp = p.  Mallows (1995) warns that for some cases, “picking the minimum Cp subset and fitting by least squares will not give a good prediction formula.”  If necessary, you can rescale the Cp axis to get a better view.


Mallows' Cp Plot Options Dialog Box

Allows you to:

•	indicate if you want the points on the plot labeled with the names of the models

•	enter a number that determines the maximum number of models that will be shown per subset size.

Label Models

Indicate if you want the points on the plot labeled with the names of the models.  This option is the default.

Maximum Number per Subset

Enter a value that will be used to determine the maximum number of models that will be shown in each subset size.  The default is 5.


MSE Plot (Regression Model Selection)

The MSE Plot graphical option displays the Mean Squared Error (MSE) for each model plotted with the number of coefficients in the model.  A line connects each number of coefficients with the models that have the smallest values of MSE.  When the line levels off, little is gained by adding variables to the model.


MSE Plot Options Dialog Box

Allows you to:

•	indicate if you want the points on the plot labeled with the names of the models

•	enter a number that determines the maximum number of models that will be shown per subset size.

Label Models

Indicate if you want the points on the plot labeled with the names of the models.   This option is the default.

Maximum Number per Subset

Enter a value that will be used to determine the maximum number of models that will be shown in each subset size.  The default is 5.


R-Squared Plot (Regression Model Selection)

The R-Squared Plot graphical option displays the value of the R-Squared statistic for each model plotted with the number of coefficients.  A line connects each number of coefficients with the models that have the largest R-Squared values.  When the line levels off, little is gained by adding variables to the model.


R-Squared Plot Options Dialog Box

Allows you to:

•	indicate if you want the points on the plot labeled with the names of the models

•	enter a number that determines the maximum number of models that will be shown in each subset size.

Label Models

Indicate if you want the points on the plot labeled with the names of the models.

Maximum Number per Subset

Enter a value that will be used to determine the maximum number of models that will be shown in each subset size.  The default is 5.


Save Results Options Dialog Box (Regression Model Selection)

The Save Results Options dialog box allows you to select the results you want to save.  There are five selections:  Model Identifiers, Adjusted R-Squared, Cp, MSE, and R-Squared.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Maximum Number per Subset

Enter a value that will determine the maximum number of models that will be shown in each subset size.  The default is 5.


Maximum Number per Subset

Allows you to indicate if the points on the plot should be labeled with the names of the models.


Label Models

Allows you to indicate if the points on the plot should be labeled with the names of the models.


Maximum Number per Subset

Indicate if the points on the plot should be labeled with the names of the models.


Regression Model Selection Tabular Options Dialog Box

This dialog box allows you to select tabular options for the analysis.

Note:  To access the Options dialog boxes, click the right mouse button on the text pane, then click the left on either Pane Options or Analysis Options.

Analysis Summary (Regression Model Selection)

Best Adjusted R-Squared (Regression Model Selection)

Best Cp (Regression Model Selection)


Nonlinear Regression Analysis Dialog Box

In STATGRAPHICS Plus, you first define the function that will be used to fit the data.  Then you select an iterative search algorithm to determine the estimates that minimize the residual sum of squares.

The methods are: Marquardt, Gauss-Newton, and Steepest Descent.  All three require you to supply initial values for the estimates of the parameters; see Draper and Smith (1981), Neter et al. (1996), and Myers (1990).  Because the method depends on these initial parameters, you should take time to develop reasonable initial estimates.

One caution regarding the initial estimates is that the model may converge to a local minimum instead of a global minimum.  To partially guard against this situation, you can perform the analysis several times using widely differing initial estimates.  Sometimes you can obtain initial estimates from estimates for a linearized form of the regression equation, or by using your own observations.  Either way, remember that different starting values can result in very different estimates for the parameters.

Estimation also sometimes fails to converge due to misplaced parentheses or other errors in the functions.  At other times, adjusting the convergence control details will help, however, there will be cases when function estimation fails because the search algorithm simply does not converge on a solution because it is not completely foolproof.

Dependent Variable

Function

Weights

Select

Sort

Delete...

Transform...

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Nonlinear Regression Analysis

Nonlinear Regression Options

Reports Options

Plot of Fitted Model Options

Response Plot Options

Residual Plots Options


Dependent Variable

Enter the name of the numeric dependent (response) variable.


Function

Enter an expression that will be used as the function that will be estimated.

You can enter the function in any of three ways:  (1) type the expression in the Function text box, (2) use the Transform… command to create a function expression (click the Transform... button), or (3) enter the name of the character variable that contains the expression.

Any variable name that is not included in the file is taken as a parameter that the program will estimate.

You have to provide a reasonable starting value for every parameter for which the program must provide an estimate (see the entry for the Initial Parameter Estimates Dialog Box).  You can include up to 12 unknowns or parameters in the function.


Weights

Enter the name of a variable that contains the values that will be applied to the residuals when the model coefficients are estimated.  The variable you enter must be numeric, which will result in a weighted least squares nonlinear regression.


Select

Select a subset of observations.  For example, to analyze the first 50 values in each variable, enter first (50) in this text box.  Or you can use this text box to select the observations the program will use to estimate the model.  The program uses the remaining complete observations (those that you do not select) to validate the model.  The validation and estimation results appear in the Residual Analysis table at the end of the Analysis Summary.


Sort

Indicate if the variables should be sorted alphabetically.  The default is sorted variables.


Initial Parameter Estimates Dialog Box

Enter the starting values for each parameter you want to estimate (each text box is labeled with the name of a parameter in the function expression).  Enter a single, reasonable, numeric starting value for each parameter.  The default values are not intended to serve as suggested values.


Nonlinear Regression Analysis Tabular Options Dialog Box

This dialog box allows you to select tabular options for the analysis.

Note:  To access the Options dialog boxes, click the right mouse button on the text pane, then click the left on either Pane Options or Analysis Options.

Analysis Summary (Nonlinear Regression)

Correlation Matrix (Nonlinear Regression)

Reports (Nonlinear Regression)

Unusual Residuals (Nonlinear Regression)

Influential Points (Nonlinear Regression)


Analysis Summary (Nonlinear Regression)

The Analysis Summary tabular option shows the results of fitting a nonlinear regression model that describes the relationship between the dependent variable and the estimated function.  Also shown is the number of iterations performed before reaching the minimum residual sum of squares. The StatAdvisor includes the equation for the fitted model.

The statistics include the following:

1.	The R-Squared statistic is shown, but it may not be meaningful for a linear model.

2. 	The Adjusted R-Squared statistic is used to compare models that have different numbers of independent variables.

3.	The Standard Error of the Estimate shows the standard deviation of the residuals.

4.	The Mean Absolute Error (MAE) is the average value of the residuals.

5.	The Durbin-Watson statistic tests the order of the residuals as they occur in the file.  If the Durbin-Watson statistic is greater than 1.4, there is probably no serious autocorrelation in the residuals.

6.	The values for the asymptotic confidence intervals are shown for each of the unknown parameters.  The intervals are approximate and most accurate for large sample sizes.  A value of 0.0 in each interval indicates whether or not an estimate is statistically significant.  Intervals that cover 0.0 correspond to coefficients that could be removed from the model without substantially affecting the fit.

If you used the optional Select text box on the Nonlinear Regression Analysis dialog box, the prediction error statistics are used to validate the accuracy of the model and displays the Residuals Table at the end of the Analysis Summary.  If you decide to validate the model, see the Advanced Regression User Manual and use one of the methods discussed in the section, “Understanding Advanced Regression,” in Chapter 1, Getting Started.

The Residuals Table includes values for the following statistics for the validation and estimation data:

1.	n —  the number of observations.

2.	MSE (Mean Square Error) — a measure of accuracy computed by squaring the individual error for each item in the data, then finding the average or mean value of the sum of those squares.  If the result is a small value, you can predict performance more accurately; if the result is a large value, you may want to use a different model.

3.	MAE (Mean Absolute Error) — the average of the absolute values of the residuals; appropriate for linear and symmetric data.  If the result is a small value, you can predict performance more accurately; if the result is a large value, you may want to use a different model.

4.	MAPE (Mean Absolute Percentage Error) — the mean or average of the sum of all the percentage errors for a given set of data without regard to sign (that is, their absolute values are summed and the average is computed).  Unlike the ME, MSE, and MAE, the size of the MAPE is independent of scale.

5.	ME (Mean Error) — the average of the residuals.  The closer the ME is to 0, the less biased, or more accurate, the prediction.

6.	MPE (Mean Percentage Error) — the average of the absolute values of the residuals divided by the corresponding estimates.  Like MAPE, it is independent of scale.


Nonlinear Regression Options Dialog Box

Allows you to enter a value for the stopping criterion, maximum iterations, maximum function calls, and the confidence level.

You also can select the method that will be used.  If you select the Marquardt method, you can enter the initial value, the scaling factor, and the maximum value.

See the Advanced Regression User Manual, Appendix B, Calculations, for more information.

Estimation

Method

Marquardt Parameter

Confidence Level (for Probability Limits)


Estimation

Enter the values that will be used to control the various estimation algorithms.

Stopping Criterion 1

Enter a number that will stop the estimation; that is the estimation stops when this value is less than the values (as a proportion) for the residual sum of squares.  The default is 1E-5.

Stopping Criterion 2

Enter a number that will stop the estimation; that is, the estimation stops when this value is less than the estimated valuess (as a proportion) for all the unknown parameters.  The default is 1E-4.

Maximum Iterations

Enter a number that will stop the iterations, based on iterations.  That is, if Stopping Criterion 1 or 2 do not stop the estimation, the estimation stops when this number of iterations is exceeded.  The default is 30.

Maximum Function Calls

Enter a number that will stop the iterations, based on function calls.  That is, the estimation stops when it exceeds this number.  The default is 200.

Confidence Level

Enter a value for the levels of the probability limits for the autocorrelations.  Enter a number greater than 0 and less than 100.  Common levels are 90, 95, or 99 percent; 95 percent is the default.


Method

Select the method that will be used to estimate the parameters.

Marquardt

Selects the Marquardt method, which utilizes the best features of the other two methods:  Gauss-Newton and Steepest Descent; that is, it provides a “middle ground” between these two methods. This option is the default.

Gauss-Newton

Selects the Gauss-Newton method, which uses a Taylor series expansion to approximate the model with linear terms and then uses ordinary least squares to estimate the parameters.

Steepest Descent

Selects the Steepest Descent method, which searches for the minimum least squares criterion measure by iteratively determining the direction in which the regression coefficients should be changed.  This method is particularly effective when the initial values are not “good”; that is, they are far from the final values.


Marquardt Parameter

Enter the values that will control the Marquardt search.

Initial Value

Enter a number that will be used as the initial value for the Marquardt parameter.  The default is 1E-2.

Scaling Factor

Enter a number that will be used to increase or decrease the Marquardt parameter during the estimation process.  The default is 20.

Maximum Value

Enter a number that will stop the estimation.  That is, the estimation stops when it exceeds this number.  The default is 120.


Correlation Matrix (Nonlinear Regression)

The Correlation Matrix tabular option displays the estimated correlations between the coefficients in the fitted model.  You can use the correlations to detect the presence of serious multicollinearity; that is, to see if there is correlation among the explanatory variables.


Reports (Nonlinear Regression)

The Reports tabular option displays information about the results generated for the regression using the current parameter, depending on your selections on the Reports Options dialog box.  Each item corresponds to the values of the independent variables in a specific row of the file.

To create forecasts (predictions) for additional combinations of values for the variables, add additional rows to the bottom of the file.  In each new row, enter values for the independent variables but leave the cell for the dependent variable empty.  The predicted values for the new rows are added to the table, but the model is left unchanged.


Standard Errors for Forecasts

Includes the values for the standard error for each predicted value.


Confidence Limits for Individual Forecasts

Includes the values for the confidence limits for new observations.


Confidence Limits for Forecast Means

Includes the values for the confidence limits for the mean response.


Unusual Residuals (Nonlinear Regression)

The Unusual Residuals tabular option lists all the observations that have unusually large studentized residuals greater than 2.0 in absolute value.  Studentized residuals measure the number of standard deviations each observed value deviates from the model fitting using all the data except that observation.


Influential Points (Nonlinear Regression)

The Influential Points tabular option identifies all the observations that have leverage values greater than three times that of an average point, or that have unusually large DFITS or Cook's distance values.

The leverage statistic helps determine the coefficients of the estimated model by measuring the amount of influence that can be attributed to each observation.  The DFITS statistic measures the amount of change for each estimated coefficient if the observation is removed from the data.  Cook's distance measures the distance between the estimated coefficients with and without each observation.


Nonlinear Regression Analysis Graphical Options Dialog Box

This dialog box allows you to select graphical options for the analysis.

Note:  The two separate options for Response Surface Plots allow you to create two different views and display them both at once.  Also, if you want to produce Response Surface Plots, you must include at least two variable names in the function you enter on the Nonlinear Regression Analysis dialog box.

Note:  To access the Options dialog boxes, click the right mouse button on the graphics pane, then click the left on either Pane Options or Analysis Options.

Plot of Fitted Model (Nonlinear Regression)

Response Surface Plots (Nonlinear Regression)

Observed versus Predicted Plot (Nonlinear Regression)

Residual Plots (Nonlinear Regression)


Plot of Fitted Model (Nonlinear Regression)

The Plot of Fitted Model graphical option displays a plot of the fitted function versus the selected independent variable.  A line is drawn over the range of the selected independent variable (X).  If there is only one independent variable, the values of the points are plotted.

Other independent variables are held constant at the levels shown in the legend on the plot.  You can change the levels of the other variables or change the variable shown on the X-axis by using the Plot of Fitted Model Options dialog box.


Plot of Fitted Model Options Dialog Box

Select a variable to plot against the fitted model, to change the limits for that variable, and select a level at which to hold all of the other variables.

[variable]

Low

High

Hold


Low

Enter a number for the lower limit of the variable you select.  Enter a number less than the number in the High text box.  The default is based on the values in the variable.


High

Enter a number for the upper limit for the variable you select.  Enter a number greater than the number in the Low text box.  The default is based on the values in the variable.


Hold

Enter a number that will be used as the level at which to hold the variables not selected for the plot.  The default is based on the values in the variable.


Response Surface Plots (Nonlinear Regression)

The Response Surface Plots graphical option allows you to select one of four types of plots:  Surface, Contour, Square, or Cube.  The Square plot is available if you have two or more variables in the function; the Cube Plot is available when you have at least three variables in the function.

Note:  The two separate options for Response Surface Plots allow you to create two different plots and display the two views at once; for example, you can create both a Surface plot and a Contour plot of the same data.


Response Plot Options Dialog Box

Select the type of plot, the settings for Contour and Surface plots, and access the Plot of Fitted Model Options dialog box, which allows you to select another variable.

Type (of Response Plot)

Contours

Resolution

Surface

Factors... Command


Type

Select the type of plot you want to create and display:  Surface, Contour, Square, or Cube.

Surface

Displays a Surface plot, which is a three-dimensional model of the relationship between the estimated dependent variable as a function of the other variables.  The height of the surface represents the value of the estimated dependent variable.

When you select this option, the Resolution and Surface options portions of the dialog box become active, which allows you to customize the plot.  You can also access the Plot of Fitted Model Options dialog box by clicking the Factors... command button.  The Factors command allows you to select another variable to plot against, to change the limits for that variable, and to select a level at which to hold all of the other variables.

To spin (rotate) the plot, click the Smooth/Rotate button on the Analysis toolbar.

Contour

Displays a Contour plot, which is a two-dimensional plot that traces the contours of the estimated dependent variable as a function of the other variables.  Each contour line represents combinations of the independent variables, which have a selected value for the estimated dependent variable.  You can predict the next value for the dependent variable by following the ridge of the contour.

When you select this option, the Contours and Resolution options portions of the dialog box become active, which allows you to customize the plot. You can also access the Plot of Fitted Model Options dialog box by clicking the Factors... command button.  The Factors command allows you to select another variable to plot against, to change the limits for that variable, and to select a level at which to hold all of the other variables.

Square

Displays a Square Plot for the observed values of the dependent variable versus the values predicted by the fitted model.  For each independent variable you select, the values for the dependent variable, including all combinations of the high and low values, are plotted.  Points close to the diagonal line are those that best predict the observed data.

You can also access the Plot of Fitted Model Options dialog box by clicking the Factors... command button.  The Factors command allows you to select a variable to plot, to change the limits for that variable, and to select levels at which to hold all of the other variables

Cube

Displays a Cube Plot of the estimated effects for three factors.  For each factor you select, the values for the response variable, including all combinations of the high and low values, are plotted.  Use the Factors... command button to select the factors and to specify the high and low values.


Surface

Displays a Surface plot, which is a three-dimensional model of the relationship between the estimated dependent variable as a function of the other variables.  The height of the surface represents the value of the estimated dependent variable.

When you select this option, the Resolution and Surface options portions of the dialog box become active, which allows you to customize the plot.  You can also access the Plot of Fitted Model Options dialog box by clicking the Factors... command button.  The Factors command allows you to select another variable to plot against, to change the limits for that variable, and to select a level at which to hold all of the other variables.

To view the plot from a different angle, click the Smooth/Rotate button on the Analysis toolbar.


Contour

Displays a Contour plot, which is a two-dimensional plot that traces the contours of the estimated dependent variable as a function of the other variables.  Each contour line represents combinations of the independent variables, which have a selected value for the estimated dependent variable.  You can predict the next value for the dependent variable by following the ridge of the contour.

When you select this option, the Contours and Resolution options portions of the dialog box become active, which allows you to customize the plot. You can also access the Plot of Fitted Model Options dialog box by clicking the Factors... command button.  The Factors command allows you to select another variable to plot against, to change the limits for that variable, and to select a level at which to hold all of the other variables.


Square

Displays a Square Plot for the observed values of the dependent variable versus the values predicted by the fitted model.  For each independent variable you select, the values for the dependent variable, including all combinations of the high and low values, are plotted.  Points close to the diagonal line are those that best predict the observed data.

You can also access the Plot of Fitted Model Options dialog box by clicking the Factors... command button.  The Factors command allows you to select a variable to plot, to change the limits for that variable, and to select levels at which to hold all of the other variables


Cube

Displays a Cube Plot of the estimated effects for three factors.  For each factor you select, the values for the response variable, including all combinations of the high and low values, are plotted.  Use the Factors... command button to select the factors and to specify the high and low values.


Contours

Select the attributes for the contours on the Contour Plot or for contours that you want to place below a Surface Plot.

From

Enter a number that will determine the first contour line.  Enter a number less than the number in the To text box.  The default is based on the values in the variables.

To

Enter a number that will determine the last contour line.  Enter a number greater than the number in the From text box.  The default is based on the values in the variables.

By

Enter a number that will determine the space of the contour lines.  This number is used with the numbers from the From and To text boxes to determine the levels of the contours.

Lines

Indicate if lines should connect the points along each contour.  This option is the default.

Painted Regions

Indicate if painted (filled-in) regions should appear in the contours.


From

Enter a number that will determine the first contour line.  Enter a number less than the number in the To text box.  The default is based on the values in the variables.


To

Enter a number that will determine the last contour line.  Enter a number greater than the number in the From text box.  The default is based on the values in the variables.


By

Enter a number that will determine the spacing of the contour lines.  This number is used with the numbers from the From and To text boxes to determine the levels of the contours.


Lines

Indicate if lines should connect the points along each contour.


Painted Regions

Indicate if painted (filled-in) regions should appear in the contours.


Resolution

Enter a value that designates the number of density values you want to calculate.  Enter a number between 1 and 100; the default is 21.


Surface

Select specific attributes for a Surface Plot.

Horizontal Division

Enter a value that indicates the number of horizontal lines you want to include on the plot.  Enter a positive integer.  The default is 10.

Vertical Division

Enter a value that indicates the number of vertical lines you want to appear on the plot.  Enter a positive integer.  The default is 10.

Contours Below

Indicate if you want to display a Contour Plot below the Surface Plot.

Show Points

Indicate if values for the points should display on the plot.  This choice is available only when you select a wire frame Surface Plot.

Wire Frame

Indicate if only horizontal and vertical lines should appear on the Surface Plot.

Solid

Indicate if a solid Surface Plot should display.

Contoured

Indicate if a topographical representation of a Surface Plot should appear, with colors corresponding to the height of the surface.


Horizontal Division

Enter a value that indicates the number of horizontal lines that should appear on the plot.  Enter a positive integer.  The default is 10.


Vertical Division

Enter a value that indicates the number of vertical lines that should appear on the plot.  Enter a positive integer.  The default is 10.


Contours Below

Indicate if a Contour Plot should display below the Surface Plot.


Show Points

Indicate if the values for the points on the plot should be displayed.  This choice is available only when you select a wire frame Surface Plot.


Wire Frame

Indicate if only horizontal and vertical lines should appear on the Surface Plot.


Solid

Indicate if you want to display a solid Surface Plot.


Contoured

Indicate if you want to display a topographical representation of a Surface Plot, with colors corresponding to the height of the surface.


Factors... Command Button
Factors... Command

Displays the Plot of Fitted Model Options dialog box, which allows you to select a variable to plot, to change the limits for that variable, and to select a level at which to hold all the other variables.


Observed versus Predicted Plot (Nonlinear Regression)

The Observed versus Predicted graphical option displays a plot of the observed values (Y) versus the values predicted by the fitted model.  The plot includes a line with slope equal to one. Points close to the diagonal line are those that best predict the observed data.

Use the plot to determine cases in which the variance is not constant, which indicates that you should probably transform the values for the dependent variable.


Residual Plots (Nonlinear Regression)

The Residual Plots graphical option includes the following:  Scatterplots (Residuals versus Predicted, Residuals versus Row Number, and Residuals versus X); Normal Probability Plot, and Autocorrelation Function.


Residuals

Plots the differences between the observed and the fitted values.


Studentized Residuals

Plots the residuals, scaled by an estimate of the variance from the data with the observation removed.  A large studentized residual value may indicate an outlier and an influential observation.  This option is the default.


Type (of Plot - Calibration Models)

Select the plot you want to display.

Scatterplot

Displays a Scatterplot of the residuals.  When you select this option, the Plot versus: list box becomes active, allowing you to select a specific residual plot.  This option is the default.

Residuals versus Predicted

Displays the residuals or the studentized residuals versus the predicted values for the observed variable (Y).  A nonrandom pattern indicates that the model you selected does not adequately describe the observed data.  The plot is helpful in showing heteroscedasticity; an indication of the variability of the changes in the residuals as the values of the dependent variable change.

Residuals versus Row Number

Displays the residuals or the studentized residuals versus the row number.  The program residuals are plotted in the order that the observations appear in the dependent variable.  The plot is helpful in determining sequential correlations among the residuals.  Any nonrandom pattern indicates serial correlation in the data, particularly if the row order corresponds to the order in which the data were collected.

Residuals versus X (where X indicates the name of each independent X variable)

Displays the residuals or studentized residuals versus the independent variable (X), where X equals the name of the independent variable you selected.  Use this plot to detect the nonlinear relationship between the dependent and independent variables.  You can also use the plot to determine if the variance of the residuals is constant.  Nonrandom patterns indicate that the model you selected does not adequately describe the data.  Any studentized residual values outside the range of -3 to +3 might be outliers.

Normal Probability Plot

Displays the residuals used to determine if the data follow a normal distribution.  A Normal Probability Plot consists of an arithmetic (interval) horizontal axis scaled for the data and a vertical axis scaled so the cumulative distribution function of a normal distribution plots as a straight line.  The closer the data are to the reference line, the more likely they follow a normal distribution.  When you select this option, the Direction and Fitter Line options become active.

Autocorrelation Function

Displays a graph of the autocorrelation estimates for the residuals.  The plot contains a pair of dotted lines and vertical bars that represent the coefficient for each lag.  The distance from the baseline is a multiple of the standard error at each lag.  Significant autocorrelations extend above or below the confidence limits.  When you select this option, the Number of Lags and Confidence Level text boxes become active.


Scatterplot
Scatterplot (Nonlinear Regression)

Displays a Scatterplot of the residuals.  When you select this option, the Plot versus: list box becomes active, allowing you to select a specific residual plot.

Residuals versus Predicted Plot (Nonlinear Regression Analysis)

Residuals versus Row Number Plot (Nonlinear Regression)

Residuals versus X Plot (Nonlinear Regression)


Residuals versus Predicted Plot (Nonlinear Regression Analysis)

Displays the residuals or the studentized residuals versus the predicted values for the observed variable (Y).  A nonrandom pattern indicates that the model you selected does not adequately describe the observed data.

The plot is helpful in showing heteroscedasticity; an indication of the variability of the changes in the residuals as the values of the dependent variable change.


Residuals versus Row Number Plot
Residuals versus Row Number Plot (Nonlinear Regression)

Displays the residuals or the studentized residuals versus the row number.  The residuals are plotted in the order that the observations appear in the dependent variable.


Residuals versus X Plot
Residuals versus X Plot (Nonlinear Regression)

Displays the residuals or studentized residuals versus the independent variable (X).

Use this plot to detect the nonlinear relationship between the dependent and independent variables.  You can also use the plot to determine if the variance of the residuals is constant.

Any nonrandom pattern indicates that the model you selected does not adequately describe the data.  Any studentized residual values outside the range of -3 to +3 might be outliers.


Normal Probability Plot
Normal Probability Plot (Nonlinear Regression)

Displays the residuals used to determine if the data follow a normal distribution.

A Normal Probability Plot consists of an arithmetic (interval) horizontal axis scaled for the data and a vertical axis scaled so the cumulative distribution function of a normal distribution plots as a straight line.  The closer the data are to the reference line, the more likely they follow a normal distribution.

When you select this option, the Direction and Fitted Line options become active.


Autocorrelation Function Plot
Autocorrelation Function Plot (Nonlinear Regression)

Displays a graph of the autocorrelation estimates for the residuals.  The plot contains a pair of dotted lines and vertical bars that represent the coefficient for each lag.  The distance from the baseline is a multiple of the standard error at each lag.

Significant autocorrelations extend above or below the confidence limits.  When you select this option, the Number of Lags and Confidence Level text boxes become active.


Plot versus:

Select the residual plot you want to generate.


Horizontal

Scales the residuals on the X-axis.


Vertical

Scales the residuals on the X-axis.


Fitted Line

Determines how the fitted line will be drawn.

None

The plot will appear without the fitted line.

Using Quartiles

The fitted line is drawn through the median at 0.5 with the slope determined by the quartiles.  This option is the default.

Using Least Squares

The line is fitted using least squares regression.


None

The plot will appear without the fitted line.


Using Quartiles

The fitted line is drawn through the median at 0.5 with the slope determined by the quartiles.  This option is the default.


Using Least Squares

The line is fitted using least squares regression.


Save Results Options Dialog Box
Save Results Options Dialog Box (Nonlinear Regression)

The Save Results Options dialog box allows you to select the results you want to save.  There are 14 selections:  Predicted Values, Standard Errors of Predictions, Lower Limits for Predictions, Upper Limits for Predictions, Standard Error of Means, Lower Limits for Forecast Means, Upper Limits for Forecast Means, Residuals, Studentized Residuals, Leverages, DFITS Statistics, Mahalanobis Distances, Coefficients, and Function.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Options Dialog Box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Number of Lags

Enter the maximum lag for estimating the autocorrelation values.  Typically, the number of lags should not exceed the number of observations divided by 4.  Enter any integer.


Reports Options Dialog Box

Select the values that will be included in the report.

Include


Residuals versus Level Codes Plot
Residuals versus Level Codes Plot (Nonlinear Regression)

Displays the residuals or the studentized residuals versus the level codes.  A nonrandom pattern indicates that the model you selected does not adequately describe the observed data.  Any values of studentized residuals outside the range of -3 to +3 might be outliers.


Ridge Regression Analysis Dialog Box

The Ridge Regression Analysis allows you to modify the least squares method to estimate the multiple regression model using slightly modified normal equations (see the Advanced Regression User Manual, Appendix B, Calculations).  The estimates that result are often more precise than those that result when you use ordinary least squares and, in the case of correlated independent variables, may be closer to the “true value” of the parameter.

The analysis provides tools for selecting a value for theta (the ridge parameter), which controls the extent of the bias that is introduced.  When theta equals zero, the estimates that result are the same as those for least squares.  As theta increases, but usually remains less than one, bias increases; however, the coefficients usually become more precise.  Ordinarily, an appropriate value for theta is the smallest value that occurs before the estimates begin to slowly change.

Dependent Variable

Independent Variable

Select

Weights

Sort

Delete...

Transform...

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Ridge Regression Analysis

Ridge Regression Options

Reports Options

Ridge Trace Options

Residual Plots Options


Dependent Variable

Enter the name of the dependent variable.  You must enter a variable that has numeric values.


Independent Variable

Enter the names of the independent variables.  You must enter variables that have numeric values.


Select

Select a subset of observations.  For example, to analyze the first 50 values in each variable, enter first (50) in this text box.  Or you can use this text box to select the observations that will be used to estimate the model.  The remaining complete observations (those that you do not select) are used to validate the model.  The validation and estimation results appear in the Residual Analysis table at the end of the Analysis Summary.


Weights

Enter the name of the variable that contains the values that will be applied to the residuals when the model coefficients are estimated.  The variable must be numeric, which will result in a weighted least squares ridge regression.


Sort

Indicate if the variables should be sorted alphabetically.  This option is the default.


Ridge Regression AnalysisTabular Options Dialog Box

This dialog box allows you to select tabular options for the analysis.

Note:  To access the Options dialog boxes, click the right mouse button on the text pane, then click the left on either Pane Options or Analysis Options.

Analysis Summary (Ridge Regression)

Regression Coefficients (Ridge Regression)

Standardized Regression Coefficients (Ridge Regression)

Variance Inflation Factors Plot (Ridge Regression)

Reports (Ridge Regression)


Analysis Summary (Ridge Regression)

The Analysis Summary tabular option shows the results for the current value of the ridge parameter.  By allowing for a small amount of bias, the precision of the estimates is greatly increased.  The summary shows the current value of the ridge parameter to be 0.0, which is equivalent to ordinary least squares.

Use the Ridge Regression Options dialog box to change the value for the ridge parameter.  The value is usually between 0 and 1.0.  To determine a good value, examine the standardized regression coefficients or the variance inflation factors.

1.	The R-Squared Statistic.  This statistic indicates the percentage of variability the dependent variable accounts for as it was fitted in the model.

2.	The Adjusted R-Squared Statistic.  This statistic is more suitable for comparing models that have different numbers of independent variables; it indicates the percentage of variability represented by the model.

3.	The Standard Error of the Estimate Statistic.  This statistic shows the value for the standard deviation of the residuals.

4.	The Mean Absolute Error (MAE) Statistic.  This statistic is the average absolute value of the residuals.

5.	The Durbin-Watson Statistic.  This statistic tests the order of the residuals as they occur in the file.  If the Durbin-Watson statistic is greater than 1.4, there is probably no serious autocorrelation in the residuals.

If you used the optional Select text box on the Ridge Regression Analysis dialog box, the prediction error statistics are used to validate the accuracy of the model and displays the Residuals Table at the end of the Analysis Summary.  If you decide to validate the model, see the Advanced Regression User Manual and use one of the methods discussed in the section, “Understanding Advanced Regression” in Chapter 1, Getting Started.

The Residuals Table includes values for the following statistics for the validation and estimation data:

1.	n — the number of observations.

2.	MSE (Mean Square Error) — a measure of accuracy computed by squaring the individual error for each item in the data, then finding the average or mean value of the sum of those squares.  If the result is a small value, you can predict performance more accurately; if the result is a large value, you may want to use a different model.

3.	MAE (Mean Absolute Error) — the average of the absolute values of the residuals; appropriate for linear and symmetric data.  If the result is a small value, you can predict performance more accurately; if the result is a large value, you may want to use a different model.

4.	MAPE (Mean Absolute Percentage Error) — the mean or average of the sum of all the percentage errors for a given set of data without regard to sign (that is, their absolute values are summed and the average is computed).  Unlike the ME, MSE, and MAE, the size of the MAPE is independent of scale.

5.	ME (Mean Error) — the average of the residuals.  The closer the ME is to 0, the less biased, or more accurate, the prediction.

6.	MPE (Mean Percentage Error) — the average of the absolute values of the residuals divided by the corresponding estimates.  Like MAPE, it is independent of scale.


Ridge Regression Options Dialog Box

Select attributes for the ridge parameter.

Ridge Parameter


Ridge Parameter

Enter a value for the current ridge parameter, and for the minimum and maximum values for the ridge parameter and the number of increments for comparing the ridge parameters.

Current

Enter a number that will determine the current value of the ridge parameter.  This value is used to calculate the model summary, the reports, and the residual plots.  The default is 0.0, which is equivalent to ordinary least squares.

Minimum

Enter a number that will display as the minimum value when the statistics for increments of the ridge parameter are compared.  The default is 0.0.

Maximum

Enter a number that will display as the maximum value when the statistics for increments of the ridge parameter are compared.  The default is 0.1.

Number of Divisions

Enter the number of increments that will display between the minimum and the maximum values.  The default is 20.


Current

Enter a number that will determine the current value of the ridge parameter.  The value is used to calculate the model summary, the reports, and the residual plots.  The default is 0.0, which is equivalent to ordinary least squares.


Minimum

Enter a number that will display as the minimum value when the statistics for increments of the ridge parameter are compared.  The default is 0.0.


Maximum

Enter a number that will display as the maximum value when the statistics for increments of the ridge parameter are compared.  The default is 0.1.


Number of Divisions

Enter the number of increments that will display between the minimum and the maximum values.  The default is 20.


Regression Coefficients (Ridge Regression)

The Regression Coefficients tabular option displays the estimated coefficients for values of the ridge parameter that are between 0.0 and 0.1 for variables that are unscaled and uncentered; that is, the variables are expressed in their original natural units.  As the ridge parameter increases from 0.0, the coefficients at first change dramatically, then become relatively stable.

Sometimes it is reasonable to use the natural units for the variables to find a good ridge parameter.  However, to eliminate problems due to extreme differences in the magnitudes of the values in the different variables, use the standardized coefficients.

A good value for the ridge parameter is the smallest value that occurs before the estimates slowly change.  This technique is subjective, but the Ridge Trace graphical option can help you make a good choice.  Use the Ridge Regression Options dialog box to change the range of the ridge parameters that will display.


Standardized Regression Coefficients (Ridge Regression)

The Standardized Regression Coefficients tabular option displays the standardized coefficients for values of the ridge parameter that are between 0.0 and 0.1.  These are coefficients of the regression model when the variables are expressed in standardized form.

As the ridge parameter increases from 0.0, the coefficients at first change dramatically, then become relatively stable.  A good value for the ridge parameter is the smallest value that occurs before the estimates slowly change.  This technique is subjective, but the Ridge Trace graphical option can help you make a good choice.  Use the Ridge Regression Options dialog box to change the range of the ridge parameters that will display.


Variance Inflation Factors (Ridge Regression)

The Variance Inflation Factors (VIF) tabular option displays the VIFs and the R-Squared statistic for each value of the ridge parameter.  The VIFs measure the amount by which the variance of the estimated coefficients would be inflated when compared with the ideal case — having all the independent variables uncorrelated.

As the ridge parameter increases from 0.0, the VIFs at first change dramatically, then become relatively stable.  This technique is subjective, but the Variance Inflation Factors graphical option can help you make a good choice.  Use the Ridge Regression Options dialog box to change the range of the ridge parameters that will display.


Reports (Ridge Regression)

The Reports tabular option displays information about the results generated for the regression using the current ridge parameter.  Depending on your selections on the Reports Options dialog box, the table includes the observed value for the dependent variable (if any), the predicted value for the dependent variable using the fitted model, and the residual (observed value minus the predicted value).  Each item corresponds to the values of the independent variables in a specific row of the file.

To create forecasts (predictions) for additional combinations of the variables, add additional rows to the bottom of the file.  In each new row, enter values for the independent variables but leave the cell for the dependent variable empty.  The predicted values for the new rows are added to the table, but the model is left unchanged.


Reports Options Dialog Box

Select the values that will be included in the report.

Include


Observed Y

Includes the observed values for Y in the report.


Fitted Y

Includes the fitted values for Y in the report. If the data include missing values of Y, the predictions are made for those values.  This option is the default.


Residuals

Includes the values for the residuals in the report.


Ridge Regression Analysis Graphical Options Dialog Box

This dialog box allows you to select graphical options for the analysis.

Note:  To access the Options dialog boxes, click the right mouse button on the graphics pane, then click the left on either Pane Options or Analysis Options.

Ridge Trace Plot (Ridge Regression)

Variance Inflation Factors Plot (Ridge Regression)

Observed versus Predicted Plot (Ridge Regression)

Residual Plots (Ridge Regression)


Ridge Trace Plot (Ridge Regression)

The Ridge Trace graphical option displays a plot of the values for the standardized or unstandardized coefficients versus the values for the ridge parameter.

As the ridge parameter increases from 0.0, the coefficients at first change dramatically, then become relatively stable.  Use the Ridge Regression Options dialog box to change the range of the ridge parameters.


Ridge Trace Options Dialog Box

Select the type of coefficients that will appear on the plot.

Display


Variance Inflation Factors Plot (Ridge Regression)

The Variance Inflation Factors graphical option displays a plot of the values for the standardized or unstandardized regression coefficients versus the values for the ridge parameter.

As the value for the ridge parameter increases from 0.0, the coefficients at first change dramatically, then become relatively stable.  Use the Ridge Regression Options dialog box to change the range of the ridge parameters.


Observed versus Predicted Plot (Ridge Regression)

The Observed versus Predicted Plot graphical option displays a plot of the observed values for the dependent variable versus the values predicted by the fitted model for the current ridge parameter.  The closer the points lie to the diagonal line, the better the model is at predicting the observed data.


Residual Plots (Ridge Regression)

The Residual Plots graphical option displays the following plots for the fitted model using the current ridge parameter:  Scatterplot (Residuals versus Predicted, Residuals versus Row Number, and Residuals versus X, where X indicates each independent variable); Normal Probability Plot; and Autocorrelation Function.Plot.


Residual Plots Options Dialog Box

Select a plot and its options.

Plot

Type

Plot versus:

Direction (for Residuals)

Fitted Line

Number of Lags

Confidence Level


Type

Select the plot you want to display.  The default is Scatterplot.

Scatterplot

Displays a Scatterplot of the residuals.  When you select this option, the Plot versus: list box becomes active, allowing you to select a specific residual plot.  This option is the default.

Residuals versus Predicted

Displays the residuals or the studentized residuals versus the predicted values for the observed variable (Y).  A nonrandom pattern indicates that the model does not adequately describe the observed data.  The plot is helpful in showing heteroscedasticity; an indication of the variability of the changes in the residuals as the values of the dependent variable change.

Residuals versus Row Number

Displays the residuals or the studentized residuals versus the row number.  The residuals are plotted in the order that the observations appear in the dependent variable.  The plot is helpful in determining sequential correlations among the residuals.  Any nonrandom pattern indicates serial correlation in the data, particularly if the row order corresponds to the order in which the data were collected.

Residuals versus X (where X indicates the name of each independent X variable)

Displays the residuals or studentized residuals versus the independent variable (X), where X equals the name of the independent variable.  Use this plot to detect the nonlinear relationship between the dependent and independent variables.  You can also use the plot to determine if the variance of the residuals is constant.  Nonrandom patterns indicate that the model you selected does not adequately describe the data.  Any studentized residual values outside the range of -3 to +3 might be outliers.

Normal Probability Plot

Displays the residuals used to determine if the data follow a normal distribution.  A Normal Probability Plot consists of an arithmetic (interval) horizontal axis scaled for the data and a vertical axis scaled so the cumulative distribution function of a normal distribution plots as a straight line.  The closer the data are to the reference line, the more likely they follow a normal distribution.  When you select this option, the Direction and Fitter Line options become active.

Autocorrelation Function

Displays a graph of the autocorrelation estimates for the residuals.  The plot contains a pair of dotted lines and vertical bars that represent the coefficient for each lag.  The distance from the baseline is a multiple of the standard error at each lag.  Significant autocorrelations extend above or below the confidence limits.  When you select this option, the Number of Lags and Confidence Level text boxes become active.


Scatterplot (Ridge Regression)

Displays a Scatterplot of the residuals.  When you select this option, the Plot versus: list box becomes active, allowing you to select a specific residual plot.

Residuals versus Predicted (Ridge Regression)

Residuals versus Row Number (Ridge Regression)

Residuals versus X (Ridge Regression)


Residuals versus Predicted Plot (Ridge Regression)

Displays the residuals versus the predicted values for the observed variable (Y).  A nonrandom pattern indicates that the model does not adequately describe the observed data.

The plot is helpful in showing heteroscedasticity; an indication of the variability of the changes in the residuals as the values of the dependent variable change.


Residuals versus Row Number Plot (Ridge Regression)

Displays the residuals versus the row number.  The residuals are plotted in the order that the observations appear in the dependent variable.

The plot is helpful in determining sequential correlations among the residuals.  Any nonrandom pattern indicates serial correlation in the data, particularly if the row number corresponds to the order in which the data were collected.


Residuals versus x Plot (Ridge Regression)

Displays the residuals versus the independent variable (X), where X equals the name of the independent variable.

Use this plot to detect the nonlinear relationship between the dependent and independent variables.  You can also use the plot to determine if the variance of the residuals is constant.  Nonrandom patterns indicate that the model you selected does not adequately describe the data.


Normal Probability Plot (Ridge Regression)

Displays a Normal Probability Plot of the residuals that you use to determine if the residuals follow a normal distribution.  A Normal Probability Plot consists of an arithmetic (interval) horizontal axis scaled for the data and a vertical axis scaled so the cumulative distribution function of a normal distribution plots as a straight line.  The closer the data are to the reference line, the more likely they follow a normal distribution.

When you select this option, the Direction and Fitted Line options become active, allowing you to select the direction of the plot and the type of values used for the fitted line.


Autocorrelation Function Plot (Ridge Regression)

Displays a plot of the autocorrelation estimates for the residuals.  The plot contains a pair of dotted lines and vertical bars that represent the coefficient for each lag.  The distance from the baseline is a multiple of the standard error at each lag.  Significant autocorrelations extend above or below the confidence limits.

When you select this option, the Number of Lags and Confidence Level text boxes are activated.


Plot versus:

Select the residual plot you want to generate.


Fitted Line

Select the type of values that will determine the fitted line on the Normal Probability Plot.

None

Plots the Normal Probability Plot without the fitted line.

Using Quartiles

Plots the Normal Probability Plot with the fitted line drawn through the median at 0.5 with the slope determined by the quartiles.  This option is the default.

Using Least Squares

Plots the Normal Probability Plot with the line fitted using least squares regression.


None

Plots the Normal Probability Plot without the fitted line.


Using Quartiles

Plots the Normal Probability Plot with the fitted line drawn through the median at 0.5 with the slope determined by the quartiles.  This option is the default.


Using Least Squares

Plots the Normal Probability Plot with the line fitted using least squares regression.


Number of Lags

Enter a value for the maximum lag for estimating the autocorrelations.  Typically, the number of lags should not exceed the number of observations divided by 4.  Enter any integer.


Save Results Options Dialog Box (Ridge Regression)

The Save Results Options dialog box allows you to select the results you want to save.  There are three selections:  Predicted Values, Residuals, and Coefficients.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Logistic Regression Analysis Dialog Box

STATGRAPHICS Plus allows you to enter dichotomous response data in either of two forms:

1.	the dependent variable can consist of individual observations of either a 0 or a 1, representing the actual outcome for each individual case

2.	the dependent variable can contain probabilities between 0 and 1 that are the proportions of successes for groups of observations, whose sizes can vary.

The independent or explanatory variables can be either categorical or continuous. Indicator variables are created for categorical factors that can simplify the use of the model when making predictions for future cases.  There are several statistics and graphs that help to assess the accuracy and usefulness of the model.

Dependent Variable

Sample Sizes

Quantitative Factors

Categorical Factors

Select

Sort

Delete...

Transform...

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Logistic Regression Analysis

Logistic Regression Options

Goodness-of-Fit Options

Predictions Options

Plot of Fitted Model Options

Histogram Options

Residual Plots Options


Dependent Variable

Enter the name of the dependent variable.  The variable can contain either binary numbers (0,1) or proportions between 0.0 and 1.0, inclusively.


Sample Sizes

Enter the name of the variables that contain the sample sizes.  You must place an entry in this text box if the variable you enter in the Dependent Variable text box is in proportions.  Leave the text box blank for 0,1 data.


Quantitative Factors

Enter the names of the variables that contain the quantitative independent variables, if there are any.  Quantitative variables must be numeric.  You must enter at least one variable in either this text box or in the Categorical Factors text box.


Categorical Factors

Enter the names of the variables that contain the categorical independent variables, if there are any.  Categorical factors can be either character or numeric.  For every categorical variable, the program sets up indicator variables for each level except the first one.  You must enter at least one variable in this text box or in the Quantitative Factors text box.


Select

Select a subset of observations.  For example, to analyze the first 50 values in each variable, enter first (50) in this text box.  Or you can use this text box to select the observations that will be used to estimate the model.  The remaining complete observations (those that you do not select) are used to validate the model.  The validation and estimation results appear in the Residual Analysis table at the end of the Analysis Summary.


Sort

Indicate if you want the variables sorted alphabetically.  The default is alphabetically sorted variables.


Logistic Regression Tabular Options Dialog Box

This dialog box allows you to select tabular options for the analysis.

Note:  To access the Options dialog boxes, click the right mouse button on the text pane, then click the left on either Pane Options or Analysis Options.

Analysis Summary (Logistic Regression)

Goodness-of-Fit (Logistic Regression)

Confidence Intervals (Logistic Regression)

Correlation Matrix (Logistic Regression)

Predictions (Logistic Regression)

Unusual Residuals (Logistic Regression)

Predictions (Logistic Regression)


Analysis Summary
Analysis Summary (Logistic Regression)

The Analysis Summary tabular option displays the results of fitting a linear logistic regression model that describes the relationship between the dependent and independent variables.  The results include estimates for each of the coefficients, approximate standard errors, and the estimated odds ratios.  If the Model p-value is less than 0.05, there is a statistically significant relationship among the variables at the 5% significance level.  If the Residual p-value is greater than or equal to 0.05, it indicates that the model is not significantly worse than the best possible model for the data you are currently using at the 5% level.

If the model was fit using weighted least squares, the results include:  t-tests with associated p-values; an ANOVA table; summary statistics, such as R-Squared; and the Type III sums of squares for each of the factors.

If the model was fit using maximum likelihood, the results include:  An analysis of model deviance and the percentage of deviance the model accounts for.  This value is similar to the R-Squared statistic.  The results also include values for the likelihood ratio tests for each of the factors.

If you used the optional Select text box on the Logistic Regression Analysis dialog box, the prediction error statistics are used to validate the accuracy of the model and to display the Residuals Table at the end of the Analysis Summary.  If you decide to validate the model, see the Advanced Regression User Manual and use one of the methods discussed in the section, “Understanding Advanced Regression” in Chapter 1, Getting Started.

The Residuals table includes values for the following statistics for the validation and estimation data:

1.	n — the number of observations.

2.	MSE (Mean Square Error) — a measure of precision computed by squaring the individual error for each item in the data, then finding the average or mean value of those squares.  If the result is a small value, you can predict performance more accurately; if the result is a large value, you may want to use a different model.

3.	MAE (Mean Absolute Error) — the average of the absolute values of the residuals.  If the result is a small value, you can predict performance more accurately; if the result is a large value, you may want to use a different model.

4.	MAPE (Mean Absolute Percentage Error) — the mean or average of the the percentage errors for a given set of data without regard to sign (that is, their absolute values are summed and the average is computed).  Unlike the ME, MSE, and MAE, the size of the MAPE is independent of scale.

5.	ME (Mean Error) — the average of the residuals.  The closer the ME is to 0, the less biased, or more accurate, the prediction.

6.	MPE (Mean Percentage Error) — the average of the absolute values of the residuals divided by the corresponding estimates.  Like MAPE, it is independent of scale.


Logistic Regression Options Dialog Box

Allows you to:

•	select the estimation method.  If you select weighted least squares, specify the smallest allowable proportion.  Any observations less than the smallest allowable proportion (or greater than 1.0 minus that proportion) are set equal to that smallest (or largest) allowable value.

•	select the type of the model to be fit and the fit

•	select the value of P to enter or remove, to select the number of steps

•	indicate how the results will be displayed.

Method

Smallest Proportion

Model

Include Constant

Fit

P-to-Enter

P-to-Remove

Max. Steps

Display

Exclude... Command


Method

Select the estimation method that will determine the regression:  Maximum Likelihood or Weighted Least Squares.

Note:  The two methods usually give different results for the same data.

Maximum Likelihood

Estimates the population parameters that will most likely result in the observed sample data.  For each possible value that a parameter might have, the method computes the probability that the particular sample statistic would have occurred if it were the true value of the parameter.  Then, for the estimate, the method chooses the parameter for which the probability of the actual observation is greatest.  This option is the default.

Weighted Least Squares

Determines a regression equation; that is, the equation that best represents the relationship among the variables.  This option is available only for proportion data.


Maximum Likelihood

Estimates the population parameters that will most likely result in the observed sample data.  For each possible value that a parameter might have, the method computes the probability that the particular sample statistic would have occurred if it were the true value of the parameter.  Then, for the estimate, the method chooses the parameter for which the probability of the actual observation is greatest.  This option is the default.


Weighted Least Squares

Determines a regression equation; that is, the equation that best represents the relationship among the variables.  This option is available only for proportion data.


Smallest Proportion

Enter a value that will be used to adjust the data, if necessary, because the Weighted Least Squares method requires all p > 0 or < exactly.  The default is 0.5.

For details, see Appendix B, Calculations in the Advanced Regression User Manual.


Model

Select the order of model to be fit:  First Order or Second Order.

First Order

Fits the independent variables as they enter the model.

Second Order

Adds the squared and two-way interaction terms to the model.


Include Constant

Indicate if the model should include the constant.  If you do not include the constant in the model, the constant in the logistic transformation is forced to 0.  In a no-constant model, the R-Squared value for the Weighted Least Squares method may be artificially inflated.  This option is the default.


Fit

Select the independent variables that will be fit in the model, and how they will be entered.

All Variables

Enter all of the variables in the model at one time.

Forward Selection

A forward stepwise regression is performed to select the variables and their order.  The regression begins with no variables in the model and adds them one at a time.

First, a simple linear regression model is fit for each of the potential X variables.  Then all the regression models with two X variables are fit and examined to determine if any of the X variables already in the model should be dropped.  Those variables are then examined to determine which X variable is the next candidate for addition, and examined to determine if any of the variables in the model now should be dropped, and so on until it is no longer feasible to add or delete any more X variables.

Backward Selection

Selects the variables by performing a backward stepwise regression, which begins with all the variables in the model and removes them one at a time.

The search procedure is the opposite of forward selection.  It begins with the model containing all potential X variables and identifies the one with the smallest p-value that is less than a predetermined limit, and drops that X variable.  It then fits the model with the remaining X variables, and identifies the next candidate to drop.  This process continues until it can drop no further X variables.


P-to-Enter

Enter the value for p at or above variables should be added into the model.  Enter a number greater than or equal to the number in the P-to-Remove text box; the default is 5E-2.


P-to-Remove

Enter the value for p below which variables should be dropped from.  Enter a number greater than or equal to 0 and less than or equal to the number in the P-to-Enter text box; the default is 5E-2.


Max. Steps

Enter the maximum number of steps that should be performed before the selection process stops.  Enter an integer greater than 0; the default is 10.


Display

Select the method that will be used to display the model for a stepwise regression.

Final Model Only

Display only the final model results.

All Steps

Display each step in the stepwise regression.  To view all the step results, scroll down the Analysis Summary pane.  This option is the default.


Exclude... Command

Displays the Exclude Options dialog box, which allows you to select the variables that will be excluded from the model.

Use this command when you have multiple independent variables and/or you choose Second Order and want to use only certain second-order terms.  Initially all the variables are listed; when you highlight the variables you want to exclude, then click the Exclude button, the highlighted variables move to the Exclude text box.


Goodness-of-Fit
Goodness-of-Fit (Logistic Regression)

The Goodness-of-Fit tabular option displays a table that divides the logistic scale into intervals, each of which contains approximately the same number of observations.

The observed versus predicted True and False observations in each interval of the observed data are compared with those predicted by the model to determine if the function adequately fits the observed data.  Small p-values indicate a significant lack of fit.


Goodness-of-Fit Options Dialog Box

Allows you to enter a value for the number of classes.

Number of Classes


Number of Classes

Enter the number of classes into which the data will be grouped; the groups may be combined to accomplish the Goodness-of-Fit test.  Enter an integer greater than 1.  The default is 5.


Confidence Intervals
Confidence Intervals (Logistic Regression)

The Confidence Intervals tabular option calculates and displays the confidence intervals for the coefficients in the model and the odds ratios using a confidence level of 95 percent.  The confidence intervals illustrate the preciseness with which the coefficients were estimated, given the amount of available data and the noise present.

The odds ratios equal the inverse natural logarithm of the coefficient and show the proportional change in the response variable as the independent variable is increased by one unit.  To change the confidence level, use the Confidence Intervals Options dialog box.


Confidence Intervals Options Dialog Box

Allows you to enter a value that will be used to calculate the confidence intervals for the mean and standard deviation.  The default is 95 percent; other common levels are 90 and 99.


Correlation Matrix
Correlation Matrix (Logistic Regression)

The Correlation Matrix tabular option displays a table of the estimated correlations between the coefficients in the fitted model.  The correlations are helpful in detecting the presence of serious multicollinearity.


Predictions
Predictions (Logistic Regression)

The Predictions tabular option displays a summary of the prediction capability of the fitted model.  The model is first used to predict the response, working with the information in each row of the file.

If the predicted value is larger than the cutoff value, the response is predicted to be True.  If the predicted value is less than or equal to the cutoff value, the response is predicted to be False.  Also shown is the percentage of observed data that were correctly predicted at various cutoff values.  Using the cutoff value that maximizes the total percentage of correct predictions may provide a good value to use when additional individuals need to be predicted.  Another approach is to predict “Success” for any observations with a predicted probability greater than .05.


Predictions Options Dialog Box

Allows you to set a range of values for the cutoff, to indicate the values that will be displayed, and to set the percentage for the confidence level.

Display

Confidence Level (for Confidence Intervalsl)


Cutoff

Allows you to set the range of values that will display in the table.

From

Enter the number that will determine the first or starting number in the range of cutoff values.  Enter a number less than the value in the To text box; the default is 0.

To

Enter a number that will determine the last or ending number in the range of cutoff values.  Enter a number greater than the value in the From text box; the default is 1.

By

Enter the number that will determine the spacing the cutoff values.  This value is used, along with the values in the From and To text boxes, to determine the rows in the table.


To

Enter a number for the last or ending number in the range of cutoff values.  Enter a number greater than the value in the From text box; the default is 1.


Display

Allows you to indicate which values will display in the table.

All Values

Displays values for all the predictions in the file.

Forecasts Only

Displays values for the forecasts only; that is, it displays the forecasts for observations that correspond to a missing value for the dependent variable.  This option is the default.


Unusual Residuals (Logistic Regression)

The Unusual Residuals tabular option displays a table that lists all the observations that have standardized residuals with values greater than 2.0 in absolute value.  Pearson residuals, the residuals divided by their estimated standard errors,.measure the number of standard deviations that each observed value of the dependent variable deviates from the the fitted model.  The Deviance residuals are the residuals scaled so that their sum of squares equals the residual deviance.


Influential Points
Influential Points (Logistic Regression)

The Influential Points tabular option displays a table that lists the observations that have leverage values greater than three times that of an average point, or that have unusually large DFITS or Cook's distance values.

Leverage is a statistic that measures the amount of influence each observation has in determining the coefficients for the estimated model.  DFITS is a statistic that measures the amount each estimated coefficient would change if each observation were removed from the data.  The Cook's distance statistic measures the distance between the estimated coefficients with and without each observation.


Logistic Regression Graphical Options Dialog Box

The Logistic Regression Graphical Options dialog box allows you to select from seven options: Plot of Fitted Model, Logit Plot, Observed versus Predicted, Observed versus Log Odds, Prediction Capability, Prediction Histograms, and Residual Plots.

Note:  To access the Options dialog boxes, click the right mouse button on the graphics pane, then click the left on either Pane Options or Analysis Options.

Plot of Fitted Model (Logistic Regression)

Logit Plot (Logistic Regression)

Observed versus Predicted Plot (Logistic Regression)

Observed versus Log Odds Plot (Logistic Regression)

Prediction Capability Plot (Logistic Regression)

Prediction Histograms Plot (Logistic Regression)

Residual Plots (Logistic Regression)


Plot of Fitted Model
Plot of Fitted Model (Logistic Regression)

The Plot of Fitted Model graphical option displays a plot of the fitted model versus the independent variable you select.  A curve is drawn over the range of X, and points are plotted for the values of the dependent variables, if there is only one independent variable.  The StatAdvisor shows the equation for the fitted model.  95% Confidence Limits are included as well.


Plot of Fitted Model Options Dialog Box

Allows you to select the variable that will be used to plot against the fitted model.  You can also enter the levels for holding the other variables or new limits for the axis for the variable you selected.  Use this dialog box to select options for both the Plot of Fitted Model and the Logit Plot.

[variable]

Low

High

Hold


[variable]

Allows you to select the variable that will be used to plot against the fitted model.  The names of the variables are listed to the right of the check boxes.


Low

Enter a value that will determine the lower limit of the axis for the selected variable.  You can use this text box as well as the High text box to switch between 0 and 1 for indicator variables.  Enter a value; the default depends on the type of data being used.


High

Enter a value that will determine the upper limit of the axis for the selected variable.  You can use this text box as well as the Low text box to switch between 0 and 1 for indicator variables.  Enter a value; the default depends on the type of data being used.


Hold

Enter a value that will determine the level at which all of the other variables will be held.  Enter any value; the default depends on the type of data being used.


Logit Plot
Logit Plot (Logistic Regression)

The Logit Plot graphical option displays a plot similar to a plot of the fitted model except that the scale has been transformed using the logit transformation.  This results in a straight regression line for a first-order model.  Points appear on the plot only if there is a single factor and you enter data as proportions and sample sizes.  The StatAdvisor displays the equation for the logit transformation.  95% Confidence Limits are included as well.


Observed versus Predicted Plot
Observed versus Predicted Plot (Logistic Regression)

The Observed versus Predicted graphical option displays a plot of the residuals from the fitted model plotted against the predicted values of the dependent variable.  Use the plot to determine any unusual patterns in the residuals.


Observed versus Log Odds Plot
Observed versus Log Odds Plot (Logistic Regression)

The Observed versus Log Odds Plot graphical option displays a plot of the values of Y versus the values of the log odds as predicted by the fitted model.  The StatAdvisor displays the equation for the logit transformation.  Use the plot to detect cases in which the variance is not constant or to determine if you need to transform the dependent variables.


Prediction Capability Plot
Prediction Capability Plot (Logistic Regression)

The Prediction Capability Plot graphical option displays a plot that summarizes the prediction capability of the fitted logistic model:  The percentages of correct values versus the cutoff values for the dependent variable that were Total, True, or False.

The model is first utilized to predict the response using the information in each row of the file.  If the predicted value is larger than the cutoff, the response is predicted to be True.  If the predicted value is less than or equal to the cutoff, the response is predicted to be False.  The plot shows the percentage of the observed data that were correctly predicted at various cutoff values.


Prediction Histograms Plot
Prediction Histograms (Logistic Regression)

The Prediction Histograms graphical option displays a plot that demonstrates the ability of the fitted logistic model to distinguish between cases when the dependent variable is True or False.

The plot shows the frequency distribution of the True and False cases in the data versus the probability predicted by the fitted model.  In an ideal situation, the model will predict a small probability for the False cases and a large probability for the True cases.  If the model works well, the larger frequencies above the line will appear to the right; larger frequencies below the line will appear to the left.


Histogram Options Dialog Box

Allows you to select the number of classes into which the data will be grouped.

Number of Classes

Lower Limit

Upper Limit

Hold

Counts


Number of Classes

Enter the number of classes into which the data will be divided.  Enter an integer between 1 and 1000.


Lower Limit

Enter a value that will determine the lower limit for the first class.  Enter any number; the default is 0.


Upper Limit

Enter a value that will determine the upper limit for the first class.  Enter any number greater than or equal to the number in the Lower Limit text box; the default is 1.


Hold

Allows you to indicate if the current scaling should be retained (if you change the values in the dialog box).

To select the option, click the check box, then display the Logistic Regression dialog box and make the changes.  When you click OK, the graph for the new data displays using the scaling from the previous graph.


Counts

Allows you to select the scale for the Y-axis.

Relative

Plots percentages in each interval.

Cumulative

Plots the sum of the frequencies at or below each interval; that is, includes the frequency of all the classes up to and including the current class.


Residual Plots
Residual Plots (Logistic Regression)

The Residual Plots graphical option displays the following plots for the fitted model:  Scatterplot (Residuals versus Predicted, Residuals versus Row Number, and Residuals versus X where X indicates each independent variable); Normal Probability Plot; and Autocorrelation Function.

Use the Residual Plots Options dialog box to select a plot and its options.


Residual Plots Options Dialog Box

Allows you to select a residual plot and its options.

Plot (Residuals or Studentized Residuals)

Type (of Residual Plot)

Plot versus:

Direction

Fitted Line

Number of Lags

Confidence Level (for Probability Limits)


Type (of Residual Plot)

Allows you to select the plot that will display.  The default is Scatterplot.

Scatterplot

Displays a Scatterplot of the residuals.  When you select this option, the Plot versus: list box becomes active, allowing you to select a specific residual plot.

Residuals versus Predicted

Displays the residuals from the fitted model versus the predicted values for the dependent variable.  Examine the residuals to look for any unusual patterns.  Remember that the response is limited to be between 0 and 1, so the residuals will not follow a normal distribution.

Residuals versus Row Number

Displays the residuals or the studentized residuals versus the row number.  The residuals are plotted in the order that the observations appear in the dependent variable.  The plot is helpful in determining sequential correlations among the residuals.  Any nonrandom pattern indicates serial correlation in the data, particularly if the row order corresponds to the order in which the data were collected.

Normal Probability Plot

Displays a Normal Probability Plot of the residuals.  To create the plot, the residuals are sorted from smallest to largest, then plotted versus the values.  If the data are from a normal distribution, the points should fall approximately along a straight line.  To help determine how close the points are to the line, a reference line is drawn on the plot, which passes through the median with the slope determined from the interquartile range.  If the points show a significant curvature, it may indicate that the residuals do not come from a normal distribution.

Autocorrelation Function

Displays a graph of the autocorrelation estimates for the residuals.  The plot contains a pair of dotted lines and vertical bars that represent the coefficient for each lag.  The distance from the baseline is a multiple of the standard error at each lag.  Significant autocorrelations extend above or below the confidence limits.  When you select this option, the Number of Lags and Confidence Level text boxes become active.


Scatterplot
Scatterplot (Logistic Regression)

Displays a Scatterplot of the residuals.  When you select this option, the Plot versus: list box becomes active, allowing you to select a specific residual plot.

Residuals versus Predicted Plot (Logistic Regression)

Residuals versus Row Number Plot (Logistic Regression)


Residuals versus Predicted Plot
Residuals versus Predicted Plot (Logistic Regression)

Displays the residuals from the fitted model versus the predicted values of the dependent variable.  Examine the residuals to look for any unusual patterns.  Remember that the response is limited to be between 0 and 1, so the residuals will not follow a normal distribution.


Residuals versus Row Number Plot
Residuals versus Row Number Plot (Logistic Regression)

Displays the residuals or the studentized residuals versus the row number.  The residuals are plotted in the order that the observations appear in the dependent variable.  The plot is helpful in determining sequential correlations among the residuals.  Any nonrandom pattern indicates serial correlation in the data, particularly if the row number corresponds to the order in which the data were collected.


Normal Probability Plot
Normal Probability Plot (Logistic Regression)

Displays a Normal Probability Plot of the residuals.  To create the plot, the residuals are sorted from smallest to largest, then plotted versus the values.  If the data come from a normal distribution, the points should fall approximately along a straight line.

To help determine how close the points are to the line, a reference line is drawn on the plot, which passes through the median with the slope determined from the interquartile range.  If the points show a significant curvature, it may indicate that the residuals do not come from a normal distribution.


Autocorrelation Function Plot
Autocorrelation Function Plot (Logistic Regression)

Displays a plot of the autocorrelation estimates for the residuals.  The plot contains a pair of dotted lines and vertical bars that represent the coefficient for each lag.  The distance from the baseline is a multiple of the standard error at each lag.  Significant autocorrelations extend above or below the confidence limits.

When you select this option, the Number of Lags and Confidence Level text boxes are activated.


Plot versus:

Allows you to select the residual plot you want to generate.


Fitted Line

Allows you to select the type of values that will determine the fitted line on the Normal Probability Plot.

None

Plots the Normal Probability Plot without the fitted line.

Using Quartiles

Plots the Normal Probability Plot with the fitted line drawn through the median at 0.5 with the slope determined by the quartiles.  This option is the default.

Using Least Squares

Plots the Normal Probability Plot with the line using least squares regression.


Number of Lags

Enter a value for the maximum lag for which the autocorrelations should be estimated.  Typically, the number of lags should not exceed the number of observations divided by 4.  Enter any integer.


Save Results Options Dialog Box
Save Results Options Dialog Box (Logistic Regression)

The Save Results Options dialog box allows you to select the results that will be saved.  There are 13 selections:  Predicted Values, Standard Errors of Predictions, Lower Limits for Predictions, Upper Limits for Predictions, Standard Errors of Means, Lower Limits for Forecast Means, Upper Limits for Forecast Means, Residuals, Studentized Residuals, Leverages, DFITS Statistics, Mahalanobis Distances, and Coefficients.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Plot versus:

Allows you to select the Residual plot you want to create.  This is available only for Scatterplots selected from the Residual Plots Options dialog box.


Confidence Interval

Displays the confidence intervals on the plot.


Analysis Summary (General Linear Models)

The Analysis Summary tabular option for the General Linear Models Analysis displays the results of fitting the general linear statistical model.  If any p-value in the first ANOVA table is less than 0.10, there is a statistically significant relationship between the variables.

The second ANOVA table tests the statistical significance for each of the factors.  If any p-value in this ANOVA table is greater than or equal to 0.10, that term is not statistically significant at the 90 percent or higher confidence level and you should consider removing it from the model.


Analysis Summary (Calibration Models)

The Analysis Summary tabular option shows the results of fitting a linear model to describe the relationship between the dependent (measured) and independent (actual) variables.  The StatAdvisor includes the equation for the fitted model.  If the data contain replicate values for X, the program also performs a lack-of-fit test.


Analysis Summary (Comparison of Regression Lines)

The Analysis Summary tabular option shows the results of the multiple regression analysis.  If the display includes the explanation provided by the StatAdvisor, the equation of the fitted model and an explanation of the terms in the equation are shown.  By default, the model contains an intercept, a coefficient for the X variable, a coefficient for the indicator variable for each group except the first, and for products of the X variable with each group indicator.  The table then shows the results of the fit:


Analysis Summary (Nonlinear Regression)

The Analysis Summary tabular option shows the results of fitting a nonlinear regression model that describes the relationship between the dependent variable and the estimated function.  Also shown is the number of iterations performed before reaching the minimum residual sum of squares. The StatAdvisor includes the equation for the fitted model.


Analysis Summary
Analysis Summary (Ridge Regression)

The Analysis Summary tabular option shows the results for the current value of the ridge parameter.  By allowing for a small amount of bias, the precision of the estimates is greatly increased.  The summary shows the current value of the ridge parameter to be 0.0, which is equivalent to ordinary least squares.

Use the Ridge Regression Options dialog box to change the value for the ridge parameter.  The value is usually between 0 and 1.0.  To determine a good value, examine the standardized regression coefficients or the variance inflation factors.


Analysis Summary (Logistic Regression)

The Analysis Summary tabular option displays the results of fitting a linear logistic regression model that describes the relationship between the dependent and independent variables.

The results include estimates for each of the coefficients, approximate standard errors, and the estimated odds ratios.  If the p-value is less than 0.01, there is a statistically significant relationship among the variables.  If the p-value for the residuals is greater than or equal to 0.10, it indicates that the model is not significantly worse than the best possible model for the data currently being used.


Display

Allows you to select the type of coefficients that will appear on the plot.

Unstandardized Coefficients

Displays unstandardized values for the coefficients

Standardized Coefficients

Displays standardized values for the coefficients.  This option is the default.


Confidence Level (for Probability Limits)

Enter a value for the confidence levels that will be used to calculate the probability limits.  Enter a number greater than 0 and less than 100.  The default is 95 percent; other common levels are 90 or 99.


Confidence Level (for Prediction Intervals)

Enter a value for the confidence level that will be used to calculate the prediction intervals for new obserservations, and the mean of the observations.  The default is 95 percent; other common levels are 90 and 99 percent.


Confidence Level (for Predictions and Confidence Limits)

Enter a value for the confidence level that will be used to calculate the prediction limits and confidence limits at the selected values of X.  The default is 95 percent; other common levels are 90 and 99.


Confidence Level (for Model Coefficients)

Enter a value for the confidence level that will be used to calculate the confidence intervals for the model coefficients.  The default is 95 percent; other common levels are 90 and 99 percent.


Confidence Level

Enter a value for the level of confidence that will be associated with the tolerance interval.  Enter a percentage greater than 0 and less than 100.  The default is 95.


Confidence Level (for Confidence Intervalsl)

Enter a value that will be used to calculate the confidence intervals.  The default is 95 percent; other common levels are 90 and 99.


Confidence Level (for Model Coefficients)

Enter a value for the confidence level that will be used to calculate the confidence intevals for the model coefficients.  The default is 95 percent; other common levels are 90 and 99 percent.


Confidence Level

Enter a value for the size of the probability limits for the autocorrelations.  Enter a number greater than 0 and less than 100.  Common levels are 90, 95, or 99 percent; 95 percent is the default.


Bubble Chart Analysis

An analysis that creates an X-Y Scatterplot consisting of circles where the size of the circles is determined by a third variable.  The plot is helpful when you want to view data in higher dimensions.


CDF (Cumulative Distribution Function)

A function that provides cumulative probabilities as an alternative way for describing the pdf for a random variable.  The height of the function indicates the probability of obtaining a value less than or equal to a specified value.


Censored Data

Data that are incomplete in some way; for example, having certain values that are unknown, or having a situation in which an event does not occur during the period of observation.


Censored Data Analysis

Data that are incomplete in some way; for example, having certain values that are unknown, or having a situation in which an event does not occur during the period of observation.


Comparison of Alternative Models

A table of the correlation coefficients and R-Squared values for several transformed model types.


Contingency Coefficient

A version of a Chi-Square test that measures the strength of the dependency between two characteristics.


Contour Plot

A two-dimensional plot of a response surface where the contours of the plot represent the height of the surface; useful for determining optimal regions.


Correlation Matrix

A table of the Pearson correlation coefficients for the estimated coefficients in a model.


Cramer's V and Conditional Gamma

Chi-square based measures of association that are helpful in determining the relationship between variables.


Cumulative Hazard Function Plot

A plot of the estimated cumulative hazard function that is helpful when you need suggestions for possible parametric models when you use failure data.


Custom Chart Analysis

An analysis that allows you to create customized charts.


Death Density Function Plot

A function that produces a plot that gives the rate at which the cumulative probability increases at a given point.


Distribution-Free Tolerance Limits

A method to create and display noparametric tolerance limits, which should be used when data are non-normal.  See Normal Tolerance Limits.


Dot Diagram Analysis

An analysis that provides an additional type of graphical display for numeric data.  The dots on the plot represent every value in a numeric column.


Durbin-Watson Statistic

A measure of the serial correlation for the residuals.


Eta

An approximate measure of association for two variables when you measure the dependent variable on an interval scale and the independent variable on a nominal or ordinal scale.


Frequency Table

A table of the number of observations that fall within each class and the relative, cumulative, and cumulative relative frequencies.


Group Comparisons

A table that shows the results of comparing groups in a study using Logrank and Wilcoxon tests.


Interaction Plot

A plot of two-factor interactions.


Interquartile Range

A range in which the middle 50 percent of the data will fall.


Kendall's Tau b and c

Statistics that measure the relative degree of agreement or disagreement between two variables.


Kurtosis

A value used to measure the flatness or steepness of a distribution with respect to a Gaussian or Normal distribution.


Lambda Values

Values that measure the degree of association on a scale from 0 to 1.  The closer Lambda is to 1, the more useful one factor is in predicting the other factor.


Life Tables (Intervals) Analysis

An analysis that creates life tables from the counts of failures in a set of intervals.


Life Tables (Times) Analysis

An analysis that creates life tables from the failure times of items, which provides an estimate of a survival function.


Locally Weighted Regression

An option that smoothes data by fitting a straight line to points using weighted least squares.


Log Survival Function Plot

A plot that shows the estimated log survival function.  The plot shows the probability of observing a value greater than a specified value (in log units).


Lower Quartile

The value below which 25 percent of the data will fall.


Maximum Likelihood

A method used to calculate an estimation.  It first calculates the probability that the sample statistic (observed value) would occur if it were the true value of the parameter, then chooses the parameter that has the greatest probability of being the actual observation.


Mean Absolute Error

The average of the absolute values of the residuals.


Means Table

A table of the sample means and standard errors for the levels in the data.


Median Notch

A notch in the box around the median on a Box-and-Whisker Plot.  The length of the notch represents an approximate confidence interval for the median.


Median Plot

A plot of the sample medians for the levels in the variables.


Mode

The value with the highest frequency.


Multiple Barchart Analysis

An analysis that creates a plot of one or more frequency bars for each classification factor (row).  The plot graphically represents a secondary classification factor within a primary classification factor.


Normal Probability Plot

A plot that consists of an arithmetic (interval) horizontal axis scaled for the data and a vertical axis scaled so the cumulative distribution function of a Normal distribution plots as a straight line.


Normal Tolerance Limits

A method for creating and displaying normal tolerance limits, which you use with normally distributed data.  See Distribution-Free Tolerance Limits.


Open Database Connectivity (ODBC)

A database-independent interface from Microsoft Corporation that allows you to access data in a variety of SQL-compliant database servers.


R-Squared

A statistic that measures the proportion of variability in a model for the dependent variables.


Range Plot

A plot of the sample ranges for the levels in the variables.


Rank Regression

A method used to calculate an estimation.  The best-fit line is drawn through the data plotted on the logarithmic (Weibull) grid to determine two parameters:  Shape and Scale.


Response Surfaces Analysis

An analysis that creates Surface and Contour plots for functions.  The plots show the shape of a response surface when it is necessary to locate optimal settings.


Robust Lowess

An option that smoothes data by repeating the smoothing process a second time, giving reduced weight to points that are the furthest from the first smoothed line.


Row-Wise Statistics Analysis

An analysis that provides the capability to calculate and save statistics on a row-wise basis for data that are in two or more columns.


Running Lines

An option that smoothes data by fitting a straight line to points.


Running Means

An option that smoothes data using a running average or a running mean.


Sigma Plot

A plot of the sample ranges for the levels of the variables.


Skewness

A value used to measure the symmetry or shape of the data.


Somer's D Statistics

Statistics that show a symmetric measure of association for variables that are measured on an ordinal scale.


StatAdvisor

A special feature unique to STATGRAPHICS Plus that allows you to display and print a short and easy-to-understand interpretation of the text and graphics options in an analysis.


StatGallery

A special feature unique to STATGRAPHICS Plus that allows you to copy text and graphics panes to multiple pages so you can view or print them.


Subset Analysis

An analysis that allows you to calculate statistics for a single column of data at each level of a second code variable; formerly known as the Codebook Analysis in STATGRAPHICS Plus.


Surface Plot

A three-dimensional plot of a response surface that is useful in locating optimal regions.


Survival Function Plot

A plot that shows the estimated survival function, which is the probability than an item will not fail before a specified length of time.


Survivor Function

A function that produces a plot of the survivor function for a distribution you select.  The function indicates the probability of obtaining a value greater than a value you select.  The survivor function is 1 - CDF.  In reliability data, the survivor function shows the probability of surviving to time x without failure.


Tolerance Limits

The values between which you can expect to find a specified proportion of a population.


Type I Sums of Squares

A method for computing additional sums of squares for each factor in the order in which they were entered.


Type II Sums of Squares

A method for computing additional sums of squares for each factor as though that factor was the last one added to the model.


Unusual Residuals

A table of the observations with studentized residuals less than -2 or greater than 2.


Upper Quartile

The value above which 25 percent of the data will lie.


Weibull Analysis

An analysis that uses the Weibull distribution modeling method to create failure-rate curves.


ANOVA Table

A standard analysis of variance table that presents the values for the variability between groups and within groups.


Boxcar Method

A method that assigns a constant density to each small interval around a value, which smoothes the density function into a series of overlapping rectangles or boxcars, similar to a simple moving average.


Brushing

A technique used to change the color of points on a Scatterplot to indicate that an additional variable has been added to the analysis.


Comments Window

A window you use to record information about a StatFolio.


Comparison of Means

An analysis whose results display the values for the 95 percent confidence intervals for the mean of two variables and for the difference between the means, assuming equal variances and not assuming equal variances.


Comparison of Medians

The results of a Mann-Whitney (Wilcoxon) test (a Rank test).


Comparison of Standard Deviation

A display of the results from an F-test, which compares the ratio of the variance for the first population with the variance of the second population.


Component Effects Plot

A plot of the residuals that is helpful in judging the relative magnitude of the residuals with respect to the explanatory power of the variable.


Contingency Tables Analysis

An analysis for determining if two classification factors are related, and if so, how closely.


Cosine Method

A method for smoothing local densities into a series of overlapping, bell-shaped intervals similar to a weighted moving average, which results in a smoother density trace.


Density/Mass Function Plot

A plot of the probability density function for a distribution.


Discrete Uniform Distribution

A distribution that allocates equal probabilities to all integer values between a lower and an upper limit.


Distribution Fitting Analysis

An analysis that determines if data follow a Normal or another type of distribution.  The analysis fits one of several distribution functions.


Distribution Functions 1 and 2

Plots that display one of several types of distribution functions:  Density Function, CDF, Survivor Function, Log Survivor Function, and Hazard Function.


Dynamic Data Exchange (DDE)

A channel through which applications pass information between each other.


Erlang Distribution

A distribution useful for random variables constrained to be greater than 0; characterized by the Shape and Scale parameters.


Exponential Value Distribution

A continuous distribution useful for characterizing random variables that can take only positive values; completely determined by its mean.


F (Variance Ratio) Distribution

A distribution useful for random variables constrained to be greater than 0; characterized by two parameters:  Numerator Degrees of Freedom and Denominator Degrees of Freedom.


Frequency Tabulation

A table created by grouping data into a default number of class intervals of frequencies and cumulative frequencies that summarize the distribution of the data.


Goodness-of-Fit Tests

A standardized Chi-Square statistic that compares observed frequencies with the expected frequencies predicted by the fitted distribution.  The program performs this analysis along with the Kolmogorov-Smirnov one-sample test.


Hazard Function

A function that produces a plot that shows the probability of failure during a small increment of time when no failure occurs before a time you select.  The Hazard Function is equal to the Probability Density Function divided by the Survivor Function.  When you model lifetime data, the function represents the instantaneous failure rate.


Hypothesis Tests (Compare Analysis)

An analysis that estimates and tests hypotheses about the sample mean, sample variance, the binomial proportion, or the rate for a single random variable.


Hypothesis Tests (Describe) Analysis

An analysis that tests hypotheses about the sample means and variances for two or more random samples.


Influential Points

A table of the observations that have leverage values above three times the average leverage value; the row numbers of the observations flagged as high leverage DFITS.


Interval Plot

A display of the dependent variable plotted against the predicted values, their row numbers, or any of the independent variables.


Key Glyph

A plot of a single glyph with individual rays labeled with the names of the corresponding variables.


Laplace Distribution

A distribution useful for random variables from a distribution that is more peaked than a Normal distribution; characterized by two parameters:  Mean and Scale.


Linear Model

A model that fits a simple linear regression equation for Y in terms of X.


Logistic Distribution

A distribution useful for random variables that are not constrained to be greater than or equal to 0; characterized by two parameters:  Mean and Standard Deviation.


Mean Marker

A symbol that denotes the location of the average on a Box-and-Whisker Plot.


Mosaic Plot

A plot that represents the frequencies in the cells of a Crosstabulation.


Multifactor ANOVA Analysis

An analysis that examines the effects of two or more factors on one variable; typically uses data collected for a designed experiment.


Multiple-Sample Comparison Analysis

An analysis used to compare several sets of data, where the observations in the samples are assumed to be independent.


Multiple-Variable Analysis

An analysis used to analyze the relationship among several numeric variables.


Negative Binomial Distribution

A distribution that characterizes the number of failures before the kth succes in a series of Bernoulli trials.


Object Linking and Embedding (OLE)

A set of program interfaces that enable you to combine objects that are supported by different applications.


One-Variable Analysis

An analysis of the data in a numeric variable.


Paired-Sample Comparison Analysis

An analysis that calculates the difference between each value in each pair of observations.


Pareto Distribution

A distribution with a decreasing density function.  One parameter, Shape, is necessary to specify the distribution.


Partial Correlations

A matrix of estimated partial correlation coefficients for a set of observed values.  A partial correlation coefficient measures the relationship between two variables while controlling for possible effects of the other variables.


Percentiles

Tabular results that show the percentage of the values that are equal to or less than a value you select.


Polynomial Regression Analysis

An analysis that calculates a model between a single dependent variable Y and a single independent variable X.


Probability Distributions

Functions that allow you to perform three basic operations:  (1) calculate probabilities, (2) create plots of the probability and cumulative distributions, (3) generate random numbers.  STATGRAPHICS Plus contains 24 distributions.  See Bernoulli, Binomial, Cauchy, Discrete Uniform, Geometric, Hypergeometric, Negative Binomial, Poisson, Beta, Chi-Square, Erlang, Exponential, Extreme Value, F (Variance Ratio), Gamma, Laplace, Logistic, Lognormal, Normal, Pareto, Student's t, Triangular, Uniform, and Weibull.


Quantile Plot

A plot that displays the quantiles for the data.  The Y-axis represents the proportion of values that are below a particular value.


Quantile-Quantile Plot

A plot of the quantile values plotted as pairs and useful for comparing the cumulative distributions for two samples.

A plot of the sample ranges for the levels in the variables.


Rank Correlations

A matrix of Spearman rank correlation coefficients similar to a correlation coefficients matrix.


Recode Data

A method for changing the values in a spreadsheet column.


Residuals versus Factor Levels Plot

A plot of the residuals versus the factor levels.


Residuals versus Observations Plot

A plot of the residuals versus the observations.


Residuals versus Row Numbers Plot

A plot of the residuals versus the row numbers.


Residuals versus Samples Plot

A plot of the residuals versus the samples.


Sample Size Determination (Compare) Analysis

An analysis that helps to determine the number of observations required to provide sufficiently powerful estimates, and to analyze the power curve for samples already drawn.  The analysis calculates sample sizes for testing five types of parameters.


Sample Size Determination (Describe) Analysis

An analysis that calculates the sampling sizes for four parameters:  Normal Mean, Normal Sigma, Binomial Proportion, and Poisson Rate.


Scatterplot Matrix

A matrix plot of the variables with points for the data; visually presents the relationships among the pairs of variables.


Simple Regression Analysis

An analysis that fits a model that relates one dependent variable to one independent variable by minimizing the sum of the squares of the residuals for the fitted line.


Skychart

A three-dimensional histogram that shows the relationship among two variables and the distribution of the data.


StatFolio

A special feature unique to STATGRAPHICS Plus that is similar to a statistical project; a file in which you can save data, analyses, a StatGallery, and comments.


Symmetry Plot

A plot helpful in determining the symmetry of the data; useful in analyses that are best applied to a symmetrical distribution.


Tail Area

The area under the density curve at specified points calculated by using the cumulative distribution function.  The function calculates the probability that a random variable will fall below a given value.


Tests for Normality

An analysis of the data to determine if they are normally distributed.  The results include the Chi-Square Goodness-of-Fit statistic, the Shapiro-Wilk's W-statistic, the z-Score for Skewness, and the z-score for Kurtosis.


Time Series Operators

Operators that calculate seasonal and backward differences.


Triangular Distribution

A distribution useful for random variables constrained to lie between two fixed limits.  This distribution peaks at some value between two limits and characterized by three parameters:  Lower Limit, Central Value (Mode), and Upper Limit.


Two-Sample Comparison Analysis

An analysis used to calculate the confidence intervals for the difference between the population means and the ratio of the population variances, and to calculate confidence intervals for the hypotheses means, variances, and medians.


Variance Check

The results of three statistical tests:  Cochran's C test, Bartlett's test, and Hartley's test.  These tests confirm the assumption that the variance of samples is equal.


Variance Components Analysis

An analysis used to analyze the effect of one or more qualitative factors on one response variable when the data are completely nested or hierarchical.


Weibull Plot

A plot of the Weibull distribution that is helpful in determining if the distribution is a good fit for a set of data.  See Weibull Distribution.


Selected Data Source

This drop-down list box allows you to select the data source you want to use.


New...

This command displays the Add Data Source dialog box, which allows you to select the ODBC driver you want to use.


Table

This drop-down list allows you to select the table (database) you want to use.


Available Fields

This text box allows you to select the fields you want to use.  As you double-click your choices, the program displays the names in the Selected Fields list box.


Selected Fields

This list box displays the names of the fields you selected.


Use Rows

This text box allows you to enter a SQL statement to specify the subset of fields.


Keypad

The keypad contains a selection of built-in SQL functions.  Use it in conjunction with the Field Names, numbers, and Functions list box to build a SQL expression in the Use Rows text box.  For example, suppose that the Field Names list box contained the entry Score; and the Functions list box contained, in addition to others, the expression BETWEEN exp AND exp.

Example:

1.	Select the Field Name Score from the untitled list box.

2.	Select the function BETWEEN exp AND exp from the Functions list box.

3.	Use the keypad to replace the first and second usages of exp, with the numbers 75 and 90, respectively.

The expression would look like this:  `Score' BETWEEN 75 AND 90

After you enter an expression and click the OK button, the program imports the data and displays the name of the table in the Data Icon taskbar in the Analysis window.  If you need more information about building an expression, see the documentation for the database you are using.


Functions

This drop-down list displays frequently used SQL functions.  After you select a function, it displays in the Use Rows text box.


Profile

This drop-down list box allows you to select or enter the profile in which the program should save the settings:  System or user-defined.  User-defined can be the name of anything, such as the name of a person or an analysis.  You can create from 1 to 10 user profiles.


Action (for Selecting Preferences)

Select your preferences for the profile.

Load

Loads the selected profile and uses it on subsequent graphs during the current working session.

Make Default

Loads the selected profile, uses it on subsequent graphs, and makes it the new default for the following and future sessions.

Save

Saves the graph with the settings for the selected profile.  This option is not available if you select the System profile.

Rename

Allows you to enter a name for the different user-defined profiles.  After you enter a name and click OK, the name appears in the Profile drop-down list box.  This option is not available if you select the System profile.


Hold

Indicates if the current scaling should be retained even if you change the values in the Analysis dialog box.  If you decide to retain the scaling, then change the data in the Analysis dialog box, the scaling remains the same when you click OK.


Rotate X-Axis Labels

This check box indicates if the program should change the position of the labels on the X-axis.  If  the check box is checked, the program rotates the labels to a vertical position on the X-axis.  If the check box is not checked, the program will display vertical labels.


Skip

This text box allows you to enter the number of tickmarks the program should skip when it creates the X-axis.  The default is 0.


Fonts...

This command displays the Font Options dialog box, which allows you to change the font and its attributes.


Labels

This text box allows you to change the name of a label, and to add or delete a name.


Rotate X-Axis Label

This check box indicates if the program should change the position of the labels on the X-axis.  If the check box is checked, the program rotates the labels to a vertical position on the X-axis.  If the check box is not checked, the program will display horizontal labels.


Skip

This text box allows you to enter the number of tickmarks the program should skip when it creates the X-axis.  The default is 0.


Fonts...

This command displays the Font Options dialog box, which allows you to change the font and its attributes.


Type

These options indicate which method the program should use to perform the smoothing.

None

This option indicates that the program should not smooth the points; it is the default.

Running Means

This option smoothes the points using the Running Means method.  The Y values correspond to X and the (k - 1)/2 values on each side of X are averaged, where k is forced to be an odd integer.  The program computes the average from the values that are available at the beginning and end of the data, where less than (k - 1)/2 values are found on one side of X.  This is basically a running average or a running mean.

This method is fast to compute, but tends to be biased at the beginning and end of the data.

Running Lines

This option smoothes the points using the Running Lines method.  The program fits a straight line to the points that correspond to X and the (k - 1)/2 points on each side of X, where k is forced to be an odd integer.

The program fits the line to the values that are available at the beginning and end of the data, where less than (k - 1)/2 values are found on one side of X.

This method takes longer to compute than the Running Means method, but it is less biased at the beginning and end of the data.

Locally Weighted Regression

This option smoothes the points using the Locally Weighted Regression method.  The program fits a straight line to the k points that are closest to X by using weighted least squares.  The weights depend on the distance from X, with the closest points getting the most weight.

This method takes longer to compute, but tends to give smoother results than either the Running Means or Running Lines methods.

Robust Lowess

This option smoothes the data using the Robust Lowess method, which is identical to the Lowess method except that the program repeats the smoothing process a second time, which gives reduced weight to points that are the furthest away from the first smoothed line.  This tends to reduce the effect of outliers, which are points that do not follow the general pattern of the other points.

This method is very time-consuming to compute due to the Lowess smoothers.


Data

Enter the name of the variable that contains the data that will be analyzed.  The variable can be from DataSheet or spreadsheet files or from data you manually enter using the DataEditor.  You must enter numeric data.


Select (Subset of Observations)

[Optional]  Select a subset of the observations.  For example, to analyze the first 50 values in each variable, enter first (50) into this text box.


Sort

Sorts the variable names alphabetically; it is the default.


Data Type

Select the type of data that will be used to create the diagram.

Discrete

Plots the observed values; it is the default.

Interval

Plots the values using intervals.


Number of Intervals

Enter the number that will be used for the increments along the X-axis.  Enter an integer between 2 and 1000.  You can use this option only if you select Interval data.


Smoothing Fraction

This text box allows you to enter a value (as a percentage of the number of values), the program will use for the size of the smoothing window.  Enter an integer from 1 to 99; 50 percent is the default.

As you increase the smoothing fraction, the line on the plot appears smoother, but it also shows less detail regarding any true curvature.


Y

Enter the name of the variable that will be plotted on the Y-axis.  You must enter numeric data.


X

Enter the name of the variable that will be plotted on the X-axis.  You must enter numeric data.


Bubble Size

Enter the name of the variable that will determine the size of the bubble. The larger the value, the larger the bubble.  The variable must contain numeric data.


Codes

[Optional]  Enter the name of the variable that contains the level codes for each of the bubbles.  The variable can contain either numeric or character data.  Each unique level displays as a bubble that contains a different pattern, all the same color; this is the default.


Filled Circles

Uses bubbles filled with color.  This option is the default.


Maximum Size

Enter a number that will determine the maximum size of the largest bubble.  Enter an number between 1 and 100; the default is 10 percent.


Columns

Enter the name of the variables that will be included in the analysis.  The number of variables should equal the number of bars that will be shown for each classification factor.  The variables can include positive or negative values.


Standard Errors

[Optional]  Enter the name of the variable that contains the values for the length of the error bars.


Labels (for Bars)

[Optional]  Enter the name of the variable that contains the labels for each bar.


Event Probability

These text boxes allow you to enter values for up to five sets of parameters the program will use for the probability of observing successes in a fixed number of independent or Bernoulli trials.  Enter numbers between 1 and 0.


Trials

These text boxes allow you to enter values for up to five sets of numbers the program will use for the number of identical trials.  Enter integers between 1 and 99,999,999.


Lower Limit

These text boxes allow you to enter values for up to five sets of parameters the program will use for the lower limit that the random variables can assume.  Enter integers from 0 to 99,999,999.


Upper Limit

These text boxes allow you to enter values for up to five sets of parameters the program will use for the upper limit that the random variables can assume.  Enter integers from 0 to 99,999,999.


Event Probability

These text boxes allow you to enter values for up to five sets of parameters the program will use for determining the probability of observing a success.  Enter numbers between 1 and 0.


Successes

These text boxes allow you to enter numbers for up to five sets of parameters the program will use for determining the number of successes.


Shape 1

These text boxes allow you to enter values for up to five sets of parameters the program will use for determining Shape 1.  Enter numbers between 1 and 0.


Shape 2

These text boxes allow you to enter values for up to five sets of parameters the program will use for determining Shape 2.  Enter numbers between 1 and 0.


Shape

These text boxes allow you to enter values for up to five sets of parameters the program will use for determining the Shape parameter.  Enter integers between 1 and 99,999,999.


Scale

These text boxes allow you to enter values for up to five sets of parameters the program will use for determining the Scale parameter.  Enter numbers between 1 and 0.


Mode

These text boxes allow you to enter values for up to five sets of parameters the program will use for determining the mode of the distribution.  Enter any numbers.


Mean

These text boxes allow you to enter values for up to five sets of parameters the program will use for determining the mean of the distribution.  Enter any numbers.


Std. Dev. (Standard Deviation)

These text boxes allow you to enter values for up to five sets of parameters the program will use for determining the standard deviation of the distribution.  Enter numbers between 1 and 0.


Center Point

These text boxes allow you to enter values for up to five sets of parameters the program will use to declare the center point of the distribution.  Enter any numbers.


Function

Enter a function that includes X and Y that will be used to create the plots.


X

Determines a range of values for the X-axis.

From

Enter the beginning value for the axis.

To

Enter the ending value for the axis.


Y

Determines a range of values for the Y-axis.

From

Enter the beginning value for the axis.

To

Enter the ending value for the axis.


Horizontal Divisions

Enter the number of horizontal lines that will be plotted on the Surface Plot.  Enter a number from 5 to 100; the default is 10.


Vertical Divisions

Enter the number of vertical lines that will be plotted on the Surface Plot.  Enter a number from 5 to 100; the default is 10.


Type (of Display)

Determines the type of plot that will be displayed.

Wire Frame

Displays horizontal and vertical lines on the plot; it is the default.

Solid

Displays a solid surface on the plot.

Contoured

Displays a topographical representation, with colors that correspond to the height of the surfaces.


Resolution

Enter the number of density values that will be calculated.  Enter a number between 1 and 100; the default is 21.


Contours Below

Determines if a Contour Plot will be displayed below the Surface Plot.


Contours

Determines the values for the attributes of the contours on the Contour Plot, or for attributes of the contours that are placed below the Surface Plot.  Note:  The options and text boxes are available only when you select the Contour Plot, Surface Plot, and Contours Below options.

From

Enter a value for the first contour line.  Enter a number less than the To value.

To

Enter a value for the last contour line.  Enter a number greater than the From value.

By

Enter a value for the spaces between the contour lines.  The contour levels are calculated using this value plus the values in the From and To text boxes.


From

Enter a value for the first contour line.  Enter a number that is less than the number you enter into the To text box; the default is function specific.


To

Enter a value for the last contour line.  Enter a number that is greater than the number you enter into the From text box; the default is function specific.


By

Enter a value for the spacing between the contour lines. This number, along with the numbers you enter into the From and To text boxes, are used to calculate the contour levels; the default is function specific.


Type

Determines what will appear on the plot.

Lines

Displays the plot with lines that connect the points along each contour; it is the default.

Painted Regions

Displays the plot with the regions of the contours painted (filled in).


Resolution

Enter a value that designates the number of density values that will be calculated.  Enter a number between 1 and 100; the default is 21.


Titles

Determines the titles that will appear on the chart.

Top

Enter the title that will appear above the chart.  Leave the text box blank if you do not want to use a title.

X-Axis

Enter the title that will appear on the horizontal (X) axis.  Leave the text box blank if you do not want to use a title.

Y-Axis

Enter the title that will appear on the vertical (Y) axis.  Leave the text box blank if you do not want to use a title.


X-Axis Scaling

Determines the values for the tickmarks that will appear on the X-axis.

From

Enter the minimum numeric value for the tickmarks; the default is 0.

To

Enter the maximum numeric value for the tickmarks; the default is 100.

By

Enter a value for the distance between each numeric tickmark.  Enter any positive numeric value; the default is 20.


Y-Axis Scaling

Determines the values for the tickmarks that will appear on the Y-axis.

From

Enter the minimum numeric value for the tickmarks; the default is 0.

To

Enter the maximum numeric value for the tickmarks; the default is 100.

By

Enter a value for the distance between each numeric tickmark.  Enter any positive numeric value; the default is 20.


Lines

Determines the position and direction for up to eight lines on the customized chart.  Use the Text Options dialog box to change the default graphics settings for the text.

Position

Enter values for the X- and Y-intercepts for a customized chart.  Enter any numeric value.  If you enter a value that does not fit within the axis scaling, the line will not appear on the chart.

Direction

Select a direction for each line.  If you select Horizontal, the line is drawn parallel to the X-axis.  If you select Vertical, the line is drawn parallel to the Y-axis.


Data

Enter the name of the variable that contains the measurement data.


Codes

Enter an expression or the name of the variable that contains the classification codes, which will be used to define the subgroups.  You must enter a code for each observation, which means that there must be one level code for each variable you enter into the Data text box.  You can enter numeric or categorical data.  The program ignores data that do not have a corresponding code.


Labels
Labels (for classification codes)

Enter the name of the variable that contains the labels for each classification code.  If you leave this text box blank, the default labels are based on the variable you enter into the Codes text box; each unique code  requires only one label.


Intervals

Determines options for the intervals that will be calculated.

None

Intervals are not calculated.

Standard Error

Calculates an Upper and Lower limit for each of the means.  The Lower and Upper limits are equal to the mean plus or minus one standard error, respectively.

Confidence Limits

Calculates confidence limits for each mean using their corresponding standard error values.


Intervals

Select options for the intervals that will be calculated.

None

Intervals will not be calculaated for the Means Table.

Standard Errors

Displays vertical lines, which represent the means plus and minus one standard error. This option is the default.

Confidence Limits

Displays the confidence intervals for the means based on their corresponding standard errors.


Show Data Values

Plots all the values on the plot, which results in a Scatterplot with the means to the right.  The default is to plot all of the data values.


Columns

Enter the names of the variables that contain the row-wise data for which you want to calculate and save statistics.


Data

Enter the name of the variable that contains the uncensored data you want to fit.


Number of Classes

Enter the number of classes into which the data will be grouped.  Enter an integer greater than 1; the default depends on the data.


Lower Limit

Enter a value for the Lower limit for the first class.  Enter any number lower than the Upper limit; the default depends on the data.


Upper Limit

Enter a value for the Upper limit for the last class.  Enter any number greater than the Lower limit; the default depends on the data.


Sample Size

Enter a value for the hypothetical sample size.  Enter an integer between 6 and 1,000,000. The default depends on the data.

When you enter a new value, the Upper and Lower interval limits are adjusted.  A larger sample size improves the precision of the parameter estimates and produces a narrower tolerance interval.


Confidence Level (for Tolerance Limits)

Enter a value for the confidence level that will be used to calculate the tolerance limits.  The default is 95 percent; other common levels are 90 and 99.


Population Proportion (for Uncensored Data)

Enter a value (as a percent), which is the proportion of observations that can be expected to fall between the limits.  Enter a number between 1.e-010 and 99.9999.


Population Proportion

This text box allows you to enter a value (as a percent), which is the proportion of observations that can be expected to fall between the limits.  Enter a number between 1.e-010 and 99.9999.  If you enter a value into this text box you cannot enter one in the Confidence Level text box.


Interval Depth

Enter a value for the interval depth.  The Upper and Lower tolerance limits are obtained by sorting the data and counting in from each end a number of observations equal to the depth value.  The default is 1, which takes the Lower and the Upper limits to the smallest and largest number, respectively.


Input

Determines if the Confidence Level or the Population Proportion will be calculated.

Confidence Level

Enter a value for the confidence level that will be used to calculate the tolerance limits.  The default is 95 percent; other common levels are 90 and 99.  If you enter a value into this text box you cannot enter one in the Population Proportion text box.  This option is the default.

Population Proportion

Enter a value (as a percent), which is the proportion of observations that can be expected to fall between the limits.  Enter a number between 1.e-010 and 99.9999.  If you enter a value into this text box you cannot enter one in the Confidence Level text box.


Method

Determines which method will be used to estimate the density trace.

Boxcar

Assigns a constant density to each small interval around each value, which smoothes the density function into a series of overlapping rectangles or boxcars, similar to a simple moving average.

Cosine

Smoothes local densities into a series of overlapping, bell-shaped intervals similar to a weighted moving average.  This method gives a smoother density trace; it is the default.


Interval Width

Enter the degree of overlap that will be used to compute the density trace.  Enter an integer between 10 and 90; the default is 60.  Increasing the interval width makes the density trace smoother, but may obscure the original data.


X-Axis Resolution

Enter a number that will be used to smooth the curve.  Enter a number from 20 to 200; the default is 30.  The higher the number, the smoother the curve.


Fitted Line

Determines if a fitted line will display on the plot; if so, which method will be used to fit the line.

None

Displays the plot without a fitted line.

Using Quartiles

Displays the plot with the fitted line drawn through the median, with the slope determined by the quartiles.  This option is the default.

Using Least Squares

Displays the plot with a fitted line, with the slope determined by using least squares regression.


Plot (Types of Functions)

Select the function that will be used to produce the plot.

Density Function

Produces a plot using a function that gives the rate at which the cumulative probability increases at a given point; it is the default for Distribution Function 1

CDF

Produces a plot using a cumulative distribution function that shows the probability of observing a value less than or equal to a value you select; it is the default for Distribution Function 2

Survivor Function

Produces a plot using a function that shows the probability of observing a value greater than a value you select.  The survivor function is 1 - CDF.  For reliability data, the survivor function shows the probability of surviving to time x without failure

Log Survivor Function

Produces a plot using a function that shows the probability of observing a value greater than a value you select (in log units); that is, the log of the survivor function

Hazard Function

Produces a plot using a function that shows the probability of failure during a small increment of time when no failure occurs before a time you select.  The hazard function is the Probability Density Function divided by the Survivor Function.


Data

Enter the name of the variable that contains the uncensored data that will be used in the analysis.


Censoring

Enter the name of the variable that contains the censored data.  Zeros indicate uncensored items; any other number, but usually -1 or 1, indicates a censored item.  Use negative numbers to indicate that the observation is left-censored (the value for the observation is less than the mean of the distribution).  Use positive numbers to indicate right-censored observations (the value for the observation is greater than the mean of the distribution).


Interval Widths

Enter the name of the variable that contains the interval widths in which the number of failures will be recorded.


Number of Failures

Enter the name of the variable that contains the number of failures in each interval.

Note:  To calculate life tables for more than one group, enter multiple entries into this text box and into the Number of Censored text box.


Number Censored

Enter the name of the variable that contains the number of censored observations in each interval.


Group Labels

[Optional]  Enter the name of the variable that contains the labels for each group.


Data (Time Entering Study)

Enter the name of the variable that contains the time that each item entered the study.


Censored (Contains Censored Data)

Enter the name of the variable that contains the censored data.  Enter a number greater than 0, usually 1.  A negative number is not recognized as a censored item.


Group (Life Tables Times Analysis)

Enter the name of the variable that contains the group codes.  A separate Life Table is created for each group.


Data

Enter the name of the variable that contains the failure or censoring times of the experimental items.  You must enter a time for all failed and unfailed items.


Censored

Enter the name of the variable that contains the censoring indicators.  Enter a number greater than 0 for any row that contains a failure time.  Enter a value greater than 0 (usually 1) for any row that contains a censored time.  Negative numbers are not recognized as censored items.


Group

[Optional]  Enter the name of the variable that contains the group codes.  A separate Weibull Analysis is performed for each group.


Starting Point

Enter a value that will be used as the starting point or origin of the Weibull distribution. Use this text box when the origin is not located at zero.  The default is 0.


Estimation Method

Determines the estimation method that will be used for the calculations.

Rank Regression

Determines the values of α and β by regrssing ln(x(i)-Δ) against specified estimates of the reliability Ri.  The reliabilities or plotting positions can be defined in any of four different ways: Median Ranks, Expected Ranks, Kaplan-Meier, Modified Kaplan-Meier (see Plotting Position).

Maximum Likelihood

Determines the values of α and β by maximizing the likelihood function of the data.  The likelihood function is given by the product of f(x(I)) for all failures times and (1 – F(x(I)) for all censored times.

Weibayes

Assuming that the user specifies the Shape parameter α, the maximum likelihood estimator of the Scale parameter β is given by

B = Σ(xIα/r)1/α


Type

Determines if lines or painted regions will be used.

Lines

Determines if lines will connect the points along each contour.  The default is lines.

Painted Regions

Determines if the regions of the contours will be painted (filled in).


X-Axis Resolution (Censored Data)

Enter the number of density values that will be calculated. Enter an integer between 20 and 500. The higher the resolution, the smoother the line.


Chart Type

Determines the format for the bars on the chart.

Clustered

Draws a separate bar for each classification.  This option is the default.

Stacked

Draws the bars for each classification, stacked one on top of the other, in a cumulative fashion.


Scaling

Determines how the types of data will appear on the plot.

Frequencies

Draws bars that represent the number of items that fall into each classification.  This option is the default.

Percentages

Draws bars that represent the percentage of observations that fall into each classification.


Direction

Determines the direction of the bars on the plot.

Horizontal

Displays the bars horizontally; this option is the default.

Vertical

Displays the bars vertically.


Error Bars

Determines the type of bar that will appear on the chart.

I-Beams

Plots the bars as I-beams, it is the default.

Lines

Plots the bars as lines.


Baseline

Enter a value for the stating point for the bars on the chart.  Enter any number; usually 0, however, you can also enter other numbers to emphasize differing relationships among the classes.  If you use a number larger than the largest class in the data, the bars descend from the baseline (on a vertical Barchart) or extend to the left of the baseline (on a horizontal Barchart).


Plotting Position

Determines the vertical position of the points on the Weibull Plot.  This also affects the estimates of the Weibull parameters when using the Rank Regression method.

Median Ranks

Uses an approximation to the median plotting position as calculated from the medians of the order statistics from a uniform distribution on (0,1).

Ri = (ji - .3)/(n + .4)

where ji is a failure order number defined by ji = ji-1 + δ and j0 = 0.  δ is initially set to 1 and modified whenever Ri corresonds to a censoring time according to δ = ((n+1) – previous failure number)/(1 + number of items before previous censored item.

Expected Ranks

Uses the expected values of the order statistics, which computes reliabilities according to the recursive relation

Ri = [ri/(ri+1)]Ri-1

where ri equals the reverse ranks of the data values and R0 = 1.

Kaplan-Meier

Uses the Kaplan-Meier method for computing the empirical c.d.f., which computes reliabilities according to

Ri = [ri-1)/ri]Ri-1

Modified Kaplan-Meier

Uses the modified Kaplan-Meier method in which reliabilities are computed from the Kaplan-Meier 	reliabilities according to

R’i = (ri + Ri+1)/2


Time Sequence Plot (Univariate Plot Analysis)

The Time Sequence Plot option creates a plot that is useful for detecting trends that occur over time, or for determining patterns in the data.  Use it only when the data are collected and stored in time order; the observations are plotted in the order in which they were entered into the DataSheet.

Use the Plot Options dialog box to indicate if points or lines will appear on the plot.  To clearly see the pattern in the plot, choose a smoothing option from the Scatterplot Smoothing Options dialog box, which is accessed by clicking the Smooth/Rotate button on the Analysis toolbar.


Analysis Summary (Dot Diagram Analysis)

The Analysis Summary tabular option creates and displays a summary of the analysis.  The summary includes the name of the selected variable, the number of observations in the variable, the mean, and the standard deviation.


Dot Diagram (Dot Diagram Analysis)

The Dot Diagram graphical option creates and displays a plot that is useful for showing the relative positions of the data in the dataset.  Every value in the numeric column is shown as a small square.


Analysis Summary (Bubble Chart Analysis)

The Analysis Summary tabular option creates and displays a summary of the analysis.  The summary displays the names of the variables that will appear on the X- and Y-axes as well as the name of the variable that contains the bubble size.  The number of observations is also shown.


Bubble Chart (Bubble Chart Analysis)

The Bubble Chart graphical option creates and displays a symbolic X-Y Scatterplot.  The size of each bubble on the chart is based on the magnitude of a third numeric variable.


Analysis Summary (Multiple Barchart Analysis)

The Analysis Summary tabular option creates and displays a summary of the analysis.  The summary contains the names of the row and column variables, the number of variables you selected (if you used this option), and the number of observations, rows, and columns.


Barchart (Multiple Barchart Analysis)

The Barchart graphical option creates and displays a Barchart with a column of numeric values for each of the variables.  The program places a single bar for each row of the column.


Analysis Summary (Response Surfaces Analysis)

The Analysis Summary tabular option displays the function that will be plotted.


Surface Plot (Response Surfaces Analysis)

The Surface Plot graphical option creates and displays a three-dimensional plot of the function.


Contour Plot (Response Surfaces Analysis)

The Contour Plot graphical option creates and displays a two-dimensional plot of the function.


Analysis Summary (Custom Charts Analysis)

The Analysis Summary tabular option creates and displays instructions for customizing the chart.


Custom Chart (Custom Charts Analysis)

The Custom Chart graphical option creates and displays a customized chart that contains the titles and axis scaling you selected on the dialog box.


Analysis Summary (Subset Analysis)

The Analysis Summary tabular option creates and displays a summary of the analysis.  The summary includes the names of the variables you selected, the number of observations and the number of levels.


Summary Statistics (Subset Analysis)

The Summary Statistics tabular option creates and displays statistical information about the center, spread, and shape of the data:  The number of values in the variable; the average, variance, standard deviation, minimum and maximum values; the standard skewness and standard kurtosis; and the sum of all the values.  This information is helpful when you need to determine if other statistical analyses might be appropriate to use with the data, or when you need to determine if you should transform the data.


Means Table (Subset Analysis)

The Means Table tabular option creates and displays a report of the sample means and standard errors for the levels in the data.  The report also shows the intervals that represent the means plus and minus one standard error.


Scatterplot (Subset Analysis)

The Scatterplot graphical option creates and displays a scatterplot that displays the pattern of points that result from plotting the values of the variable.  The levels are shown on the X-axis while the numeric values of the data are shown on the Y-axis.


Means Plot (Subset Analysis)

The Means Plot graphical option creates and displays a plot that shows the sample means for the levels.  The vertical lines represent the means plus and minus one standard error.


Median Plot (Subset Analysis)

The Median Plot graphical option creates and displays a plot of the sample medians for the levels in the variables you selected.


Sigma Plot (Subset Analysis)

The Sigma Plot graphical option creates and displays a plot that shows the sample ranges for the levels of the variables you selected.


Range Plot (Subset Analysis)

The Range Plot graphical option creates and displays a plot of the sample ranges for the levels in the variables you selected.


Box-and-Whisker Plot (Subset Analysis)

The Box-and-Whisker Plot graphical option creates and displays a Box-and-Whisker Plot for each level of the variable you selected.

The rectangular part of the plot extends from the lower quartile to the upper quartile, covering the center half of each sample.  The center lines within each box show the location of the sample medians.  The plus signs represent the location of the sample means.

The whiskers extend from the box to the minimum and maximum values in each sample, except for any outside or far-outside points, which are plotted separately.  Outside points lie more than 1.5 times the interquartile range above or below the box; they are shown as small squares.  Far-outside points lie more than 3.0 times the interquartile range above or below the box; they are shown as small squares with plus signs through them.


Analysis Summary (Row-Wise Statistics Analysis)

The Analysis Summary tabular option creates and displays the names of the variables you selected (the data columns), and the number of rows.


Summary Statistics (Row-Wise Statistics Analysis)

The Summary Statistics tabular option creates and displays a table that shows the sample statistics for the rows in the file that have at least one nonmissing value.


Means Table (Row-Wise Statistics Analysis)

The Means Table tabular option creates and displays a table that shows the sample means and standard errors for the rows in the file that have at least one nonmissing value.  The table also shows the intervals that represent the means plus or minus one standard error.


Scatterplot (Row-Wise Statistics Analysis)

The Scatterplot graphical option creates and displays a scatterplot that displays the pattern of points that result from plotting the values of the variable.


Means Plot (Row-Wise Statistics Analysis)

The Means Plot graphical option creates and displays a plot that shows the sample means for the rows in the file that have at least one nonmissing value.  The vertical lines represent the means plus and minus one standard error.


Median Plot (Row-Wise Statistics Analysis)

The Median Plot graphical option creates and displays a plot of the sample medians for the rows in the file that have at least one nonmissing value.


Sigma Plot (Row-Wise Statistics Analysis)

The Sigma Plot graphical option creates and displays a plot that shows the sample standard deviations for the rows in the file that have at least one nonmissing value.


Range Plot (Row-Wise Statistics Analysis)

The Range Plot graphical option creates and displays a plot of the sample ranges for the rows in the file that have at least one nonmissing value.


Box-and-Whisker Plot (Row-Wise Statistics Analysis)

The Box-and-Whisker Plot graphical option creates and displays a Box-and-Whisker plot for each of the rows of data you selected.  The rectangular part of the plot extends from the lower quartile to the upper quartile, covering the center half of each sample.

The centerlines within each box show the location of the sample medians.  The plus signs represent the location of the sample means.  The whiskers extend from the box to the minimum and maximum values in each sample except for any outside or far-outside points, which are plotted separately.

Outside points are points that lie more than 1.5 times the interquartile range above or below the box; they are shown as squares on the plot.  Far-outside points lie more than 3.0 times the interquartile range above or below the box; they are shown as small squares with plus signs through them.


Analysis Summary (Uncensored Data Analysis)

The Analysis Summary tabular option creates a summary of the analysis that includes the name of the variable you selected, the number of values and their range, the name of the distribution you are currently using, and the estimated parameters for that distribution.

Use the Probability Distributions Options dialog box to choose options for the analysis,


Tests for Normality (Uncensored Data Analysis)

The Tests for Normality tabular option calculates the results for several tests that determine if the data can be adequately modeled by the distribution you are using.  The results include the values and the p-values for these tests: Chi-Square goodness-of-fit and Shapiro-Wilk's W, the z-score for skewness, and the z-score for kurtosis.

Chi-Square Goodness-of-Fit

Compares the frequency of the data (observed frequency) with a distribution you select (expected frequency).  This is an updated version of the standard chi-square goodness-of-fit statistic (see Madansky, 1988).

Shapiro-Wilk's W-Statistic

Tests the assumption that the data follow a Normal rather than another distribution (see Madansky, 1988).

z-Score for Skewness

Determines if the data are symmetrically distributed; and, if so, how likely they are to be normally distributed.  Unlike standardized skewness, the z-score for skewness is valid for small sample sizes (n is less than or equal to 8) (see D'Agostino and Stephens, 1986).

z-Score for Kurtosis

Determines the degree of peakedness of the distribution.  Unlike standardized kurtosis, the z-score for kurtosis is valid for small sample sizes (n is less than or equal to 20) (see D'Agostino and Stephens, 1986).


Goodness-of-Fit Tests (Uncensored Data Analysis)

The Goodness-of-Fit Tests option calculates results for tests of fit based on the Empirical Distribution Function (EDF).  EDF is a step function that is calculated from the sample, which estimates the population distribution function.  EDF statistics are used for testing the fit of the sample to the distribution (D'Agostino and Stephens, 1986).  The tests are: Chi-Square Goodness of Fit, Kolmogorov-Smirnov D, Kuiper V, Cramer-von Mises W2, Watson U2, and Anderson-Darling A2.

D'Agostino and Stephens (1986) provide the following explanation of these EDF statistics:

The first two EDF statistics, D+ and D-, are respectively, the largest vertical difference when Fn(x) is smaller than F(x), and the largest vertical difference when Fn(x) is smaller than F(x). . . . The most well-known EDF statistic is D, introduced by Kolmogorov (1933)....  A closely related statistic V, given by Kuiper (1960), is useful for observations on a circle. . . . A second and wide class of measures of discrepancy is given by the Cramer-von Mises family . . . when y(x) = 1, the statistic is the Cramer-von Mises statistic, now usually called W2, and when

y(x) =[{F(x)}{1 - F(x)}]-1

the statistic is the Anderson-Darling statistic, called A2.  A modification of W2, also devised originally for the circle, is the Watson statistic U2.

Chi-Square

The chi-square statistic divides the range of the data into nonoverlapping intervals and compares the number of observations in each class with the number of expected frequencies, based on the fitted distribution.

Kolmogorov-Smirnov D

The Kolmogorov-Smirnov D statistic calculates the maximum distance between the cumulative distribution of the data and the cumulative distribution function of the fitted distribution.  This calculation is a nonparametric method that tests the overall goodness of fit between the distribution of the data and the distribution you choose.

Kuiper V

The Kuiper V statistic improves the Kolmogorov-Smirnov test in the tails of a distribution.  If there are only two class levels, it is a scaled value for an asymptotic distribution, and determines the probability of observing a larger test statistic.

Cramer-von Mises W2

The Cramer-von Mises W2  statistic determines if a one-dimensional data sample is compatible with being a random sample from a given distribution.  It determines if two data samples are compatible with being random samples from the same unknown distribution.  It is similar to the Kolmogorov-Smirnov test except it is more complex.

Watson U2

The Watson U2 statistic is a modification of the Cramer-von Mises statistic; it was originally devised for a circle.

Anderson-Darling A2

The Anderson-Darling statistic is a general test for complete datasets (without censored observations) that compares the fit of an observed cumulative distribution function with an expected cumulative distribution function.

Use the Goodness-of-Fit Tests Options dialog box to choose an EDF statistic.


Tail Areas (Uncensored Data Analysis)

The Tail Areas tabular option calculates the area under the density curve at specified points.  The test uses the cumulative distribution function to calculate the probability that a random variable will fall below a given value.  The test calculates tail areas for up to five critical values.

Use the Tail Areas Options dialog box to choose options for the test,


Critical Values (Uncensored Data Analysis)

The Critical Values tabular option calculates the critical values for the distribution.  Critical values are the smallest values for the area that fall under the distribution curve.  The values for the distribution curve are those that are no less than the values you selected for the probability.  The test calculates critical values for up to five lower tail areas.

Use the Critical Values Options dialog box to Choose options for the table,


Normal Tolerance Limits (Uncensored Data Analysis)

The Normal Tolerance Limits tabular option creates normal tolerance limits for normally distributed data.  Tolerance limits are the values between which you can expect to find a specified proportion of the population.  The results show the sample size you selected, the estimated parameters for the Normal distribution, and the Upper and Lower tolerance limits for the specified population proportion and confidence level.

The program calculates the Upper and Lower tolerance limits by taking the mean of the data, plus or minus, respectively, K times the standard deviation, where K is a constant whose value is based on the sample size, the confidence level, and the population proportion specified for the test.  The value of K is also shown in the results.  The analysis uses the estimated parameters for a column of data to determine the tolerance limits for future samples taken from the same population.

If yiou believe your data do not follow a Normal distribution and you want nonparametric tolerance limits, use the Distribution-Free Tolerance Limits option.

Use the Normal Tolerance Limits Options dialog box to enter values for the size of the sample, the confidence level, and the population proportion.


Distribution-Free Tolerance Limits (Uncensored Data Analysis)

The Distribution-Free Tolerance Limits option creates nonparametric limits, as well as the number of counts; the minimum, maximum, and median of the data; and the confidence level for the limits and population proportion.  The program calculates the interval using the smallest and largest value(s) from the dataset.  Use nonparametric tolerance limits when you believe that the data may not be from a Normal distribution.

Use the Distribution-Free Tolerance Limits Options dialog box to choose options for the test,


Density Trace (Uncensored Data Analysis)

The Density Trace option creates a plot, which is a smoothed histogram of the shape of the distribution, especially the variations in density over the range of the data.  The plot uses overlapping intervals and a weight function to smooth the densities, which results in a continuous line rather than a group of rectangles

Use the Density Trace Options dialog box to choose options for the plot.


Symmetry Plot (Uncensored Data Analysis)

The Symmetry Plot option creates a plot that helps assess the symmetry of the data.  The program constructs the plot by first sorting the values from smallest to largest.  It then selects the values to the left and right of the median and plots them as points a respective distance from the median.  It repeats this process for the pair of points that are second closest to the median, then third closest, and so on.

If the distribution is symmetric, the points will lie close to the diagonal line.  If the distribution is positively skewed, the points will deviate above the line.  If the distribution is negatively skewed, the points will deviate below the line


Frequency Histogram (Uncensored Data Analysis)

The Frequency Histogram option creates a histogram that shows the distribution curve shown as an overlay.  The program divides the data into sets of nonoverlapping intervals and plots bars for each interval; the height of each bar is proportional to the number of observations that fall within that interval.  Use the plot to determine if the data follow the distribution you selected.

Use the Frequency Tabulation Options dialog box to choose options for the plot.

Note:  Changes you make to this plot can affect the Goodness-of-Fit tabular option.


Distribution Functions 1 and 2 (Uncensored Data Analysis)
Distribution Functions 1 and 2

The Distribution Functions 1 and 2 graphical options each create and display one of several different types of distribution function plots.

The type of functions you can display are the Density Function, Cumulative Distribution Function, Survivor Function, Log Survivor Function, and Hazard Function.

The default for Distribution Function 1 is the Density Function plot.  The default for Distribution Function 2 is the Cumulative Distribution Function plot.

Use the Options dialog box to select the type of function distribution you want to plot.

To select options for the plot, use the Distribution Functions Options dialog box.


Analysis Summary (Censored Data Analysis)

The Analysis Summary tabular option creates and displays a summary of the results, which includes the number of values and their ranges, as well as the number of left- and right-censored (positive/negative) observations.  It then displays the results of the fitted distribution; for example, it shows the values for the mean and standard deviation of a Lognormal distribution.

To select a distribution for the analysis, use the Probability Distribution dialog box.


[Chi-Square] Goodness-of-Fit Tests (Censored Data Analysis)

The [Chi-Square] Goodness-of-Fit Tests tabular option calculates and displays the results of a Chi-Square test, which helps to determine if the data can be adequately modeled by a selected distribution.

The Chi-Square test divides the range of data into nonoverlapping intervals and compares the number of observations in each class with the number of expected frequencies, based on the fitted distribution.  If the p value is less than .05 (for a 95 percent confidence level), the data do not fit the distribution.

To select options for the test, use the Frequency Tabulation Options dialog box.


Tail Areas (Censored Data Analysis)

The Tail Areas tabular option calculates and displays the area under the density curve at specified points.  The test uses the cumulative distribution function to calculate the probability that a random variable will fall below a given value.  The test calculates tail areas for up to five critical values.

To select options for the test, use the Tail Areas Options dialog box.


Critical Values (Censored Data Analysis)

The Critical Values tabular option calculates and displays the critical values for the distribution.  Critical values are the smallest values for the area that fall under the distribution curve.  The values for the distribution curve are those that are no less than the values you selected for the probability.  The test calculates critical values for up to five lower tail areas.

To select options for the table, use the Critical Values Options dialog box.


Frequency Histogram (Censored Data Analysis)

The Frequency Histogram graphical option creates and displays a histogram with the distribution curve shown as an overlay.  The data are divided into sets of nonoverlapping intervals and plots bars for each interval; the height of each bar is proportional to the number of observations that fall within that interval.  Use the plot to determine if the data follow the selected distribution.

To select options for the plot, use the Frequency Tabulation Options dialog box.


Distribution Functions 1 and 2 (Censored Data Analysis)
Distribution Functions 1 and 2

The Distribution Functions 1 and 2 options each create one of several different types of distribution function plots.

The type of functions you can display are:  Density Function, Cumulative Distribution Function, Survivor Function,  Log Survivor Function, and Hazard Function.

The default for Distribution Function 1 is the Density Function plot.  The default for Distribution Function 2 is the Cumulative Distribution Function plot.

Use the Distribution Functions Options dialog box to indicate the type of function distribution you want to plot, and to enter the number of density values that will be calculated.


Analysis Summary (Life Tables Intervals Analysis)

The Analysis Summary tabular option displays a summary of the estimated survival probabilities in each of the intervals.  The results include the number of items at risk at the start of each interval as well as the number that were withdrawn (censored) during the interval.

The Cumulative Survival column shows the values for the estimated probability that an item would survive at least as long as the beginning of the interval.

The Hazard column contains the values for the estimated hazard function (the instantaneous failure rate) during each interval.

The Density column contains estimates of the density function for the corresponding lifetime distribution.

The report also includes the standard errors (in parentheses) for each of the three functions.


Percentiles (Life Tables Intervals Analysis)

The Percentiles tabular option calculates and displays a table of the estimated percentiles for the lifetime distribution.  The percentiles estimate the length of time that a selected percentage of the items will survive.

The standard errors of the percentiles provide an estimate of how well the percentiles were estimated given the available data.

To select options for the table, use the Percentiles Options dialog box.


Group Comparisons (Life Tables Intervals Analysis)

The Group Comparisons tabular option creates and displays the results of comparing the groups in the study.

The table displays the total number of items in the table, the number of items that failed, and the number that were withdrawn or censored.  It also displays the proportion of the censored items.


Survival Function (Life Tables Intervals Analysis)

The Survival Function graphical option creates and displays a plot of the estimated survivor function.  The survival function is the probability that an item will not fail before a specified length of time.

To select options for the plot, use the Life Table Plots Options dialog box.


Log Survival Function (Life Tables Intervals Analysis)

The Log Survival Function graphical option creates and displays a plot of the estimated log survival function.  The plot shows the cumulative survival function on a logarithmic scale.


Cumulative Hazard Function (Life Tables Intervals Analysis)

The Cumulative Hazard Function graphical option creates and displays a plot of the estimated cumulative hazard function.  The hazard function is helpful when you need suggestions for possible parametric models when you use failure data.


Death Density Function (Life Tables Intervals Analysis)

The Death Density Function graphical option creates and displays a plot of the estimated death density function.  The death density function corresponds to the probability distribution of item lifetimes.

To select options for the plot, use the Life Table Plots Options dialog box.


Hazard Function (Life Tables Intervals Analysis)

The Hazard Function graphical option creates and displays a plot of the estimated hazard function.  The hazard function shows the failure rate conditional to an item's survival to a certain point in time; that is, it plots the probability that an item that has survived to the beginning of the interval will experience failure in that interval.

To select options for the plot, use the Life Table Plots Options dialog box.


Analysis Summary (Life Tables Times Analysis)

The Analysis Summary tabular option creates and displays a table that shows the estimated survival probabilities.

Each row of the table represents a single value shown in increasing order.  If the value represents a failure or death, the Status column reads FAILED.  If the value represents a censored observation, the Status column reads WITHDRAWN.

The Time column displays the time an item failed or was withdrawn, while the Number at Risk column displays the number of items that did not fail or were not withdrawn or that were not censored before the observed time.

The Cumulative Survival values represent the probability that an item will survive to a particular point in time.  The values in the Standard Error and Cumulative Hazard columns represent respectively, the standard deviation of the product-limit estimates, and one minus the cumulative survival probability.


Percentiles (Life Tables Times Analysis)

The Percentiles tabular option calculates and displays a table of the estimated percentiles for the lifetime distribution.

The percentiles estimate the length of time that a selected percentage of the items will survive.  The standard errors of the percentiles provide an estimate of how well the percentiles were estimated given the available data.


Group Comparisons (Life Tables Times Analysis)

The Group Comparisons tabular option creates and displays the results of a comparison of the groups in the study using the Logrank and Wilcoxon tests.  The table displays the number of items at risk and the number of terminations for each group that you analyze.

The Chi-Square statistic shows the results of testing for the equivalence of death rates between the groups.  Other values show the associated significance level so you can determine if the survival rates are significantly different between the groups.


Survival Function (Life Tables Times Analysis)

The Survival Function graphical option creates and displays a plot of the estimated survival function.  The survival function is the probability that an item will not fail before a specified length of time.

To select options for this plot, use the Life Table Plots Options dialog box.


Log Survival Function (Life Tables Times Analysis)

The Log Survival Function graphical option creates and displays a plot of the log survival function.  The survival function is the probability that an item will not fail before a specified length of time.


Cumulative Hazard Function (Life Tables Times Analysis)

The Cumulative Hazard Function graphical option creates and displays a plot of the cumulative hazard function.  This plot is helpful when you are using failure data and need suggestions for possible parametric models.


Analysis Summary (Weibull Analysis)

The Analysis Summary option creates a summary of the results of fitting a Weibull distribution to a set of data.  The summary includes the name of the data and the censoring variables, as well as the name of the estimation method used.  The summary then displays the sample size, the number of failures, the estimated parameters for the distribution you selected, and the starting point.

Use the Weibull Analysis Options dialog box to choose an origin for the distribution starting point, an estimation method, and a plotting position.  The estimation methods include rank regression, maximum likelihood, and Weibayes.  The methods used to calculate the plotting position are median ranks, expected ranks, Kaplan-Meier, and modified Kaplan-Meier.


Tail Areas

The Tail Areas tabular option uses the cumulative distribution function to calculate and display the tail areas — the areas under the density curve at specified points.  This function calculates the probability that a random variable will fall below a given value.

Use the Critical Values Options dialog box to select options for the table.


Critical Values (Weibull Analysis)

The Critical Values tabular option calculates and displays the critical values for the fitted Weibull distribution(s).  Critical values are the smallest values for the area that falls under the distribution curve.  These values are no less than the value you select for the probability.


Weibull Plot (Weibull Analysis)

The Weibull Plot graphical option creates and displays a plot that is helpful in determining if the data can be modeled using a Weibull distribution.

The values are plotted along the horizontal axis using a logarithmic scale, and the median ranks that correspond to each value along the vertical axis.  The plot also shows the best-fitting straight line for the points.

If the points fall approximately on the straight line, the Weibull distribution is a good fit.


Frequency Histogram (Weibull Analysis)

The Frequency Histogram graphical option creates and displays a Frequency Histogram of the data.

The number of values in each interval are calculated and plotted as frequencies.  The plot also includes an overlay of the probability density function for the fitted Weibull distribution.

If the distribution fits well, the top of the bars should be relatively close to the line. The height of each bar is proportional to the number of observations that fall within that interval.

To select options for the plot, use the Frequency Tabulation Options dialog box.


Density Function (Weibull Analysis)

The Density Function graphical option creates and displays a plot that shows the probability density function for the fitted Weibull distribution.

The probability of attaining the values within the specified intervals is calculated by computing the areas under the function.


CDF (Weibull Analysis)

The CDF graphical option creates and displays a plot that shows the cumulative distribution function for the fitted Weibull distribution.  The height of the function indicates the probability of attaining a value less than or equal to the value on the X-axis.


Survival Function (Weibull Analysis)

The Survival Function graphical option creates and displays a plot that shows the survival function for the fitted Weibull distribution.  The survival function indicates the probability of attaining a value greater than or equal to the value on the X-axis.


Log Survival Function (Weibull Analysis)

The Log Survival Function graphical option creates and displays a plot that shows the log survival function for the fitted Weibull distribution.  The survival function indicates the probability of attaining a value greater than or equal to the value on the X-axis.


Hazard Function (Weibull Analysis)

The Hazard Function graphical option creates and displays a plot that shows the hazard function for the fitted Weibull distribution.

The hazard function is equal to the probability density function divided by the survival function.  When you model lifetime data, the hazard function represents the instantaneous failure rate.


SQL Data Sources Dialog Box

This dialog box allows you to select the data source you want to use and to use the New… command to access the Add Data Source dialog box to select an ODBC driver.  This is a standard Windows dialog box; see Microsoft's documentation for further information.

Selected Data Source

New...


Query Databases Dialog Box

This dialog box allows you to select a table (database), and to select and view fields on the table.  This is a standard Windows dialog box; see Microsoft's documentation for further information.

Table

Available Fields

Selected Fields


Query Database (ODBC) - Use Rows Dialog Box

This dialog box allows you to build or select a SQL statement to specify the subset you want to use.  The syntax rules may vary depending on the data source you are using.

Use Rows

Keypad

Functions


Scatterplot Smoothing Options Dialog Box

This dialog box allows you to select the method the program will use to perform the smoothing and to enter a value for the size of the smoothing window.

Type

Smoothing Fraction


Dot Diagram Analysis Dialog Box

Allows you to enter data that will be used to perform the analysis.

Data

Select

Sort

Delete...

Transform...

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Dot Diagram Analysis

Dot Diagram Options


Dot Diagram Options Dialog Box

Select the type of data that will be used to create the diagram, and to enter a number for the increments along the X-axis.

Data Type

Number of Intervals


Bubble Chart Analysis Dialog Box

This dialog box allows you to:

•	select the names of the variables that will be plotted on Y- and X-axes

•	enter the name of the variable that will be shown as the bubble

•	enter the name of the variable that contains the level codes for each of the bubbles

•	select a subset of the observations

•	sort the variables.

Y

X

Bubble Size

Codes

Select (Subset of Observations)

Sort

Delete...

Transform...

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Bubble Chart Analysis

Bubble Chart Options


Bubble Chart Options Dialog Box

Allows you to indicate whether or not you want filled bubbles on the chart, and to enter a number that will determine the maximum size of the largest bubble.

Filled Circles

Maximum Size


Multiple Barchart Analysis Dialog Box

The Multiple Barchart analysis creates one or more frequency bars for each classification factor (row).  The analysis is helpful when you need to graphically represent a secondary classification factor within a primary classification factor.

Columns

Standard Errors

Labels

Select (Subset of Observations)

Sort

Delete...

Transform...

To select options for the analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Multiple Barchart Analysis

Barchart Options


Bernoulli Options Dialog Box

Enter values for up to five sets of parameters that will be used for the probability of observing successes (Event Probability) in a fixed number of independent or Bernoulli trials.  Enter numbers between 0 and 1.


Binomial Options Dialog Box

Enter values for the event probability and the number of identical trials.

Event Probability

Enter values for up to five sets of parameters that will be used for determining the probability of observing successes in a fixed number of independent or Bernoulli trials.  Enter numbers between 1 and 0.

Trials

Enter values for up to five sets of numbers that will be used for determining the number of identical trials.  Enter integers between 1 and 99,999,999.


Discrete Uniform Options Dialog Box

Enter values for the Lower and Upper limits.

Lower Limit

Enter values for up to five sets of parameters that will be used for the Lower Limit that the random variables can assume.  Enter integers from 0 to 99,999,999.

Upper Limit

Enter values for up to five sets of parameters that will be used for the Upper Limit that the random variables can assume.  Enter integers from 0 to 99,999,999.


Geometric Options Dialog Box

Enter values for up to five sets of parameters that will be used for the probability of observing a success (Event Probability).  Enter numbers between 1 and 0.


Negative Binomial Options Dialog Box

Enter values for the event probability and successes.

Event Probability

Enter values for up to five sets of parameters that will be used for determining the probability of observing a success.  Enter numbers between 1 and 0.

Successes

Enter values for up to five sets of parameters that will be used for determining the number of successes.


Poisson Options Dialog Box

Enter values for up to five sets of parameters that will be used for determining the average number of events (Mean) that will occur during a specific period of time.  Enter numbers between 1 and 0.


Beta Options Dialog Box

Enter values for determining Shape 1 and Shape 2.

Shape 1

Enter values for up to five sets of parameters that will be used for determining Shape 1.  Enter numbers between 1 and 0.

Shape 2

Enter values for up to five sets of parameters that will be used for determining Shape 2.  Enter numbers between 1 and 0.


Chi-Square Options Dialog Box

Enter the degrees of freedom associated with each distribution in the five sets of parameters.  Enter integers between 1 and 99,999,999.


Erlang Options Dialog Box

Enter values for determining the Shape and Scale parameters.

Shape

Enter values for up to five sets of parameters that will be used for determining the Shape parameter.  Enter integers between 1 and 99,999,999.

Scale

Enter values for up to five sets of parameters that will be used for determining the Scale parameter.  Enter numbers between 1 and 0.


Exponential Options Dialog Box

Enter values for up to five sets of parameters that will be used for determining the mean time and distance between the occurrences of random events.  Enter numbers between 1 and 99,999,999.


Extreme Value Options Dialog Box

Enter values for determining the mode of the distribution and the Scale parameter.

Mode

Enter values for up to five sets of parameters that will be used to determine the mode of the distribution.  Enter any numbers.

Scale

Enter values for up to five sets of parameters that will be used to determine the Scale parameter.  Enter numbers between 1 and 0.


F (Variance Ratio) Options Dialog Box

Enter values for up to five sets of parameters that will used for determining the degrees of freedom for the numerator and the denominator.


Gamma Options Dialog Box

Enter values for determining the Shape and Scale parameters.

Shape

Enter values for up to five sets of parameters for determining the Shape parameter for the distribution.  Enter numbers between 1 and 0.

Scale

Enter values for up to five sets of parameters for determining the Scale parameter for the distribution.  Enter numbers between 1 and 0.


Laplace Options Dialog Box

Enter values determining the mean of the distribution and the Scale parameter.

Mean

Enter values for up to five sets of parameters for determining the mean of the distribution.  Enter any numbers.

Scale

Enter values for up to five sets of parameters for determining the Scale parameter for the distribution.  Enter numbers between 1 and 0.


Logistic Options Dialog Box

Enter values for determining the Mean and Standard Deviation parameters.

Mean

Enter values for up to five sets of parameters that will be used for determining the mean of the distribution.  Enter any numbers.

Standard Deviation

Enter values for up to five sets of parameters that will be used for determining the standard deviation of the distribution.  Enter numbers between 1 and 0.


Lognormal Options Dialog Box

Enter values for determining the Mean and the Standard Deviation.

Mean

Enter values for up to five sets of parameters that will be used for determining the mean of the distribution.  Enter numbers between 1 and 0.

Standard Deviation

Enter values for up to five sets of parameters that will be used for determining the standard deviation of the distribution.  Enter numbers between 1 and 0.


Pareto Options Dialog Box

This dialog box allows you to enter values for up to five sets of parameters that will be used for determining the Shape parameter for the distribution.  Enter numbers between 1 and 0.


Student's t Options Dialog Box

Enter values for up to five sets of parameters that will be used for determining the number of degrees of freedom associated with the distribution.  Enter integers between 1 and 0.


Triangular Options Dialog Box

Enter values for determining the Lower Limit, Center Point, and Upper Limit.

Lower Limit

Enter values for up to five sets of parameters that will be used for determining the Lower Limit that the random variables can assume.  Enter any numbers.

Center Point

Enter values for up to five sets of parameters that will be used for determining the Center Point that the random variables can assume.  Enter any numbers.

Upper Limit

Enter values for up to five sets of parameters that will be used for determining the Upper Limit that the random variables can assume.  Enter any numbers.


Uniform Options Dialog Box

Enter values for determining the Lower Limit and the Upper Limit.

Lower Limit

Enter values for up to five sets of parameters that will be used for determiming the Lower Limit that the random variables can assume.  Enter any numbers.

Upper Limit

Enter values for up to five sets of parameters that will be used for determining the Upper Limit that the random variables can assume.  Enter numbers up to 99,999,999.


Weibull Options Dialog Box

Enter values for determining Shape and Scale.

Shape

Enter values for up to five sets of parameters for determining the Shape parameter for the distribution.  Enter numbers between 1 and 0.

Scale

Enter values for up to five sets of parameters for determining the Scale parameter for the distribution.  Enter numbers between 1 and 0.


Cumulative Distribution Options Dialog Box

Enter up to five values that will be used for determining the random variables.


Inverse CDF Options Dialog Box

This dialog box allows you to enter values for the tail area you want to use.  You can enter up to five values.


Random Numbers Options Dialog Box

This dialog box allows you to enter the number of observations the program will include in the random sample.


Response Surfaces Analysis Dialog Box

The Response Surfaces analysis allows you to create Surface and Contour plots for functions that you specify.  You must write the functions involving X and Y; for example:

10 + 2*X + 3*Y - 10*X*Y

The plots are helpful when you need to visualize the shape of a response surface and when you need to locate optimal settings.

This dialog box allows you to enter a function that will be used to create the plots.  It also allows you to enter the range of values for X- and Y-axes.

Function

X

Y

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Response Surface Plots Analysis

Surface Plot Options

Contour Plot Options


Surface Plot Options Dialog Box

This dialog box allows you to:

•	enter a number for the horizontal and vertical divisions for the plot

•	select the type of plot that will display

•	enter the number of density values that will be calculated

•	indicate if you want a Contour Plot displayed below the Surface Plot

•	enter values for the attributes of the contours on the Contour Plot.

Horizontal Divisions

Vertical Divisions

Type

Resolution

Contours Below

Contours

Type


Contour Plot Options Dialog Box

This dialog box allows you to enter values for the first and last contour lines, to enter a value for the spacing of the contour lines, to indicate if you want lines or painted regions on the plot, and to enter a value for number of density values.

From

To

By

Type

Resolution


Custom Chart Analysis Dialog Box

The Custom Chart analysis allows you to create charts with custom titles, scaling, and horizontal and vertical lines.  Its primary purpose is to let you create charts you can use to overlay on other plots when you use the StatGallery.  A control chart is an example of a customized chart you could create.

This dialog box allows you to enter information that will be used to create charts with custom titles, scaling, and horizontal and vertical lines.

Titles

X-Axis Scaling

Y-Axis Scaling

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Custom Charts Analysis

Custom Chart Options


Custom Chart Options Dialog Box

This dialog box allows you to select the position and direction of up to eight lines on a customized chart.

Lines


Subset Analysis Dialog Box

The Subset Analysis (formerly known as the Codebook Analysis) provides the ability to calculate statistics for a single column of data at each level of a second code variable.  You can calculate separate summary statistics and plot means and confidence intervals for the subsets of data.

You define the subsets using the values in any variable that can partition the observations into subsets; for example, country, fiscal year, age, sex.  Doing this allows you to compare the central tendency, spread, and shape among the groups of data.  For example, using the Cardata sample dataset, you might want to calculate statistics on the mileage ratings for each of three regions of origin.  This is easily done using this analysis, which can calculate summary statistics for each level of a variable.

This dialog box allows you to enter information the program will use to calculate statistics for a single column of data at each level of a second code variable.

Data

Codes

Labels

Select (Subset of Observations)

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left mouse button on either Pane Options or Analysis Options.

See also

Using the Subset Analysis

Summary Statistics Options

Means Table Options

Means Plot Options

Plot Options

Box-and-Whisker Plot Options


Means Table Options Dialog Box

Select options for the intervals that will be calculated and enter a value for the confidence level.

Intervals

Confidence Level


Means Plot Options Dialog Box

Allows you to indicate how the data will appear on the plot, to enter the confidence level that will be used to calculate the confidence intervals, to select options for the intervals that will be calculated, and to indicate if you want to plot all of the values.

Plot (Points or Lines)

Confidence Level

Intervals

Show Data Values


Plot Options Dialog Box

Determines how the data will appear on the plot.

Points

Plots points; this option is the default.

Lines

Plots lines.


Row-Wise Statistics Analysis Dialog Box

The Row-Wise Statistics Analysis provides the capability to calculate and save statistics on a row-wise basis for data that are in two or more columns.  The analysis calculates summary statistics for each row of a set of columns.  It is designed to save the statistics so you can use them in other analyses when the data are not arranged in the usual column-wise manner.

Columns

Select

Sort

To select options for the analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Row-Wise Statistics Analysis

Summary Statistics Options

Means Table Options

Means Plot Options

Plot Options

Box-and-Whisker Plot Options


Frequency Tabulation Options Dialog Box (Uncensored/Censored Data Analyses)

Allows you to:

•	enter the number of classes into which the data will be grouped

•	enter a value for the Lower Limit and the Upper Limit

•	indicate if you want to retain the current scaling even if you change values on the Analysis dialog box.

Number of Classes

Lower Limit

Upper Limit

Hold


Tail Areas Options Dialog Box (Censored Data Analysis)
Tail Areas Options Dialog Box

Enter the values that will be used to calculate the areas under the curve.


Critical Values Options Dialog Box

Enter values for the probabilities that will be used to calculate the areas under the curve.  You can enter from one to five values.


Normal Tolerance Limits Options Dialog Box

Allows you to enter a value for the number of samples that will be taken, to enter a value for the confidence level the program will use to calculate the tolerance limits, and to enter a value, which is the proportion of observations expected to fall between the limits.

Sample Size (Number of Samples)

Confidence Level (for Tolerance Limits)

Population Proportion (for Uncensored Data)


Distribution-Free Tolerance Limits Options Dialog Box (Uncensored Data)

Allows you to enter a value that will be used to calculate either the Confidence Level or the Population Proportion, and to enter a value for the interval depth.

Input

Interval Depth


Density Trace Options Dialog Box (Uncensored Data Analysis)

Select the options that will determine the method, interval width, and X-axis resolution for the plot.

Method

Interval Width

X-Axis Resolution


Normal Probability Plot Options Dialog Box (One-Analysis Variable Analysis)

Indicate how the plot will be displayed and select the method that will be used to plot the fitted line.

Direction

Fitted Line


Distribution Functions Options Dialog Box (Uncensored/Censored Data Analyses)

Allows you to select the function that will be used to produce the plot, and to enter the number of density values the program will calculate.

Plot

X-Axis Resolution


Censored Data Analysis Dialog Box

The Censored Data analysis allows you to fit censored (lifetime) data to one of 22 probability distribution functions.  Censored data are data or samples that are incomplete in some way, such as when certain values are unknown or ignored, or in a situation when an event does not occur during the period of observation and the items have to be withdrawn before a study ends.

The analysis determines if the censored data follow a normal (the default) or another type of distribution.  It then calculates and displays the estimated parameters for the distribution you are currently using.

Data

Censoring

Select

Sort

Delete...

Transform...

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Censored Data Analysis

Probability Distribution Dialog Box

Frequency Tabulation Options

Tail Areas Options

Critical Values Options

Distribution Functions Options


Life Tables (Intervals) Analysis Dialog Box

The Life Tables (Intervals) analysis creates a life table from the counts of failures in a set of intervals.  The life table is created using a random sample of censored data to estimate the survival probabilities for a population over time; that is, a calculation is made of the probability that items in the sample group will survive at least as long as the beginning of an interval.  The analysis allows you to plot survival probabilities versus time.

Sample items lost from a study are called censored data, which means you know only that the sample items survive until they leave the study.  For example, imagine that you want to study a sample of 100 automobile tires to determine their average expected tread life.  During the study, some tires are lost; for example, when a nail pierces and flattens a tire — the tire can no longer be used for the duration of the study.

Or you may want to study 100 individuals to determine the effects of a pain-relieving medication.  During the study, some portion of the sample group moves to other cities and you lose contact with them; they can no longer be used for the duration of the study.

Interval Widths

Number of Failures

Number Censored

Group Labels

Sort

Delete...

Transform...

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Life Tables (Intervals) Analysis

Percentiles Options

Life Table Plots Options


Percentiles Options Dialog Box (Life Tables Intervals Analysis)

Enter values for other percentiles.  If you do not want to calculate a percentile, enter 0.


Life Table Plots Options Dialog Box

Indicate if you want to include the confidence limits, and to enter a value for the confidence level.

Include Confidence Limits

Indicate if you want to include the confidence limits.  The default is non-included confidence limits.

Confidence Level

Enter a value for the confidence level that will be used to calculate the confidence intervals for the data.  The default is 95 percent; other common levels are 90 and 99.


 Life Tables (Times) Analysis Dialog Box

The Life Tables (Times) analysis creates a life table from the failure times of items, which provides a nonparametric estimate of an empirical survival function.  The analysis is helpful when you must obtain survival probabilities for multicensored data.  It is also particularly useful in reliability studies when there is a need to estimate the lifetime of products and when, for various reasons, items must be withdrawn from a test.  Another use is in studying and comparing clinical trials of survival rates for patients who are undergoing different treatments for the same condition.

Data (Time Entering Study)

Censored (Contains Censored Data)

Group (Weibull Analysis)

Select

Sort

Delete...

Transform...

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Life Tables (Times) Analysis

Life Table Plots Options


Weibull Analysis Dialog Box

The Weibull analysis creates estimates for distribution parameters that are based on one of two estimation methods:  Rank Regression or Maximum Likelihood.  It then calculates and displays tail areas, critical values, and graphic displays that help you determine how the survival rate will change over time.

Weibull Analysis originated in 1951 when Weibull claimed that his distribution or his “family” of distributions was applicable to a wide variety of problems that ranged from yield strength of steel to the size of adult males born in the British Isles.  Weibull never claimed that the distributions always worked or that they were always the best choice; time, however, has shown that his statements were right (Abernethy, Breneman, Medlin, and Reinman, 1983).

Today his analyses are used in numerous applications, particularly in fitting failure-time distributions to lifetime data.  The flexible shape of the distribution makes it an appropriate fit for modeling the failure times of many different and diverse processes; therefore, most observed lifetimes can be accurately described by the distribution.

In STATGRAPHICS Plus, the analysis handles various types of censoring, which frequently occurs when you are using lifetime data.  Lifetime data can include time-to-failure of manufactured items or survival times of individuals undergoing treatment in clinical trials.  The basis for most applications of the analysis is a single failure class or mode from a single part or component.  Usually the analysis begins with a few failures embedded in a large number of successful, unfailed, or censored units where the age of each part is required.

Data

Censored

Group

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Weibull Analysis

Weibull Analysis Options

Goodness-of-Fit Options

Tail Areas Options

Critical Values Options

Frequency Tabulation Options


Weibull Analysis Options Dialog Box

This dialog box allows you to choose an origin for the distribution starting point, an estimation method, and a plotting position.

Starting Point

Estimation Method

Plotting Position


Dot Diagram Tabular Options Dialog Box

Allows you to select tabular options for the Dot Diagram analysis.

Analysis Summary (Dot Diagram Analysis)


Dot Diagram Graphical Options Dialog Box

Allows you to select graphical options for the Dot Diagram analysis.

Dot Diagram (Dot Diagram Analysis)


Bubble Chart Analysis Tabular Options Dialog Box

This dialog box allows you to select tabular options for the Bubble Chart Analysis.

Analysis Summary (Bubble Chart Analysis)


Bubble Chart Analysis Graphical Options Dialog Box

This dialog box allows you to select graphical options for the Bubble Chart Analysis.

Bubble Chart (Bubble Chart Analysis)


Multiple Barchart Analysis Tabular Options Dialog Box

This dialog box allows you to select tabular options for the Multiple Barchart Analysis.

Analysis Summary (Multiple Barchart Analysis)


Multiple Barchart Analysis Graphical Options Dialog Box

This dialog box allows you to select graphical options for the Multiple Barchart Analysis.

Barchart (Multiple Barchart Analysis)


Response Surfaces Analysis Tabular Options Dialog Box

Allows you to select tabular options for the Response Surfaces analysis.

Analysis Summary (Response Surfaces Analysis)


Response Surfaces Analysis Graphical Options Dialog Box

Allows you to select graphical options for the Response Surfaces analysis.

Surface Plot (Response Surfaces Analysis)

Contour Plot (Response Surfaces Analysis)


Custom Charts Analysis Tabular Options Dialog Box

This dialog box allows you to select tabular options for the Custom Charts Analysis.

Analysis Summary (Custom Charts Analysis)


Custom Charts Analysis Graphical Options Dialog Box

This dialog box allows you to select graphical options for the Custom Charts Analysis.

Custom Chart (Custom Charts Analysis)


Subset Analysis Tabular Options Dialog Box

This dialog box allows you to select tabular options for the Subset Analysis.

Analysis Summary (Subset Analysis)

Summary Statistics (Subset Analysis)

Means Table (Subset Analysis)


Subset Analysis Graphical Options Dialog Box

Allows you to select graphical options for the Subset analysis.

Scatterplot (Subset Analysis)

Means Plot (Subset Analysis)

Median Plot (Subset Analysis)

Sigma Plot (Subset Analysis)

Range Plot (Subset Analysis)

Box-and-Whisker Plot (Subset Analysis)


Row-Wise Statistics Analysis Tabular Options Dialog Box

Allows you to select tabular options for the Row-Wise Statistics analysis.

Analysis Summary (Row-Wise Statistics Analysis)

Summary Statistics (Row-Wise Statistics Analysis)

Means Table (Row-Wise Statistics Analysis)


Row-Wise Statistics Analysis Graphical Options Dialog Box

This dialog box allows you to select graphical options for the Row-Wise Statistics analysis.

Scatterplot (Row-Wise Statistics Analysis)

Means Plot (Row-Wise Statistics Analysis)

Median Plot (Row-Wise Statistics Analysis)

Sigma Plot Option (Row-Wise Statistics Analysis)

Range Plot (Row-Wise Statistics Analysis)

Box-and-Whisker Plot (Row-Wise Statistics Analysis)


Save Results Options Dialog Box (Row-Wise Statistics)

The Save Results Options dialog box for the Row-Wise Statistics Analysis allows you to select the results you want to save.  There are five selections:  Counts, Means, Medians, Standard Deviations, and Ranges.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Save Results Options Dialog Box (Subset Analysis)

The Save Results Options dialog box for the Subset Analysis allows you to select the results you want to save.  There are six selections:  Labels, Counts, Means, Medians, Sigmas, and Interquartile Range.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results button on the Analysis toolbar (the fourth button from the left).


Censored Data Analysis Tabular Options Dialog Box

Allows you to select tabular options for the Censored Data analysis.

Analysis Summary (Censored Data Analysis)

[Chi-Square] Goodness-of-Fit Tests (Censored Data Analysis)

Tail Areas (Censored Data Analysis)

Critical Values (Censored Data Analysis)


Censored Data Analysis Graphical Options Dialog Box

Allows you to select graphical options for the Censored Data analysis.

Frequency Histogram (Censored Data Analysis)

Distribution Functions 1 and 2 (Censored Data Analysis)


Life Tables (Intervals) Analysis Tabular Options Dialog Box

Allows you to select tabular options for the Life Tables (Intervals) analysis.

Analysis Summary (Life Tables Intervals Analysis)

Percentiles (Life Tables Intervals Analysis)

Group Comparisons (Life Tables Intervals Analysis)


Life Tables (Intervals) Analysis Graphical Options Dialog Box

Allows you to select graphical options for the Life Tables (Intervals) analysis.

Survival Function (Life Tables Intervals Analysis)

Log Survival Function (Life Tables Intervals Analysis)

Cumulative Hazard Function (Life Tables Intervals Analysis)

Death Density Function (Life Tables Intervals Analysis)

Hazard Function (Life Tables Intervals Analysis)


Life Tables (Times) Analysis Tabular Options Dialog Box

Allows you to select tabular options for the Life Tables (Times) analysis.

Analysis Summary (Life Tables - Times Analysis)

Percentiles (Life Tables - Times Analysis)

Group Comparisons (Life Tables - Times Analysis)


Life Tables (Times) Analysis Graphical Options Dialog Box

This dialog box allows you to select graphical options for the Life Tables (Times) Analysis.

Survival Function (Life Tables Times Analysis)

Log Survival Function (Life Tables Times Analysis)

Cumulative Hazard Function (Life Tables Times Analysis)


Weibull Analysis Tabular Options Dialog Box

Allows you to select tabular options for the Weibull analysis.

Analysis Summary (Weibull Analysis)

Goodness-of-Fit

Tail Areas (Weibull Analysis)

Critical Values (Weibull Analysis)


Weibull Analysis Graphical Options Dialog Box

This dialog box allows you to select graphical options for the Weibull analysis.

Weibull Plot (Weibull Analysis)

Frequency Histogram (Weibull Analysis)

Density Function (Weibull Analysis)

CDF (Weibull Analysis)

Survival Function (Weibull Analysis)

Log Survival Function (Weibull Analysis)

Hazard Function (Weibull Analysis)


Save Results Options Dialog Box (Subset Analysis)

The Save Results Options dialog box allows you to select the results you want to save.  There are five selections:  Labels, Counts, Means, Medians, and Sigmas.

You can also use the Target Variables text boxes on the dialog box to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results Options button on the Analysis toolbar (the fourth button from the left).


Data (Uncensored)

Enter the name of the variable that contains the uncensored data you want to fit.


Data

Enter the name of the variable that contains the data will be fit.


Labels (Axis Scaling)

This text box allows you to change the name of a label, and to add or delete a name.


Plot

Determines the function that will be used to produce the Distribution Function Plot.

Density Function

Produces a plot using a function that gives the rate at which the cumulative probability increases at a given point; it is the default for Distribution Function 1.

CDF

Produces a plot using a cumulative distribution function that shows the probability of observing a value less than or equal to a value you select; it is the default for Distribution Function 2.

Survivor Function

Produces a plot using a function that shows the probability of observing a value greater than a value you select.  The survivor function is 1 – CDF.  For reliability data, the survivor function shows the probability of surviving to time x without failure.

Log Survivor Function

Produces a plot using a function that shows the probability of observing a value greater than a value you select (in log units); that is, the log of the survivor function.

Hazard Function

Produces a plot using a function that shows the probability of failure during a small increment of time when no failure occurs before a time you select.  The hazard function is the Probability Density Function divided by the Survivor Function.


Axis Scaling Options (Numeric) Dialog Box

This dialog box allows you to change scaling options for graphs that plot numeric data on the specified axis.  Use the options to set the range, format and direction of the axis labels.


Axis Scaling Options (Character) Dialog Box

This dialog box allows you to change scaling options for graphs that plot character data on the specified axis.  Use the options to set the range, format and direction of the axis labels.


Using the Statistical Analyses in STATGRAPHICS Plus

These topics provide step-by-step instructions for learning the basics about the analyses in the Standard Edition of STATGRAPHICS Plus.

The organization follows the arrangement on the Analysis toolbar; that is, from left to right.

Using the Analyses in the Plot Menu

Using the Analyses in the Describe Menu

Using the Analyses in the Compare Menu

Using the Analyses in the Relate Menu


Using Analyses in the Base Program
Using Standard Edition Analyses

These topics provide instructions for learning the analyses in the base program of STATGRAPHICS Plus.  The organization follows the buttons on the Analysis toolbar, from left to right.  To view the topics specific to the analyses in each menu, go to that topic.

Using the Analyses in the Plot Menu

Using the Analyses in the Describe Menu

Using the Analyses in the Compare Menu

Using the Analyses in the Relate Menu


Analysis Summary (Box-Cox Transformations Analysis)

The Analysis Summary option creates a summary of the analysis, which shows the results of fitting a linear model that describes the relationship between the two variables.  The equation of the fitted linear model is: Y = a + b*X.  In the regression model, the estimate for the intercept is the value for “a”; the estimate for the slope is the value of “b”.

The summary includes the standard error, t-statistic, and p-value for each estimate.  The t-statistic tests to see if the true value of the coefficient is equal to 0, which is equivalent to concluding that there is no linear relationship between the independent and dependent variables.  Low probability levels (less than .05 for a 95 percent confidence level) for the intercept and slope suggest significant values.

The summary also includes an ANOVA Table for the model.  The F-ratio in the summary indicates the significance of the results; a high F-ratio suggests a significant model.  The summary also shows the correlation coefficient that measures the linear relationship between the independent and dependent variables, the R-Squared value (the square of the correlation coefficient, expressed as a percentage), and the standard error of estimation.  The standard error of estimation is the square root of the residual mean square, which is the estimated standard deviation of the variable that is not explained by the estimated model.  The R-Squared value shows the percentage of variability in the Y values explained by the X variable.

Use the Simple Regression Options dialog box to select the type of model that will be fit.


Lack-of-Fit Test (Box-Cox Transformation Analysis)

The Lack-of-Fit Test option creates a table that displays the results of a test designed to determine whether the selected model adequately describes the observed data, or whether a more complicated model should be used instead.  The analysis compares the variability of the residuals for the current model with the variability between observations at replicate values of the independent variable X.  If the p-value is greater than or equal to .05, the current model should be adequate for the observed data at the 95 percent confidence level.


Forecasts (Box-Cox Transformation Analysis)

The Forecasts option creates a table of the predicted values for the Y (dependent) variable using the fitted model.  In addition to the best predictions, the table displays the prediction intervals for the new observations and the confidence intervals for the mean of many observations (at a given percentage).

Use the Forecasts Options dialog box to enter values to change the confidence level that will be used to calculate the confidence limits, and to enter values for X for which you want to predict a Y value.


MSE Comparison Table (Box-Cox Transformation Analysis)

The MSE Comparison Table option creates a table that displays the mean squared error (MSE) for various values of the power transformation parameter (Lambda1) between -2 and +2.  The MSE Table shows the estimated model MSE for a range of lambda values.  By default, this analysis will always choose the optimal Lambda1.  Using the table you can determine the value of Lambda1, which minimizes the model MSE.  You can also see the MSE for other values of lambda, other than the optimal.

Use the MSE Comparison Table Options dialog box to enter values for the minimum and maximum Lambda1, and for the resolution.


Unusual Residuals (Box-Cox Transformations Analysis)

The Unusual Residuals option creates a table that lists all the observations that have studentized residuals greater than 2.0 in absolute value.  Studentized residuals measure the number of standard deviations each observed value of the dependent variable deviates from a model fitted using all the data except that observation.  Take a close look at any values greater than 3 in absolute value to determine if they are outliers, which you should remove from the analysis.


Influential Points (Box-Cox Transformations Analysis)

The Influential Points option creates a table that lists all the observations that have leverage values greater than three times the average.  Leverage is a statistic that measures the amount of influence of each observation in determining the coefficients for the estimated model.


Plot of Fitted Model (Box-Cox Transformations Analysis)

The Plot of Fitted Model creates a plot of the results of fitting a linear model that describes the relationship between two selected variables.  The equation of the fitted model is shown as a solid line.  The plot includes both confidence limits for the means (the middle lines) and prediction limits (the outer lines).

Use the Plot of Fitted Model Options dialog box to indicate the type of limits that will be included, to enter a value for the confidence level, and to enter a number that will be used to change the resolution of the lines.


Observed versus Predicted (Box-Cox Transformations Analysis)

The Observed versus Predicted option creates a plot of the observed values versus the predicted values for the dependent variable (the fitted model).  The closer the points lie to the diagonal line, the better the model (at predicting the observed data).

Look for various anomalies, such as increases in variability around the line, as the value of the variable (the observed data) increases.  This is known as heteroscedasticity.  Also look for individual points that lie far away from the line, which are known as outliers.  You can use the plot to detect cases in which the variance is not constant, which indicates you may need to transform the dependent variable.


MSE Comparison Plot (Box-Cox Transformations Analysis)

The MSE Comparison Plot option creates a plot of the mean squared error (MSE) for various values of the power transformation parameter Lambda1 between -2 and +2.  The analysis, by default, will always choose Lambda1.

Use the MSE Comparison Plot Options dialog box to enter values for the minimum and maximum Lambda1, and for the resolution.


Residuals versus X (Box-Cox Transformations Analysis)

The Residuals versus X option creates a plot of the studentized residuals versus the values for the independent variable.

Nonrandom patterns could indicate that the model you selected does not adequately describe the observed data, and any values outside the range of -3 to +3 are outliers.  Use the plot to detect the nonlinear relationship between Y and X.  You can also use the plot to determine if the variance of the residuals is constant.  If the model is correct, and if all the assumptions are satisfied, the residuals should appear structureless; that is, no pattern will be apparent.

Use the Residual Plot Options dialog box to indicate the type of residuals that will appear on the plot.


Residuals versus Predicted (Box-Cox Transformations Analysis)

The Residuals versus Predicted option creates a plot of the studentized residuals versus the predicted values of the variable you selected.  Nonrandom patterns indicate that the model you selected does not adequately describe the observed data.

This plot is especially helpful in showing heteroscedasticity, in which the variability of the residuals change as the values of the dependent variables change.  If the model is correct and if all the assumptions are satisfied, the residuals should be structureless.

Use the Residual Plot Options dialog box to indicate the type of residuals that will appear on the plot.


Residuals versus Row Number (Box-Cox Transformations Analysis)

The Residuals versus Row Number option creates a plot of the studentized residuals versus their row number. If the row order corresponds to the order in which the data were collected, any nonrandom pattern could indicate serial correlation in the data.  Ideally, the points should appear structureless.

Use the Residual Plot Options dialog box to indicate the type of residuals that will appear on the plot.


Save Results Options (Box-Cox Transformations Analysis)

The Save Results Options dialog box allows you to select the results you want to save.  There are nine selections: Predicted Values, Lower Limits for Predictions, Upper Limits for Predictions, Lower Limits for Forecast Means, Upper Limits for Forecast Means, Residuals, Studentized Residuals, Leverages, and Transformed Data.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results Options button on the Analysis toolbar (the fourth button from the left).


Box-Cox Transformations Analysis Dialog Box

The Box-Cox Transformations Analysis automatically identifies a transformation from a family of power transformations.  The analysis determines the appropriate transformation parameter, Lambda1, which minimizes the mean squared error (MSE) of the fitted model.

X

Y

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Box-Cox Transformations Analysis

Box-Cox Transformations Options

Lack-of-Fit Tests

Forecasts

Forecasts Options

MSE Comparison Table

MSE Comparison Table Options

Unusual Residuals

Influential Points

Plot of Fitted Model

Observed versus Predicted

MSE Comparison Plot

MSE Comparison Plot Options

Residuals versus X

Residual Plot Options

Residuals versus Predicted

Residuals versus Row Number


Box-Cox Transformations Options Dialog Box

This dialog box allows you to enter values for power (Lambda1) and Shift (Lambda2), and to indicate if Lambda1 should be optimized.

Power (Lambda1)

Shift (Lambda2)

Optimize


MSE Comparison Table Options Dialog Box

This dialog box allows you to enter values for the minimum and maximum Lambda1, and for the resolution.

Minimum Lambda1

Maximum Lambda1

Resolution


MSE Comparison Plot Options Dialog Box

This dialog box allows you to enter values for the minimum and maximum Lambda1, and for the resolution.

Minimum Lambda1

Maximum Lambda1

Resolution


Box-Cox Transformations Analysis Tabular Options Dialog Box

This dialog box allows you to select tabular options for the Box-Cox Transformations Analysis.

Analysis Summary (Box-Cox Transformations Analysis)

Lack-of-Fit Test (Box-Cox Transformation Analysis)

Forecasts (Box-Cox Transformation Analysis)

MSE Comparison Table (Box-Cox Transformation Analysis)

Unusual Residuals (Box-Cox Transformations Analysis)

Influential Points (Box-Cox Transformations Analysis)


Box-Cox Transformations Analysis Graphical Options Dialog Box

This dialog box allows you to select graphical options for the Box-Cox Transformations Analysis.

Plot of Fitted Model (Box-Cox Transformations Analysis)

Observed versus Predicted (Box-Cox Transformations Analysis)

MSE Comparison Plot (Box-Cox Transformations Analysis)

Residuals versus X (Box-Cox Transformations Analysis)

Residuals versus Predicted (Box-Cox Transformations Analysis)

Residuals versus Row Number (Box-Cox Transformations Analysis)

Skewness and Kurtosis Plot (Box-Cox Transformations)


Forecasts Options Dialog Box

This dialog box allows you to enter values to change the confidence level, and to enter values for X for which you want to predict a Y value.

Confidence Level

Forecast at X


Multiple Dot Diagram Analysis Dialog Box

The Multiple Dot Diagram Analysis creates a dot diagram for data that are divided into more than one group.  It displays summary statistics and confidence intervals for each group.

This plot is a way to summarize data that are often used in exploratory data analysis to illustrate the major features of the distribution of data in a convenient form.  A Multiple Dot Diagram can also help detect any unusual observations (outliers), or gaps in the dataset.

Data

Sample Code

Labels

Upper Limit

Lower Limit

Select

Sort


Multiple Dot Diagram Analysis Options Dialog Box

This dialog box allows you to indicate the type of mean or median statistics, if any, that will appear on the plot.  You can also enter values for the mean, median, standard deviation, and coefficient of variation; indicate if a line representing the Grand Average should appear on the plot; enter the confidence level that will be used to calculate the intervals around each group mean; and enter a value for the confidence level that will be used to calculate the intervals around each group mean.

Group Statistics

Number of Decimals

Display Grand Average

Confidence Level


Multiple Dot Diagram Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Multiple Dot Diagram Analysis)


Multiple Dot Diagram Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Multiple Dot Diagram


Multiple Barchart Options Dialog Box

This dialog box allows you to choose options for the format of the Multiple Barchart.

Chart Type

Scaling

Direction

Error Bars

Baseline


Component Line Chart Analysis Dialog Box

The Component Line Chart Analysis is useful for displaying one or more sets of time-series data, which are useful for investigating trends, patterns, or other nonrandom behavior in the time series; for example stock prices.  You can plot original values individually or cumulatively.

Columns

Sampling Interval

Select

Sort


Component Line Chart Analysis Options Dialog Box

This dialog box allows you to indicate if the variables should be plotted cumulatively, which is the default.


Component Line Chart Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary


Component Line Chart Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Component Line Chart


High-Low-Close Plot Analysis Dialog Box

The High-Low-Close Plot Analysis is valuable when you want to display stock, commodity, currency, and other market data that fluctuate greatly from hour-to-hour, day-to-day, or week-to-week.  To convey a sense of short-term change while also viewing long-term change requires that each category of data show a range of values.

High Values

Low Values

Closing Values

Sampling Interval

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the High-Low-Close Plot Analysis

High-Low-Close Plot


High-Low-Close Plot Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (High-Low-Close Plot)


High-Low-Close Plot Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

High-Low-Close Plot


Hypergeometric Options Dialog Box

This dialog box allows you to enter values for the event probability, trials, and population size.

Event Probability

Trials

Population Size


Cauchy Options Dialog Box

This dialog box allows you to enter values for the Mode and Scale parameters.

Mode

Scale


Power Transformations Analysis Dialog Box

If, after performing an exploratory analysis on a set of data, the normality of the data appears to be questionable, a transformation of the data is in order even though it is often difficult to determine what type of transformation will have the most beneficial effect.  The Box-Cox power transformation automatically identifies the optimal transformations.

The program determines the optimal Box-Cox transformation by finding the value of the Lambda1 parameter, which minimizes the mean squared error.  The StatAdvisor displays the transformation for the value of Lambda 1 you selected.  You can compare the results of the transformation with other values of Lambda1 by choosing the MSE Comparison Table option.

Data

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Power Transformations Options

MSE Comparison Table

MSE Comparison Table Options

Tests for Normality

Normal Probability Plot

Normal Probability Plot Options

MSE Comparison Plot

MSE Comparison Plot Options

Skewness and Kurtosis Plot

Skewness and Kurtosis Plot Options


Power Transformations Tabular Options Dialog Box

Use this dialog box to choose tabular options for the analysis.

Analysis Summary (Power Transformations)

MSE Comparison Table (Power Transformations Analysis)

Tests for Normality (Power Transformations Analysis)


Power Transformations Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Normal Probability Plot (Power Transformations Analysis)

Skewness and Kurtosis Plot (Power Transformations)

MSE Comparison Plot (Power Transformations Analysis)


Power Transformations Options Dialog Box

This dialog box allows you to change the values for Lambda1 and Lambda2; and to indicate if you want the value for Lambda1 optimized.

Power (Lambda1)

Shift (Lambda2)

Optimize


MSE Comparison Table Options Dialog Box

This dialog box allows you to set the values for which the MSE will be determined and to enter a value for the resolution.

Minimum Lambda1

Maximum Lambda1

Resolution


Normal Probability Plot Options Dialog Box

This dialog box allows you to indicate if the plot will display in a horizontal or vertical direction and to indicate if a fitted line will appear on the plot; if so, whether quartiles or least squares will be the method used to fit the line.

Direction

Fitted Line


MSE Comparison Plot Options Dialog Box

This dialog box allows you to set the values for which the MSE will be determined, and to enter a value for the resolution.

Minimum Lambda1

Maximum Lambda1

Resolution


Save Results Options Dialog Box (Power Transformations Analysis)

Use the Save Results Options dialog box to choose the results you want to save.  There is one selection: Transformed Data.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results Options button on the Analysis toolbar (the fourth button from the left).


Statistical Tolerance Limits Analysis Dialog Box

The Statistical Tolerance Limits Analysis computes statistical tolerance limits, given a sample size, mean, and standard deviation.  The analysis also determines the sample size needed to obtain nonparametric limits for a given proportion of the population.

Statistical tolerance limits are limits that contain a certain proportion of the distribution of a quality characteristic.  When the parameters of a distribution are known, these limits are easily calculated.  However, usually the distribution and its parameters are unknown, and you must estimate the tolerance limits from a sample of population data.

This analysis provides both normal tolerance limits and nonparametric tolerance limits.  Use normal tolerance limits when it can reasonably be assumed that the data collected are well described by a normal distribution.  When the normality of the data cannot be assumed, use Nonparametric limits.

Data Sample


Statistical Tolerance Limits Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Statistical Tolerance Limits Analysis)

Nonparametric Limits (Statistical Tolerance Limits Analysis)


Statistical Tolerance Limits Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Tolerance Plot (Statistical Tolerance Limits Analysis)


Statistical Tolerance Limits Options Dialog Box

This dialog box allows you to enter values for the confidence level and the population proportion, and to indicate if two-sided, upper, or lower limits will be used.

Confidence Level

Population Proportion

Limits


Probability Plots Analysis Dialog Box

The Probability Plots Analysis allows you to create seven different types of probability plots to help determine if one variable comes from a particular type of distribution.  After you create and examine the plots, you can fit a distribution using a Distribution Fitting Analysis for either uncensored or censored data.

Data

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Probability Plot Options

Uniform Plot

Normal Plot

Lognormal Plot

Weibull Plot

Extreme Value Plot

Logistic Plot

Exponential Plot


Probability Plots Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Probability Plots Analysis)


Probability Plots Graphical Options Dialog Box

This dialog box allows you to choose options for the analysis.

Uniform Plot (Probability Plots Analysis)

Normal Plot (Probability Plots Analysis)

Lognormal Plot (Probability Plots Analysis)

Weibull Plot (Probability Plots Analysis)

Extreme Value Plot (Probability Plots Analysis)

Logistic Plot (Probability Plots Analysis)

Exponential Plot (Probability Plots Analysis)


Probability Plots Options Dialog Box

This dialog box allows you to enter a number for the values above maximum and a number for the values below maximum.

 Number of Values Below Minimum

 Number of Values Above Maximum


Distribution Fitting (Uncensored Data) Analysis Dialog Box

Raw data are seldom suitable for performing an analysis, so it is necessary to convert it into a suitable form that can undergo meaningful analysis.  The goal is to understand the random variability that exists in each measurement of the data.  Uncensored data are data that are present throughout the entire duration of an experiment, or data that do not have to be excluded from an experiment for any reason.

The Uncensored Data Analysis allows you to create a relevant summary by fitting one of the 24 probability distribution functions in STATGRAPHICS Plus to a set of data.  The analysis provides a way to determine if uncensored data follow a Normal (the default), or another type of distribution.  The analysis calculates and displays estimated parameters for each distribution you choose.

Data

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on Pane Options or Analysis Options.

See also

Using the Distribution Fitting (Uncensored Data) Analysis

Probability Distributions Options

Tests for Normality

Goodness-of-Fit Tests

Goodness-of-Fit Tests Options

Tail Areas

Tail Areas Options

Critical Values

Critical Values Options

Normal Tolerance Limits

Normal Tolerance Limits Options

Distribution-Free Tolerance Limits

Distribution-Free Tolerance Limits Options

Density Trace

Density Trace Options

Symmetry Plot

Frequency Histogram

Quantile Plot

Quantile/Quantile Plot

Distribution Functions 1 and 2


Distribution Fitting (Uncensored Data) Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Uncensored Data Analysis)

Tests for Normality (Uncensored Data Analysis)

Goodness-of-Fit Tests (Uncensored Data Analysis)

Tail Areas (Distribution Fitting - Uncensored Data)

Critical Values (Uncensored Data Analysis)

Normal Tolerance Limits (Uncensored Data Analysis)

Distribution-Free Tolerance Limits (Uncensored Data Analysis)


Distribution Fitting (Uncensored Data) Graphical Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Density Trace (Uncensored Data Analysis)

Symmetry Plot (Uncensored Data Analysis)

Frequency Histogram (Uncensored Data Analysis)

Quantile Plot (Distribution Fitting - Uncensored Data)

Quantile/Quantile Plot (Distribution Fitting - Uncensored)

Distribution Functions 1 and 2 (Uncensored Data Analysis)


Goodness-of-Fit Tests Options Dialog Box

This dialog box allows you to choose an EDF statistic.

EDF Statistics

Determines the EDF statistic that will be used to calculate the goodness-of-fit test.

Kolmogorov-Smirnov

Calculates the maximum distance between the cumulative distribution of the data and the cumulative distribution function of the fitted distribution.  This option is one of the defaults.

Kuiper V

Improves the Kolmogorov-Smirnov V test in the tails of a distribution.  If there are only two class levels, it is a scaled value for an asymptotic distribution and determines the probability of observing a larger test statistic.

Cramer-von Mises W2

Determines if a one-dimensional data sample is compatible with being a random sample from a given distribution.  It determines if two data samples are compatible with being random samples from the same unknown distribution.  It is similar to the Kolmogorov-Smirnov test except it is more complex.

Watson U2

A modification of the Cramer-von Mises statistic; it was originally devised for a circle.

Anderson-Darling A2

A general test for complete datasets (without censored observations) that compares the fit of an observed cumulative distribution with an expected cumulative distribution function.


Critical Values Options Dialog Box

Enter values for the probabilities that will be used to calculate the corresponding critical values.  You can enter from one to five values.


Normal Tolerance Limits Options Dialog Box

This dialog allows you to enter values for the size of the sample, the confidence level, and the population proportion.

Sample Size

Confidence Level

Population Proportion


Distribution-Free Tolerance Limits Options Dialog Box

This dialog box allows you to enter values for the confidence level, population proportion, and the interval depth.

Input


Density Trace Options Dialog Box

This dialog box allows you to indicate the method that will be used to estimate the density trace; to enter the degree of overlap that will be used to compute the density trace; and to enter the number of density values that will be calculated.

Method

X-Axis Resolution


Frequency Tabulation Options Dialog Box

This dialog box allows you to enter the number of classes into which the data will be grouped and to enter values for the Lower and Upper limits.  You can also indicate if the current scaling should be retained if you change the data in the Analysis dialog box.

Number of Classes

Lower Limit

Upper Limit

Hold


Distribution Functions Options Dialog Box

This dialog box allows you to indicate the type of function distribution you want go plot and to enter the number of density values that will be calculated.

Plot

X-Axis Resolution


Distribution Fitting (Censored Data) Analysis Dialog Box

Censored data are data or samples that are incomplete in some way, such as when certain values are unknown or ignored.  For example, in a study of the 1993 college graduation rate of individuals born in 1970, some of those born then may not have completed college by 1993; however, they could easily have done so after the end of the study.  The data in the study would be censored because the number of individuals from the 1970 group who finished their degrees after 1993 would be unknown.

The Censored Data Analysis fits censored data to one of the 24 probability distribution functions available in STATGRAPHICS Plus.  The analysis fits a given distribution to a set of data, then calculates the estimated parameters for the distribution.

Data

Censoring

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Distribution Fitting (Censored Data) Analysis

Goodness-of-Fit Tests

Goodness-of-Fit Options

Tail Areas

Tail Areas Options

Critical Values

Critical Values Options

Frequency Histogram

Quantile Plot

Quantile/Quantile Plot

Distribution Functions 1 and 2


Distribution Fitting (Censored Data) Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Distribution Fitting - Censored Data)

Goodness-of-Fit Tests (Distribution Fitting - Censored)

Tail Areas (Distribution Fitting - Censored Data)

Critical Values (Distribution Fitting - Censored)


Distribution Fitting (Censored Data) Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Frequency Histogram (Distribution Fitting - Censored Data)

Quantile Plot (Distribution Fitting - Censored Data)

Quantile/Quantile Plot (Distribution Fitting - Censored Data)

Distribution Functions 1 and 2 (Distribution Fitting - Censored Data)


Percentiles Options Dialog Box

This dialog box allows you to enter values for other percentiles.  If you do not want to calculate percentiles, enter 0.


Goodness-of-Fit Tests Options Dialog Box

This dialog box allows you to choose the EDF statistics you want to calculate, as well as a censoring method.

EDF Statistics

Censoring


Weibull Plot Options Dialog Box

This dialog box allows you to indicate if you want to calculate confidence intervals and tail areas, and if so, to enter values that will be used to calculate them.  You can also indicate if a histogram of the censored values will be created and, if so, you can enter values for the number of classes and the lower and upper limits.

Include

Hold


Frequency Tabulation Options Dialog Box

This dialog box allows you to enter values for the number of classes into which the data will be grouped, as well as for the Lower and Upper limits, and the group number.  You can also indicate if the X-axis will be scaled logarithmically and if the scaling should be retained if you change values on the Analysis dialog box.

Number of Classes

Lower Limit

Upper Limit

Group Number

Log Scale for X-Axis

Hold


Density Function Options Dialog Box

This dialog box allows you to indicate if the X-axis should be scaled logarithmically.

Log Scale for X-Axis


CDF Function Options Dialog Box

This dialog box allows you to indicate if the X-axis should be scaled logarithmically.

Log Scale for X-Axis


Survival Function Options Dialog Box

This dialog box allows you to indicate if the X-axis should be scaled logarithmically.

Log Scale for X-Axis


Log Survival Function Options Dialog Box

This dialog box allows you to indicate if the X-axis should be scaled logarithmically.

Log Scale for X-Axis


Hazard Function Options Dialog Box

This dialog box allows you to indicate if the X-axis should be scaled logarithmically.

Log Scale for X-Axis


Arrhenius Plot Analysis

When operating under normal conditions, it is often not possible to obtain sufficient amounts of data for fitting life distributions.  However, by increasing stress levels, you can fail an adequate number of items, collect the data you need, and attempt to fit the distribution.

The Arrhenius Plot Analysis in STATGRAPHICS Plus fits an Arrhenius model to a set of percentiles taken at two or more study temperatures.  The fitted model is then used to predict the corresponding percentile at a normal temperature.  The analysis models the relationships between failure rates at high stress levels and normal operating levels.  This analysis is a Physical Acceleration model that is useful when thermal stresses are significant.  You can use this analysis to estimate the constants in an Arrhenius model.

The form of the Arrhenius model is:

P = AeΔ/kT

where

P = the estimated percentile

A and Δ= the unknown constants to be estimated

k = Boltzmann's Constant (8.617 10-5 EV/degrees Kelvin)

T = the temperature in degrees (Kelvin)

Using the estimated percentiles at the temperature at which it carries out the tests, the program calculates the unknown constants in the Arrhenius model.

Percentiles

Temperatures (in Kelvin)

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

      Using the Arrhenius Plot Analysis

Arrhenius Plot Options

Arrhenius Plot


Arrhenius Plot Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Arrhenius Plot Analysis)


Arrhenius Plot Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Arrhenius Plot


Arrhenius Plot Options Dialog Box

This dialog box allows you to enter the temperature at which the prediction will be made and a confidence level.

Predict at

Confidence Level


Comparison of Proportions Analysis Dialog Box

The Comparison of Proportions Analysis uses an ANOM (analysis of means) statistical technique, which is conceptually similar to a control chart.  The plot shows the observed proportions plotted against the decision limits.  This type of analysis uses critical values from a sampling distribution, which lend power that is comparable to an ANOVA under similar conditions.  While an ANOM is not the best test from a mathematical perspective, it is easier to use and understand, which gives it an advantage over ANOVA.

The Comparison of Proportions Analysis compares the proportion of items that have a particular characteristic of an attribute.  For example, at some time or another, manufacturers face the problem of having a variable that turns out to also be an attribute such as a light bulb that will or will not light or a battery whose life is or is not below standard (Ott, 1979).

The data for this analysis should meet these criteria: (1) the sampling distribution of the proportion should be a binomial distribution; and (2) if np and n (1 - p ) are both greater than 5, you should be able to use a normal distribution to approximate the sampling distribution of a portion.

If the variable you are using consists of attribute data, you can use an ANOM to compare the proportion of the items to test for differences between the proportions.

The analysis uses three or more proportions to test the hypothesis that all the proportions are equal.  The results include several reports as well as an ANOM (analysis of means) plot.

Sample Proportions

Sample Sizes

Sample Labels

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Analysis of Means (ANOM) Report

Analysis of Means Report Options

Analysis of Means (ANOM) Plot

Analysis of Means Plot Options


Comparison of Proportions Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Comparison of Proportions Analysis)

Analysis of Means Report (Comparison of Proportions)


Comparison of Proportions Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Analysis of Means (ANOM) Plot (Comparison of Proportions Analysis)


Analysis of Means Report Options Dialog Box

This dialog box allows you to enter a value for the confidence level that will be used to calculate the confidence intervals and to enter the number of decimal places that will be used for the decision limits.

Confidence Level

Decimal Places for Limits


Analysis of Means Plot Options Dialog Box

This dialog box allows you to enter a value for the confidence level that will be used to calculate the confidence intervals and to enter the number of decimal places that will be used for the decision limits.

Confidence Level

Decimal Places for Limits


Comparison of Counts Analysis Dialog Box
Comparison of Rates Analysis Dialog Box

The Comparison of Rates Analysis uses an ANOM (analysis of means) technique for comparing several populations you use when the response is count data.  This analysis is essentially the same as the Comparison of Proportions Analysis, except that the input data consists of rates rather than counts.

Ott (1979) provides this example of a quality control environment, where workers are monitoring the number of defective items from a production line.  An inspection unit is first defined for each of the populations, which might be defined as a period of time, a fixed number of items, or a fixed unit of measurement; for example, an inspection unit of a square-foot section of material from a weaving loom.

Periodically, a square-foot section of the material is examined and the number of flaws is recorded.  The number of defects is noted as c1,...,k.  The results are then calculated and plotted to see if any count falls outside the decision lines, which means there is a statistically significant difference among the counts.

Sample Rates

Sample Labels

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Comparison of Counts Analysis

Analysis of Means (ANOM) Report

Analysis of Means (ANOM) Report Options

Analysis of Means (ANOM) Plot

Analysis of Means (ANOM) Plot Options


Comparison of Counts Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Comparison of Counts Analysis)

Analysis of Means (ANOM) Report (Comparison of Counts Analysis)


Comparison of Counts Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Analysis of Means (ANOM) Plot (Comparison of Counts Analysis)


Edit Preferences Dialog Box

This dialog box allows you to set system-wide edit preferences that will override the defaults for various aspects of the program.  You can set behavioral preferences for some system, graphics, and link options from this dialog box.

System Options

Graphics

Suppress Ticmark Gap

Link Behavior


Fill Tab Page

If you view and print a graph in color, you can coordinate the color of the outline and fill area of a graph.  If you view and print the graph in black and white, you can use different fill patterns to achieve the same effect.  You use the Fill tab page on the Graphics Options dialog box to change the style and color of fill patterns to distinguish the bars, boxes, wedges, and other fill areas on a graph.

Fill

Fill Types

Color

Colors...

To Change the Style and Color of Fill Patterns

1.	Double-click the graph to maximize it.

2.	Place the mouse pointer on a fill area on the graph.

3.	Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box, which should open to the tab page that corresponds to the area of the graph you selected in Step 2.

4.	In the Fill options portion of the dialog box, click the number of the area you want to change.

5.	Choose one of the eight Fill styles: Empty (no fill pattern), Solid, Horizontal Lines, Vertical Lines, Left- and Right-Facing Diagonal Lines, Cross-Hatch Lines, or Diagonal Cross-Hatch Lines.

6.	For the Color option, click either Fill or Outline to indicate whether you want color applied to the fill pattern or to the outline of the filled area.

7.	Click the Colors... button to display the Color dialog box.

8.	Choose the color you want to use for the fill or outline, then click OK.

9.	Click Apply, then OK on the Fills tab page to process the changes.


Grid Tab Page

A grid, which is a series of lines that extend from an axis to an area on a plot, helps guide your eye from a point on a graph to its corresponding value or category on an axis.  Using the proper grid, or using no grid, can make points easier to see, which visually enhances a graph.

The Grid tab page allows you to change the appearance of a grid by changing its direction, changing the type of the lines on it, changing its color and/or line thickness, and indicating if a back grid should display on three-dimensional plots.

Direction

Colors...

Line Thickness

To Change the Direction, Style, and Color of Grid Lines

1.	Double-click the graph to maximize it.

2.	Place the mouse pointer on an empty portion inside the graph frame.

3.	Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box.  Click the Grid tab page.

4.	Choose one of the four Direction styles:  Horizontal, Vertical, Both, or None.

5.	Click the Colors... button to display the Color dialog box.

6.	Choose the color you want to use.

7.	Place the mouse pointer on the slider control for the line thickness and move the control from Thinnest to Thickest to change the width of the line.  Release the control.

Note:  The line thickness feature is available only for solid lines.

If the Back Grid on 3D Plots option is active and you are using a 3D plot that would look better with a back grid, click the box.

8.	Click Apply, then OK on the Grid tab page to process these changes.


Label Tab Page

The Label tab page is available for plots, such as the Pareto Chart in the Quality and Design product, for which you want to create labels.  Labels refer to text that appears on a graph as an identifier.  A series of text boxes appear on the page, which allow you to enter names for the labels.  The letter between the braces, for example, {A}, is an internal system reference to variable names.  The Fonts... command lets you change the font.

Label

Fonts...

To Change the Name of a Label

1.	Double-click the graph to maximize it.

2.	Move the mouse pointer to the label you want to change.

3.	Click the left button to select the name of the label; markers appear at the corners of the selected label.

4.	Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the Label tab page.

5.	In the Label text box, enter the new name for the label, then click OK to process the change.

6.	Continue entering names until you finish.

7.	Click the Fonts... button to display the Windows Font dialog box.

8.	Choose the font, font style, size, color, and other attributes, then click OK.

9.	Click Apply and OK on the Label tab page to process the changes.


Layout Tab Page

The Layout tab page allows you to customize a graph by choosing a style and color for the tickmarks, the type of frame that will surround the graph, the color of the background

and/or border of the graph, and the thickness of the axis line.

Tickmarks and Colors

Tickmarks

Mode

Line Thickness

Colors...

3-d effects

To Change Tickmarks

1.	Double-click the graph to maximize it.

2.	Place the mouse pointer on an empty portion inside the graph frame.

3.	Click the left button, then the right on Graphics Options on the pop-up menu to display the Graphics Options dialog box opened to the Layout page.

4.	Click the option that corresponds to the axis whose tickmarks you want to change (X-, Y-, or Z-Axis).

5.	Choose one of the three Tickmark styles:  No Tickmarks, Tickmarks Inside, or Tickmarks Outside.

6.	Click the Colors... button to display the Color dialog box.

7.	Choose the color you want to use, then click OK on the Color dialog box.

8.	Click Apply, then OK on the Layout tab page to process all the changes.

To Change the Background and/or Border of a Graph

1.	Double-click the graph to maximize it.

2.	Place the mouse pointer on an empty portion inside the graph frame.

3.	Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box, opened to the Layout page.

4.	Click either the background or the border option.

5.	Click the Colors... button to display the Color dialog box.

6.	Choose the color you want to use, then click OK on the Color dialog box.

7.	Click Apply, then OK on the Layout tab page to process all the changes.

To Change the Shape of a Graph

1.	Double-click the graph to maximize it.

2.	Place the mouse pointer on an empty portion inside the graph frame.

3.	Click the left button, then the right on Graphics Options on the pop-up menu to display the Graphics Options dialog box opened to the Layout tab page.

4.	Choose one of the two shape styles: L-Shaped or Square.

5.	Click Apply, then OK on the Layout tab page to process the change.


Legend Tab Page

Many of the analyses you use to plot data for two or more variables contain a legend; for example, a Multiple X-Y-Z Plot or a Barchart.  A legend lists and explains the symbols on a graph.  You use the Legend tab page on the Graphics Options dialog box to change the title of a legend, change the names of the individual variables that apply to a legend, and to change the font attributes such as the style, point size, and color.  A series of text boxes appear on the page, which allows you to enter names for the legends.  The letter between the braces, for example, {A}, is an internal system reference to variable names.

Title

Legend

Fonts...

To Change a Legend Title and Variable Names

1.	Double-click the graph to maximize it.

2.	Move the mouse pointer to the legend title you want to change.

3.	Click the left button, then the right on Graphics Options on the pop-up menu to display the Graphics Options dialog box opened to the Legend tab page.

4.	Enter a title into the Title text box.

5.	Click in the {A} Legend text box, then enter a name for the first variable.

6.	Continue entering names until you finish.

7.	Click the Fonts... button to display the Windows Font dialog box.

8.	Choose the color you want to use, then click OK.

9.	Click Apply and OK on the Legend tab page to process the changes.


Line Tab Page

Changing the look of the lines that appear on a graph is useful when you need to enhance and clarify the graphical results.  You use the Line tab page on the Graphics Options dialog box to set the style and color of the lines on a graph.

Line

Line Types

Line Thickness

Colors...

3-d effects

To Change the Type, Thickness, and Color of Lines

1.	Double-click the graph to maximize it.

2.	Place the mouse pointer on the line you want to change.

3.	Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the Line tab page.

4.	In the Line options portion of the dialog box, click the number of the line you want to change.

5.	Choose one of the five Line styles: Solid, Dashed, Dotted, Dash-Dot, or Dash-Dot-Dot.

6.	If you chose a Solid line, place the mouse pointer on the slider control for the line thickness and move the control from Thinnest to Thickest to change the width of the line.  Release the control.

7.	Click the Colors... button to display the Color dialog box.

8.	Choose the color you want to use, then click OK.

9.	Click Apply, then OK on the Lines tab page to process the changes.


Point Tab Page

When you create two- and three-dimensional scatterplots or similar types of plots, it is helpful to be able to change the shape, size, and color of the individual points.  You use the Point tab page on the Graphics Options dialog box to set the style and color of points.

Point

Point Types

Fill Point

Point Size

Point Thickness

Colors...

To Change the Shape, Size, and Color of Points

1.	Double-click the graph to maximize it.

2.	Place the mouse pointer on the point you want to change.

3.	Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the Points tab page.

4.	In the Point options portion of the dialog box, click the number of the point you want to change.

5.	Choose one of the eight Point styles: Square, Plus, X, Star, Diamond, Up Arrowhead, Down Arrowhead, or Circle.

6.	Click the Fill Point check box or leave it blank to indicate if you want filled points.  An unchecked box (the default), means the points will not be filled.

7.	Place the mouse pointer on the slider control for the Point Size and move the control from Smallest to Largest to change the size of the point, then release the control.

8.	Place the mouse pointer on the slider control for the Point Thickness and move the control from Thinnest to Thickest, then release the control.

9.	Click the Colors... button to display the Color dialog box.

10.	Choose the color you want to use, then click OK.

11.	Click Apply, then OK on the Points tab page to process the changes.


Profile Tab Page

The Profile tab page on the Graphics Options dialog box lets you set up and save graphics profiles.  The first two options, System (Color, White Background) and System (Color, Dark Background) describe the two predefined choices for choosing the color and background of the graphs you produce; the choices are self-explanatory.  System (Black and White) means that the graphs will always display in black and white format.

You can set up or edit up to 12 user profiles.  When you set them up or edit them, you can either use numbers, letters, names, or a combination of them to create the name of the profile.

Profile (Profile Tab Page)

Load

Make a Default

To Set Up a User Profile

1.	Access the Graphics Options dialog box.

2.	Select your graphics preferences using the tabs on the Graphics Options dialog box.

3.	Return to the Profile tab page; use Load..., Save..., or Save As....  Load loads the profile; Save, saves it; and Save As saves the profile as a specific name.

For example, you might set up one profile for scatterplots, and another one for 3-dimensional plots.  After choosing your preferences for each type of plot:

4.	Click the first User # option.

5.	Click Save As... to display the Save Profile dialog box.

6.	In the text box, type Scatterplot to save the profile for scatterplots; click OK; the program displays the current graphics settings saved in a saved profile message.  Click OK.

7.	Repeat Steps 4, 5, and 6, using 3-D Plots as the name for the User #2 option.  When you click OK, names are displayed on the Profile tab page as the names for the two user options.

8.	If you want to make one of the profiles the default:

9.	Click the option button next to the setting you want to make the default.

10.	Click Make Default..., then Load.... The D default indicator to the left of the option buttons, moves to the left of the new profile, indicating the default.


Right Axis Tab Page

Some plots, such as the Multiple X-Y-Z Plot, contain a right axis.  The Right Axis tab page lets you change the scale for this axis.

Title

Vertical

From

To

By

Skip

No Power

Log

Hold

Title Fonts

Tickmark Fonts

Labels

Rotate Axis Labels

To Change the Scaling for the Right Axis

1.	Double-click the graph to maximize it.

2.	Position the mouse pointer on one of the values on the right axis.

3.	Click the left button to select the axis; markers appear at the corners of the axis.

4.	Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the Right Axis tab page.

5.	In the From text box, enter a number that will determine the minimum value for the axis.

6.	In the To text box, enter a number that will determine the maximum value for the axis.

7.	In the By text box, enter a number that will determine the distance between each tickmark on the axis scale.

8.	In the Skip text box, enter the number of tickmarks that should be skipped when the axis is created.

9.	Use the No Power check box to indicate if the axis scale for the tickmarks should be calculated using a power of 10.

10.	Use the Log check box to indicate if the axis scale for the tickmarks should be calculated using decimal log scaling.

11.	Use the Hold check box to indicate if the current scaling should be retained, even if you change the data in the Analysis dialog box.

12.	Click the Tickmark Fonts... button to display the Font dialog box, then choose the font you want to use for the tickmarks, and click OK.

13.	Click Apply and OK on the Right Axis tab page to process the changes.


Spinning Tab Page

You can view three-dimensional graphs from different horizontal and vertical angles by spinning a graph to change the location of the viewpoint.  To set preferences for spinning, use the Spinning tab page of the Graphics Options dialog box.

You can set your preferences to indicate if text should be displayed on the graph while it is spinning; and to enter values that control the number of frames per second (fps) and the degrees per frame the graph will display while it is spinning.

To actually spin the graph, click the Smooth/Rotate button on the Analysis toolbar.

Draw Test

Maximum Speed

Degrees per Frame

To Spin Graphs

1.	Double-click a three-dimensional graph to maximize it.

2.	Click the Smooth/Rotate button on the Analysis toolbar (the third button from the right), to display a slidebar/button combination on the toolbar that allows you to spin the graph.

Spin the Graph Horizontally: Click the Horizontal button (the horizontal, double-headed arrow), to begin spinning the graph horizontally.

Spin the Graph Vertically: Click the Vertical button (the vertical double-headed arrow), to begin spinning the graph vertically.

3.	Click the button a second time or click on the graph to stop the spinning.  Use the slidebars beside the two buttons to control the horizontal and vertical angles of the graph.  The range of the horizontal angle is from -90 to +90 degrees.  The range of the vertical angle is from -180 to +180 degrees.

4.	Click the right button, then click the left on the Reset Scaling/Viewpoint... command on the pop-up menu to return the graph to its original viewpoint.


Text Tab Page

On certain graphs or if you add text to a graph, the Text tab page allows you to edit the text.

Text

Edit

Direction

Fonts...

To Add Miscellaneous Text to a Graph

1.	Double-click the graph to maximize it.

2.	Place the mouse pointer on an empty portion inside the graph frame.

3.	Click the left button, then the right on Graphics Options on the pop-up menu to display the Graphics Options dialog box opened to the Text tab page.

4.	In the Text text box, enter the text you want to add to the graph.

5.	Click one of the Direction options to choose the way the text will display; either horizontally or vertically.

6.	Click the Fonts... button if you want to make changes to the font or its attributes.

7.	Click OK to process the changes.


Top Title Tab Page

Top title refers to the title that displays at the top of a graph.  You can change the entire name of the title or add or delete words from it.  You use the Top Title tab page in the Graphics Options dialog box to make the text changes.  You can indicate the direction in which the title will appear; change fonts for the one- or two-line title, and indicate if the font should be changed for both titles if you are using a two-line title.

Title

Vertical

Line 1 Fonts...

Line 2 Fonts...

Change Font for All Titles

To Change a Top Title

1.	Double-click the graph to maximize it.

2.	Place the mouse pointer on the title you want to change.

3.	Click the left on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the Top Title tab page.

4.	In the first Title text box, enter either a new title or make changes to the current title.

Note:  If the plot you are working with contains a title on a second line, the second text box will be activated and you can make changes there also.

5.	Click the Vertical check box if you want the title to display vertically on the graph.  If the box is checked, the title will display in that direction

6.	Click the Line 1 Fonts... button to display the Font dialog box you use to change the font for the text in line 1.

7.	Click the Line 2 Fonts... button to display the Font dialog box you use to change the font for the text in line 2.

8.	Click the Change Font for All Titles check box if you want to change to a font that will be used for all the titles on the graph.

9.	Click Apply and OK to process the changes.


X-Axis Tab Page

The scales against which a graph is plotted are known as axes.  The X- Y-, and Z-Axis tab pages are identical except for defaults.  You must change each axis independently; for example, if you want to make changes to the X-axis and the Y-axis, you must first access the X-Axis tab page, make the necessary changes, then access the Y-Axis tab page and make the necessary changes on that page.

To Change the Axis Scaling

1.	Double-click the graph to maximize it.

2.	Position the mouse pointer on one of the values on the axis whose scale you want to change (the X-, Y-, or Z-axis).

3.	Click the left button to select the axis; markers appear at the corners of the selected axis.

4.	Click the left on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the n Axis tab page (n indicates the selected axis).

5.	Enter a title for the axis in the Title text box.

6.	Indicate if the title should display vertically or horizontally.

7.	In the From text box, enter a number that will determine the minimum value for the axis.

8.	In the To text box, enter a number that will determine the maximum value for the axis.

9.	In the By text box, enter a number that will determine the distance between each tickmark on the axis scale.

10.	In the Skip text box, enter the number of tickmarks that should be skipped when the axis is created.

11.	In the No Power check box, indicate if the axis scale for the tickmarks should be calculated using a power of 10.

12.	In the Log check box, indicate if the axis scale for the tickmarks should be calculated using decimal log scaling.

13.	In the Hold check box, indicate if the current scaling should be retained, even if you change the data in the Analysis dialog box.

14.	Click the Title Fonts... button to display the Font dialog box you use to change the font for the title.

15.	Click the Tickmark Fonts... button to display the Font dialog box you use to change the font for the tickmarks.

16.	Click Apply and OK on the n Axis tab page to process the changes.


Y-Axis Tab Page

The scales against which a graph is plotted are known as axes.  The X- Y-, and Z-Axis tab pages are identical except for defaults.  You must change each axis independently; for example, if you want to make changes to the X-axis and the Y-axis, you must first access the X-Axis tab page, make the necessary changes, then access the Y-Axis tab page and make the necessary changes on that page.

To Change the Axis Scaling

1.	Double-click the graph to maximize it.

2.	Position the mouse pointer on one of the values on the axis whose scale you want to change (the X-, Y-, or Z-axis).

3.	Click the left button to select the axis; markers appear at the corners of the selected axis.

4.	Click the left on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the n Axis tab page (n indicates the selected axis).

5.	Enter a title for the axis in the Title text box.

6.	Indicate if the title should display vertically or horizontally.

7.	In the From text box, enter a number that will determine the minimum value for the axis.

8.	In the To text box, enter a number that will determine the maximum value for the axis.

9.	In the By text box, enter a number that will determine the distance between each tickmark on the axis scale.

10.	In the Skip text box, enter the number of tickmarks that should be skipped when the axis is created.

11.	In the No Power check box, indicate if the axis scale for the tickmarks should be calculated using a power of 10.

12.	In the Log check box, indicate if the axis scale for the tickmarks should be calculated using decimal log scaling.

13.	In the Hold check box, indicate if the current scaling should be retained, even if you change the data in the Analysis dialog box.

14.	Click the Title Fonts... button to display the Font dialog box you use to change the font for the title.

15.	Click the Tickmark Fonts... button to display the Font dialog box you use to change the font for the tickmarks.

16.	Click Apply and OK on the n Axis tab page to process the changes.


Z-Axis Tab Page

The scales against which a graph is plotted are known as axes.  The X- Y-, and Z-Axis tab pages are identical except for defaults.  You must change each axis independently; for example, if you want to make changes to the X-axis and the Y-axis, you must first access the X-Axis tab page, make the necessary changes, then access the Y-Axis tab page and make the necessary changes on that page.

To Change the Axis Scaling

1.	Double-click the graph to maximize it.

2.	Position the mouse pointer on one of the values on the axis whose scale you want to change (the X-, Y-, or Z-axis).

3.	Click the left button to select the axis; markers appear at the corners of the selected axis.

4.	Click the left on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the n Axis tab page (n indicates the selected axis).

5.	Enter a title for the axis in the Title text box.

6.	Indicate if the title should display vertically or horizontally.

7.	In the From text box, enter a number that will determine the minimum value for the axis.

8.	In the To text box, enter a number that will determine the maximum value for the axis.

9.	In the By text box, enter a number that will determine the distance between each tickmark on the axis scale.

10.	In the Skip text box, enter the number of tickmarks that should be skipped when the axis is created.

11.	In the No Power check box, indicate if the axis scale for the tickmarks should be calculated using a power of 10.

12.	In the Log check box, indicate if the axis scale for the tickmarks should be calculated using decimal log scaling.

13.	In the Hold check box, indicate if the current scaling should be retained, even if you change the data in the Analysis dialog box.

14.	Click the Title Fonts... button to display the Font dialog box you use to change the font for the title.

15.	Click the Tickmark Fonts... button to display the Font dialog box you use to change the font for the tickmarks.

16.	Click Apply and OK on the n Axis tab page to process the changes.


StatWizard Dialog Boxes

The StatWizard feature is especially useful to novice or new users who need help matching data with analyses. The default behavior is that the StatWizard opens each time you open STATGRAPHICS Plus.  To turn the StatWizard off, click the Show the StatWizard at Startup checkbox on the initial dialog box.

Using the StatWizard Before You Enter Data or Open a Data File

If you click the StatWizard button before you enter data into a data file or before you open a data file, the first StatWizard dialog box you see inquires about the type of task you want to perform.  There are three choices: Analyze Existing Data or Enter New Data, Design a New Experiment or Sampling Plan, and Perform an Analysis that Does Not Require Data.

The task you want to perform controls the next dialog box you use.

For example, if you want to analyze existing data or enter new data, the dialog box you use begins with the statement: “The data to be analyzed can come from various sources,” then asks where the data are currently located.  The location you choose determines the path the program will take; that is, you can pick your choice from the following list, which appears on the dialog box:

• Already Loaded in the STATGRAPHICS Plus Datasheet

•	In an Existing StatFolio

•	In an Existing STATGRAPHICS Plus Data File

•	In a Plain Text or Spreadsheet File

•	In an ODBC Database

•	In the Windows Clipboard

•	I Want to Enter New Data

Using the StatWizard After You Enter Data or Open a Data File

If you entered or loaded data into a DataSheet, another set of dialog boxes let you choose analyses from a Standard Menu or from a Quick Pic list.  Depending on the task you choose, a different series of dialog boxes will display.

Selecting Analyses from a Standard Menu

When you use this option, you complete a series of dialog boxes that describe the data you are using.  Because the dialog boxes are data-driven, they are too numerous to document separately.

The StatWizard - Data Selection dialog box, lists the names of the variables in the file you have chosen.  You are asked to enter a variable name for the Response Variable, Quantitative Explanatory Factor, the Categorical Explanatory Factor, and the Labels.  You also choose the type of variable you are using — general numeric, counts (integers), proportions (0-1), or categorical.

Use the StatWizard - Row Selection dialog box when you want to analyze all the rows in the DataSheet or when you want to select a subset of the rows.

The StatWizard - Variable Transformations dialog box is used when it is necessary to transform data to achieve an approximate normality.  You first select the name of the variable you want to transform, then choose the method that will be used to perform the transformation.

The StatWizard - Analysis Selection dialog box displays the type of variable you selected and asks you to select the analyses you want to perform).

Selecting Analyses from the Quick Pic List

The Quick Pic list contains 12 tasks, such as “Summarize a Single Column of Data,” “Compare Two Data Columns,” and “Fit a Multiple Regression Model.”  When you choose a task, then click OK, the appropriate Analysis dialog box displays.  For example, when you choose, “Summarize a Single Column of Data,” the One-Variable Analysis dialog box displays.


Capability Indices Options Dialog Box

This dialog box allows you to choose the indices that will be computed and indicate if 6-sigma limits or user-specified limits will be used in the calculations.  You can also enter a value for the confidence level and indicate how the indices will be labeled.

Indices

Based On

Confidence Level

Label As


Probability Plot Options Dialog Box

The Probability Plot Options dialog box allows you to indicate if the plot will display horizontally or vertically and if the fitted line should display on the plot.

Direction

Fitted Line


CuSum Chart (H-K) Analysis Dialog Box

The CuSum Chart (H-K) Analysis is also called the algorithmic or tabular CuSum.  The technique accumulates deviations above the target separately from deviations below the target.  Those accumulated deviations above the target become the one-sided upper CuSums.  The accumulated deviations below the target become the one-sided lower CuSums.  The process is determined to be out of control when other types of CuSum exceed the decision interval, called H.

Data

Subgroup Numbers or Size

Subgroup Labels

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the CuSum Chart (H-K) Analysis

CuSum (H-K) Chart Options

CuSum Chart Report

CuSum Chart Report Options

CuSum Chart

CuSum Chart Options

Range Chart

Control Chart Options

ARL Curve


CuSum Chart (H-K) Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (CuSum Chart (H-K) Analysis)

CuSum Chart Report (CuSum Chart (H-K) Analysis)


CuSum Chart (H-K) Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Cumulative Sum Chart (CuSum Chart (H-K) Analysis)

Range Chart (CuSum Chart (H-K) Analysis)

ARL Curve (CuSum Chart (H-K) Analysis)


CuSum (H-K) Chart Options Dialog Box

This dialog box allows you to indicate the type of study and the type of control limits as well as to set values for other options.

Type of Study

Decision Interval (h)

Reference Value (k)

ARL at n Sigma = x

Headstart n Sigma

Target

CuSum Control Limits

Range Control Limits

Control to Standard

Design...


CuSum Chart Report Options Dialog Box

This dialog box allows you to choose the report you want to create.

Display


CuSum Chart Options Dialog Box

This dialog box allows you to enter the number of decimal points that will display for the control limits.

Decimal Places for Limits


Save Results Options Dialog Box (CuSum [H-K] Chart Analysis
Save Results Options Dialog Box (CuSum Individuals [H-K] Chart Analysis

The Save Results Options dialog box allows you to choose the results you want to save.  There are six selections: Cumulative Sum, Moving Ranges, Labels, Process Mean, Process Sigma, Included Observations.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results Options button on the Analysis toolbar (the fourth button from the left).


CuSum Individuals Chart (H-K) Analysis Dialog Box

The CuSum Chart (H-K) Analysis is also called the algorithmic or tabular CuSum.  The technique accumulates deviations above the target separately from deviations below the target.  Those accumulated deviations above the target become the one-sided upper CuSums.  The accumulated deviations below the target become the one-sided lower CuSums.  The process is determined to be out of control when other types of CuSum exceed the decision interval, called H.

The CuSum Individuals Chart (H-K) Analysis produces a time-weighted chart of the individual observations.  This analysis plots the cumulative sums of the deviations of the sample from the target value.  Use this analysis when the subgroup size is 1.

You can use the analysis to maintain current control of a process.  An upward or downward trend in the data indicates that the process mean has shifted and the process is out of control.  The CuSum Individuals Chart allows you to detect sudden and persistent change in the process average more rapidly than variables controls charts.  By detecting the changes sooner, you can adjust the process before large variations occur.  This analysis is particularly useful in chemical and process industries where individual items may be difficult to form into subgroups.

Observations

Labels

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the CuSum Individuals Chart (H-K) Analysis

CuSum Individuals (H-K) Chart Options

CuSum Individuals Chart Report

CuSum Individuals Chart Report Options

CuSum Chart

CuSum Chart Options

ARL Curve


CuSum Individuals Chat (H-K) Tabular Options Dialog Box
CuSum Individuals Chart (H-K) Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (CuSum Individuals Chart (H-K) Analysis)

CuSum Individuals Chart Report (CuSum Individuals Chart (H-K) Analysis


CuSum Individuals Chart (H-K) Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

CuSum Chart

Scale Chart

ARL Curve


CuSum Individuals (H-K) Chart Options Dialog Box

This dialog box allows you to indicate the type of study, enter values for sigma, enter a number to calculate the ARL and that will shift the initial values of the upper and lower CuSums, to indicate the type of control limits and if the data should be normalized, and to enter values for the upper and lower control limits.  For a control-to-standard study, you can specify values for the mean and sigma parameters.

Type of Study

Decision Interval (h)

Reference Value (k)

ARL at n Sigma = x

Headstart n Sigma

Target

Mean Control Limits

Scale Control Limits

Design...


Design CuSum Chart Dialog Box

This dialog box displays when you click the Design… button.  It allows you to enter values for the options on the dialog box.

In-Control ARL

Enter a numeric value for the in-control ARL.

Sigma Shift to Detect

Enter a positive numeric value for the size of the sigma shift the CuSum Chart should detect.


CuSum Individuals Chart Report Options Dialog Box

This dialog box allows you to choose the report that will be created and enter the number of decimal places that will be used to display the limits.

Display


Save Results Options Dialog Box (CuSum Individuals [H-K] Chart Analysis)
Save Results Options Dialog Box (CuSum [H-K] Chart Analysis)

The Save Results Options dialog box allows you to choose the results you want to save.  There are six selections: Cumulative Sum, Ranges, Sizes, Labels, Process Mean, and Process Sigma.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results Options button on the Analysis toolbar (the fourth button from the left).


ARIMA Chart Analysis Dialog Box

The ARIMA and ARIMA Individuals charts analyses in STATGRAPHICS Plus, use Montgomery’s approach.  The analyses are designed to handle serially correlated subgroup or individuals data.  They also provide complete ARIMA modeling without limits on the order of autoregressive or moving-average processes.

Data

Subgroup Numbers or Size

Subgroup Labels

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the ARIMA Analysis

ARIMA Chart Options

ARIMA Chart Report

ARIMA Chart Report Options

Runs Tests

Runs Tests Options

Capability Indices

Process Capability Indices Options

ARIMA Chart

ARIMA Chart Options

Range Chart

Control Chart Options

Residual Autocorrelation Function Plot

Residual Autocorrelation Function Options

Residual Partial Autocorrelation Function Plot

Residual Partial ACF Options

Tolerance Chart

Tolerance Chart Options


ARIMA Chart Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (ARIMA Chart Analysis)

ARIMA Chart Report (ARIMA Chart Analysis)

Runs Tests

Capability Indices


ARIMA Chart Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

ARIMA Chart

Range Chart

Residual Autocorrelation Function Plot

Residual Partial Autocorrelation Function Plot

Tolerance Chart


ARIMA Chart Options Dialog Box

This dialog box allows you to choose options for the ARIMA Chart Report and ARIMA Chart.

Type of Study

ARIMA Control Limits

Range Control Limits

Control to Standard

Model

Estimate Sigma From

Chart Type


ARIMA Chart Report Options Dialog Box

This dialog box allows you to choose the information that will display in the report.

Display


Process Capability Indices Options Dialog Box

This dialog box allows you to choose the indices that will be included and to enter values for the upper and lower specification limits and the target for the nominal.

Indices

Specifications


Residual Autocorrelation Function Options Dialog Box

This dialog box allows you to enter values for the number of lags and the confidence level.

Number of Lags

Confidence Level


Residual Partial ACF Options Dialog Box

This dialog box allows you to enter values for the number of lags and the confidence level.

Number of Lags

Confidence Level


Tolerance Chart Options Dialog Box

This dialog box allows you to set the specification limits for the Tolerances chart.

Specifications

Plot

Decimal Places for Limits


Save Results Options Dialog Box (ARIMA Chart Analysis)

The Save Results Options dialog box allows you to choose the results you want to save.  There are seven selections: Means, Ranges, Sizes, Labels, Process Mean, Process Sigma, and Residuals.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results Options button on the Analysis toolbar (the fourth button from the left).


ARIMA Individuals Chart Analysis Dialog Box

Auto-Regressive Integrated Moving Average (ARIMA) models are a complex set of statistical techniques for time-series analysis that combines autoregressive analysis procedures with those of moving averages.  A researcher, in using ARIMA models, is able to construct a trend line that accounts for both systematic error (autocorrelation) and nonsystematic (random) error.

The ARIMA and ARIMA Individuals charts analyses in STATGRAPHICS Plus, use Montgomery’s approach.  The analyses are designed to handle serially correlaed subgroup or individuals data.  They also provide complete ARIMA modeling without limits on the order of autogressive or moving-average processes.

The functionality in the ARIMA Individuals Chart Analysis is identical to that in the ARIMA Chart Analysis, except you use for observations instead of subgroups.

Observations

Labels

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the ARIMA Individuals Analysis

ARIMA Individuals Chart Options

ARIMA Individuals Chart Report

ARIMA Individuals Chart Report Options

Runs Tests

Runs Tests Options

Capability Indices

Process Capability Indices Options

ARIMA Chart

ARIMA Chart Options

Range Chart

Control Chart Options

Residual Autocorrelation Function Plot

Residual Autocorrelation Function Options

Residual Partial Autocorrelation Function Plot

Residual Partial ACF Options

Tolerance Chart

Tolerance Chart Options


ARIMA Individuals Chart Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (ARIMA Individuals Chart Analysis)

ARIMA Individuals Chart Report

Runs Tests (ARIMA Individuals Chart Analysis)

Capability Indices (ARIMA Individuals Chart Analysis)


ARIMA Individuals Chart Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

ARIMA Chart (ARIMA Individuals Chart Analysis)

MR(2) Chart (ARIMA Individuals Chart Analysis)

Residual Autocorrelation Function Plot

Residual Partial Autocorrelation Function Plot


ARIMA Individuals Charts Options Dialog Box

This dialog box allows you to indicate the type of study that will be performed and to enter values for the upper and lower sigma for the ARIMA Control Limits and M(2) Control Limits.

Type of Study

ARIMA Control Limits

MR(2) Control Limits

Control to Standard

Model

Estimate Sigma From

Chart Type


ARIMA Individuals Chart Report Options Dialog Box

This dialog box allows you to choose the report you want to create.

Display


Save Results Options Dialog Box (ARIMA Individuals Chart Analysis)

The Save Results Options dialog box allows you to choose the results you want to save.  There are seven selections: Observations, Moving Ranges, Labels, Process Mean, Process Sigma, and Residuals.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results Options button on the Analysis toolbar (the fourth button from the left).


Toolwear Chart Analysis Dialog Box

Montgomery (1997) reports research by others who confirm that adapting control charts for the tool-wear problem is a good approach.  This concept calls for an initial tool setting at some multiple of sigma above the lower specification limit, while the maximum permissible process average is at the same multiple of sigma, below the upper specification limit.  If the rate of wear is known or can be estimated from the data, a set of slanting control limits about the tool-wear trend can be constructed.  If the sample values of X-bar fall within these limits, the tool wear is in control.  When the trend line exceeds the maximum permissible process average, the process should be reset or the tool replaced.

Data

Subgroup Numbers or Size

Subgroup Labels

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Toolwear Chart Analysis

Toolwear Chart Options

Toolwear Chart Report

Toolwear Chart Report Options

Runs Tests

Runs Tests Options

Toolwear Chart

Control Chart Options

Range Chart

Tolerance Chart

Tolerance Chart Options


Toolwear Chart Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Toolwear Chart Analysis)

Toolwear Chart Report

Runs Tests


Toolwear Chart Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Toolwear Chart

Range Chart

Tolerance Chart


Toolwear Chart Options Dialog Box

This dialog box allows you to choose the type of study, enter values for the upper and lower sigma, and for the upper and lower specification limits.

Type of Study

Estimate Sigma From

Control to Standard

X-bar Control Limits

Range Control Limits

Specification Limits


Toolwear Chart Report Options Dialog Box

This dialog box allows you to choose the type of report you want to produce.

Display


Save Results Options Dialog Box (Toolwear Chart Analysis)

The Save Results Options dialog box allows you to choose the results you want to save.  There are seven selections: Means, Ranges, Sizes, Labels, Process Mean, Process Sigma, and Residuals.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results Options button on the Analysis toolbar (the fourth button from the left).


Toolwear Individuals Chart Analysis Dialog Box

Montgomery (1997) reports research by others who confirm that adapting control charts for the tool-wear problem is a good approach.  This concept calls for an initial tool setting at some multiple of sigma above the lower specification limit, while the maximum permissible process average is at the same multiple of sigma, below the upper specification limit.  If the rate of wear is known or can be estimated from the data, a set of slanting control limits about the tool-wear trend can be constructed.  If the sample values of X-bar fall within these limits, the tool wear is in control.  When the trend line exceeds the maximum permissible process average, the process should be reset or the tool replaced.

The functionality in the Toolwear Individuals Chart Analysis is identical to that in the Toolwear Chart Analysis, except that you use observations instead of subgroups.

Observations

Labels

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Toolwear Individuals Chart Analysis

Toolwear Individuals Chart Options

Toolwear Chart Report

Toolwear Chart Report Options

Runs Tests

Runs Tests Options

Toolwear Chart

Control Chart Options

Range Chart

Tolerance Chart

Tolerance Chart Options


Toolwear Individuals Chart Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Toolwear Individuals Chart Analysis)

Toolwear Individuals Chart Report

Runs Tests


Toolwear Individuals Chart Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Toolwear Chart

MR(2) Chart


Toolwear Individuals Chart Options Dialog Box

This dialog box allows you to choose the type of study and to enter values for the upper and lower sigma for the X Control Limits, MR(2) Control Limits, and values for the upper and lower specification limits.

Type of Study

Estimate Sigma From

Include Model Estimation Error

Control to Standard

X Control Limits

MR(2) Control Limits

Specification Limits


Toolwear Individuals Chart Report Options Dialog Box

This dialog box allows you to choose the report that will be created.

Display


Save Results Options Dialog Box (Toolwear Individuals Chart Analysis)

The Save Results Options dialog box allows you to choose the results you want to save.  There are seven selections: Observations, Moving Ranges, Labels, Process Mean, Process Sigma, Included Observations, and Residuals.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results Options button on the Analysis toolbar (the fourth button from the left).


Acceptance Chart Analysis Dialog Box

Acceptance charts are one of two methods used for relaxing the level of surveillance provided by a standard control chart (Montgomery, 1997).  The purpose of the analysis is to monitor processes that tend to operate well within process specifications (with high Cp).  Rather than place the control limits at +/- 3 sigma from the centerline, STATGRAPHICS Plus places them relative to the specification limits.  This allows the process to drift around the centerline, while still ensuring that little if any product is out of specification.

The basis of the Acceptance Chart is controlling both the risk of rejecting a satisfactory process (α-risk), and the risk of accepting an unsatisfactory process (β-risk).

Data

Subgroup Numbers or Size

Subgroup Labels

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Acceptance Chart Analysis

Acceptance Chart Options

Acceptance Chart Report

Acceptance Chart Report Options

Capability Indices

Process Capability Indices Options

Acceptance Chart

Control Chart Options

S Chart

Tolerance Chart

OC Curve

ARL Curve


Acceptance Chart Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Acceptance Chart Analysis)

Acceptance Chart Report

Capability Indices


Acceptance Chart Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Acceptance Chart

S Chart

Tolerance Chart

OC Curve

ARL Curve


Acceptance Chart Options Dialog Box

This dialog box allows you to choose the type of study and to enter values for the upper and lower sigma for the X-bar Control Limits, Sigma Control Limits, and values for the upper and lower specification limits.

Type of Study

Specify

X-bar Control Limits

Sigma Control Limits

Specification Limits


Acceptance Chart Report Options Dialog Box

This dialog box allows you to choose the report that will be created.

Display


Tolerance Chart Options Dialog Box

This dialog box allows you to enter values for the Nominal and the number of decimal places that will be used to display the limits, and to indicate if points or the nominal will display on the plot.

Specifications

Plot

Decimal Places for Limits


Save Results Options Dialog Box (Acceptance Chart Analysis)

The Save Results Options dialog box allows you to choose the results you want to save.  There are six selections: Means, Sigmas, Sizes, Labels, Process Mean, and Process Sigma.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results Options button on the Analysis toolbar (the fourth button from the left).


Acceptance Individuals Chart Analysis Dialog Box

Acceptance charts are one of two methods used for relaxing the level of surveillance provided by a standard control chart (Montgomery, 1997).  The purpose of the analysis is to monitor processes that tend to operate well within process specifications (with high Cp).  Rather than place the control limits at +/- 3 sigma from the centerline, STATGRAPHICS Plus places them relative to the specification limits.  This allows the process to drift around the centerline, while still ensuring that little if any product is out of specification.

The basis of the Acceptance Chart is controlling both the risk of rejecting a satisfactory process (α-risk), and the risk of accepting an unsatisfactory process (β-risk).

The functionality in the Acceptance Individuals Chart Analysis is identical to that in the Acceptance Chart Analysis, except that you use individual observations instead of subgroups.

Observations

Labels

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Acceptance Chart Analysis

Acceptance Chart Options

Acceptance Chart Report

Acceptance Chart Report Options

Capability Indices

Process Capability Indices Options

Acceptance Chart

Control Chart Options

S Chart

Tolerance Chart

OC Curve

ARL Curve


Acceptance Individuals Chart Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Acceptance Individuals Chart Analysis)

Acceptance Individuals Chart Report

Capability Indices


Acceptance Individuals Chart Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Acceptance Chart

MR(2) Chart

OC Curve

ARL Curve


Specification Limits Dialog Box

This dialog box determines the specifications for the Acceptance Individuals Chart.

Upper

Enter a numeric value for the upper specification limit.  The value you enter must be greater than the value in the Lower text box.

Lower

Enter a value for the lower specification limit.  The value you enter must be less than the value in the Upper text box.


Acceptance Individuals Chart Options Dialog Box

This dialog box allows you to choose options for the chart.

Type of Study

Specify

Control to Standard

X-Control Limits

MR(2) Control Limits

Specification Limits


Acceptance Individuals Chart Report Options Dialog Box

This dialog box allows you to choose the type of report that will be displayed.

Display


Save Results Options Dialog Box (Acceptance Individuals Chart Analysis)

The Save Results Options dialog box allows you to choose the results you want to save.  There are six selections: Observations, Moving Ranges, Labels, Process Mean, Process Sigma, and Included Observations.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results Options button on the Analysis toolbar (the fourth button from the left).


Fishbone Diagram Analysis

A noted Japanese quality expert, Dr. Kaoru Ishikawa, originally developed the Fishbone diagram for solving quality problems.  A major benefit of the diagram is that it forces all that is known about a subject to be noted, which is also a major weakness because its accuracy depends on the person or group who creates the diagram.  It is critical that input be gathered from everyone involved with the process because the varying ideas often lead to a better picture of the actual causes.

There are other benefits for using this type of diagram.

•	All the factors are known, instead of only those suspected.

•	The diagram provides a plan of attack that allows deletion of causes that may not 	turn out to be important.

•	The diagram provides an ongoing record of when the actual relationships occur 	and when they are corrected.

•	When the analysis is complete, it is reasonable to assume that you have 	accounted for all the information.

Labels

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Fishbone Analysis

Setting Up a DataSheeet for Creating a Fishbone Diagram

Fishbone Diagram


Fishbone Diagram Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Fishbone Diagram Analysis)


Fishbone Diagram Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Fishbone Diagram


Acceptance Sampling - Attributes Analysis Dialog Box

Acceptance sampling for attributes includes developing sampling plans for attribute data based on the Binomial and Poisson distributions.  The metric for the Operating Curve (OC) can be either the fraction defective, as in the Binomial case of Go/No-Go data, or counts, as in the Poisson case of defect count.

The Acceptance Sampling for Attributes Analysis has several useful applications.  It can:

•	determine if a process can meet a proposed quality requirement

•	determine the required inspection effort

•	improve tough recall decisions

•	calculate one- and two-sided confidence limits based on fraction defectives and 	counts.

A description of standard sampling procedures for inspection by attributes that were developed during World War II are discussed in Montgomery (1997) and are the basis for the Acceptance Sampling by Attributes Analysis in STATGRAPHICS Plus.  Today the most widely used version of the standard is MIL STD 105E and its civilian counterpart standard ANSI/ASQC Z14, which is quite similar.

Action

Quality Levels

Lot Size

Desired Features

Current Plan

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Acceptance Sampling – Attributes Analysis

OC Curve

AOQ Curve

ATI Curve


Acceptance Sampling - Attributes Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Acceptance Sampling - Attributes)


Acceptance Sampling - Attributes Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

OC Curve

AOQ Curve

ATI Curve


Acceptance Sampling - Variables Analysis Dialog Box

Acceptance sampling by variables has a primary advantage in that you can obtain the same operating-characteristic curve using a smaller sample size than you would using an attributes sampling plan.  Therefore, a variables acceptance-sampling plan requires fewer samples.  Another advantage is that measurement data usually provide more information about the manufacturing process.  And, when acceptable quality levels are small, the required sample sizes are usually very large.

MIL STD 414 is a lot-by-lot acceptance sampling-sampling plan for variables introduced in 1957.  The primary focus of this standard is the acceptable quality level (AQL).  Again, Montgomery (1997) provides an informative and in-depth discussion.

Action

Quality Levels

Lot Size

Process Sigmas

Desired Features

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Acceptance Sampling – Variables Analysis

OC Curve

AOQ Curve

ATI Curve


Acceptance Sampling - Variables Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Acceptance Sampling - Variables)


Acceptance Sampling - Variables Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

OC Curve

AOQ Curve

ATI Curve


Multilevel Factorial Design Options Dialog Box

This dialog box allows you to choose options for the design.

Runs

Error d.f.

Replicate Design

Randomize


Inner/Outer Arrays Options Dialog Box

This dialog box allows you to choose an Inner Array.  If you entered a value for the noise factors on the Response Definition Options dialog box, you can choose an Outer Array.

Control Design (Inner Array)

Noise Design (Outer Array)

Randomize


Column Assignments Dialog Box

This dialog box allows you to enter a number for each factor in the Inner Array.

Column Design (Inner Array)

Factor

Column

Noise Design (Outer Array)

Factor

Column


Control/Noise Factor Definition Options Dialog Box

Allows you to choose a factor and enter a name for it, or optionally, enter a value for the units of measure.

Factor

Name

Units

Labels...


Factor Levels Dialog Box

This dialog box allows you to enter a number or an alphanumeric string up to 20 characters for each factor level.


Single Factor Categorical Design Options Dialog Box

This dialog box allows you to either accept the defaults or choose a design type and choose other options for the design.  If you use the Combinatoric BIB or Small BIB options in the Design Type section, two additional options are available: Number of Blocks and Block Size.

Runs

Blocks

Error d.f.

Design Type

Replicate Design

Randomize

Number of Blocks

Block Size

Back


Multi-Factor Categorical Design Options Dialog Box

This dialog box allows you to enter or choose options for the design.

Runs

Error d.f.

Replicate Design

Randomize

Back


Variance Components Design Options Dialog Box

This dialog box allows you to choose options regarding replicating and randomizing.

Runs

Error d.f.

Replicate Design

Randomize

Back


Multiple Response Optimization Dialog Box

This dialog box allows you to enter the names of the response variables that will be used in the optimization.

Responses

Sort


Multiple Response Optimization Options Dialog Box

This dialog box allows you to further define the optimization.

Response

Low

High

Max/Min/Hit

Target

Weights

Impact


Optimize Response Options Dialog Box

This dialog box allows you to choose the type of optimization that will be used, choose the type of additional starting points, and enter the Low, High, and Start values for the factor(s).

Type of Optimization

Additional Starting Points

Low

High

Start


Response Plot Factors Dialog Box

This dialog box allows you to set values for the factors.

[Factor]

Low

High

Hold


Optimization

The Optimization option shows the combination of factor levels that maximize the selected variable over an indicated region.  You can set the value for one or more factors to a constant by setting the low and high limits to that value.


Analyze Design Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the design.

Analysis Summary

ANOVA Table

Regression Coefficients

Correlation Matrix

Predictions

Path of Steepest Ascent

Optimization


Analyze Design Graphical Options Dialog Box

This dialog box allows you to choose graphical options.

Pareto Charts

Main Effects Plots

Interaction Plots

Normal Probability Plots of Effects

Response Plots

Diagnostic Plots


Multiple Response Optimization Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Multiple Response Optimization)

Optimization


Multiple Response Optimization Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Response Plots

Response Plots

Overlaid Contour Plots


Skewness and Kurtosis Plot Options Dialog Box

This dialog box allows you to enter the lowest and highest values for Lambda1, and enter a value for the resolution that will smooth the curve.

Minimum Lambda1

Maximum Lambda1

Resolution


Weibull Analysis Options Dialog Box

This dialog box allows you to choose an origin for the distribution starting point, an estimation method, and a plotting position.

Starting Point

Plotting Position


Polar Coordinates Plot Analysis Dialog Box

The Polar Coordinates Plot Analysis creates a two-dimensional scatterplot or line plot for pairs of points that are defined by radius and angle positions.  In other words, it provides information about the location of a point on a graph; for example, finding (x,y) in polar coordinates.  This type of plot is useful in manufacturing environments where a polar coordinate system rather than, or in addition to, a rectangular coordinate system might be used to label points on the plane.

A polar coordinate system differs from a rectangular coordinate system in the way it represents points on the plane.  In a rectangular coordinate system, a point, (x,y), is defined as the point derived from moving from the origin horizontally x units and vertically y units.  In a polar coordinates system, a point, (x,y), is defined by beginning at the origin, finding the ray that comes from the origin that is an angle of y with the positive X-axis, and goes out a distance of y, on this ray (The Math Forum, 1997).

Radius

Angle

Point Codes

Select

Sort

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left o either Pane Options or Analysis Options.

See also

Using the Polar Coordinates Analysis

Polar Coordinates Plot Options

Polar Coordinates Plot


Polar Coordinates Plot Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Polar Coordinates Plot Analysis)


Polar Coordinates Plot Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Polar Coordinates Plot (Polar Coordinates Plot Analysis)


Polar Coordinates Plot Options Dialog Box

This dialog box allows you to choose options for this analysis.

Plot

Angular Units

Labels

Direction

Origin


Radar/Spider Plot Analysis Dialog Box

The Radar/Spider Plot Analysis is a simple visualization technique often considered valuable in meeting the demands of multivariate data because of its ability to simultaneously portray numerous aspects of the data.  This technique plots multiple measurements on equally spaced radii that are linked to create a star-like form.  The radii extend from the center of a circle and give an overall impression of changing values across subjects.

A Radar Plot is much like a Star Plot.  In a Radar Plot, radii that stretch from the center of a circle represent the value of the measurement. Each radius stands for a subject instead of a variable.  Points of different colors represent the response for each variable.  When there are too many variables and subjects, the pattern of the data is concealed.

Columns

Row Labels

Select

Sort


Radar/Spider Plot Tabular Options Dialog Box

This dialog box allows you to choose tabular options for the analysis.

Analysis Summary (Radar/Spider Plot)


Radar/Spider Plot Graphical Options Dialog Box

This dialog box allows you to choose graphical options for the analysis.

Radar/Spider Plot


Radar/Spider Plot Analysis Options Dialog Box

This dialog box allows you to make changes to the analysis.  You can indicate the type of scale and grid that will be used for a plot; indicate if spokes will be drawn; and if filled polygons will be used.

Scaling


Analysis Summary (Multiple Dot Diagram Analysis)

The Analysis Summary option creates a summary that includes the names of the variables that contain the data and the level codes.  It also displays the number of levels and observations in the analysis, as well as the selected values for the upper and lower limits.

Use the Multiple Dot Diagram Analysis Options dialog box to choose options for the plot.


Multiple Dot Diagram (Multiple Dot Diagram Analysis)

The Multiple Diagram option creates a plot that shows the location for each level mean, as well as the confidence intervals for the means.  The X-axis shows the mean and standard deviation for each level.

A vertical line is drawn at the grand mean of the total observations.  The plot displays the grand mean and the standard deviation at the top of the vertical line.


Analysis Summary (Radar/Spider Plot)

The Radar/Spider Plot option creates a summary of the analysis that displays the names of the data variables.


Overlay Plot
Radar/Spider Plot

The Radar/Spider Plot option creates a plot that shows the data in each row, with the size of each of the variables plotted along one of the spokes.  You can plot up to 16 cases on a single diagram, which is helpful in comparing cases from a multivariate perspective.


Analysis Summary (Component Line Chart Analysis)

The Analysis Summary option creates a summary of the analysis that displays the names of the variables in the columns, the start index, and the sampling interval.  It also displays the number of periods that contain data.

Use the Component Line Chart Analysis Options dialog box to indicate if the variables should be plotted cumulatively, which is the default

.

If you choose Cumulative, the patterns for the variables appear vertically stacked, one on top of the other.  In plots that contain positive data, the values are added at each time point.  In plots that contain negative data, the values are subtracted from the values for the previous variable.

If you deselect the default (remove the checkmark), the patterns for each variable appear as overlays and points in one variable may hide the points for variables that are plotted later.  To minimize this problem, first enter the variable with the smallest values; then the variable with the second smallest values; and so on.  The program plots the last variable first, the second-to-last on top of the last variable, and so on until all the variables appear on the plot.


Component Line Chart

The Component Line Chart option creates a filled polygon with the values plotted against time.  The values appear on the plot in the order in which they appear in the DataSheet.  The area under any specific time series is filled with a unique color.  You can create a cumulative or noncumulative plot.


Analysis Summary (High-Low-Close Plot)

The Analysis Summary option creates a summary of the analysis that displays the names of the variables for High, Low, and Close values; and the values for the Starting Index and Sampling Interval.

It also displays the number of periods that contain data; and values for the Maximum High, Minimum Low, and Average Close.


High-Low-Close Plot

The High-Low-Close Plot option creates a plot with a vertical line that extends from each low value to its corresponding high value.  A horizontal line is drawn at each of the closing values.


Analysis Summary (Power Transformations)

The Analysis Summary option creates a summary of the analysis that displays the name of the variable, the number of observations, the values for the Box-Cox transformation (Lambda1 and Lambda2 optimized), and the value for the geometric mean.

Use the Power Transformations Options dialog box to change the values for Lambda1 and Lambda2; and to indicate if you want the value for Lambda1 optimized.


MSE Comparison Table (Power Transformations Analysis)

The MSE Comparison Table option creates a table that shows the Mean Squared Error (MSE) for various values of the power transformation parameter, Lambda1.  The table shows the values for MSE for a range of different Lambdas.

Use the MSE Comparison Table Options dialog box to set the values for which the MSE will be determined, and to enter a value for the resolution.


Tests for Normality (Power Transformations Analysis)

The Tests for Normality option displays the results of tests run to determine if the transformed values of the variable adequately model a normal distribution.

The Chi-Square Test divides the range of the transformed values of the variable into equal probability classes, and compares the number of observations in each class with the expected number, based on the fitted distribution.

The Shapiro-Wilks test is based on the comparison of the quantiles for the fitted normal distribution with the quantiles of the data.

The Standardized Skewness test looks for lack of symmetry in the data, while the Standardized Kurtosis test looks for distributional shape that is either flatter or more peaked than a normal distribution.

The Tests for Normality table shows the lowest p-value among the tests performed.  If the p value is less than 0.05, you can reject the idea that the transformed values come from a normal distribution at the 95 percent confidence level.


Normal Probability Plot (Power Transformations Analysis)

The Normal Probability Plot option creates a plot of the transformed values for the selected variable.  The program sorts the values from smallest to largest, then plots them versus the values (i-0.375)/(n+0.25), where n = equals the sample size.

If the data come from a normal distribution, the points should fall approximately along a straight line.  To help determine the closeness of the points to the straight line, a reference line is drawn on the plot.  The reference line, by default, is fit to the data using least squares.  Additional tests for normality are also available in this analysis.

Use the Normal Probability Plot Options dialog box to choose options for the plot.


Skewness and Kurtosis Plot (Power Transformations)

The Skewness and Kurtosis Plot option creates a plot that shows the values for the standardized skewness and standardized kurtosis at various values of Lambda1. A vertical line is drawn at the optimal value; horizontal lines are drawn at 0 and +/-2.

Use the Skewness and Kurtosis Plot Options dialog box to choose options for the plot.


MSE Comparison Plot (Power Transformations Analysis)

The MSE Comparison Plot option creates a plot that shows the various values of the power transformation parameter, Lambda1, between -2.0 and +2.0.  It also shows the smallest value for MSE at Lambda1.

Use the MSE Comparison Plot Options dialog box to set the values for which the MSE will be determined, and to enter a value for the resolution.


Analysis Summary (Statistical Tolerance Limits Analysis)

The Analysis Summary option creates a summary of the analysis that shows the size, mean, and standard deviation for the sample.  It then displays the specified tolerance limits, confidence interval, and population proportions.

Use the Statistical Tolerance Limits Options dialog box to enter values for the confidence level and the population proportion, and to indicate if two-sided, upper, or lower limits will be used.


Nonparametric Limits (Statistical Tolerance Limits Analysis)

The Nonparametric Limits option displays the specified tolerance limits (always the sample maximum and minimum), confidence level, and population proportion.  The required sample size represents the number of observations that must be taken to ensure that, with the specified confidence level, at least the specified proportion of the population lies between the minimum and maximum values.


Tolerance Plot (Statistical Tolerance Limits Analysis)

The Tolerance Plot option displays a normal density function with vertical lines drawn at the location of the tolerance limits.


Analysis Summary (Probability Plots Analysis)

The Analysis Summary option creates a summary that shows the name of the selected variable, the number of non-missing observations, and the number of values below minimum and above maximum.

Use the Probability Plot Options dialog box to enter a number for the values above maximum and a number for the values below maximum.


Uniform Plot (Probability Plots Analysis)

The Uniform Plot option creates a plot for the variable you selected that helps determine if the data can be reasonably modeled using a Uniform distribution.

To create the plot, the program sorts the values from smallest to largest, then plots them versus the values (i - 0.375)/(n + 0.25), where n is the size of the sample.  If the data come from a Uniform distribution, the points will lie approximately along a straight line.  A reference line is superimposed on the plot to determine the closeness of the points to the line.  The reference line was fit to the plot using least squares.


Normal Plot (Probability Plots Analysis)

The Normal Plot option creates a plot for the variable you selected that helps determine if the data can be reasonably modeled using a Normal distribution.

To create the plot, the program sorts the values from smallest to largest, then plots them versus the values (i- 0.375)/(n + 0.25), where n is the size of the sample.  If the data come from a Normal distribution, the points will lie approximately along a straight line.  A reference line is superimposed on the plot to determine the closeness of the points to the line.  The reference line was fit to the plot using least squares.


Lognormal Plot (Probability Plots Analysis)

The Lognormal Plot option creates a plot for the variable you selected that helps determine if the data can be reasonably modeled using a Lognormal distribution.

To create the plot, the program sorts the values from smallest to largest, then plots them versus the values (i - 0.375)/(n + 0.25), where n is the size of the sample.  If the data come from a Lognormal distribution, the points will lie approximately along a straight line.  A reference line is superimposed on the plot to determine the closeness of the points to the line.  The reference line was fit to the plot using least squares.


Weibull Plot (Probability Plots Analysis)

The Weibull Plot option creates a plot for the variable you selected that helps determine if the data can be reasonably modeled using a Weibull distribution.

To create the plot, the program sorts the values from smallest to largest, then plots them versus the values (i - 0.375)/(n + 0.25), where n is the size of the sample.  If the data come from a Weibull distribution, the points will lie approximately along a straight line.  A reference line is superimposed on the plot to determine the closeness of the points to the line.  The reference line was fit to the plot using least squares.


Extreme Value Plot (Probability Plots Analysis)

The Extreme Value Plot option creates a plot for the variable you selected that helps determine if the data can be reasonably modeled using an Extreme Value distribution.

To create the plot, the program sorts the values from smallest to largest, then plots them versus the values (i - 0.375)/(n + 0.25), where n is the size of the sample.  If the data come from an Extreme Value distribution, the points will lie approximately along a straight line.  A reference line is superimposed on the plot to determine the closeness of the points to the line.  The reference line was fit to the plot using least squares.


Logistic Plot (Probability Plots Analysis)

The Logistic Plot option creates a plot for the variable you selected that helps determine if the data can be reasonably modeled using a Logistic distribution.

To create the plot, the program sorts the values from smallest to largest, then plots them versus the values (i - 0.375)/(n + 0.25), where n is the size of the sample.  If the data come from a Logistic distribution, the points will lie approximately along a straight line.  A reference line is superimposed on the plot to determine the closeness of the points to the line.  The reference line was fit to the plot using least squares.


Exponential Plot (Probability Plots Analysis)

The Exponential Plot option creates a plot for the variable you selected that helps determine if the data can be reasonably modeled using an Exponential distribution.

To create the plot, the program sorts the values from smallest to largest, then plots them versus the values (i - 0.375)/(n + 0.25), where n is the size of the sample.  If the data come from an Exponential distribution, the points will lie approximately along a straight line.  A reference line is superimposed on the plot to determine the closeness of the points to the line.  The reference line was fitted to the plot using least squares.


Quantile Plot (Distribution Fitting - Uncensored Data)
Quantile Plot

The Quantile Plot option creates a plot of the quantiles for the data.  The Y-axis represents the proportion of values that are below a particular value.


Quantile/Quantile Plot (Distribution Fitting - Uncensored)
Quantile/Quantile Plot

The Quantile/Quantile Plot option creates a plot of the sorted values against the corresponding quartiles of the fitted distribution so you can compare the cumulative distributions for the two samples.  If the distributions are a good fit, the points fall along the line.


Analysis Summary (Distribution Fitting - Censored Data)

The Analysis Summary option creates a summary of the results, which includes the number of values and their ranges, as well as the number of left- and right-censored (positive/negative) observations.  It then displays the results of the fitted distribution; for example, it shows the values for the mean and standard deviation for a Lognormal distribution if that is the distribution you are using.

Use the Probability Distributions Options dialog box to choose a different distribution, to enter the number of trials, and to enter the number of successes.  Each of the 24 distributions has its’ own Options dialog box.


Goodness-of-Fit Tests (Distribution Fitting - Censored)

The Goodness-of-Fit Tests option calculates results for tests of fit based on the Empirical Distribution Function (EDF).  EDF is a step function that is calculated from the sample, which estimates the population distribution function.  EDF statistics are used for testing the fit of the sample to the distribution (D'Agostino and Stephens, 1986).  The tests are: Kolmogorov-Smirnov D, and Kuiper V.

The Kolmogorov-Smirnov D test calculates the maximum distance between the cumulative distribution of the data and the cumulative distribution function of the fitted distribution.  This calculation is a nonparametric method used to test the overall goodness of fit between the distribution of the data and the distribution you choose.  If the p value is less than .05 (for a 95 percent confidence level), the data do not fit the distribution.  The Kolmogorov-Smirnov test is available when you are fitting data to continuous distributions.

The Kuiper V statistic improves the Kolmogorov-Smirnov test in the tails of a distribution.  If there are only two class levels, it is a scaled value for an asymptotic distribution, and determines the probability of observing a larger test statistic.

Use the Goodness-of-Fit Tests Options dialog box to choose the EDF statistic and the censoring method.


Critical Values (Distribution Fitting - Censored)

The Critical Values option calculates critical values for the distribution.  Critical values are the smallest values for the area that fall under the distribution curve.  The values for the distribution curve are those that are no less than the values you selected for the probability.  The test calculates critical values for up to five lower tail areas.

Use the Critical Values Options dialog box to enter values for the probabilities that will be used to calculate the corresponding critical values.


Tail Areas (Distribution Fitting - Censored Data)

The Tail Areas option calculates the area under the density curve at specified points.  The test uses the cumulative distribution function to calculate the probability that a random variable will fall below a given value.  The test calculates tail areas for up to five critical values.

Use the Tail Areas Options dialog box to enter values that will be used to calculate the areas under the curve.


Frequency Histogram (Distribution Fitting - Censored Data)

The Frequency Histogram option creates a histogram with the distribution curve shown as an overlay.  The program divides the data into sets of nonoverlapping intervals and plots bars for each interval; the height of each bar is proportional to the number of observations that fall within that interval.  Use the plot to determine if the data follow the distribution you selected.

Use the Frequency Tabulation Options dialog box to enter the number of classes into which the data will be grouped, and to enter values for the Lower and Upper limits.  You can also indicate if the current scaling should be retained if you change the data in the Analysis dialog box.


Quantile Plot (Distribution Fitting - Censored Data)
Quantile Plot

The Quantile Plot option creates a plot of the quantiles for the data.  The Y-axis represents the proportion of values that are below a particular value.


Quantile/Quantile Plot (Distribution Fitting - Censored Data)
Quantile/Quantile Plot

The Quantile/Quantile Plot option creates a plot of the sorted values against the corresponding quartiles of the fitted distribution so you can compare the cumulative distributions for the two samples.  If the distributions are a good fit, the points fall along the line.


Distribution Functions 1 and 2 (Distribution Fitting - Censored Data)
Distribution Functions 1 and 2

The Distribution Functions 1 and 2 options each create one of several different types of distribution function plots.  The type of functions you can display are: Density Function, Cumulative Distribution Function, Survivor Function, Log Survivor Function, and Hazard Function.  The default for Distribution Function 1 is the Density Function plot.  The default for Distribution Function 2 is the Cumulative Distribution Function plot.

Use the Distribution Functions Options dialog box to indicate the type of function distribution you want to plot and to enter the number of density values that will be calculated.


Tail Areas (Distribution Fitting - Uncensored Data)

The Tail Areas option calculates the area under the density curve at specified points.  The test uses the cumulative distribution function to calculate the probability that a random variable will fall below a given value.  The test calculates tail areas for up to five critical values.


Goodness-of-Fit Options Dialog Box

This dialog box allows you to choose an EDF statistic and the censoring method.

EDF Statistics

Censoring


Analysis Summary (Arrhenius Plot Analysis)

The Analysis Summary option creates a summary of the analysis that shows the names of the variables as well as the equation for the fitted model, the regression statistics, including the number of observations, and values for the intercept, slope, and R-Squared.  It also shows the predictions, including values for the temperature, the estimated percentile, and the upper and lower limits.

The analysis fits an Arrhenius model to a set of percentiles taken at two or more study temperatures.  You can then use the fitted model to predict the corresponding percentile at a normal temperature.

Use the Arrhenius Plot Options dialog box to enter the temperature at which the prediction will be made and a confidence level.


Arrhenius Plot

The Arrhenius Plot option creates a plot that shows the predicted percentile with the data and the fitted model.


Analysis Summary (Comparison of Proportions Analysis)

The Analysis Summary option creates a summary of the analysis that shows the calculated decision limits, the average proportion, and the observed proportions.  Any proportions outside the decision limits are noted with an asterisk. The lower portion of the table displays the results of a chi-square test, which compares each sample value with its grand mean.  If the p-value is less than 0.05, there are significant differences between the samples at the 95 percent confidence level.


Analysis of Means (ANOM) Report (Comparison of Proportions Analysis)

The Analysis of Means (ANOM) Report option creates a table of the observed proportions for each of the samples.  The ANOM for proportions is performed by first calculating the average proportion, then calculating an estimate of the variation, based on the average proportion.

The top portion of the table shows the values for the decision limits at a given confidence level, and the number of samples beyond the limits.  An asterisk indicates values that are beyond the limits.  The bottom portion of the table displays the sample sizes and the observed proportions.

Use the Analysis of Means Report Options dialog box to enter a value for the confidence level that will be used to calculate the confidence intervals and to enter the number of decimal places that will be used for the decision limits.


Analysis of Means Report Options Dialog Box

This dialog box allows you to enter a value for the confidence level that will be used to calculate the confidence intervals and to enter the number of decimal places that will be used for the decision limits.

Confidence Level

Decimal Places for Limits


Analysis of Means (ANOM) Plot (Comparison of Proportions Analysis)

The Analysis of Means (ANOM) Plot option creates a plot that shows each group mean, the centerline at the grand mean, and the decision limits, which, determine the groups that differ significantly at the grand mean.  If any points are outside the decision limits, it can be concluded that there is a statistically significant difference between the proportions.

Use the Analysis of Means Plot Options dialog box to enter a value for the confidence level that will be used to calculate the confidence intervals and to enter the number of decimal places that will be used for the decision limits.


Analysis of Means Plot Options Dialog Box

This dialog box allows you to enter a value for the confidence level that will be used to calculate the confidence intervals and to enter the number of decimal places that will be used for the decision limits.

Confidence Level

Decimal Places for Limits


Analysis Summary (Comparison of Counts Analysis)

The Analysis Summary option creates a summary of the analysis that shows the name of the variable, the number of samples, and the mean count. The lower portion of the table displays the results of a chi-square test, which compares each sample value with its grand mean.  If the p-value is less than 0.05, there are significant differences between the samples at the 95 percent confidence level.


Analysis of Means (ANOM) Report (Comparison of Counts Analysis)

The Analysis of Means (ANOM) Report option creates a table of the observed counts for each of the samples.  The ANOM for counts is performed by first calculating the average count, then calculating an estimate of the variation, based on the average count.

The top portion of the table shows the values for the decision limits at a given confidence level, and the number of samples beyond the limits.  An asterisk indicates values that are beyond the limits.  The bottom portion of the table displays the decision limits and the observed counts.

Use the Analysis of Means Report Options dialog box to enter a value for the confidence level that will be used to calculate the confidence intervals and to enter the number of decimal places that will be used for the decision limits.


Analysis of Means Report Options Dialog Box

This dialog box allows you to enter a value for the confidence level that will be used to calculate the confidence intervals and to enter the number of decimal places that will be used for the decision limits.

Confidence Level

Decimal Places for Limits


Analysis of Means (ANOM) Plot (Comparison of Counts Analysis)

The Analysis of Means (ANOM) Plot option creates a plot that shows each group mean, the centerline at the grand mean, and the decision limits, which determine the groups that differ significantly at the grand mean.  If any points are outside the decision limits, it can be concluded that there is a statistically significant difference between the counts.

Use the Analysis of Means Plot Options dialog box to enter a value for the confidence level that will be used to calculate the confidence intervals and to enter the number of decimal places that will be used for the decision limits.


Analysis of Means Plot Options Dialog Box

This dialog box allows you to enter a value for the confidence level that will be used to calculate the confidence intervals and to enter the number of decimal places that will be used for the decision limits.

Confidence Level

Decimal Places for Limits


Graphics Options Dialog Box

This dialog box allows you to access various graphics tab pages to change or enhance a graph or chart.  The tab pages are graph-specific; for example, if you are creating a Piechart and want to make changes to it, first create the chart, then access the Graphics Options dialog box, which should display all the tab pages applicable for modifying that specific chart.

If you make changes to a graph, leave any tab page, then decide you do not want to make the changes, clicking the right mouse button, then Undo… on the pop-up menu reverses all the changes.

Fill Tab Page

Grid Tab Page

Label Tab Page

Layout Tab Page

Legend Tab Page

Line Tab Page

Point Tab Page

Point Tab Page

Profile Tab Page

Right Axis Tab Page

Spinning Tab Page

Text Tab Page

Top Title Tab Page

X-Axis Tab Page

Y-Axis Tab Page

Z-Axis Tab Page


Fill Tab Page

The Fill tab page allows you to change the style and color of fill patterns to distinguish the bars, boxes, wedges, and other fill areas on a graph or plot.  If you view and print the graph in color you can coordinate the color of each outline and area of the graph.  If you view and print the graph in black and white, you can use different fill patterns to achieve the same effect.

Fill

Fill Types

Color

Colors...

To Change the Style and Color of Fill Patterns

Double-click the graph to maximize it.

Place the mouse pointer on a fill area on the graph.

Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box, which should open to the tab page that corresponds to the area of the graph you selected in Step 2.

In the Fill options portion of the dialog box, click the number of the area you want to change.

Choose one of the eight Fill styles: Empty (no fill pattern), Solid, Horizontal Lines, Vertical Lines, Left- and Right-Facing Diagonal Lines, Cross-Hatch Lines, or Diagonal Cross-Hatch Lines.

For the Color option, click either Fill or Outline to indicate whether you want color applied to the fill pattern or to the outline of the filled area.

Click the Colors... button to display the Color dialog box.

Choose the color you want to use for the fill or outline, then click OK.

Click Apply, then OK on the Fills tab page to process the changes.


Grid Tab Page

The Grid tab page allows you to change the appearance of a grid by changing its direction, changing the type of lines on it, changing its color and/or line thickness, and indicating if a back grid should display on three-dimensional plots.

Direction

Type

Colors...

Line Thickness

Back Grid on 3D Plots

To Change the Direction, Style, and Color of Grid Lines

Double-click the graph to maximize it.

Place the mouse pointer on an empty portion inside the graph frame.

Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box.  Click the Grid tab page.

Choose one of the four Direction styles: Horizontal, Vertical, Both, or None.

Click the Colors... button to display the Color dialog box.

Choose the color you want to use.

Place the mouse pointer on the slider control for the line thickness and move the control from Thinnest to Thickest to change the width of the line.  Release the control.  Note:  The line thickness feature is available only for solid lines.

If the Back Grid on 3D Plots option is active and you are using a 3D plot that would look better with a back grid, click the box.

9.	Click Apply, then OK on the Grid tab page to process these changes.


Label Tab Page

The Label tab page allows you to create labels for plots and graphs.  Labels refer to text that appears on a graph as an identifier.  A series of text boxes appear on the page, which allow you to enter names for the labels.  The letter between braces, for example, {A}, is an internal system reference to variable names.

Label

Fonts...

To Change the Name of a Label

Double-click the graph to maximize it.

Move the mouse pointer to the label you want to change.

Click the left button to select the name of the label; markers appear at the corners of the selected label.

Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the Label tab page.

In the Label text box, enter the new name for the label, then click OK to process the change.

Continue entering names until you finish.

Click the Fonts... button to display the Windows Font dialog box.

Choose the font, font style, size, color, and other attributes, then click OK.

Click Apply and OK on the Label tab page to process the changes.


Layout Tab Page

The Layout tab page allows you to customize a graph by choosing a style and color for the tickmarks, the type of frame that will surround the graph, the color of the background and/or border of the graph, and the thickness of the axis line.

Tickmarks and Colors

Tickmarks

Mode

Line Thickness

Colors...

3D Effects

To Change Tickmarks

Double-click the graph to maximize it.

Place the mouse pointer on an empty portion inside the graph frame.

Click the left button, then the right on Graphics Options on the pop-up menu to display the Graphics Options dialog box opened to the Layout page (see Figure 5-6).

Click the option that corresponds to the axis whose tickmarks you want to change (X-, Y-, or Z-Axis).

Choose one of the three Tickmark styles:  No Tickmarks, Tickmarks Inside, or Tickmarks Outside.

Click the Colors... button to display the Color dialog box.

Choose the color you want to use, then click OK on the Color dialog box.

Click Apply, then OK on the Layout tab page to process all the changes.

To Change the Background and/or Border of a Graph

Double-click the graph to maximize it.

Place the mouse pointer on an empty portion inside the graph frame.

Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box, opened to the Layout page.

Click either the background or the border option.

Click the Colors... button to display the Color dialog box.

Choose the color you want to use, then click OK on the Color dialog box.

Click Apply, then OK on the Layout tab page to process all the changes.

To Change the Shape of a Graph

Double-click the graph to maximize it.

Place the mouse pointer on an empty portion inside the graph frame.

Click the left button, then the right on Graphics Options on the pop-up menu to display the Graphics Options dialog box opened to the Layout tab page.

Choose one of the two shape styles: L-Shaped or Square.

Click Apply, then OK on the Layout tab page to process the change.


Legend Tab Page

Many of the analyses you use to plot data for two or more variables contain a legend; for example, a Multiple X-Y-Z Plot or a Barchart.  A legend lists and explains the symbols on a graph.  You use the Legend tab page on the Graphics Options dialog box to change the title of a legend, change the names of the individual variables that apply to a legend, and to change the font attributes such as the style, point size, and color.  A series of text boxes appear on the page, which allow you to enter names for the legends.

Title

Legend

Fonts

To Change a Legend Title and Variable Names

Double-click the graph to maximize it.

Move the mouse pointer to the legend title you want to change.

Click the left button, then the right on Graphics Options on the pop-up menu to display the Graphics Options dialog box opened to the Legend tab page.

Enter a title into the Title text box.

Click in the {A} Legend text box, then enter a name for the first variable.

Continue entering names until you finish.

Click the Fonts... button to display the Windows Font dialog box.

Choose the color you want to use, then click OK.

Click Apply and OK on the Legend tab page to process the changes.


Line Tab Page

Changing the look of the lines that appear on a graph is useful when you need to enhance and clarify the graphical results.  You use the Line tab page on the Graphics Options dialog box to set the style and color of the lines on a graph.

Line Types

Line Thickness

Colors...

3D Effects

To Change the Type, Thickness, and Color of Lines

Double-click the graph to maximize it.

Place the mouse pointer on the line you want to change.

Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the Line tab page.

In the Line options portion of the dialog box, click the number of the line you want to change.

Choose one of the five Line styles: Solid, Dashed, Dotted, Dash-Dot, or Dash-Dot-Dot.

If you chose a Solid line, place the mouse pointer on the slider control for the line thickness and move the control from Thinnest to Thickest to change the width of the line.  Release the control.

Click the Colors... button to display the Color dialog box.

Choose the color you want to use, then click OK.

Click Apply, then OK on the Lines tab page to process the changes.


Points Tab Page

When you create two- and three-dimensional scatterplots or similar types of plots, it is helpful to be able to change the shape, size, and color of the individual points.  You use the Point tab page on the Graphics Options dialog box to set the style and color of points.

Point

Point Types

Fill Point

Point Size

Point Thickness

Colors...

To Change the Shape, Size, and Color of Points

Double-click the graph to maximize it.

Place the mouse pointer on the point you want to change.

Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the Points tab page.

In the Point options portion of the dialog box, click the number of the point you want to change.

Choose one of the eight Point styles: Square, Plus, X, Star, Diamond, Up Arrowhead, Down Arrowhead, or Circle.

Click the Fill Point check box or leave it blank to indicate if you want filled points.  An unchecked box (the default), means the points will not be filled.

Place the mouse pointer on the slider control for the Point Size and move the control from Smallest to Largest to change the size of the point, then release the control.

Place the mouse pointer on the slider control for the Point Thickness and move the control from Thinnest to Thickest, then release the control.

Click the Colors... button to display the Color dialog box.

Choose the color you want to use, then click OK.

Click Apply, then OK on the Points tab page to process the changes.


Profile Tab Page

The Profile tab page on the Graphics Options dialog box lets you set up and save graphics profiles.  The first two options, System (Color, White Background) and System (Color, Dark Background) describe the two predefined choices for choosing the color and background of the graphs you produce; the choices are self-explanatory.  System (Black and White) means that the graphs will always display in black and white format.

You can set up or edit up to 12 user profiles.  When you set them up or edit them, you can either use numbers, letters, names, or a combination of them to create the name of the profile.

Profile

Make a Default

Load

To Set Up a User Profile

Access the Graphics Options dialog box.

Select your graphics preferences using the tabs on the Graphics Options dialog box.

Return to the Profile tab page; use Load..., Save..., or Save As....  Load loads the profile; Save, saves it; and Save As saves the profile as a specific name.

For example, you might set up one profile for scatterplots, and another one for 3-dimensional plots.  After choosing your preferences for each type of plot:

Click the first User # option.

Click Save As... to display the Save Profile dialog box.

In the Profile Name text box, type Scatterplot to save the profile for scatterplots; click OK to save the current graphics settings.

Repeat Steps 4, 5, and 6, using 3-D Plots as the name for the User #2 option.  When you click OK, names are displayed on the Profile tab page as the names for the two user options.

If you want to make one of the profiles the default:

Click the option button next to the setting you want to make the default.

Click Make Default..., then Load.... The D default indicator to the left of the option buttons, moves to the left of the new profile, indicating the default.


Right Axis Tab Page

Some plots, such as the Multiple X-Y-Z Plot, contain a right axis.  The Right Axis tab page lets you change the scale for this axis.

Title

Vertical

From

To

By

Skip

No Power

Log

Hold

Tickmark Fonts

Labels

Rotate Axis Labels

Title Fonts

To Change the Scaling for the Right Axis

Double-click the graph to maximize it.

Position the mouse pointer on one of the values on the right axis.

Click the left button to select the axis; markers appear at the corners of the axis.

Click the left button on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the Right Axis tab page.

In the From text box, enter a number that will determine the minimum value for the axis.

In the To text box, enter a number that will determine the maximum value for the axis.

In the By text box, enter a number that will determine the distance between each tickmark on the axis scale.

In the Skip text box, enter the number of tickmarks that should be skipped when the axis is created.

Use the No Power check box to indicate if the axis scale for the tickmarks should be calculated using a power of 10.

Use the Log check box to indicate if the axis scale for the tickmarks should be calculated using decimal log scaling.

Use the Hold check box to indicate if the current scaling should be retained, even if you change the data in the Analysis dialog box.

Click the Tickmark Fonts... button to display the Font dialog box, then choose the font you want to use for the tickmarks, and click OK.

Click Apply and OK on the Right Axis tab page to process the changes.


Spinning Tab Page

You can view three-dimensional graphs from different horizontal and vertical angles by spinning a graph to change the location of the viewpoint.  To set preferences for spinning, use the Spinning tab page of the Graphics Options dialog box.

You can set your preferences to indicate if text should be displayed on the graph while it is spinning; and to enter values that control the number of frames per second (fps) and the degrees per frame the graph will display while it is spinning.

To actually spin the graph, click the Smooth/Rotate button on the Analysis toolbar. To Spin Graphs

Draw Test

Maximum Speed

Degrees per Frame

To Spin Graphs

Double-click a three-dimensional graph to maximize it.

Click the Smooth/Rotate button on the Analysis toolbar (the third button from the right), to display a slidebar/button combination on the toolbar that allows you to spin the graph).

Spin the Graph Horizontally: Click the Horizontal button (the horizontal, double-headed arrow), to begin spinning the graph horizontally.

Spin the Graph Vertically: Click the Vertical button (the vertical double-headed arrow), to begin spinning the graph vertically.

Click the button a second time or click on the graph to stop the spinning.  Use the slidebars beside the two buttons to control the horizontal and vertical angles of the graph.  The range of the horizontal angle is from -90 to +90 degrees.  The range of the vertical angle is from -180 to +180 degrees.

Click the right button, then click the left on the Reset Scaling/Viewpoint... command on the pop-up menu to return the graph to its original viewpoint.


Text Tab Page

On certain graphs or if you add text to a graph, the Text tab page allows you to edit the text.

Text

Edit

Direction

Fonts...

To Add Miscellaneous Text to a Graph

Double-click the graph to maximize it.

Place the mouse pointer on an empty portion inside the graph frame.

Click the left button, then the right on Graphics Options on the pop-up menu to display the Graphics Options dialog box opened to the Text tab page.

In the Text text box, enter the text you want to add to the graph.

Click one of the Direction options to choose the way the text will display; either horizontally or vertically.

Click the Fonts... button if you want to make changes to the font or its attributes.

Click OK to process the changes.


Top Title Tab Page

This title refers to the title that displays at the top of a graph.  You can change the entire name of the title or add or delete words from it.  Use the To Title tab page in the Graphics Options dialog box to make the text changes.  You can indicate the direction in which the title will appear; change fonts for the one-or two-line title; and indicate if the font should be changed for both titles if you are using a two-line title.

Title

Vertical

Line 1 Fonts...

Line 2 Fonts...

Change Font for All Titles

To Change a Top Title

Double-click the graph to maximize it.

Place the mouse pointer on the title you want to change.

Click the left on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the Top Title tab page.

In the first Title text box, enter either a new title or make changes to the current title.

Note:  If the plot you are working with contains a title on a second line, the second text box will be activated and you can make changes there also.

Click the Vertical check box if you want the title to display vertically on the graph.  If the box is checked, the title will display in that direction

Click the Line 1 Fonts... button to display the Font dialog box you use to change the font for the text in line 1.

Click the Line 2 Fonts... button to display the Font dialog box you use to change the font for the text in line 2.

Click the Change Font for All Titles check box if you want to change to a font that will be used for all the titles on the graph.

Click Apply and OK to process the changes.


X-Axis Tab Page

The scales against which a graph is plotted are known as axes.  Although the X- Y-, and Z-Axes tab pages are identical except for defaults, you must change each axis independently.  For example, if you want to make changes to the X-axis and the Y-axis, you must first access the X-Axis tab page, make the necessary changes, then access the Y-Axis tab page and make the necessary changes on that page.

Title

Vertical

From

To

By

Skip

No Power

Log

Hold

Tickmark Fonts

Labels

Rotate Axis Labels

Title Fonts

To Change the Axis Scaling

Double-click the graph to maximize it.

Position the mouse pointer on one of the values on the axis whose scale you want to change.

Click the left button to select the axis; markers appear at the corners of the selected axis.

Click the left on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the X-Axis tab page.

Enter a title for the axis in the Title text box.

Indicate if the title should display vertically or horizontally.

In the From text box, enter a number that will determine the minimum value for the axis.

In the To text box, enter a number that will determine the maximum value for the axis.

In the By text box, enter a number that will determine the distance between each tickmark on the axis scale.

In the Skip text box, enter the number of tickmarks that should be skipped when the axis is created.

In the No Power check box, indicate if the axis scale for the tickmarks should be calculated using a power of 10.

In the Log check box, indicate if the axis scale for the tickmarks should be calculated using decimal log scaling.

In the Hold check box, indicate if the current scaling should be retained, even if you change the data in the Analysis dialog box.

Click the Title Fonts... button to display the Font dialog box you use to change the font for the title.

Click the Tickmark Fonts... button to display the Font dialog box you use to change the font for the tickmarks.

Click Apply and OK on the X-Axis tab page to process the changes.


Y-Axis Tab Page

The scales against which a graph is plotted are known as axes.  Although the X- Y-, and Z-Axes tab pages are identical except for defaults, you must change each axis independently.  For example, if you want to make changes to the X-axis and the Y-axis, you must first access the X-Axis tab page, make the necessary changes, then access the Y-Axis tab page and make the necessary changes on that page.

Title

Vertical

From

To

By

Skip

No Power

Log

Hold

Title Fonts

Tickmark Fonts

Rotate Axis Labels

To Change the Axis Scaling

Double-click the graph to maximize it.

Position the mouse pointer on one of the values on the axis whose scale you want to change.

Click the left button to select the axis; markers appear at the corners of the selected axis.

Click the left on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the Y-Axis tab page.

Enter a title for the axis in the Title text box.

Indicate if the title should display vertically or horizontally.

In the From text box, enter a number that will determine the minimum value for the axis.

In the To text box, enter a number that will determine the maximum value for the axis.

In the By text box, enter a number that will determine the distance between each tickmark on the axis scale.

In the Skip text box, enter the number of tickmarks that should be skipped when the axis is created.

In the No Power check box, indicate if the axis scale for the tickmarks should be calculated using a power of 10.

In the Log check box, indicate if the axis scale for the tickmarks should be calculated using decimal log scaling.

In the Hold check box, indicate if the current scaling should be retained, even if you change the data in the Analysis dialog box.

Click the Title Fonts... button to display the Font dialog box you use to change the font for the title.

Click the Tickmark Fonts... button to display the Font dialog box you use to change the font for the tickmarks.

Click Apply and OK on the Y-Axis tab page to process the changes.


Z-Axis Tab Page

The scales against which a graph is plotted are known as axes.  Although the X- Y-, and Z-Axes tab pages are identical except for defaults, you must change each axis independently.  For example, if you want to make changes to the X-axis and the Y-axis, you must first access the X-Axis tab page, make the necessary changes, then access the Y-Axis tab page and make the necessary changes on that page.

Title

Vertical

From

To

By

Skip

No Power

Log

Hold

Title Fonts

Tickmark Fonts

Rotate Axis Labels

To Change the Axis Scaling

Double-click the graph to maximize it.

Position the mouse pointer on one of the values on the axis whose scale you want to change.

Click the left button to select the axis; markers appear at the corners of the selected axis.

Click the left on the graph, the right to display the pop-up menu, then the left on Graphics Options to display the Graphics Options dialog box opened to the Z-Axis tab page.

Enter a title for the axis in the Title text box.

Indicate if the title should display vertically or horizontally.

In the From text box, enter a number that will determine the minimum value for the axis.

In the To text box, enter a number that will determine the maximum value for the axis.

In the By text box, enter a number that will determine the distance between each tickmark on the axis scale.

In the Skip text box, enter the number of tickmarks that should be skipped when the axis is created.

In the No Power check box, indicate if the axis scale for the tickmarks should be calculated using a power of 10.

In the Log check box, indicate if the axis scale for the tickmarks should be calculated using decimal log scaling.

In the Hold check box, indicate if the current scaling should be retained, even if you change the data in the Analysis dialog box.

Click the Title Fonts... button to display the Font dialog box you use to change the font for the title.

Click the Tickmark Fonts... button to display the Font dialog box you use to change the font for the tickmarks.

Click Apply and OK on the Z-Axis tab page to process the changes.


Analysis Summary (Polar Coordinates Plot Analysis)

The Analysis Summary option creates a summary of the analysis that displays the names of the variables that contain the values for the radius and angle; it also displays the number of observations.

Use the Polar Coordinates Plot Options dialog box to make changes.  You can indicate if points or lines will appear on the plot; if the angles will be in degrees, radians, or grads; if the angular locations will be labeled; if the angles should increase clock wise or counter-clock wise; if 0 degrees will be at 12:00 or 3:00.


Polar Coordinates Plot (Polar Coordinates Plot Analysis)

The Polar Coordinates Plot option creates a two-dimensional scatterplot or line plot for pairs of points that are defined by radius and angle positions.  The values for the radius variable are plotted against the values for the angle variable.


Analysis Summary (CuSum Chart (H-K) Analysis)

The Analysis Summary option creates a summary of the analysis for either an initial or a control-to-standard study that helps determine if the data come from a process that is in statistical control.   The program constructs the control charts under the assumption that the data come from a normal distribution with values for the mean and standard deviation, which are estimated from the data.

For the CuSum Chart and the Range Chart, the report displays the values for the upper and lower control limits, the centerline, and the number of subgroups beyond the limits.  The report also shows the number of subgroups, the subgroup size, and the number of subgroups excluded from the study.  It provides estimates for the process mean, and process sigma.  For a control-to-standard study, the report includes standard statistics.

For a control-to-standard study, you can specify the values that will be used for the mean and sigma parameters.  This dialog box is available from all the tabular and graphical panes so you can make changes that will affect the analysis.


CuSum Chart Report (CuSum Chart (H-K) Analysis)

The CuSum Chart Report option creates a report of the subgroups based on your selection on the CuSum Chart Report Options dialog box.  The report shows the values that are plotted on the control chart, including values for the subgroup size, CuSum value, and range.  It notes points that are beyond the control limits with an asterisk, and points that are excluded with an X.  You can create a report that displays all the subgroups; subgroups beyond the control limits, CuSums beyond the limits, ranges beyond the limits, or subgroups that were excluded.

Use the Subgroup Reports Options dialog box to choose the report you want to create.  The choices are listed in the above explanation.


Cumulative Sum Chart (CuSum Chart (H-K) Analysis)

The Cumulative Sum Chart option creates a plot of the cumulative sum designed to monitor deviations from target for each of the subgroups.  The chart detects shifts in the process mean and notes points that are beyond the control limits.

Use the CuSum Chart Options dialog box to enter the number of decimal points that will display for the control limits.


Range Chart (CuSum Chart (H-K) Analysis)

The Range Chart option creates a plot of the ranges for each of the subgroups.  It notes the points that are beyond the control limits and flags points that violate the runs rules.

Use the Control Chart Options dialog box to choose options for the chart.


ARL Curve (CuSum Chart (H-K) Analysis)

The ARL (Average Run Length) Curve option creates a plot that shows the ARL for the CuSum Chart (H-K) as a function of the process mean.  For example, if the process is actually running at the centerline, the chart will create an out-of-control signal on average for the number of samples.  If the process moves away from the centerline, the ARL will change accordingly.  The plot is helpful when you need to select an adequate sampling plan to monitor the process.


Analysis Summary (CuSum Individuals Chart (H-K) Analysis)

The Analysis Summary option creates a summary of the analysis for either an initial or a control-to-standard study that helps determine if the data come from a process that is in statistical control.  The program constructs the control charts under the assumption that the data come from a normal distribution with values for the mean and standard deviation, which are estimated from the data.

For the Mean CuSum Chart and the Scale CuSum Chart, the report displays the values for the upper and lower control limits, the centerline, and the number of observations beyond the limits.  The report also shows the number of observations, the observation size, and the number of observations excluded from the study.  It provides estimates for the process mean and process sigma.  For a control-to-standard study, the report includes standard statistics.

Use the CuSum (H-K) Chart Options dialog box to choose options for the analysis.


CuSum Individuals Chart Report (CuSum Individuals Chart (H-K) Analysis
CuSum Individuals Chart Report (CuSum Individuals Chart (H-K)) Analysis

The CuSum Individuals Chart Report option creates a report of the observations based on your selection on the CuSum Individuals Chart Report Options dialog box.  The report shows the values that are plotted on the control chart, including values for the Mean CuSum and Scale CuSum.  It notes points that are beyond the control limits with an asterisk, and points that are excluded with an X. You can create a report that displays all the observations; observations beyond the control limits, CuSum values beyond the limits, Scale CuSum values beyond the limits, or observations that were excluded.

Use the Subgroup Reports Options dialog box to choose the report you want to create.


CuSum Chart (CuSum Individuals Chart (H-K) Analysis)
CuSum Chart (CuSum Individuals Chart (H-K)) Analysis

The CuSum Chart option creates a plot of the cumulative sum that monitors deviations from target for each of the measurements).  Upper and lower control limits are displayed and determine if the process in statistical control.  If the process is in control, all of the points should be within the control limits.

Use the CuSum Chart Options dialog box to enter the number of decimal places that should be used for displaying the control limits.


Scale CuSum Chart (CuSum Individuals Chart Analysis)

The Scale CuSum Chart option creates a cumulative sum plot for the scaled values of the measurements.  The plot is designed to detect changes in the standard deviation of the process; it notes points that are beyond the control limits and flags points that violate the runs rules.

Use the CuSum Chart Options dialog box to enter the number of decimal places that should be used for displaying the control limits.


ARL Curve

The ARL (Average Run Length) Curve option creates a plot that shows the ARL as a function of the process mean.  For example, if the process is actually running at Centerline, the chart should generate an out-of-control signal on an approximate average based on the number of samples.  If the process moves away from the centerline, the ARL will change.  The plot is helpful in choosing an adequate sampling plan to monitor a process.


ARIMA Chart

The ARIMA Chart option creates an ARIMA Chart or a plot of the residuals for each of the subgroups and shows the points that are beyond the control limits.  The default chart plots the data with 3-sigma limits, based on the marginal distribution of the data and a constant centerline.  With a moving centerline, the limits are based on the one-ahead forecast errors.  The last two types of plots are a plot of the residuals from the fitted model and a plot that shows normalized residuals calculated by dividing them by the estimated white noise sigma.  The plot flags points that violate the runs rules.


Residual Autocorrelation Function Plot

The Residual Autocorrelation Function Plot option creates a plot of the estimated autocorrelations between the residuals at various lags.  The lag k autocorrelation coefficient measures the correlation between the residuals at time t and time t-k.  If the probability limits at a particular lag do not contain the estimated coefficient, there is a statistically significant correlation at that lag at the given confidence level.


Residual Partial Autocorrelation Function Plot

The Residual Partial Autocorrelation Function Plot option creates a plot you can use to determine the order of autoregressive model needed to fit the data.  If the probability limits at a particular lag do not contain the estimated coefficient there is a statistically significant correlation at that lag at the given confidence level.


Tolerance Chart

The Tolerance Chart option creates a plot of the individual values, organized by subgroup.  The horizontal line indicates the grand mean of the observations.  The vertical lines indicate the subgroup ranges.  Because you use this option to examine individual observations, the chart is available only when you select Observations from the Data options on the Analysis dialog box.


Analysis Summary (ARIMA Chart Analysis)

The Analysis Summary option creates a summary of the analysis for either an initial or a control-to-standard study that helps determine if the data come from a process that is in statistical control.  The summary shows the location of the limits on standard ARIMA and Range charts.  The charts are constructed using the assumption that the data come from a normal distribution with values for the mean and standard deviation estimated from the data.

For both the ARIMA Chart and the Range Chart, the report displays the values for the upper and lower control limits, the centerline, and the number of subgroups beyond the limits.  It also shows the number of subgroups, the subgroup size, and the number of subgroups excluded from the study.  It provides estimates for the process mean, process sigma, and the mean range.

The ARIMA Model Summary table displays the parameters used in the ARIMA model and the values of the estimated coefficients and their associated standard error, t-statistic, and p-values.  The t-statistics and the p-values indicate if the coefficients are significant.  For example, when testing at a 95 percent level of confidence, a coefficient with a p-value less than .05 is statistically significant.  The table also shows if Backforecasting was used in the calculation, and provides values for the estimated white noise variance and standard deviation.

Use the ARIMA Chart Options dialog box to indicate if the study will be an initial or a control to standard; and to enter values for the upper and lower sigma for the ARIMA Control Limits and Range Control Limits.


ARIMA Chart Report (ARIMA Chart Analysis)

The ARIMA Chart Report option creates a report of the subgroups based on your selection on the ARIMA Chart Report Options dialog box.  The report shows the values that are plotted on the control chart, including values for the subgroup size, X-bar, and range.  It notes points that are beyond the control limits with an asterisk, and points that are excluded with an X.

Use the ARIMA Chart Report Options dialog box to choose the report you want to create.    You can create a report that displays all the subgroups; subgroups beyond the control limits, X-bars beyond the limits, ranges beyond the limits, or subgroups that were excluded.


Runs Tests

The Runs Tests option performs a battery of tests that help determine if a sequence of observations is in a nonrandom pattern, which indicates that a process is out of control.  To use this option, choose either Residuals or Normalized Residuals from the Chart Type portion of the ARIMA Chart Options dialog box.

The tests search for and identify any unusual patterns in the residuals, which are helpful in detecting processes that are slowly drifting away from target, even though no points may be outside the control limits.  The Runs Tests table shows the subgroup or observation at which the unusual pattern was detected, as well as the particular rule that was violated.  The rules are identified by letters (A, B, C, D, etc.); the subgroups or observations by numbers (1, 2, 3, 4, etc.).  If the table shows Rule D in Subgroup 2 in violation, it means that rule D was violated at point 2.

Use the Runs Tests Options dialog box to choose the rules you want to include in the tests.


Analysis Summary (ARIMA Individuals Chart Analysis)

The Analysis Summary option creates a summary of the analysis for either an initial or a control-to-standard study that helps determine if the data come from a process that is in statistical control.  The summary shows the location of the limits on standard ARIMA and MR(2) charts.  The charts are constructed using the assumption that the data come from a normal distribution with values for the mean and standard deviation estimated from the data.

For both the ARIMA Chart and the MR(2), the report displays the values for the upper and lower control limits, the centerline, and the number of observations beyond the limits.  It also shows the number of observations and provides estimates for the process mean, process sigma, and the mean MR(2).

The ARIMA Model Summary table displays the parameters in the ARIMA model and the values of the estimated coefficients and their associated standard error, t-statistic, and p-values.  The t-statistics and the p-values indicate if the coefficients are significant.  For example, when testing at a 95 percent level of confidence, a coefficient with a p-value less than .05 is statistically significant.  The table also shows if Backforecasting was used in the calculation, and provides values for the estimated white noise variance and standard deviation.

Use the ARIMA Individuals Charts Options dialog box to indicate if the study will be an initial or a control to standard; and to enter values for the upper and lower sigma for the ARIMA Control Limits and MR(2) Control Limits.

For both types of studies, you can also choose the order of the ARIMA model, allowing for up to fourth-order AR and MA terms and up to second-order differencing.  You use the Model options and choose from each of the three columns, the parameters you want estimated; that is, from the AR column, the number of nonseasonal autoregressive parameters; from the I column, the number of integrated parameters; and from the MA column, the number of nonseasonal moving-average parameters.

You can also indicate if you want sigma estimated from the MR(2) Chart or the Model MSE; and choose the type of chart you want to create:  Data with long-term limits, Data with one-step limits, Residuals, or Normalized residuals.

For a Control-to-Standard Study, you can enter values for the Mean and Sigma, and for each of the AR and MA terms you choose from the Model options portion of the dialog box.


ARIMA Individuals Chart Report

The ARIMA Individuals Chart Report option creates a report of the observations based on your selection on the ARIMA Individuals Chart Report Options dialog box.  The report shows the values that are plotted on the control chart, including the observation number, and values for X and MR(2).  It notes points that are beyond the control limits with an asterisk.

Use the ARIMA Individuals Chart Report Options dialog box to choose the report you want to create.  You can create a report that displays all the observations; observations beyond the control limits, X’s beyond the limits, or MR(2)’s beyond the limits.


Runs Tests (ARIMA Individuals Chart Analysis)

Available Only for Residuals or Normalized Residuals

The Runs Tests option performs a battery of tests that help determine if a sequence of observations is in a nonrandom pattern, which indicates that a process is out of control.  To use this option, choose either Residuals or Normalized Residuals from the Chart Type portion of the ARIMA Individuals Chart Options dialog box.

The tests search for and identify any unusual patterns in the residuals, which are helpful in detecting processes that are slowly drifting away from target, even though no points may be outside the control limits.  The Runs Tests table shows the subgroup or observation at which the unusual pattern was detected, as well as the particular rule that was violated.  The rules are identified by letters (A, B, C, D, etc.); the subgroups or observations by numbers (1, 2, 3, 4, etc.).  If the table shows Rule D in Subgroup 2 in violation, it means that rule D was violated at point 2.

Use the Runs Tests Options dialog box to choose the rules you want to include in the tests.


Capability Indices

The Capability Indices option calculates several process capability indices based on the estimated process mean and standard deviation. These indices help determine the capability of a process to produce products that must meet a quality standard.  The capability indices will not be calculated until you enter values for the USL, Nominal, and LSL values on the Process Capability Indices Options dialog box.

Use the Process Capability Indices Options dialog box to choose the indices you want to include, and to enter values for the upper and lower specification limits and the target for the nominal.


ARIMA Chart (ARIMA Individuals Chart Analysis)

The ARIMA Chart option creates an ARIMA Chart or a plot of the residuals for each of the observations and shows the points that are beyond the control limits.  The default chart plots the data with 3-sigma limits, based on the marginal distribution of the data and a constant centerline.  With a moving centerline, the limits are based on the one-ahead forecast errors.  The last two types of plots are a plot of the residuals from the fitted model and a plot that shows normalized residuals calculated by dividing them by the estimated white noise sigma.  The plot flags points that violate the runs rules.

Use the ARIMA Chart Options dialog box to choose the type of chart you want to plot and other options for the chart.  Use the Control Chart Options dialog box if you are using the Control-to-Standard option.


MR(2) Chart

The MR(2) Chart option creates a plot of the moving ranges for each of the observations and shows the points that are beyond the control limits.

Use the Control Chart Options dialog box to choose options for the chart.


Analysis Summary (Toolwear Chart Analysis)

The Analysis Summary option creates a summary of the analysis for either an initial or a control-to-standard study that helps determine if the data come from a process that is in statistical control.  The summary shows the location of the limits on the Toolwear and Range charts.  The charts are constructed using the assumption that the data come from a normal distribution with values for the mean and standard deviation estimated from the data.

For both the Toolwear Chart and the Range Chart, the report displays the values for the upper and lower control limits, the centerline, and the number of subgroups beyond the limits.  It also shows the number of subgroups, the subgroup size, and the number of subgroups excluded from the study.  It provides values for the intercept, slope, USL and LSL, as well as estimates for the process mean, process sigma, and the mean range.

Use the Toolwear Chart Options dialog box to indicate if the study will be an initial or a control to standard; and to choose options for the analysis.  For a Control-to-Standard Study, you can enter values for the Intercept, Slope, and Sigma.


Toolwear Chart Report

The Toolwear Chart Report option creates a report of the subgroups based on your selection on the Toolwear Chart Report Options dialog box.  The report shows the values that are plotted on the control chart, including values for the subgroup size, X-bar, and range.  It notes points that are beyond the control limits with an asterisk.

Use the Toolwear Chart Report Options dialog box to choose the report you want to create.  You can create a report that displays all the subgroups; subgroups beyond the control limits, X-bars beyond the limits, and ranges beyond the limits.


Toolwear Chart

The Toolwear Chart option creates a plot of the means for each of the subgroups and shows points beyond the control limits.

Use the Control Chart Options dialog box to indicate if you want to plot outer and/or inner warning limits, and if so, to enter the number of sigmas from the centerline the inner and/or outer warning limits will be plotted.  You can also enter the number of decimal places that will be displayed for the limits.


Range Chart

The option creates a plot of the ranges for each of the subgroups and shows points beyond the control limits.

Use the Control Chart Options dialog box to indicate if you want to plot outer and/or inner warning limits, and if so, to enter the number of sigmas from the centerline the inner and/or outer warning limits will be plotted.  You can also enter the number of decimal places that will be displayed for the limits.


Analysis Summary (Toolwear Individuals Chart Analysis)

The Analysis Summary option creates a summary of the analysis for either an initial or a control-to-standard study that helps determine if the data come from a process that is in statistical control.  The summary shows the location of the limits on the Toolwear and MR(2) charts.  The charts are constructed using the assumption that the data come from a normal distribution with values for the mean and standard deviation estimated from the data.

For both the Toolwear Chart and the MR(2) Chart, the report displays the values for the upper and lower control limits, the centerline, and the number of observations beyond the limits.  It also shows the number of observations, and the number of observations excluded from the study.  It provides values for the intercept, slope, USL and LSL, as well as estimates for the process mean, process sigma, and the mean MR(2).

Use the Toolwear Individuals Chart Options dialog box to choose the type of study and to enter values for other options.  For a Control-to-Standard Study, you can enter values for the Intercept, Slope, and Sigma.


Toolwear Individuals Chart Report

The Toolwear Individuals Chart Report option creates a report of the observationss based on your selection on the Toolwear Individuals Chart Report Options dialog box.  The report notes the observation number, and shows the values that are plotted on the control chart, including values for X and MR(2).  It notes points that are beyond the control limits with an asterisk, and points that are excluded with an X.

Use the Toolwear Individuals Chart Report Options dialog box to choose the report you want to create.


Toolwear Chart

The Toolwear Chart option creates a plot of the individual measurements and shows points beyond the control limits.

Use the Control Chart Options dialog box to indicate if you want to plot outer and/or inner warning limits, and if so, to enter the number of sigmas from the centerline the inner and/or outer warning limits will be plotted.  You can also enter the number of decimal places that will be displayed for the limits.


Analysis Summary (Acceptance Chart Analysis)

The Analysis Summary option creates a summary of the analysis for either an initial or a control-to-standard study that helps determine if the data come from a process that is in statistical control.  The summary shows the location of the limits on standard X-bar and S charts.  The charts are constructed using the assumption that the data come from a normal distribution with values for the mean and standard deviation estimated from the data.

For both the X-bar Chart and the S Chart, the report displays the values for the upper and lower control limits, the centerline, and the number of subgroups beyond the limits.  It shows the number of subgroups, the subgroup size, and the number of subgroups excluded from the study.  Also shown are the values used for the maximum fraction defective, and sigma multiple (or unacceptable fraction defective and beta risk) and the upper and lower specification limits.  Estimates are also displayed for the process mean, process sigma, and mean sigma.

Use the Acceptance Chart Options dialog box to choose the type of study and to enter values for other options.  For a Control-to-Standard Study, you can enter values for the Mean and Sigma.


Acceptance Chart Report

The Acceptance Chart Report option creates a report of the subgroups based on your selection on the Acceptance Chart Report Options dialog box.  The report shows the values that are plotted on the control chart, including values for the subgroup size, X-bar, and S.  It notes points that are beyond the control limits with an asterisk, and points that are excluded with an X.

Use the Acceptance Chart Report Options dialog box to choose the report you want to create.


Specification Limits Dialog Box

Determines the upper and lower specification limits.

Upper

Enter a numeric value for the upper specification.  The value you enter must be greater than the value in the Lower text box.

Lower

Enter a value for the lower specification.  The value you enter must be less than the value in the Upper text box.


Acceptance Chart

The Acceptance Chart option creates a plot of the observations.  It notes the points that are beyond the control limits.

Use the Control Chart Options dialog box to choose options for the chart.


Analysis Summary (Acceptance Individuals Chart Analysis)

The Analysis Summary option creates a summary of the analysis for either an initial or a control-to-standard study that helps determine if the data come from a process that is in statistical control.  The summary shows the location of the limits on standard X and MR(2) charts.  The charts are constructed using the assumption that the data come from a normal distribution with values for the mean and standard deviation estimated from the data.

For both the X Chart and the MR(2) Chart, the report displays the values for the upper and lower control limits, the centerline, and the number of observations beyond the limits.  It shows the number of observations, and the number of observations excluded from the study.  Also shown are the values used for the maximum fraction defective and sigma multiple (or unacceptable fraction defective and beta risk) and the upper and lower specification limits.  Estimates are also displayed for the process mean, process sigma, and mean MR(2).

Use the Acceptance Individuals Chart Options dialog box to choose the type of study and to enter values for other options.  For a Control-to-Standard study, you can enter values for the Mean and Sigma.


Acceptance Individuals Chart Report

The Acceptance Individuals Chart Report option creates a report of the values that were plotted on the control chart, including values for X and MR(2), as well as a list of the observation number.  It notes points that are beyond the control limits with an asterisk, and points that are excluded with an X.

Use the Acceptance Individuals Chart Report Options dialog box to choose the report you want to create.


Analysis Summary (Fishbone Diagram Analysis)

The Analysis Summary option creates a summary that shows the name of the variable that contains the label names, the name of the effect, and the number of primary, secondary, and tertiary causes.


Fishbone Diagram

The Fishbone Diagram option displays a cause-and-effect diagram that shows the name of the effect and the primary, secondary, and tertiary causes.


Analysis Summary (Acceptance Sampling - Attributes)

The Analysis Summary option creates a summary of the sampling plan.  A summary of the desired features is created, depending on the type of plan you choose.  The summary shows the lot size, desired features, generated plan, and the plan attributes.

The Desired Features list includes the producer and consumer risk (alpha and beta), respectively, in percentages.  The Generated Plan includes the sample size and the acceptable number of defective items (c).  The values for the Plan Attributes include the acceptable quality level (AQL), the producer’s risk (alpha), the Lot tolerance percent defective (LTPD), and the Consumer’s risk (beta), all in percentages.  Also shown are values for the Average Outgoing Quality Limit (AOQL), and the Average Total Inspection (ATI) at units per lot at the AQL, units per lot at the AOQL, and units per lot at the LTPD.


AOQ Curve

The AOQ (Average Outgoing Quality) Curve option creates a plot that shows the average percentage of defective items shipped when using the sampling plan (assuming the rejected lots are subjected to 100 percent inspection) as a function of the true percentage of defective items in the lot.


ATI Curve

The ATI (Average Total Inspection) Curve option creates a plot that shows the average number of units inspected when using the sampling plan (assuming that the rejected lots are subjected to 100 percent inspection) as a function of the true percentage of defective items in the plot.


OC Curve

The OC (Operating Characteristic) Curve option creates a plot that shows the probability of accepting the lot when using the sampling plan as a function of the true percentage of defective items in the lot.   The plot helps determine the adequacy of the current sampling plan.


Analysis Summary (Acceptance Sampling - Variables)

The Analysis Summary option creates a summary of the sampling plan).  A summary of the desired features is created, depending on the type of plan you choose.  The summary shows the lot size, desired features, generated plan, and the plan attributes.

The Desired Features list includes the producer and consumer risk (alpha and beta), respectively, in percentages.  The Generated Plan includes the sample size and the value of the critical distance (k).  The values for the Plan Attributes include the acceptable quality level (AQL), the producer’s risk (alpha), the Lot tolerance percent defective (LTPD), and the Consumer’s risk (beta), all in percentages.  Also shown are values for the Average Outgoing Quality Limit (AOQL), and the Average Total Inspection (ATI) at units per lot at the AQL, units per lot at the AOQL, and units per lot at the LTPD.


Optimize Experiment Window

This window displays several times when you are optimizing an experiment.  When you begin the optimization, the program displays the window with a message that tells you to choose Analysis Options.  When you click the right mouse button, one of two Optimize Design Options dialog boxes will display.  One is used for Mixture designs; the other for all the remaining types of designs.

After you process the Optimize Design Options dialog box, the Optimize Experiment Window redisplays, this time displaying a report of the optimization.


Optimize Design Options Dialog Box (Non-Mixture Designs)

This dialog box allows you to choose options for the optimization.

Maximum Order Effect

Ignore Block Numbers

Confounding Pattern

Desired Number of Runs

Method

Exclude... Command


Optimize Design Options Dialog Box (Mixture Designs)

This dialog box allows you to choose options for the optimization.

Model to Fit

Desired Number of Runs

Method

Exclude... Command


Candidates List

The Candidates List option displays all the candidate lists considered by the program.  Runs marked with an asterisk (*), can achieve D-optimality if you obtain the data for them.


Analysis Summary (Optimization)

The Analysis Summary option displays the file name and comment, the type of criterion you chose, the number of desired runs, the selection method, and model type.  It also displays the number of runs already completed and any additional candidate runs.

It also displays the number of runs that the design has been reduced to and either lists other possible reductions or shows that no further reduction is possible.

To perform the optimization, the program chooses a subset of the runs in the current experiment for which it will attempt to achieve D-optimality.  D-optimality is a criterion that measures the variability of all the estimated parameters.


Analysis Summary (Multiple Response Optimization)

The Analysis Summary option shows the results of combining experimental factors, which simultaneously optimizes several responses by maximizing a desirability function.  The summary also shows the desirability function evaluated at each point in the design and the run at which maximum desirability is achieved.


Optimize Design Tabular Options Dialog Box

This dialog box allows you to choose tabular options for an optimization.  The options will vary depending on the type of design you are using.

Three options are available: Analysis Summary, Candidates List, and Worksheet.  All the options may not be available for all the designs.

Analysis Summary

Candidates List

Worksheet


Control Ellipse (Multivariate Control Chart Analysis)

The Control Ellipse option displays a plot that shows the points outside the control ellipse, which corresponds to points outside the control limit.  This plot is available only when you analyze two variables.


S Chart

The S Chart option creates a plot of the standard deviations for each of the subgroups and shows the points that are beyond the control limits.

A process is out of control if points are shown outside the control limits, or if the points are shown within the control limits but arranged in a nonrandom sequence.


Create/Augment Design (Multilevel Factorial) Tabular Options Dialog Box
Create/Augment Design (Multilevel Factorial) Tabular Options Dialog Box  Don’t use – use generic instead

TO DO: Enter topic text here!


Create/Augment Design (Multilevel Factorial) Graphical Options Dialog Box
Create/Augment Design (Multilevel Factorial) Graphical Options Dialog Box   Don’t use – use generic instead


Create/Augment Design (Mixture) Graphical Options Dialog Box
Create/Augment Design (Mixture) Graphical Options Dialog Box Don’t use – use generic instead


Optimize Design Tabular Options Dialog Box
Optimize Design Tabular Options Dialog Box - duplicate


Optimize Design Graphical Options Dialog Box

This dialog box allows you to choose graphical options for an optimization. A Power Curve is available for Screening Designs.

Power Curve


Analyze Design Dialog Box (Inner/Outer Arrays Design)

This dialog box allows you to choose the name of the variable that contains the response data you want to analyze.  You can also choose the performance measure that will be analyzed.

Data

Select

Sort


Save Results Options Dialog Box (Inner/Outer Arrays)


Save Results Dialog Box

The Save Results Options dialog box allows you to select the results you want to save.  There is one selection: Desirabilities.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis.  You can enter new names or accept the defaults.

Note:  To access the Save Results Options dialog box, click the Save Results Options button on the Analysis toolbar (the fourth button from the left).


Create Design Options Dialog Box

This dialog box allows you to choose a design class and enter or choose other options for the design you want to create.  Depending on the design you are creating, some of the fields on the dialog box will vary.

Number of Response Variables

Number of Experimental Factors

Number of Components

Number of Control Factors

Number of Noise Factors

Comment


Design Generators Dialog Box

This dialog box lists the design generators that are used to create the last column(s) of the design matrix.  You can change the signs (plus or minus) of the design generators.  When you click OK, the Composite Design Options dialog box redisplays.  You can use the Back… command to return to the previous dialog box.


Open StatGallery Dialog Box

This dialog box allows you to choose the experiment file you want to open.

Look In

Allows you, if necessary, to choose the drive and folder in which the file you want to open resides.

File Name

Choose or enter the name of the file you want to open.

Files of Type

Choose or enter the name of the type of file you want to open


Open StatReporter Dialog Box

This dialog box allows you to choose the experiment file you want to open.

Look In

Allows you, if necessary, to choose the drive and folder in which the file you want to open resides.

File Name

Choose or enter the name of the file you want to open.

Files of Type

Choose or enter the name of the type of file you want to open


Save StatGallery As Dialog Box

This dialog box allows you to choose or enter a name for the current StatGallery file you want to save.

Save In

Allows you, if necessary, to choose a drive and folder to which you want to save the StatGallery file on your hard disk.

File Name

Choose or enter the name of the file you want to save.

Save as Type

Choose or enter the name of the type of file you want to save.


Save StatReporter As Dialog Box

This dialog box allows you to choose or enter a name for the current StatReporter file you want to save.

Save In

Allows you, if necessary, to choose a drive and folder to which you want to save the StatReporter file on your hard disk.

File Name

Choose or enter the name of the file you want to save.

Save as Type

Choose or enter the name of the type of file you want to save.


StatLink - Open Data Source Dialog Box

This dialog box allows you to choose the data source you want to use.

Data Source


StatLink - Set Update Interval Dialog Box

This dialog box allows you to choose the duration of time between polling updates.  The program first reads the data, then automatically updates it in all the views of the Analysis windows and StatGalleries.

The Stop Polling menu item immediately and automatically halts the polling.

Duration between Updates


Jittering Dialog Box

This dialog box allows you to jitter the points on a graph.  When you plot data that contains many repeated values, it is likely that some points will occupy the same position.  This causes two or more points to be plotted one on top of the other, which may make the graph difficult to interpret.

Jittering prevents this and also allows you to see the density of the points in various locations on the plot.  Jittering adds a small, random offset to each point.  You can select the amount of horizontal and/or vertical offset that will affect each point.

Horizontal Jittering

Vertical Jittering


Point Identification Dialog Box

This dialog box allows you to choose the name of the variable that contains the labels that will be used to identify points on a graph.

When you create two- and three-dimensional scatterplots or similar types of plots, it is helpful to be able to identify and display individual points.  For example, you may want to identify a point by its row number or its label.  In addition to displaying the values you use to create the plot (for example, the X-, Y-, and Z-axes), you can also choose another variable to use as a label for each of the points.  You can also highlight the DataSheet row that corresponds to a point on a graph to see other related values.

Identify by

Sort


Goodness-of-Fit Tests (Weibull Analysis)

The Goodness-of-Fit Tests option calculates results for tests based on the Empirical Distribution Function (EDF).  EDF is a step function that is calculated from the sample, which estimates the population distribution function.  The tests are: Chi-Square, Kolmogorov-Smirnov D, Kuiper V, Cramer-von Mises W2, Watson U2, and Anderson-Darling A2.

The methods used to calculate the statistics are Random, Type I, or Type II.

Use the Goodness-of-Fit Tests Options dialog box to choose the EDF statistics that will be calculated and the censoring method that will be used to calculate the statistics

.


Overlaid Contour Plots

The Overlaid Contour Plots option creates an overlay plot that shows the contour functions for each of the response variables.


Intervals

Determines options for the intervals that will be calculated for the Means Table.

None

Intervals are not calculated.

Standard Error

Calculates an Upper and Lower limit for each of the means.  The Lower and Upper limits are equal to the mean, plus or minus one standard error, respectively.

Confidence Limits

Calculates confidence limits for each mean using its corresponding values for the standard error.


Overlaid Contour Plots (Multiple Response Optimization)
Overlaid Contour Plots (Multiple Response Optimization) duplicate – don’t use

The Overlaid Contour Plots option creates an overlay plot that shows the contour functions for each of the response variables.


Analysis of Means (ANOM) Plot (One Way ANOVA)
Analysis of Means (ANOM) Plot (One-Way ANOVA)

The Analysis of Means (ANOM) Plot option creates a plot that shows each group mean, the centerline at the grand mean, and the decision limits, which determine the groups that differ significantly at the grand mean.  If any points are outside the decision limits, it can be concluded that there is a statistically significant difference between the counts.

Use the Analysis of Means Plot Options dialog box to enter a value for the confidence level that will be used to calculate the confidence intervals and to enter the number of decimal places that will be used for the decision limits.


Identify by

Enter the name of the variable that will be used as a label.  You can also choose a variable name from the list box.  Enter a character or a numeric variable.


Horizontal Jittering

Sets the amount of jittering applied to points along the horizontal plane of a graph.  The range is from less to more.


Vertical Jittering

Sets the amount of jittering applied to points along the vertical plane of a graph.  The range is from less to more.


StatGallery Options Dialog Box

This dialog box allows you to choose an arrangement for the splitter windows in the StatGallery and to arrange the StatGallery window into different sized panes within the columns of the window.

Arrangement

By Columns


Blocking Factor Definition Options Dialog Box

This dialog box allows you to indicate the active factor, enter a name and the number of levels for it, and optionally, enter the label that will be used for each factor unit.

The dialog box is active when you choose the Graeco-Latin Square (3 Blocking) option on the Single-Factor Categorical Design Options dialog box.

Factor

Name

Number of Levels

Units

Back


Read Clipboard Dialog Box

This dialog box allows you to choose the source of the variable names for the data source.

From First Row

Indicates that the variable names will be from the first row of data.

Generate Default

Indicates that the variable names will be created as defaults by the program.  This option is the default.


Paste to Gallery Dialog Box

This dialog box allows you to indicate the action that should be taken when you are overlaying graphs.

Action


Comparison of Means Options Dialog Box

This dialog box allows you to enter a value for the null hypothesis, to choose an alternative hypothesis

Null Hypothesis

Alternative Hypothesis

Alpha

Assume Equal Sigmas


Comparison of Standard Deviations Options Dialog Box

This dialog box allows you to enter a value for the null hypothesis, to choose an alternative hypothesis, and to enter a percentage for alpha.

Null Hypothesis

Alternative Hypothesis

Alpha


Comparison of Medians Options Dialog Box

This dialog box allows you to choose an alternative hypothesis and enter a percentage for alpha.

Alternative Hypothesis

Alpha


ARIMA Control Limits

Determines the values for the location of the control limits on the ARIMA Chart.

Upper Sigma

Enter a value for the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10.  The default is 3.0.

Lower Sigma

Enter a value for the multiple of sigma that will be used to calculate the LCL.  Enter a numeric value greater than or equal to -10 and less than or equal to 0.  The default is -3.0.


X-bar and S Charts Subgroup Report Options

This dialog box allows you to choose the contents of the report.

Display

Determines what will display in the Subgroup Report

All Subgroups

Includes all the subgroups.

Subgroups Beyond Limits

Includes a list of the subgroups that are beyond the control limits.

X-bars Beyond Limits

Includes a list of the subgroups that have means of the sample beyond the control limits.

Sigmas Beyond Limits

Includes a list of the subgroups that have standard deviations beyond the control limits.

Excluded Subgroups

Includes a list of the excluded subgroups.


X-bar and S-Squared Charts Subgroup Reports Options

This dialog box allows you to choose the contents of the report.

Display

Determines what will display in the Subgroup Report

All Subgroups

Includes all the subgroups.

Subgroups Beyond Limits

Includes a list of the subgroups that are beyond the control limits.

X-bars Beyond Limits

Includes a list of the subgroups that have means of the sample beyond the control limits.

Variances Beyond Limits

Includes a list of the subgroups that have variances beyond the control limits.

Excluded Subgroups

Includes a list of the excluded subgroups.


Discriminant Function Options Dialog Box

Use this dialog box to select the functions that will be plotted on the Plot of Discriminant Functions.  Select the functions by the number in which they were entered into the Discriminant Function Analysis dialog box.


Y

Enter the name of the dependent variable whose values will be predicted by the estimated model.  Enter a numeric variable.


X

Enter the name of the independent variable whose values will be used to predict the values for the dependent variable.  Enter a numeric variable.


Select

[Optional]   Select a subset of the observations.  For example, to analyze the first 50 values in each variable, enter first (50) into this text box.


Sort

Sorts the variable names alphabetically; sorted is the default.


Power (Lambda1)

Enter a value for the power adjustment (Lambda1, the Box-Cox parameter) that will be used to transform the preliminary data.  By default, the program calculates the optimal Lambda, which minimizes the mean squared error (MSE).


Shift (Lambda2)

Enter a value for the shift adjustment (Lambda2) that will be used to shift the preliminary data.  Enter any positive numeric value.  The default is 0 (no shift).


Optimize

Determines the optimal setting of Lambda, the default, which minimizes the model MSE.  Deselect the option if you want to enter your own value.


Confidence Level

Enter the number that will be used to calculate the prediction limits and confidence limits at the selected values of X.  The default is 95 percent; other levels are 90 and 99.


Forecast at X

Enter the values for X for which the program will predict a value for Y.


Minimum Lambda1

Enter a value for the lowest value of Lambda1 that will appear in the MSE Comparison Table.  Enter a number that is less than the Maximum Lambda1.  The default is –2.


Maximum Lambda1

Enter a value for the highest value of lambda1 that will appear on the MSE Comparison Table.  Enter a number that is greater than the Minimum Lambda1.  The default is 2.


Resolution

Enter a value that will determine how Lambda1 will be divided between Minimum and Maximum Lambda.  The range for Lambda1 should be divided so it results in a number of estimated MSEs for a given Lambda, equal to the resolution, if possible.  The default is 100.


Include

Determines what will be included on the plot.

Prediction Limits

Includes the prediction limits.  If you want to include both prediction and confidence limits on the plot, click both options.

Confidence Limits

Includes the confidence limits.  If you want to include both prediction and confidence limits on the plot, click both options.


Confidence Level

Enter a value for the confidence level that will be used to calculate the prediction limits and the confidence limits at the selected values of X.  The default is 95 percent; other common levels are 90 and 99.


X-Axis Resolution

Enter the number that will be used to change the resolution of the lines on the graph.  Enter an integer between 20 and 200; the default is 30.  Higher values give smoother lines.


Minimum Lambda1

Enter a value for the lowest value of Lambda1 that will appear in the MSE Comparison Plot.  Enter a number that is less than the Maximum Lambda1.  The default is -2.


Maximum Lambda1

Enter a value for the highest value of Lambda1 that will appear on the MSE Comparison Plot.  Enter a number that is greater than the Minimum Lambda1.  The default is 2.


Resolution

Enter a value that will determine how Lambda1 will be divided between Minimum and Maximum Lambda.  The range for Lambda1 should be divided so it results in a number of estimated MSEs for a given Lambda, equal to the resolution, if possible.  The default is 100.


Radius

Enter the name of the variable that contains the radial values for each point.


Angle

Enter the name of the variable that contains the angular values for each point.


Point Codes

[Optional]  Enter the name of the variable that contains the column that defines the labels for the points.


Select

[Optional]  Select a subset of the variables.  For example, to analyze the first 50 values in each variable, enter first (50) into this text box.


Sort

Sorts the variable names alphabetically; sorted is the default.


Plot

Determines if points or lines will appear on the Polar Coordinates Plot.

Points

Plots points; it is one of the defaults.

Lines

Plots lines; it is one of the defaults.


Angular Units

Determines the type of angular units that will appear on the plot.

Degrees

Plots the angles in degrees (0° - 360°); it is the default.

Radians

Plots the angles in radians (0 - 2 pi).

Grads

Plots the angles in grads (0 - 100).


Labels

Determines how the angular locations will be labeled.

Angular

Labels the angular locations numerically; it is the default.

Compass

Labels the angular locations using compass directions (N-S-E-W).


Direction

Determines the direction in which the angles will increase.

Clock Wise

Increases the angles in a clock-wise direction; it is the default.

Counter Clock Wise

Increases the angles in a counter clock-wise direction.


Origin

Determines the position of 0 degrees.

12:00

Places 0 degrees at the 12:00 position; it is the default.

3:00

Places 0 degrees at the 3:00 position.


Data

Enter the name of the variable that contains the data that will be analyzed.  You must enter numeric data.


Sample Code

Enter the name of the variable that contains the level codes.


Labels

[Optional]  Enter the name of the variable that contains the names for the labels.


Upper Limit

[Optional]  Enter a number that will be used to draw vertical lines on the chart.


Lower Limit

[Optional]  Enter a number that will be used to draw vertical lines on the chart.


Select

[Optional]  Select a subset of the observations.  For example, to analyze the first 50 values in each variable, enter first (50) into this text box.


Sort

Sorts the variable names alphabetically; sorted is the default.


Group Statistics

Determines the type of statistics that will appear on the plot.

Mean

Calculates and displays the mean for each group.

Mean (Stdev)

Calculates and displays the mean and standard deviation for each group.  This option is the default.

Mean (Stdev) Count

Calculates and displays the mean, standard deviation, and count for each group.

Mean (% CV)

Calculates and displays the mean and coefficient of variation (CV) for each group.

Mean (% CV) Count

Calculates and displays the mean, coefficient of variation (CV), and count for each group.

Median

Calculates and displays the median for each group.

Median/Count

Calculates and displays the median and count for each group.

Median/Mean

Calculates and displays the median and mean for each group.

Median/Mean (Stdev)

Calculates and displays the median, mean, and standard deviation for each group.

None

Displays no summary statistics.


Number of Decimals

Determines the number of decimal places for the mean, median, standard deviation, and coefficient of variance.

Mean

Enter a number that will be used for the decimal place in the mean.  The default is 3.

Median

Enter a number that will be used for the decimal place in the median.  The default is 3.

Stdev

Enter a number that will be used for the decimal place in the standard deviation.  The default is 3.

CV

Enter a number that will be used for the decimal place in the coefficient of variance.  The default is 3.


Display Grand Average

Indicates if the grand mean of the data will be calculated and displayed on the graph; Displayed on the Graph is the default.


Confidence Level

Enter a value for the confidence level that will be used to calculate confidence intervals for the mean and standard deviation.  The default is 95 percent; other common levels are 90 and 99.


Columns

Enter the name of one or more variables that contain the values for each column.


Row Labels

Enter the name of the variable that contains the name of the labels for each case.


Model to Fit

Determines the type of model the program assumes it is using when the experimental runs are chosen.

Linear

Chooses experimental runs for a Linear model.

Quadratic

Chooses experimental runs for a Quadratic model.  A Quadratic model includes second-order terms; for example, AB, AC, and BC.

.

Special Cubic

Chooses experimental runs for a Special Cubic model.  A Special Cubic model includes special third-order terms; for example, ABC.

Cubic

Chooses experimental runs for a Cubic model.  A Cubic model is a Special Cubic model with additional terms; for example, AB(A – B).


Desired Number of Runs

Enter the number of runs (experimental trials) you want to use to optimize the base design.  Enter an integer that is at least one less than the existing number of runs.


Scaling

Determines the scale for the variables.

Common

Uses the same scale for all the variables; it is the default.

From

Enter a number for the start of the scale; the default depends on the data.

To

Enter a number for the end of the scale; the default depends on the data.

By

Enter a number for the increments of the scale; the default depends on the data.

Separate

Uses a separate scale for each of the variables.  You can enter separate scales for

16 separate cases.

From

Enter a number for the start of the scale; the default depends on the data.

To

Enter a number for the end of the scale; the default depends on the data.


High Values

Enter the name of the variable that contains the high values.


Low Values

Enter the name of the variable that contains the low values.


Closing Values

Enter the name of the variable that contains the closing values.


Event Probability

Enter values for up to five sets of parameters that will be used for the probability of observing a success.  Enter numbers between 1 and 0; the default is 0.1.


Trials

Enter values for up to five sets of numbers that will be used for the number of identical trials.  Enter integers between 1 and 99,999,999; the default is 10.


Population Size

Enter values for up to five sets of populations that will be used for the sample.  Enter a number less than the number of trials.  The default is 1000.


Mode

Enter values for up to five sets of parameters that will be used for determining the mode of the distribution.  Enter any numbers; the default is 1.


Scale

Enter values for up to five sets of parameters that will be used for determining the Scale parameter.  Enter numbers between 1 and 0; the default is 1.


Data

Enter the name of the variable that contains the column of data that will be analyzed.  Enter a numeric variable with values greater than 0.


Power (Lambda1)

Enter a value for the power adjustment (Lambda1, the Box-Cox parameter) that wiull be used to transform the preliminary data.  By default, the program calculates Lambda, which minimizes the mean squared error (MSE).


Shift (Lambda2)

Enter a value for the shift adjustment (Lambda2) that will be used to shift the preliminary data.  Enter any positive numeric value.  The default is 0 (no shift).


Optimize

Determines if the default, power (Lambda1), will be used automatically to transform the preliminary data, or if you want to enter your own value for power (Lambda1).


Minimum Lambda1

Enter a number for the lowest value of Lambda1 that will appear in the MSE Comparison Table.  Enter a number that is less than the Maximum Lambda1.  The default is -2.


Maximum Lambda1

Enter a number for the highest value of Lambda1 that will appear on the MSE Comparison Table.  Enter a number that is greater than the Minimum Lambda1.  The default is 2.


Resolution

Enter a number that will be used to smooth the curve.  Enter a number from 20 to 200; the default is 100.  The higher the number, the smoother the curve.


Direction

Determines the direction of the plot.

Horizontal

Displays the plot horizontally.

Vertical

Displays the plot vertically; it the default.


Fitted Line

Determines if a fitted line will display on the plot; if so, which method will be used to fit the line.

None

Displays the plot without a fitted line.

Using Quartiles

Displays the plot with a fitted line drawn through the median, with the slope determined by the quartiles.

Using Least Squares

Displays the plot with a fitted line using least squares regression.  This option is the default.


Minimum Lambda1

Enter a number for the lowest value of Lambda1 that will appear on the MSE Comparison Plot.  Enter a number that is less than the Maximum Lambda1.  The default is -2.


Maximum Lambda1

Enter a number for the highest value of Lambda1 that will appear on the MSE Comparison Plot.  Enter a number that is greater than the Minimum Lambda1.  the default is 2.


Minimum Lambda1

Enter a number for the lowest value of Lambda1 that will appear on the Skewness and Kurtosis Plot.  Enter a number that is less than the Maximum Lambda1.  The default is -2.


Maximum Lambda1

Enter a number for the highest value of Lambda1 that will appear on the Skewness and Kurtosis Plot.  Enter a number that is greater than the Minimum Lambda1.  The default is 2.


Data Sample

Enter information about the sample data.

Size

Enter a number for the sample size.  Enter any number 5 or greater; the default is 100.

Mean

Enter a number for sample mean that will be used to calculate the statistical tolerance limits.  Enter any positive or negative number; the default is 10.

Standard Deviation

Enter a number for the standard deviation that will be used to calculate the statistical tolerance limits.  Enter any positive number; the default is 2.


Confidence Level

Enter a value for the confidence level that will be used to calculate the interval.  Enter a percentage between 50 and 99.999; the default is 95 percent.


Population Proportion

Enter a value for the proportion of the population that can be expected to fall within the interval.  Enter a percentage between 0.0000001 and 99.9999999; the default is 99 percent.


Limits

Determines the type of limits that will be calculated.  The program allows for both one- and two-sided limits.

Two-Sided

Calculates two-sided tolerance limits, with the Lower and Upper limits estimated for the interval.  This option is the default.

Upper Only

Calculates one-sided tolerance limits, with the Upper limits estimated for the interval.

Lower Only

Calculates one-sided tolerance limits, with the Lower limits estimated for the interval.


Data

Enter the name of the variable that contains the column of data you want to analyze.


Number of Values Below Minimum

Enter the number of additional values below the smallest included in the column.


Number of Values Above Maximum

Enter the number of additional values above the largest included in the column.


Sample Size

Enter a value for the number of samples that will be taken.  Enter an integer between 6 and 1000000.


Confidence Level

Enter a value for the confidence level that will be used to calculate the tolerance limits.  The default is 95 percent; other common levels are 90 and 99.


Population Proportion

Enter a value (as a percent), which is the proportion of observations that can be expected to fall between the limits.  Enter a number between 1.e-010 and 99.9999.


Input

Determines if the Confidence Level or the Population Proportion will be calculated.

Confidence Level

Enter a value for the confidence level that will be used to calculate the tolerance limits.  The default is 95 percent; other common levels are 90 and 99.  If you enter a value into this text box you cannot enter one in the Population Proportion text box.

Population Proportion

Enter a value (as a percent), which is the proportion of observations that can be expected to fall between the limits.  Enter a number between 1.e-010 and 99.9999.  If you enter a value into this text box you cannot enter one in the Confidence Level text box.

Interval Depth

Enter a value for the interval depth.  The Upper and Lower tolerance limits are obtained by sorting the data and counting in from each end a number of observations equal to the depth value.  The default is 1, which takes the Lower and Upper limits to the smallest and largest number, respectively.


Method

Determines which method will be used to estimate the density trace.

Boxcar

Assigns a constant density to each small interval around each value, which smoothes the density function into a series of overlapping rectangles or boxcars, similar to a simple moving average.

Cosine

Smoothes local densities into a series of overlapping, bell-shaped intervals similar to a weighted moving average.  This method gives a smoother density trace; it is the default.

Interval Width

Enter the degree of overlap that will be used to compute the density trace.  Enter an integer between 10 and 90; the default is 60.  Increasing the interval width makes the density trace smoother, but may obscure the original data.

X-Axis Resolution

Enter a number that will be used to smooth the curve.  Enter a number from 20 to 200; the default is 30. The higher the number, the smoother the curve.


X-Axis Resolution

Enter a number that will be used to smooth the curve.  Enter a number from 20 to 200; the default is 30. The higher the number, the smoother the curve.


Number of Classes

Enter the number of classes into which the data will be grouped.  Enter an integer greater than 1; the default depends on the data.


Lower Limit

Enter a value for the Lower limit for the first class.  Enter any number lower than the Upper limit; the default depends on the data.


Upper Limit

Enter a value for the Upper limit for the last class.  Enter any number greater than the Lower limit; the default depends on the data.


Hold

Indicates if the current scaling should be retained even if you change the values in the Analysis dialog box. If you decide to retain the scaling, then change the data in the Analysis dialog box, the scaling remains the same when you click OK.


Plot

Determines the function that will be used to produce the plot.

Density Function

Produces a plot using a function that gives the rate at which the cumulative probability increases at a given point; it is the default for Distribution Function 1.

CDF

Produces a plot using a cumulative distribution function that shows the probability of observing a value less than or equal to a value you select; it is the default for Distribution Function 2.

Survivor Function

Produces a plot using a function that shows the probability of observing a value greater than a value you select.  The survivor function is 1 - CDF.  For reliability data, the survivor function shows the probability of surviving to time x without failure.

Log Survivor Function

Produces a plot using a function that shows the probability of observing a value greater than a value you select (in log units); that is, the log of the survivor function.

Hazard Function

Produces a plot using a function that shows the probability of failure during a small increment of time when no failure occurs before a time you select.  The hazard function is the Probability Density Function divided by the Survivor Function.


X-Axis Resolution

Enter a number that will be used to smooth the curve.  Enter a number from 20 to 200; the default is 30. The higher the number, the smoother the curve.


Censoring

Enter the name of the variable that contains the censored data.  Zeros indicate uncensored items; any other number, but usually –1 or 1, indicates a censored item.

Use negative numbers to indicate that the observation is left-censored (the value for the observation is less than the mean of the distribution).  Use positive numbers to indicate right-censored observations (the value for the observation is greater than the mean of the distribution.


EDF Statistics

Determines the EDF statistic that will be used to calculate the goodness-of-fit test.

Kolmogorov-Smirnov D

Calculates the maximum distance between the cumulative distribution of the data and the cumulative distribution function of the fitted distribution.  This option is one of the defaults.

This option is available for Random and Type I and Type II censoring.

Kuiper V

Improves the Kolmogorov-Smirnov V test in the tails of a distribution.  If there are only two class levels, it is a scaled value for an asymptotic distribution and determines the probability of observing a larger test statistic.

This option is available for Random, Type I, and Type II censoring.

Cramer-von Mises W2

Determines if a one-dimensional data sample is compatible with being a random sample from a given 	distribution.  It determines if two data samples are compatible with being random samples from the same unknown distribution.  It is similar to the Kolmogorov-Smirnov test except it is more complex.

This option is available for Type I and Type II censoring.

Watson U2

A modification of the Cramer-von Mises statistic; it was originally devised for a circle.

This option is available for Type I and Type II censoring.

Anderson-Darling A2

A general test for complete datasets (without censored observations) that compares the fit of an observed cumulative distribution with an expected cumulative distribution function.

This option is available for Type I and Type II censoring.


Censoring

Determines the type of censoring that will be used to calculate the tests.

Random

Specifies the effects in the model that are random.  When you choose this option, the expected value of each Type I and Type II effect used in the analysis is included.

When you choose this option, the Kolmogorov-Smirnov D and Kuiper V statistics are activated; the default is Kolmogorov-Smirnov D.

Type I

Measures the contribution of a variable to the reduction in error sums of squares.  Type I sums of squares measure the reduction in error sums of squares as the variable sequentially enters the model.  It calculates the sums of squares by fitting the model in steps, then recording the error difference at each step.   Also called sequential sums of squares.

When you choose this option, all five EDF statistics are activated; the defaults are Kolmogorov-Smirnov D and Cramer-von Mises W2.

Type II

Measures the contribution of a variable to the reduction in error sums of squares.   Type II sums of squares are the increment in error sums of squares that result when variables are removed from the full model.

When you choose this option, all five EDF statistics are activated; the defaults are Kolmogorov-Smirnov D and Cramer-von Mises W2.


Include

Determines what will be included on the plot.

Confidence Intervals

Includes confidence limits for the fitted line.  Enter a percentage for the value that will be used in the Levels text box.

Tail Areas

Includes the calculation of the percentile (0-100).  Enter a percentage for the value that will be used in the Percentile text box.

Histogram of Censored Values

Determines values for the histogram.

Number of Classes

Enter the number of classes into which the data will be grouped.  Enter an integer greater than 1.

Lower Limit

Enter a value for the Lower limit for the first class.  Enter any number lower than the Upper limit.

Upper Limit

Enter a value for the Upper limit for the last class.  Enter any number greater than the Lower limit.


Number of Classes

Enter the number of classes into which the data will be grouped.  Enter an integer greater than 1.


Lower Limit

Enter a value for the Lower limit for the first class.  Enter any number lower than the Upper limit.


Upper Limit

Enter a value for the Upper limit for the last class.  Enter any number greater than the Lower limit.


Group Number

Enter the number of the group for which you want to create a Histogram.  Enter either 1 or 2; the default is 1.


Log Scale for X-Axis

Determines if the X-axis will be scaled logarithmically (using a log scale). If the check box is marked, a log scale will be used.  Deselect the option to scale the axis numerically.


Hold

Indicates if the current scaling will be retained even if you change the data on the Analysis dialog box


Percentiles

Enter the name of the variable that contains the estimated percentile at each testing temperature.  You must have at least two values in the variable.


Temperatures (in Kelvin) (Arrhenius Plot Analysis dialog Box

Enter the name of the variable that contains the temperatures at which you want to test the units.  The program expects the temperatures to be in degrees Kelvin.  If you record the temperatures in Celsius, add 273.16 to the value of the temperatures.  The variable must contain at least two values.  The number of entries in this variable must equal the number of variables in the Percentiles column.


Predict at

Enter the temperature at which the prediction will be made.  The default is 300.


Confidence Level

Enter a value for the confidence level that will be used to calculate the confidence intervals.  The default is 95 percent; other common percentages are 90 and 99.


Sample Proportions

Enter the name of the variable that contains the sample proportions.  When you create the variables, all the data must be between 0 and 1.


Sample Sizes

Enter the name of the variable that contains the observations.  If all the observations are the same size, enter a single number.  Enter integers greater than or equal to 1.


Sample Labels

 [Optional]  Enter the name of the variable that contains the labels for the observations.  These labels identify the observations on reports.  You must enter one label for each observation in the data; include labels for observations you plan to remove from the analysis.  The program assigns the first label to the first observation, the second label to the second observation, and so on.  If you leave the text box blank, the program creates default labels.


Confidence Level

Determines the confidence level that will be used to calculate the confidence intervals for the data.  The default is 95 percent; other levels are 90 and 99.


Decimal Places for Limits

Enter the number of decimal places that will be used for the decision limits.  Enter an integer between 0 and 20; the default is 2.


Sample Counts

Enter the name of the variable that contains the Count data.  When you create the variables, the data must be integers.


Sample Labels

[Optional]  Enter the name of the variable that contains the labels for the count data.  These labels identify the observations on reports.  You must enter one label for each observation in the data; include labels for observations you plan to remove from the analysis.  The program assigns the first label to the first observation, the second label to the second observation, and so on.  If you leave the text box blank, the program creates default labels.


Select

[Optional]  Select a subset of the observations.  For example, to compare the first 50 values in each variable, enter first (50) into this text box.  The entry in this text box applies to all the variable names you enter into the Sample Counts text box.


System Options

Determines the system behavioral preferences you can make system-wide.

Sort Variable Names on Dialog Boxes

Allows you to either retain or not retain settings for sorting variable names on dialog boxes.  By default, variable names are sorted.  You can change that setting system-wide instead of changing it later one-by-one later or changing it on individual dialog boxes.  Always sorted is the default.

4-Digit Dates

Allows you to either always use or not always use four-digit date format in Date variables.  Changing the setting allows you to enter four-digit dates when you create or modify DataSheets instead of using a two-digit date format.  The change takes place after you exit the current STATGRAPHICS Plus session and re-enter the program.  Four-digit date format is the default.

Autosave Enabled

Allows you to either	 enable or disable the automatic save feature and set specific time limits by entering minutes in the text box. Autosave enabled at every 10 minutes is the default.


Graphics

Determines the graphics behavioral preferences you can make system-wide.

Maintain 1:1 Aspect Ratio

Allows you to either retain or not retain a graphics aspect ratio of 1:1, which means that graphs will be created in a square shape.

Always Black and White

Allows you to either retain or not retain black and white graphs, which means that you can override the default setting on the Profile tab page of the Graphics Options dialog box.

Suppress Ticmark Gap

Allows the gap between the intersection of the of the axes and the first tickmark to be eliminated.

Decimal Places for Labels

Determines the number of decimal places that will appear in labels on charts.  Enter the number of decimal places in the text box.  The default is 4.


Link Behavior

Determines the link behavioral preferences you can make system-wide.

Update Analyses While Iconic

Allows you to either update or not update analyses while they are in the nature of an icon.

Update Analyses on Each New Data Value

Allows you to either update or not update analyses whenever a new data value is generated.


Fill

Determines the area of the graph whose fill pattern and/or color you want to change.  The number on the dialog box refers to an internal tracking system feature.


Fill Types

Determines the fill pattern: Empty (no fill pattern), Solid, Horizontal Lines, Vertical Lines, Diagonal Lines, Cross-Hatch Lines, or Diagonal Cross-Hatch Lines.


Color

Determines if the fill or the fill outline will be in color.


Colors...

Displays the Windows Color dialog box that you use to choose a color for the fill pattern or outline.


Direction

Determines how the grid will display on the graph.

Horizontal

Displays the grid horizontally.

Vertical

Displays the grid vertically.

Both

Displays the grid both horizontally and vertically; this option is the default.

None

Displays the graph without a grid.


Type

Determines the type of line that will appear on the grid.  There are five options:  Solid Line, Dashed Line, Dotted Line, Dash-Lot Line, or Dash-Dot-Dot Line.


Colors...

Displays the Windows Color dialog box that you use to change the color of the lines on the graph.


Line Thickness

Determines the thickness of the line on the graph.  Use the slider control to move from thinnest to thickest.  This feature is available only for the Solid Line option.


Back Grid on 3D Plots

Determines if a grid should always be included on the back and left side of a three-dimensional plot.  You can also use the Edit Preferences dialog box to override the default.


Label

Enter names for the labels that will appear on the graph.  You can enter as many as 33 names.  The letter between the braces, for example, {A}, is an internal system reference to variable names.


Fonts...

Displays the Windows Font dialog box that you can use to change to a different font, or to change an attribute of the font such as its style or size.


Tickmarks and Colors

Determines options for axes, background, and border of a graph.

X-Axis

Changes the style of the tickmarks on the X-axis or to their color.

Y-Axis

Changes the style of the tickmarks on the Y-axis or to their color.

Z-Axis

Changes the style of the tickmarks on the Z-axis or to their color.

Background

Changes the color of the background inside the axes.

Border

Changes the color of the border around the graph.


Tickmarks

Determines the type of tickmarks that will appear on the graph: No Tickmarks, Tickmarks Inside the Frame, or Tickmarks Outside the Frame.  These options are available only when you choose one of the three axes: X, Y, or Z.


Mode

Determines the shape of the graph: L-Shaped (Two-Sided), or Square (Four-Sided).


Line Thickness

Determines the thickness of the line that forms the shape of the graph.  Use the slider control to move from thinnest to thickest.


Colors...

Displays the Windows Color dialog box you use to choose a color for the tickmarks.


Title

Enter the name of the title for the legend.


Legend

Enter a name for the variables.  The letter between the braces; for example, {A}, is an internal reference to variable names you enter into the text box(es) on an Analysis or Options dialog box.


Line Types

Determines the type of line that will appear.  There are five options:  Solid Line, Dashed Line, Dotted Line, Dash-Dot Line, or Dash-Dot-Dot Line.


Line Thickness

Determines the thickness of the lines on the graph. Use the slider control to move from thinnest to thickest.


Colors...

Displays the Windows Color dialog box you use to choose a color for the lines.


Point

Determines the point whose type and/or color will be changed.  The number on the dialog box refers to an internal tracking system feature.


Point Types

Determines the shape of the points that will appear on the graph: Square, Plus, X, Star, Diamond, Up Arrowhead, Down Arrowhead, or Circle.


Fill Point

Determines whether the point will or will not be filled; the default is unfilled.  If you deselect the option, the point will appear only as an outline.


Point Size

Determines the size of the point.  Use the slider control to move from Smallest to Largest.


Point Thickness

Determines the thickness of the point the graph.  Use the slider control to move from thinnest to thickest.  This feature is available only for the Solid Line option.


Colors...

Displays the Windows Color dialog box you use to choose a color for the points.


Profile

Determines the system profile you want to set up.

System (Color, White Background)

Uses a predefined profile to display plots always in color on a white background.

System (Color, Dark Background)

Uses a predefined profile to display plots always in color on a dark background.

System (Black and White)

Uses a predefined profile to display plots always in black and white.  You can override this default using the Edit Preferences dialog box.

User #3…User #12

Uses a profile you set up.  You can set up or edit from 1 to 12 user profiles.  When you set them up or edit them, you can either use numbers, letters, names, or a combination of the three to create the name of the profile.


Make a Default

Moves the default indicator (letter D) to the left of a profile.  When you click Make Default… then Load, the indicator moves to the left of a profile, which indicates that this profile is the default.


Load

Loads a profile for a new user.


Title

Enter a title for the axis.


Vertical

`Enter a number for the minimum value of the axis.  Enter a number less than the number you enter into the To text box.


From

Enter a number for the minimum value of the axis.  Enter a number less than the number you enter into the To text box.


To

Enter a number for the maximum value of the axis.  Enter a number greater than the number you enter into the From text box.


By

Enter a number that will be used to calculate the distance between each tickmark.  Enter any positive value less than the difference between the number you enter into the To and From text boxes.


Skip

Enter the number of tickmarks that will be skipped when the X-axis is created.  The default is 0.


No Power

Indicates if the axis scale will be changed for the tickmarks.  If the check box is not checked, a power of 10 is used to calculate the axis scale.


Log

Indicates if the axis scale will be changed for the tickmarks using Log option, which means that decimal logarithmic scaling will be used to calculate the scale.


Hold

Indicates if the program will retain the current scaling even if you change the data on the Analysis dialog box.


Title Fonts

Displays the Windows Font dialog box that you use to change the font for the title.


Tickmark Fonts

Displays the Windows Font dialog box that you use to change the font for the tickmarks.


Labels

Enter the name of the label you want to add or delete.  This portion of the Right-Axis Scaling tab page displays automatically when the program determines that it is appropriate for the values you are entering.


Rotate Axis Labels

Indicates that the position of the labels should be rotated.  This portion of the Right-Axis Scaling tab page displays automatically when the program determines that it is appropriate for the values you are entering.


Draw Test

Indicates if the text should be drawn (displayed) on the graph.  If the check box is marked, text will display on the drawn while the graph is spinning.


Maximum Speed

Enter a value that will be used to control to number of frames per second the graph will be redrawn while it is spinning.  The default is 20.


Degrees per Frame

Enter a value that will be used to control the degrees per frame the graph will rotate while it is spinning.  The default is 3.


Text

Enter the text for the title or label that will be changed.  When you want to edit the text or label, the text currently on the graph displays in this text box.


Edit

Displays the text you highlighted in the Text text box so you can edit it.


Direction

Determines the direction in which the text for the title and/or label will display on the graph.

Horizontal

Displays the text horizontally; this option is the default.

Vertical

Displays the text vertically.


Fonts...

Displays the Windows Font dialog box that you can use to change to a different font, or to change an attribute of the font such as its style or size.


Line

Determines the line that will be changed.  The number on the dialog box refers to an internal tracking system feature.


Title

Enter the name that will be used for the new or changed title.


Vertical

Reverses the title and places it vertically instead of horizontally.


Line 1 Fonts...

Displays the Windows Font dialog box that you can use to change the fonts for line 1 of the title.


Line 2 Fonts...

Displays the Windows Font dialog box that you can use to change the fonts for line 2 of the title.


Change Font for All Titles

Changes the font for all the titles on the chart.


Plot

Determines what will appear on the plot.

Points

Plots points; it is one of the defaults.

Lines

Plots lines; it is one of the defaults.


Angular Units

Determines the type of angular units that will appear on the plot.

Degrees

Plots the angles in degrees (0° - 360°); it is the default.

Radians

Plots the angles in radians (0 - 2 pi).

Grads

Plots the angles in grads (0 - 100).


Labels

Determines how the angular locations will be labeled.

Angular

Labels the angular locations numerically; it is the default.

Compass

Labels the angular locations using compass directions (N-S-E-W).


Direction

Determines the direction in which the angles will increase.

Clock Wise

Increases the angles in a clock-wise direction; it is the default.

Counter Clock Wise

Increases the angles in a counter clock-wise direction.


Origin

Determines the position of 0 degrees.

12:00

Places 0 degrees at the 12:00 position; it is the default.

3:00

Places 0 degrees at the 3:00 position.


Radius

Enter the name of the variable that contains the radial values for each point.


Angle

Enter the name of the variable that contains the angular values for each point.


Point Codes

[Optional]  Enter the name of the variable that contains the column that defines the labels for the points.


Indices

Determines the indices that will appear on the Capability Indices report and the Capability Plot.  If you use a one-sided specification, you cannot calculate capability indices for Cp, Cr, Cpm, or K.  If you use an asymmetric two-sided specification, interpret the Cp, Cr, and Cpm indices with caution because they are based on symmetric limits.

Cp

Displays a value for the inherent capability of the process.  In general, if the mean of the data is located close to the midpoint of the tolerances, then a Cp less than 1.00 indicates that the process is not capable; a Cp above 1.33 indicates that the process is capable; a Cp between 1.00 and 1.33 indicates that the process is capable, but should be monitored as Cp approaches 1.00.

Cpk

Displays a value for the capability in relation to the mean. Cpk is a worse-case index of the process.  It is the ratio of the distance from the UCL to the mean or the LCL to the mean, whichever is smaller, to half the sigma range. Cpk is useful even if the mean of the data is not close to the midpoint of the tolerances.  A Cpk larger than 1.33 indicates that both sigma limits fall within the specification limits and the process is capable of performing to specification; a Cpk of less than 1.00 means that at least one of the sigma limits is outside of a specification limit and the process may not be capable of performing to specification.

Cp (upper)

Displays a value for the distance from the USL to the mean, divided by half the sigma range.

Cp (lower)

Displays a value for the distance from the LSL to the mean, divided by half the sigma range.

Cr

Displays a value for the capability ratio of the process; it is the reciprocal of the Cp index.  If the mean of the data is located close to the midpoint of the tolerances, then a Cr greater than 1.00 indicates that the process is not capable; a Cr less than 0.75 indicates that the process is capable; a Cpr between 0.75 and 1.00 indicates that the process is capable, but should be monitored as Cr approaches 1.00.

Cpm

Displays a value for the modified Cp index.  The program calculates Cpm using the nominal value instead of the calculated mean.  It is a more conservative index than Cp; you interpret it in the same manner.  For small sample sizes, Cpm is a better measure than Cp.

K

Displays a value for the comparison ratio of the process mean to the nominal specification.  K is a measure of how far the center of the process is from the nominal or target of the process.  If K is 0, the mean and the nominal value are identical; if K is positive, the mean is above the nominal value; if K is negative, the mean is below the nominal value.  When the absolute value of K is small, the process mean is close to the nominal specification.  A small value of K can occur even if the process is not capable.


Based On

Determines if 6 sigma limits or user-specified limits will be used to calculate the capability indices.  You can use User-Specified Limits only when you select the Normal distribution.

6.0 Sigma Limits

Uses 6.0 sigma limits to calculate the capability indices; this option is the 	default.

User-Specified Limits

Uses the value you enter as the sigma limits to calculate the capability indices.  For example, if you enter 8 sigma limits, the program calculates Cp by dividing by 8 standard deviations rather than by 6 standard deviations.


Confidence Level

Enter a value that will be used to calculate the confidence levels for the intervals.  Enter a numeric value greater than 0 and less than 100.


Label As

Determines how the indices will be labeled.

Cp, Cpk, etc.

An alternative way some analysts use to label Process Capability indices.

Pp, Ppk, etc.

Alternative way some analysts use to label Process Capability indices.


Direction

Determines the direction in which the plot will display.

Horizontal

Displays the plot horizontally; this option is the default.

Vertical

Displays the plot vertically.


Fitted Line

Indicates if a fitted line will appear on the plot; a fitted line on the plot is the default.


Data

Determines the type of data that will be analyzed.

Observations

Choose this option if you are entering individual observations.  In the text box, enter the name of the variable that contains the observations.  This option is the default.

Subgroup Statistics

Choose this option if you will be entering subgroup statistics.  In the text box, enter the name of the variable that contains the subgroup statistics; you must enter means and corresponding ranges.


Subgroup Numbers or Size

Enter a number for the size of the subgroups.  If all the subgroups are the same size, enter a single number.  If you are using Observations, and the subgroups are of different sizes, enter a numeric variable that identifies the subgroup to which each observation belongs.  The observations are organized into subgroups automatically.  If you are using Subgroup Statistics, enter one subgroup size for each subgroup statistic.  Enter values between 2 and 25.


Subgroup Labels

 [Optional]  Enter the name of the variable that contains the labels that will be used for the subgroups.  The labels are used to identify the subgroups on reports.  Enter one label for each subgroup; include labels for subgroups that you plan to remove from the analysis.  The first label is assigned to the first subgroup, the second label to the second subgroup, and so on.  If you leave the text box blank, the program creates default names for the subgroup labels.


Select

[Optional]  Select a subset of the observations or subgroups.  For example, to analyze the first 50 values in each variable, enter first (50) into this text box.


Sort

Sorts the variable names alphabetically; sorted is the default.


Decimal Places for Limits

Enter a positive integer for the number of decimal places that will display for the limits.


Type of Study

Determines the type of study; either Initial Study or Control to Standard.  The default is Initial Study.

Initial Study

Computes the control limits based on the data.

Control to Standard

Computes the control limits based on the mean and sigma you enter.  In this type of study, the control limits are fixed and the data do not influence the control limits.


Decision Interval (h)

Enter a value for the multiple of sigma that will be used to calculate the control limits for the CuSum Chart.  Enter a value greater than 0; the default is 5.


Reference Value (k)

Enter a value for K that will be used to calculate the Upper and Lower one-sided specifications.  Normally this value is chosen about half-way between the target value and the value of the mean that corresponds to the out-of-control state.  Enter a value greater than 0; the default is 0.5.


ARL at n Sigma = x

Enter a value to specify the shift in the mean as a multiple of sigma for estimating the average run length.  Enter a value greater than or equal to 0; the default is 0.


Headstart n Sigma

Enter a value for the headstart parameter that shifts the initial values of the Upper and Lower CuSums.  This improves the sensitivity of a CuSum at process startup.  Enter a value greater than or equal to 0; the default is 0.


CuSum Control Limits

Determines the type of CuSum control chart that will be created.

Two-Sided

Creates a two-sided CuSum Chart with both a lower CuSum and an upper CuSum.  This option is the default.

Upper Only

Creates a one-sided CuSum Chart with only an upper CuSum calculated.

Lower Only

Creates a one-sided CuSum Chart with only a lower CuSum calculated.

Normalize

Standardizes the data and produces a normalized CuSum Chart and a normalized Range Chart.  A normalized CuSum Chart can be used for monitoring variability.


Range Control Limits

Determines the location of the control limits on the Range Chart.

Upper Sigma

Enter a value for the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10.  The default is 3.0.

Lower Sigma

Enter a value for the multiple of sigma that will be used to calculate the LCL.  Enter a numeric value greater than or equal to -10 and less than or equal to 0.  The default is -3.0.


Control to Standard

Determines the values for a control-to-standard study.  The options are available only when you choose Control to Standard from the Type of Study option.

Specify Parameters

Enter the values that will be used to calculate the control limits.

Mean

Enter a value for the process mean.  Enter any numeric value.

Sigma

Enter a value for the process sigma.  Enter any positive numeric value.


Design...

This command displays the Design CuSum Chart dialog box that determines the best values for K and h for a resulting ARL Chart, given a specified sigma shift to detect and the in-control ARL.


Display

Determines what will display in the CuSum Chart Report.

All Subgroups

Includes all the subgroups.

Subgroups Beyond Limits

Includes a list of the subgroups that are beyond the control limits.

CuSum Beyond Limits

Includes a list of the subgroups that are beyond the CuSum control limits.

Ranges Beyond Limits

Includes a list of the subgroups that have ranges beyond the control limits.

Excluded Subgroups

Includes a list of the excluded subgroups.


Observations

Enter the name of the variable that contains the individual observations.


Labels

[Optional]  Enter the name of the variable that contains the labels that will be used to label the individual observations.  Enter one label for each observation in the data; include labels for the observations you plan to remove from the analysis.  The program assigns the first label to the first observation, the second label to the second observation, and so on.  If you leave this text box blank, the program creates default labels.


Target

Enter a value for the target of sigma.


Mean Control Limits

Determines the type of CuSum control chart that will be created.

Two-Sided

Creates a two-sided CuSum Chart with both a lower CuSum and an upper CuSum.  This option is the default.

Upper Only

Creates a one-sided CuSum Chart with only an upper CuSum calculated.

Lower Only

Creates a one-sided CuSum Chart with only a lower CuSum calculated.

Normalize

Standardizes the data and produces a normalized CuSum Chart and a normalized Scale Chart.  A normalized CuSum Chart can be used for monitoring variability.


Scale Control Limits

Determines the Scale control charts used for detecting changes in the mean and standard deviation.

Two-Sided

Creates a two-sided Scale Chart with both an UCL and an LCL calculated.

Upper Only

Creates a one-sided Scale Chart with only a UCL calculated.

Lower Only

Creates a one-sided Scale Chart with only a LCL calculated.


Display

Determines what will display in the CuSum Individuals Chart Report.

All Observations

The report includes all the observations.

Observations Beyond Limits

The report includes a list of the observations that are beyond the control limits.

CuSum Beyond Limits

The report includes a list of the observations that have a mean CuSum beyond the control limits.

Scale CuSum Beyond Limits

The report includes a list of the observations that have a Scale CuSum beyond the control limits.

Excluded Observations

The report includes a list of the excluded observations.


Runs Tests (ARIMA Chart Analysis)

The Runs Tests option performs a battery of tests that help determine if a sequence of observations is in a nonrandom pattern, which indicates that a process is out of control.  To use this option, choose either Residuals or Normalized Residuals from the Chart Type portion of the ARIMA Chart Options dialog box.

The tests search for and identify any unusual patterns in the residuals, which are helpful in detecting processes that are slowly drifting away from target, even though no points may be outside the control limits.  The Runs Tests table shows the subgroup or observation at which the unusual pattern was detected, as well as the particular rule that was violated.  The rules are identified by letters (A, B, C, D, etc.); the subgroups or observations by numbers (1, 2, 3, 4, etc.).  If the table shows Rule D in Subgroup 2 in violation, it means that rule D was violated at point 2.  For more information, see the AT&T Statistical Quality Control Handbook.

Use the Runs Tests Options dialog box to choose the rules you want to include in the tests.


X-bar Control Limits

Determines the values for the location of the control limits on the ARIMA Chart.

Upper Sigma

Enter a value for the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10.  The default is 3.0.

Lower Sigma

Enter a value for the multiple of sigma that will be used to calculate the LSL.  Enter a numeric value greater than or equal to -10 and less than or equal to 0.  The default is -3.0.


Range Control Limits

Determines the values for the UCL and LCL on the Range Chart.

Upper Sigma

Enter a value for the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10.  The default is 3.0.

Lower Sigma

Enter a value for the multiple of sigma that will be used to calculate the LCL.  Enter a numeric value greater than or equal to -10 and less than or equal to 0.  The default is -3.0.


Control to Standard

Determines the values for a control-to-standard study.

Mean

Enter a value for the process mean.  Enter any numeric value.

Sigma

Enter a value for the process sigma.  Enter any positive numeric value.

AR(1)

Enter a numeric value for the first-order autoregressive parameter.

AR(2)

Enter a numeric value for the second-order autoregressive parameter.

AR(3)

Enter a numeric value for the third-order autoregressive parameter.

AR(4)

Enter a numeric value for the fourth-order autoregressive parameter.

MA(1)

Enter a numeric value for the first-order moving average parameter.

MA(2)

Enter a numeric value for the second-order moving average parameter.

MA(3)

Enter a numeric value for the third-order moving average parameter.

MA(4)

Enter a numeric value for the fourth-order moving average parameter.


Model

Determines the order of the ARIMA model, allowing for up to fourth-order AR and MA terms, and up to second-order differencing.

AR 0-4

Choose the order of the autoregressive terms in the model: none, or first through fourth.

I

Choose the order of the differencing: none, first, or second.

Constant

Indicates that a constant term will be estimated for the model.

MA 0-4

Choose the order of the moving average terms in the model: none, or first 	through fourth.


Estimate Sigma From

Determines what will be used to calculate sigma.

Range Chart

Choose this option if the Range Chart should be used to estimate sigma.

Model MSE

Choose this option if the mean squared error of the model should be used to estimate sigma.


Chart Type

Determines the type of chart that will be created.

Data with Long-Term Limits

Creates a plot with constant UCL and LCL limits and the centerline set at the 	estimate for the process mean.

Data with One-Stop Limits

Creates a plot with constant UCL and LCL limits calculated for each subgroup.

Residuals

Creates a plot of the ARIMA residuals.

Normalized Residuals

Creates a plot of the normalized ARIMA residuals.


Display

Determines what will display in the ARIMA Chart Report.

All Subgroups

The report includes all the subgroups.

Subgroups Beyond Limits

The report includes a list of the subgroups that are beyond the control limits.

X-bars Beyond Limits

The report includes a list of the subgroups that have X-bars beyond the control limits.

Ranges Beyond Limits

The report includes a list of the subgroups that have ranges beyond the control limits.


Indices

Determines the capability indices that will be calculated for the Capability Indices Report.  If you use a one-sided specification, capability indices are not calculated for Cp, Cr, Cpm, or K.  If you use an asymmetric, two-sided specification, Cp, Cr, and Cpm should be interpreted with caution because the indices are based on symmetric limits.

Cp

Displays the inherent capability of the process.  In general, if the mean is located 	close to the midpoint 	of the tolerances, a Cp less than 1.00 indicates the process is not capable.  A Cp above 1.33 indicates that the process is capable.  A Cp between 1.00 and 1.33 indicates that the process is capable but should be monitored as Cp approaches 1.00.

Cpk

Displays the capability in relation to the mean.  Cpk is a worst-case index of the process; it is the ratio of the smaller of the distance from the USL to the mean or the USL to the mean, whichever is smaller, to half of the sigma range.  Cpk is useful even if the mean of

the data is not close to the midpoint of the tolerances.  A Cpk larger than 1.00 indicates that both sigma limits fall within the specification limits and the process is capable of performing to specification.  A Cpk of less than 1.00 means that at least one of the sigma limits is outside a specification limit and the process may not be capable of performing to specification.

Cpk (upper)

Displays the distance from the USL to the mean, divided by half the sigma range.

Cpk (lower)

Displays the distance from the LSL to the mean, divided by half the sigma range.

Cr

Displays the capability ratio of the process.  It is the reciprocal of the Cp index.  If the mean of the data is located close to the midpoint of the tolerances, the data are located close to the midpoint of the 	tolerances, then a Cr greater than 1.00 indicates the process is not capable.  A Cr less than 0.75 indicates that the process is capable.  A Cr between 0.75 and 1.00 indicates that the process is capable, but should be monitored as Cr approaches 1.00.

Cpm

Displays the modified Cpk index.  The program calculates Cpm using the nominal values instead of the calculated mean.  It is a more conservative index than Cp, and you can interpret it in the same manner.  For small sample sizes, Cpm is a better measure than Cp.

K

Displays the comparison ratio of the process mean to the nominal specification.  K is a measure of the distance the center of the process is from the nominal midpoint of the process.  If K is 0, the mean and the nominal value are identical.  If K is positive, the mean is above the nominal value.  If K is negative, the mean is below the nominal value.  When the absolute value of K is small, the process mean is close to the nominal specification.  A small value of K can occur even if the process is not capable.


Specifications

Determines the specification limits.  Some options may not be available.

USL

Enter a numeric value for the upper specification.  The value you enter must be greater than the values in the LSL and Nominal text boxes.

Nominal

Enter a numeric value for the target value for the process.  The value you enter must be greater than the value in the LSL text box and less than the value in the USL text box.

LSL

Enter a value for the lower specification.  The value you enter must be less than the values in the USL and Nominal text boxes.


Number of Lags

Enter the maximum number of lags that should be used for estimating the autocorrelations.  Typically, the number of lags should not exceed the number of observations divided by 4.  Enter any positive integer.


Confidence Level

Enter a value that will be used to calculate the size of the probability limits for the autocorrelations.  Enter a number greater than 0 and less than 100; common levels are 90, 95, or 99 percent; 95 percent is the default.


Specifications

Sets the specification limits for the Tolerance Chart.

Upper

Enter a numeric value for the upper specification limit.  The value you enter must be greater than the values in the Lower and Nominal text boxes.

Nominal

Enter a numeric value for the target value for the process.  The value you enter must be greater than the value in the Lower text box and less than the value in the Upper text box.

Lower

Enter a value for the lower specification.  The value you enter must be less than the values in the Upper and Nominal text boxes.


Plot

Determines whether points or the nominal specification will be plotted on the chart.  The default is both options.


Decimal Places for Limits

Enter a number that will be used for the decimal places for the limits.  The default is 4.


Observations

Enter the name of the variable that contains the individual observations.


Labels

 [Optional]  Enter the name of the variable that contains the labels that will be used to identify the individual observations on reports.  You must enter one label for each observation; include labels for observations you plan to remove from the analysis.  The first label is assigned to the first observation; the second label to the second observation; and so on.  If you leave this text box blank, default labels are created.


X-Control Limits

Determines the location of the control limits on the ARIMA Individuals Chart.  If you enter a value of 0 in either option, the corresponding control limit is removed from the analysis.

Upper Sigma

Enter a value for the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10.  The default is 3.0.

Lower Sigma

Enter a value for the multiple of sigma that will be used to calculate the LCL.  Enter a numeric value less than or equal to 0 and greater than or equal to -10.  The default is -3.0.


MR(2) Control Limits

Determines the location of the control limits on the MR(2) Chart.

Upper Sigma

Enter a value for the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10.  The default is 3.0.

Lower Sigma

Enter a value for the multiple of sigma that will be used to calculate the LCL.  Enter a numeric value less than or equal to 0 and greater than or equal to -10.  The default is -3.0.


Estimate Sigma From

Determines what will be used to calculate sigma.

MR(2) Chart

Choose this option if the MR(2) Chart should be used to estimate sigma.

Model MSE

Choose this option if the mean squared error of the model should be used to estimate sigma.


Display

Determines what will display in the ARIMA Individuals Chart Report.

All Observations

The report includes all the observations.

Observations Beyond Limits

The report includes a list of the observations that are beyond the control limits.

X Beyond Limits

The report includes a list of the observations that have values beyond the control limits.

MR(2) Beyond Limits

The report includes a list of the observations that have moving ranges beyond the control limits.


Data

Determines the type of data measurements that will be analyzed.

Observations

Choose this option if you are entering individual observations.  In the text box, enter the name of the variable that contains the individual observations; that is, if the data contain individual measurements, enter the variable name that contains that data.  This option is the default.

Subgroup Statistics

Choose this option if you will be entering subgroup statistics.

Means

Enter the means (X-bars) of the subgroups that will be included in the analysis.

Ranges

Enter the ranges that will be included in the analysis.  The values you enter must correspond to the values you enter into the Means text box.


X-bar Control Limits

Determines the values for the location of the control limits on the Toolwear Chart.

Upper Sigma

Enter a value for the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10.  The default is 3.0.

Lower Sigma

Enter a value for the multiple of sigma that will be used to calculate the LCL. Enter a numeric value greater than or equal to -10 and less than or equal to 0. The default is

-3.0.


Control to Standard

Determines the parameters for the control to standard study.

Intercept

Enter a numeric value for the intercept parameter.

Slope

Enter a numeric value for the slope parameter.

Sigma

Enter a positive numeric value for sigma.


Specification Limits

Determines the specification limits for the Toolwear Chart.

Upper

Enter a numeric value for the upper specification.

Lower

Enter a value for the lower specification.


Estimate Sigma From

Determines what will be used to calculate sigma.

Range Chart

Uses the Range Chart to estimate sigma.

Model MSE

Uses the mean squared error of the model to estimate sigma.

Include Model Estimation Error

Includes the model estimation error when calculating the control limits for the Toolwear Chart.


Display

Determines what will display in the Toolwear Chart Report.

All Subgroups

Includes all the subgroups.

Subgroups Beyond Limits

Includes a list of the subgroups that are beyond the control limits.

X-bars Beyond Limits

Includes a list of the subgroups that have X-bars beyond the control limits.

Ranges Beyond Limits

Includes a list of the subgroups that have ranges beyond the control limits.

Excluded Subgroups

Includes a list of the excluded subgroups.


X Control Limits

Determines the values for the location of the control limits on the Toolwear Chart.

Upper Sigma

Enter a value for the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10.  The default is 3.0.

Lower Sigma

Enter a value for the multiple of sigma that will be used to calculate the LCL.  Enter a numeric value greater than or equal to -10 and less than or equal to 0.  The default is -3.0.


Include Model Estimation Error

Includes the model estimation error when calculating the control limits for the Toolwear Chart.


Display

All Observations

Includes all the observations

Observations Beyond Limits

Includes a list of the observations that are beyond the control limits.

X Beyond Limits

Includes a list of the observations that are beyond the X control limits.

MR(2) Beyond Limits

Includes a list of the observations that have moving ranges beyond the control limits.

Excluded Observations

Includes a list of the excluded observations.


Specify

Determines of you specify the multiple of sigma or beta risk for calculating the X-bar control limits.

Sigma Multiple

Places the control limits a number of standard errors away from the means.  Choose this option if you want to specify the number of standard errors away from the means at which the control limits will be placed (sometimes called a “modified control chart).”

Beta Risk

Places the control limits using the probability of incorrectly accepting a process 	at those means.   Choose this option if you want to specify the beta risk for calculating the X-bar control limits.


X-bar Control Limits

Determines the location of the control limits on the Acceptance Chart.

Fraction Nonconforming

Enter a small positive decimal value for the ratio of the number of nonconforming items in the population to the total number of items in the population.

Sigma Multiple

Enter a numeric value greater than or equal to 1 and less than or equal to 10 for the number of standard errors away from the means at which the control limits will be placed.  The default is 3.0.


Sigma Control Limits

Determines the values for the UCL and LCL.

Upper Sigma

Enter a value for the multiple of sigma that will be used to calculate the UCL.  Enter a numeric value greater than or equal to 0 and less than or equal to 10.  The default is 3.0.

Lower Sigma

Enter a value for the multiple of sigma that will be used to calculate the LCL.  Enter a numeric value greater than or equal to -10 and less than or equal to 0.  The default is -3.0.


Specification Limits

Determines the specification limits.

Upper

Enter a numeric value for the upper specification.  The value you enter must be greater than the value in the Lower text box.

Lower

Enter a value for the lower specification.  The value you enter must be less than the value in the Upper text box.


Display

Determines what will display in the Acceptance Chart Report.

All Subgroups

Includes all the subgroups.

Subgroups Beyond Limits

Includes a list of the subgroups that are beyond the control limits.

X-bars Beyond Limits

Includes a list of the subgroups that have X-bars beyond the control limits.

Sigmas Beyond Limits

Includes a list of the subgroups that have standard deviations beyond the control limits.

Excluded Subgroups

Includes a list of the excluded subgroups.


Specifications

Determines the settings for the specification limits. Some settings may not be available.

USL

Enter a value for the USL.  Enter one numeric value.  The value you enter must be greater than the values you enter into the LSL and Nominal text boxes.

Nominal

Enter a value for the target of the process.  Enter one numeric value.  The value you enter must be greater than the value in the LSL and less than the USL.

LSL

Enter a value for the LSL.  Enter one numeric value.  The value you enter must be less than the values in the USL and Nominal text boxes.


Plot

Determines whether points or the nominal specification will be plotted on the chart.  The default is both options.


Decimal Places for Limits

Enter a positive integer to indicate the number of decimal places that will be displayed for the control limits.


Select

[Optional]  Select a subset of observations.  For example, to analyze the first 50 observations, enter first 50) into this text box.


X-Control Limits

Determines the location of the control limits on the Acceptance Individuals Chart.

Fraction Nonconforming

Enter a small positive decimal value for the ratio of the number of nonconforming items in the population to the total number of items in the population.

Sigma Multiple

Enter a numeric value greater than or equal to 1 and less than or equal to 10 for 	the number of standard errors away from the means at which the control limits 	will be placed.  The default is 3.


Control to Standard

Determines the values for a control-to-standard study.

Mean

Enter a numeric value for the process mean.

Sigma

Enter a positive numeric value for the process sigma.


Display

Determines what will display in the Acceptance Individuals Chart Report.

All Observations

The report includes all the observations

Observations Beyond Limits

The report includes a list of the observations that are beyond the control limits.

X Beyond Limits

The report includes a list of the observations that are beyond the X control limits.

MR(2) Beyond Limits

The report includes a list of the observations that have moving ranges beyond the control limits.

Excluded Observations

The report includes a list of the excluded observations.


Labels

Enter the name of the variable that contains the labels for the diagram.


Setting Up a DataSheet For Creating a Fishbone Diagram

STATGRAPHICS Plus lets you create a Fishbone Diagram using the computer rather than pencil and paper; however, you must know how to correctly enter the data.

1.	Access a blank untitled DataSheet.

2.	Access the Modify Column dialog box, and define a single character column 	with a width adequate for the labels you will be entering.

3.	Enter primary-cause category names flush with the left edge of the column.  	Enter rank-ordered, secondary-cause categories with a beginning period (.) 	preceding the name; and enter rank-ordered, tertiary-cause categories with 	double periods (..) preceding the name.

For an example of a DataSheet set up this way, see Figure 10-1 in the User Manual.  After you create the diagram, you can use the graphics editing options to change its look.  For example, you could change the primary-cause category names to a larger point size, make them bold, or change their color to make them stand out.  You can also move the labels to provide more or less white space.


Action

Determines the type of sampling plan that will be created; or analyzes an existing plan.

Create OC Plan

Creates an OC (Operating Characteristic) Plan whose objective is to assure quality levels for consumer/producer.  Allows you to select a plan for a specific OC curve.

Create AOQL

Creates an AOQL Plan whose objective is to assure average outgoing quality levels.  Attribute procedures include AOQL System and Dodge-Romig plans.

Create LTPD Plan

Creates a Lot Tolerance Percent Defective (LTPD) plan, whose objective is to assure quality no worse than a specified target.  Attribute procedures include LTPD plans and Dodge-Romig plans.

Analyze Existing Plan

Analyzes a sampling plan that was previously created, and currently exists.


Quality Levels

Determines the elements that define the type of OC Curve that will be used in the analysis.

Acceptable Quality Level (AQL)

Enter a value for an element that defines an OC Curve.  It is the smallest percentage of defectives that will make the lot definitely acceptable; a level that the customer prefers.  Enter a numeric value greater than 0 and less than 100.

Lot Tolerance Percent Defective

Enter a value for an element that defines an OC Curve.  It is the largest percentage of defectives that will make the lot definitely unacceptable.  Customers cannot tolerate more defectives than this percentage.  Enter a numeric value greater than the value for AQL and less than 100.


Lot Size

Enter a value for the size of the lot or batch that is being inspected.  Enter a positive integer.


Desired Features

Determines the characteristics of the items that will make up the sampling plan.

Producer’s Risk (Alpha)

Enter a value for the probability that a lot will meet the AQL and will not be accepted.  This is the Type I error; the error committed when rejecting a good lot, and is frequently set at 5 percent.  Enter a value greater than 0 and less than 100.

Consumer’s Risk (Beta)

Enter a value for the probability that a lot will exceed the LTPD and still be accepted.  This is the Type II error; the error committed when accepting a bad lot, and is frequently set at 10 percent.  Enter a value greater than 0 and less than 100.


Current Plan

Determines the characteristics of items that make up the current sampling plan.  These options are available only when you select Analyze Existing Plan from the Action option list.

Sample Size (n)

Enter a value for the previously determined sampling plan size.  The disposition of the lot is determined based on the information contained in that sample.  Enter a positive integer.

Acceptance Number (c)

Enter a value for the number of acceptable defective items.  Enter a positive integer.

Each quality characteristic inspected is an attribute, and each unit in the sample is judged to be either conforming or nonconforming.  One or several attributes can be inspected in the same sample; generally, a unit that is nonconforming to specifications on one or more attributes is said to be a defective unit.  The procedure is called a single-sampling plan because the lot is sentenced based on the information contained in one sample of size n.


Create AOQL

Creates an AOQL Plan whose objective is to assure average outgoing quality levels.  Attribute procedures include AOQL System and Dodge-Romig plans.


Create LTPD Plan

Creates a Lot Tolerance Percent Defective (LTPD) plan, whose objective is to assure quality no worse than a specified target.  Attribute procedures include LTPD plans and Dodge-Romig plans.


Process Sigmas

Indicates whether you already know the process sigma or whether you will estimate sigma using the sample standard deviation.

Assume Known Value

Indicates that you already know the process standard deviation.

Use Sample Estimate

Indicates that you plan to estimate the process standard deviation using the sample standard deviation.  This option creates a larger sample size than the Assume Known Value option.


Action

Determines the type of sampling plan that will be created; or analyzes an existing plan.

Create OC Plan

Creates an OC (Operating Characteristic) Plan whose objective is to assure quality levels for consumer/producer.  Allows you to select a plan for a specific OC curve.

Create AOQL

Creates an AOQL (Average Outgoing Quality Limit) plan whose objective is to maintain quality at a target.

Create LTPD Plan

Creates an LTPD (Lot Tolerance Percent Defective) plan, whose objective is to assure quality no worse than a specified target.

Analyze Existing Plan

Analyzes a sampling plan that was previously created, and currently exists.


Saving Designs

After you create a design, you must name and save it permanently to the hard disk or to a diskette.  STATGRAPHICS Plus saves experimental design files as *.sfx files.

To Save Experimental Designs

1.	Choose FILE... SAVE AS... SAVE DESIGN FILE AS... from the Menu bar to display the Save Design As dialog box.

2.	Type the name for the title of the experimental design and click OK.  The program adds the *.sfx extension, saves the file, and displays the Data icon in a Taskbar at the bottom of the Application window.

After the file is saved, the design remains open so you can continue working; the new file name appears on the title bar.


Method

Determines the algorithm that will be used in the optimization.

Forward

Selects candidates using a forward selection algorithm.

Backward

Selects candidates using a backward selection algorithm.

Exchange at End

Uses an exchange algorithm after you choose the initial set of runs.


Maximum Order Effect

Enter the maximum order effect that will be used in the model.  Effect is the change in the average of the responses between two factor-level combinations or two experimental settings.  For a two-level factor, the effect of the factor is the average response at the high level of the factor, minus the average of the response at the low level of the factor.  Enter an integer between 1 and 3; the default is 2.


Ignore Block Numbers

Indicates if the program will ignore block numbers when it optimizes the design.  Click the check box if you want the block numbers ignored; de-select it if not.


Confounding Pattern

Determines how the program will decide the confounding pattern in the design.  Confounding is confusing two or more factors so you cannot separate their effects.  Also called aliasing.

From Original Design

From Data


Start Row

Enter the number of row in the DataSheet that will be used to start the Worksheet.

By default, STATGRAPHICS Plus generates a worksheet for either the number of runs in the design, or for large designs, the first 128 runs in the design.  Our suggested approach to generating worksheets for large designs is to put together a series of worksheet in groups of 128 (1-128, 129-256, 257-384, etc.) by setting the Start Row and End Row values accordingly.


End Row

Enter the number of the row in the DataSheet that will be used to end the Worksheet.

By default, STATGRAPHICS Plus generates a worksheet for either the number of runs in the design, or for large designs, the first 128 runs in the design.  Our suggested approach to generating worksheets for large designs is to put together a series of worksheet in groups of 128 (1-128, 129-256, 257-384, etc.) by setting the Start Row and End Row values accordingly.


Type of Optimization

Determines the optimization criteria.

Maximize

Maximizes the response variable; this option is the default.

Minimize

Minimizes the response variable.

Maintain at

Maintains the response variable at the value you enter into the text box.


Additional Starting Points

Determines the starting location(s) for the optimization process.

Best Design Point

Makes the best design point available as a starting point for the optimization process.  By default, this option is chosen.

All Design Points

Makes all the design points available as starting points for the optimization process.

Best Vertex

Makes the best vertex from the design available as a starting point for the optimization process.

All Vertices

Makes all the vertices from the design available as starting points for the optimization process.


Low

Enter a numeric value for the minimum constraint for the factor.


High

Enter a numeric value for the maximum constraint for the factor.


Start

Enter a starting value for the factor.


Runs

Displays the total number of runs (experimental trials) necessary to complete the base design.


Error d.f.

Displays the degrees of freedom available for the error if you run the base experiments.  Error degrees of freedom are necessary for testing the significance of factor effects using confidence intervals, ANOVA, and the Standardized Pareto Chart.  You can increase the error degrees of freedom by replicating the design.


Replicate Design

Determines if the design will be replicated.  If you replicate, the number of runs and the degrees of freedom available for error are updated.

Note:  In some designs, each replicate design is placed in its own block.

Number

Enter the number of times the design will be repeated.  Enter a positive integer; the default is 0.


Randomize

Indicates if the runs will be created in random order.  The program prints the Worksheet and stores the responses in that same order.  Randomized is the default.

In a blocked design, the order of the blocks as well as the order of runs within each block is randomized.


Number of Control Factors

Enter the number of control factors that will be used in the experiment.  Enter any integer from 2 to 16; the default is 3.

The total number of factors (Control Factors plus Noise Factors) cannot exceed 16.  For example, if you enter 16 into the Control Factor text box, you cannot enter any value other than 0 in the Noise Factor text box.


Number of Noise Factors

Enter the number of noise factors that will be used in the experiment.  Enter any integer from 0 to 14; the default is 0.

The total number of factors (Control Factors plus Noise Factors) cannot exceed 16.  For example, if you enter 16 into the Control Factor text box, you cannot enter any value other than 0 in the Noise Factor text box.


Control Design (Inner Array)

Determines which of the family of orthogonal arrays will be used for the control design.  Chose one orthogonal array.


Noise Design (Outer Array)

Determines which of the family of orthogonal arrays will be used for the noise design.  Choose one orthogonal array.


Randomize

Indicates if the runs will be randomized.  If the check box is marked, the runs will be randomized; if it is not marked, the runs will not be randomized.


Column Design (Inner Array)

Determines the column assignment for each factor in the Inner Array.


Factor

Displays the letter that identifies the factor.


Column

Enter the number that determines the column assignment for the factor.  Enter a positive integer.


Noise Design (Outer Array)

Determines the column assignment for each factor in the Outer Array.


Labels...

Displays the Factor Levels dialog box, which you use to enter a value for each factor level.


Data

Enter the name of the variable that contains the response data you want to analyze.  You can use only response variables, not factor names or blocking variables.


Performance Measure

Determines the performance measure that will be analyzed.

Mean

Analyzes the mean response for each run in the inner array.  Use this option to isolate location effects when they are confounded with dispersion effects.

Log Variance

Analyzes the log variance of the response variable.  Use this option to isolate dispersion effects when they are confounded with location effects.

Signal-to-Noise Ratio (-10 log s^2)

Analyzes the signal-to-noise ratio (-10 log s^2) when response values can be negative as well as positive.

Signal-to-Noise Ratio (Target Value)

Analyzes the signal-to-noise ratio, where the objective is to minimize the variability around a target.

Signal-to-Noise Ratio (Larger the Better)

Analyzes the signal-to-noise ratio, where the objective is to maximize the response variable.

Signal-to-Noise Ratio (Smaller the Better)

Analyzes the signal-to-noise ratio, where the objective is to minimize the response variable.

Noise Factors

Analyzes the factors in the outer array.

Crossed Array

Analyzes control and noise factors together.


Select

[Optional]  Select a subset of the response variable.  For example, to analyze the first 50 values of a variable, enter first (50) into this text box.


From Original Design

Uses the original base design to determine the confounding pattern.


From Data

Looks at all the current experimental runs to determine the confounding pattern.


Blocks

Displays the number of blocks in the design.

Blocking is a technique that increases the precision of an experiment.  A block is a portion of experimental material that should be more homogeneous than the entire set of material.  Blocking involves making comparisons in each block among common conditions in the experiment.  Blocking is often necessary to remove the effects of different batches of material, different experimenters, or experiments run on different days.


Design Type

Determines the type of available designs that will be used in the experiment.  The designs include:

Completely Randomized (No Blocking)

Randomized Block (1 Blocking Factor)

Combinatonic BIB (1 Blocking Factor)

Small BIB (1 Blocking Factor)

Latin Square (2 Blocking Factors)

Graeco-Latin Square (3 Blocking Factors)

Hyper-Graeco-Latin Square (4 Blocking Factors)


Number of Blocks

Enter the number of blocks that will be used.  This option is activated when you choose Randomized Block in the Design Type options section of the dialog box.  The default is 1.


Block Size

Enter the size of the block that will be created.  This option is activated when you choose Combinatonic BIB or Small BIB options in the Design Type options section of the dialog box.  The default is 2.


Number of Components

Enter the number of components that will be used in the experiment.  Enter an integer from 2 to 12; the default is 3.


Responses

Enter the names of two or more response variables from the current experimental file.


Response

Lists the names of the response variables.


Low

Enter a numeric value for the lowest value of the response variable.  The default is the minimum value in the current experiment file.


High

Enter a numeric value for the highest value of the response variable.  The default is the maximum value in the current experiment file.


Max/Min/Hit

Choose one of the options to Maximize (Max), Minimize (Min), or Hit a target for the response variable.


Target

Enter a numeric value for the target of the response variable.  This option is available only when you choose the Hit option.


Weights

Enter a numeric value to specify weights for the response variable.  Enter a value between 0.1 and 10; the default is 1.


Impact

Enter a numeric value for the impact.  Enter a number between 1 and 5.


[Factors]

Indicates the factors that will be plotted on the Square, Cube, Contour, or Surface plots.  The Square, Contour, and Surface plots require two factors; the Cube Plot requires three.  You can also enter values into the Hold text boxes for the factors you do not choose.


Low

Enter a value for the lowest level for the factor you want to use on the Response Plot.  Enter a number less than the value you enter into the High text box.


High

Enter a value for the highest level for the factor you want to use on the Response Plot.  Enter a number higher than the value you enter into the Low text box.


Hold

Enter a value at which the factors that were not chosen for the plot will be held.


Data Source

Determines the data source that will be used.

SG Plus DataSheet

Links data to a DataSheet.  To check to see if the link was made, use StatLinks to display the Status message box.

File

Displays the Open Data File dialog box so you can choose the file you want to use.

ODBC Query

Displays the Select Data Source dialog box.  Use the dialog box to choose the data source that describes the driver you want to connect to.  You can use any data source that refers to an ODBC driver that is installed on your computer.

Clipboard

Displays the Read Clipboard dialog box that lets you indicate if the variable names will be from the first row of data of if defaults should be created by the program.

Demo

Generates a single column of random numbers.


Duration between Updates

Sets the duration of time between polling updates.  Enter a number in the text box to indicate the duration of time that will be used: Seconds, Minutes, or Hours.


Arrangement

Adds additional splitter windows to the StatGallery window or arranges the placement of the splitter windows within the StatGallery window.

Two by Two

Arranges the StatGallery window into four equally sized panes; two on the top and two on the bottom.  This option is the default.

Top and Bottom

Arranges the StatGallery window into two equally sized, horizontal panes; one on the top and one on the bottom.

Left and Right

Arranges the StatGallery window into two equally sized, side-by-side panes.

Two Left, One Right

Arranges the StatGallery window into two equally sized, top and bottom panes on the left and one pane on the right.

One Left, Two Right

Arranges the StatGallery window into two equally sized, top and bottom panes on the right and one pane on the left.  The arrangement is the opposite of Two Left, One Right.

Three by Three

Arranges the StatGallery window into nine equally sized panes.

One Position Only

Arranges the StatGallery window into nine different sized panes within the columns of the window.


By Columns

Arranges the StatGallery window into different sized panes within the columns of the window.

The Rows text boxes let you change the number of panes that will be displayed within each column.  For example, if you enter 3 for Column 1, 2 for Column 2, and 1 for Column 3, the StatGallery window will contain Top, Middle, and Bottom panes in Column 1; Top and Bottom panes in Column 2; and a One Position Only pane in Column 3.


Null Hypothesis

Enter a value for the null hypothesis mean, which is used to determine if it can be reasonably assumed that the true population mean is equal to a given value.  The default is 0.


Alternative Hypothesis

Determines the type of alternative hypothesis test that will be used.

Not Equal

Performs a two-tailed test, which tests the null hypothesis that two sample means are equal versus the alternative hypothesis that the two sample means are unequal.  This option is the default.

Less Than

Performs a one-tailed test, which tests the null hypothesis that two sample means are equal versus the alternative hypothesis that Sample 1 is less than Sample 2.

Greater Than

Performs a one-tailed test, which tests the null hypothesis that the two sample means are equal versus the alternative hypothesis that Sample 1 is greater than Sample 2.


Assume Equal Sigmas

Determines if the variance of the two samples is assumed to be equal.  Assumed to be equal is the default.


Action

Determines the action the program will take when you are overlaying graphs.

Replace

Replaces the graph, but does not overlay it.

Overlay

Places the graph on top of the current graph, creating an overlay.  This option is the default.


Decimal Places for Indices

Enter a value for the number of decimal places that will be used in the indices.


Box-Cox Transformation Shift

One of the two parameters of the Box-Cox Transformation, namely its shift.


Box-Cox Transformation Power

One of the two parameters of the Box-Cox Transformation, namely its exponent.


Publish StatFolio

Publishes a StatFolio to a web site for access by web browsers. Output from all analyses, the comments window, the StatGallery, and the StatReporter is saved in HTML format on a local disk or Internet server. Tables and graphs are saved as JPEG files, PNG files, or interactive Java applets. Sites may be configured to update automatically at periodic intervals.

HTML file on local directory: the table of contents page for the publication, with full path. Example: c:\data\mystatfolio.htm

FTP site URL: the web address for the published files, if any.  To upload files to this site, it must contain a valid FTP server.  Example: www.mywebsite.com

FTP username: for secure Internet sites.

FTP password: for secure access.

Include: the STATGRAPHICS StatFolio components to be published, namely the Analyses, Comments, StatGallery, StatReporter, and the data sheet.  (To view the data sheet, a browser must support Java applets).

Graph width in pixels: the width of published graphs.

Graph height in pixels: the height of published graphs.

Image Format: the format in which graphs are saved. JPEG and PNG are common formats supported by most browsers.  If Java applets are selected, the tables and graphs will be updated from within the browser at the interval specified; otherwise, they will be loaded by the browser only once.  Adding interactivity to an applet allows the viewer to click on points while in the browser to identify their location.

NOTE: to view published pages containing Java applets, users must have Java enabled within their browsers.  If you do not need to use the special features which Java provides, choose the JPEG or PNG format instead, since your pages will load faster and be viewable by any browser.


StatFolio Start-Up Script

The StatFolio Start-Up Script allows you to define a script that will be run whenever the current StatFolio is loaded, either manually through the File menu or on program startup via the command line.  You can also execute the script at any time by pressing the F10 key after the StatFolio is loaded.

Any of six operations may be specified:

Execute – runs the specified analysis.  Select from a list of the analyses contained in the StatFolio.

Assign – assigns the specified STATGRAPHICS expression to a target column of the data file, which may or may not exist. If the column exists, its are replaced.  Otherwise, a new column is created.

Print – prints the specified item, which may be “All Analyses”, “StatReporter”, “StatGallery”, “Data File”, “StatFolio Comments”, or a specified analysis. The current default print settings are used (no dialog box is displayed).

Publish – publishes the StatFolio to the last location used by StatPublish. An error message is displayed if the StatFolio has never been published.

Shell – instructs Windows to execute the specified command line.

Exit – causes STATGRAPHICS to terminate. This command is ignored except when  loading the StatFolio from the Windows Document menu or via a command line.


Using SnapStats

Contains one-step analyses for many commonly encountered data analysis problems. The output is specially formatted to create one printed page containing both tabular and graphical output. These procedures are designed to produce quick, standardized output and thus have more limited options than the corresponding analyses found under other sections of the main menu.


Publishing

Publishes a StatFolio to a web site for access by web browsers. Output from all analyses, the comments window, the StatGallery, and the StatReporter is saved in HTML format on a local disk or Internet server. Tables and graphs are saved as JPEG files, PNG files, or interactive Java applets. Sites may be configured to update automatically at periodic intervals.


Data Input (Matrix Plot)

The Matrix Plot analysis produces a matrix of two-variable scatterplots for a set of numeric variables.  It also displays box-and-whisker plots for each variable.

To run the analysis, specify two or more numeric data variables.

Data

Select


Analysis Options (Outlier Identification)

Specify options for the analysis:

Confidence Level: a value such as 90, 95, or 99 for the standard and Winsorized confidence intervals.

Trimming: the percentage of data values to be trimmed for each end of the data when computing the trimmed and Winsorized statistics.  The default value of 15% removes the smallest 15% and largest 15% of the data values.

Display on Either Side: specifies how many values are displayed in the list of sorted data values. The default of 5 requests that the 5 smallest and the 5 largest values be included in the table.


Tabular Options Dialog Box (Matrix Plot)

Allows you to select tabular options for the Matrix Plot.

Analysis Summary (Matrix Plot)


Graphical Options Dialog Box (Matrix Plot)

Allows you to select graphical options for the Matrix Plot

Scatterplot Matrix (Matrix Plot)


Analysis Summary (Matrix Plot)

The Analysis Summary lists the variables used in the Matrix Plot.


Outlier Plot (Outlier Identification)

The Outlier Plot shows the data values together with lines at the sample mean plus and minus 1, 2, 3, and 4 times the sample standard deviation.

You may exclude observations from the analysis by clicking on them on this plot and then pressing the +/- button on the analysis toolbar.


Scatterplot Matrix (Matrix Plot)

The Scatterplot Matrix consists of all pairwise scatterplots of the variables, including all of their respective transposed plots. For example, the first row of the matrix contains plots of the first variable specified on the data input dialog box on the Y axis versus each of the other variables on the X axis. The first column of the matrix contains plots of the first variable on the X axis versus each of the other variables on the Y axis.

The main diagonal shows Box-and-Whisker plots for each of the variables.  Use Pane Options to change the style of these plots.


Data Input (Outlier Identification)

The Outlier Identification analysis allows you to detect unusual observations  in a numeric variable. The procedures included expose outliers and quantify the extent of the evidence against their validity. They also provide estimates of common parameters, such as the mean and standard deviation, which are designed to be resistant to the potential presence of such outliers.

To run the analysis, specify a single numeric data variable.

Data

Select

Sort


Tabular Options Dialog Box (Outlier Identification)

Allows you to select tabular options for the Outlier Identification Analysis.

Analysis Summary (Outlier Identification)

Summary Statistics

Tests for Normality


Graphical Options Dialog Box (Outlier Identification)

Allows you to select graphical options for the Outlier Identification Analysis

Outlier Plot (Outlier Identification)

Box-and-Whisker Plot

Normal Probability Plot


Analysis Summary (Outlier Identification)

The Analysis Summary Table displays several statistics and tests:

The number of data values included in the analysis and their range.

•	The number of data values excluded from the analysis, if any.  You can exclude values by maximizing the Outlier Plot, clicking on points to be removed, and then pressing the +/- button on the analysis toolbar.

•	Several estimates of the central location of the data, including the usual sample mean, the sample median, the trimmed mean (which excluded a fixed percentage of the smallest and largest data values), and a Winsorized mean (which replaces a fixed percentage of the smallest and largest data values with a more interior value).  Use Analysis Options to specify the percentage used by the last two estimators.

•	Several estimates of the spread or scale of the data, including the usual sample standard deviation, an estimate based on the MAD (median absolute deviation), an estimator based on the biweight estimator of location (Sbi), and a Winsorized standard deviation (which replaces a fixed percentage of the smallest and largest data values with a more interior value).  Use Analysis Options to specify the percentage used by the last estimator.

•	Confidence intervals for the mean, based on both the usual method and using the Winsorized mean and sigma.

•	A table of sorted values. The table includes Studentized values (Xi-Xbar)/s where Xbar and s are estimated with and without each individual data value. It also includes a modified z-score based on the median absolute deviation. (The StatAdvisor notes any modified z-scores which exceed 3.5 in absolute value, which are typically considered to be very unusual)  Use Analysis Options to specify how many data values should be displayed in this list.

•	The results of Grubb’s test for a single outlier (if n>2) and several of Dixon’s tests for 1 or 2 outliers (if n is between 4 and 30).  Small P-values (below 0.05 if operating at 95% confidence) for any of these tests indicates the presence of a significant outlier in the data.


Save Results Options (Outlier Identification)

The Save Results Dialog Box allows you to save calculated statistics. There are five selections:

Trimmed Data – the original data with any excluded values removed.

Select Flags - set to 0 for any excluded data value and 1 for any value not excluded. Intended to be used in the Select field on data input dialog boxes.

Studentized Values (No Deletion) – Studentized values based on the sample mean and standard deviation of all non-excluded data values.

Studentized Values (With Deletion) – Studentized values based on the sample mean and standard deviation of all non-excluded data values other than the current data value.

Modified Z-Scores – Z-scores based on the Median Absolute Deviation.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values generated during the analysis. You can enter new names or accept the defaults.

Note: To access the Save Results Options dialog box, click on the Save Results Options on the Analysis Toolbar (the fourth button from the left)


Data Input (Factor Means Plot)

The Factor Means Plot displays the main effects and interactions for one or more factors in a designed experiment.  It displays means plots (on the diagonal) and interaction plots (off the diagonal) for each of the factors specified, similar to that generated by a multifactor analysis of variance.

The input fields are:

Dependent variable: the name of the variable containing response values.

Factors: the names of one or more variables containing the levels of more predictive factors at which the response values are to be analyzed.

See also

Dependent Variable

Select

Sort

Quantitative Factors

Categorical Factors


Tabular Options Dialog Box (Factor Means Plot)

Allows you to select tabular options for the Factor Means Plot Analysis.

Analysis Summary

Means Table


Graphical Options Dialog Box (Factor Means Plot)

Allows you to select graphical options for the Factor Means Plot Analysis.

Means Plot


Analysis Summary (Factor Means Plot)

The Analysis Summary displays the name of the dependent variables, the names of the factors, and the number of complete cases in the plot.


Means Table (Factor Means Plot)

The Means Table shows means and counts at each factor level and pair of levels.


Means Plot (Factor Means Plot)

The Means Plot shows the means at different combinations and levels of the factors. The plots on the diagonals show the overall level means, and the off-diagonal plots show the means for all pairs of factor levels.

In each row, there is a line connecting all means corresponding to the same level of the factor which defines that row.

In contrast to the Multifactor ANOVA, this procedure plots unadjusted means, not least squares means.


Skewness and Kurtosis Plot (Box-Cox Transformations)

The Skewness and Kurtosis Plot Option creates a plot that shows the values for the standardized skewness and standardized kurtosis at various values of lambda1. A vertical line is drawn at the optimal value; horizontal lines are drawn at 0 and +/-2.

Values of lambda1 which correspond to standardized skewness and standardized kurtosis values both with the range of –2 to +2 are yield transformations for which the residuals are approximately normally distributed.

Use the Pane Options dialog box to choose options for the plot.


Data Input (Gage Linearity and Accuracy)

The Gage Linearity and Accuracy Analysis is designed to study the bias in a measurement process.  It estimates the linearity  of the process, which is the difference in the bias of the measurements over the expected operating range. This is a standard technique in Measurement Systems Analysis, in which repeated measurements are made on a selection of items with known characteristics. To execute this analysis, construct a file containing one row for each measurement made on each item.  The columns in the file should contain:

Part Numbers: the name of a column containing item or part identifiers.

Measurements: the name of a column containing the measurements.

Reference Values: the true value of the characteristic being measured.

You may also enter:

Process Variation: the assumed value for 5.15 times the process sigma, typically obtained from a Gage R&R study.


Tabular Options Dialog Box (Gage Linearity and Accuracy)

Allows you to select tabular options for the Gage Linearity and Accuracy Analysis.

Analysis Summary (Gage Linearity and Accuracy)


Graphical Options Dialog Box (Gage Linearity and Accuracy)

Allows you to select graphical options for the Gage Linearity and Accuracy Analysis.

Fitted Model Plot (Gage Linearity and Accuracy)

Linearity Plot (Gage Linearity and Accuracy)

Barchart


Analysis Summary (Gage Linearity and Accuracy)

The Analysis Summary shows the input variables, the specified Process Variation (if any), and summaries of the estimated accuracy of the gage. It includes:

1. 	Bias model - the equation of the fitted model relating bias to the reference values x.

2. 	Linearity - a measure of the linearity of the gage, which is computed by

linearity = slope * process sigma

3. 	The percentage of linearity, which is related to the slope of the regression line by

% linearity = 100 * slope

 A lower slope (closer to 0) implies better gage linearity.

4. 	R-squared - measures the correlation between the average measurement for each part and the reference values.

5. 	Bias - average bias of the gage, i.e., the average difference between the mean measurement for each part and its reference value.  Lower values of bias (closer to 0) imply better gage linearity.

6. 	The percentage of bias, calculated by

% bias = 100 * bias / process variation

The linearity and percent bias are only computed if the process variation is entered.


Fitted Model Plot (Gage Linearity and Accuracy)

The Fitted Model Plot graphical option plots the individual measurements (squares), the average measurement for each item (circles), and the fitted regression line.


Linearity Plot (Gage Linearity and Accuracy)

The Linearity Plot graphical option plots the average bias for each item (circles), and the fitted regression line.


Barchart (Gage Linearity and Accuracy)

The Barchart graphical option displays the percent linearity and percent bias. It is only available if the process variation has been entered on the data input dialog box.


Data Input (Multi-Vari Charts)

A Multi-Vari Chart is designed to display multiple sources of variability in a way which enables the analyst to identify easily which factors are the most important.

The required fields consist of the dependent variable and up to four categorical factors.


Tabular Options Dialog Box (Multi-Vari Charts)

Allows you to select tabular options for the Multi-Vari Charts Analysis.

Analysis Summary (Multi-Vari Charts)


Graphical Options Dialog Box (Multi-Vari Charts)

Allows you to select graphical options for the Multi-Vari Charts Analysis.

Multi-Vari Plot (Multi-Vari Charts)


Analysis Summary (Multi-Vari Charts)

The Analysis Summary displays the name of the dependent variable used in the analysis, as well as all the independent factors, and the total number of complete cases.


Multi-Vari Plot (Multi-Vari Charts)

The Multi-Vari Plot displays the mean levels of the dependent variable at various combinations of the independent factors, and can help visualize the contribution of each factor to the overall variability.


Tabular Options Dialog Box (Automatic Forecasting)

Allows you to select tabular options for the Automatic Forecasting Analysis.

Analysis Summary (Automatic Forecasting)

Model Comparisons (Automatic Forecasting Analysis)

See also

Residual Autocorrelations

Residual Partial Autocorrelations

Residual Periodogram Table

Residual Tests for Randomness


Graphical Options Dialog Box (Automatic Forecasting)

Allows you to select graphical options for the Automatic Forecasting Analysis.

Time Sequence Plot

Forecast Plot

Residual Plots

Residual Autocorrelation Function

Residual Partial Autocorrelation Function

Residual Periodogram

Residual Crosscorrelation Function


Analysis Summary (Automatic Forecasting)

The Analysis Summary shows information about the selected forecasting model.  It shows:

Data variable: the name of the variable for which forecasts have been generated.

Forecast model selected: the model selected as the best for the input time series.  This model was selected from amongst those specified on the Analysis Options dialog box.

Statistics: the root mean squared error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), mean error (ME), and mean percentage error (MPE). These statistics are computed from the one-ahead  forecast errors, which are the errors made in forecasting the observation at time t from time t-1. If some time periods were withheld from the fit for validation purposes, the statistics are computed for both the observations used to estimate the model and those withheld for validation.


Analysis Options (Automatic Forecasting)

The Analysis Options Dialog Box allows you to choose:

Models Included: which models should be included as candidates when searching for the best forecasts.  In the case of the ARMA models, ARMA(p,p-1) models will be fit up to the maximum order p specified.

Information Criterion: which criterion should be used to choose between the different models.  Each of the selections is based upon a penalized likelihood function, where a higher penalty is assessed for models with more unknown coefficients. AIC is the default.

Transformation: the type of transformation to be performed on the data before the models are fit. If Box-Cox is selected, the program will find the optimal power transformation given the addend specified.

NOTE: if a large number of models are selected, the model selection procedure may be very time-consuming, particularly if the Box-Cox transformation is chosen.


SnapStats General Tab

The SnapStats General Tab lets you select the confidence level at which SnapStats intervals and tests are constructed, and the number of significant digits for displaying numeric results.


SnapStats Box Plot Tab

The SnapStats Box Plot Tab lets you select whether you want the box plot to be displayed vertically or horizontally, and whether you want a mean marker, a median notch, and outlier symbols.

Note: these settings specify default values for all box-and-whisker plots throughout the system, not just in the SnapStats.


SnapStats Prob Plot Tab

The SnapStats Prob Plot tab allows you to select whether you want percentage on probability plots to be displayed along the horizontal or vertical axis, whether the plot should contain a fitted line, and if so, whether the line should be computed using Least Squares or based on the sample Quartiles and median.

Note: these settings specify default values for all probability plots throughout the system, not just in the SnapStats.


SnapStats Control Charts Tab

The SnapStats Control Charts tab lets you select between a range (R) chart and a sigma (S) chart, the type of smoother if any to include on the charts, how many subgroups to display, and whether or not to display warning limits.  These options correspond to those available in the control charts under the Special, Quality Control menu.


SnapStats Gage R&R Tab

The SnapStats Gage R&R tab lets you select the method used to perform a gage repeatability and reproducibility analysis: either the Average and Range method, the ANOVA method with an operator-by-part interaction, or the ANOVA method without that interaction.

It also allows you to specify the terminology to be used on all output to label the appraisers, samples, and trials.  Note: these settings specify default values for all gage R&R analyses, not just in the SnapStats.


SnapStats Forecasting Tab

The SnapStats Forecasting tab lets you select options for the Automatic Forecasting SnapStat, including:

Forecast Limits - the percentage confidence for the forecast limits.

Models - the type of models to be considered.  You may fit Trend models (mean, linear, quadratic and S-curve), Smoothing models (moving average and various exponential smoothers), and ARMA models (stepwise fit of ARMA(p,p-1) models up to the maximum order specified).

Information Criterion - which criterion should be used to choose between the different models.  Each of the selections is based upon a penalized likelihood function, where a higher penalty is assessed for models with more unknown coefficients. AIC is the default.

Transformation - the type of transformation to be performed on the data before the models are fit. If Box-Cox is selected, the program will find the optimal power transformation given the addend specified.

NOTE: if a large number of models are selected, the model selection procedure may be very time-consuming, particularly if the Box-Cox transformation is chosen.


SnapStats Comparisons Tab

The SnapStats Comparisons tab lets you select the type of Intervals to be displayed by the Multiple Comparisons SnapStat: none, Standard Errors (Pooled s or Individual s), Confidence Intervals (Pooled s or Individual s), LSD Intervals, Tukey HSD Intervals, Scheffe Intervals or Bonferroni Intervals.

You also choose the type of Variance Check to be conducted: Cochran’s, Bartlett’s, Hartley’s, or Levene’s.


SnapStats Curve Fit Tab

The SnapStats Curve Fit tab lets you choose whether to include Confidence Limits and/or Prediction Limits on the plot, and whether to plot Ordinary or Studentized Residuals.


Data Input (SnapStats One Variable Analysis)

The One-Variable Analysis SnapStats analyzes the data in a single numeric variable.

Specify the name of the numeric variable containing the data.

Data

Select

Sort

Delete...

Transform...

To select options for the analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left mouse button on either Pane Options or Analysis Options.


Analysis Summary (SnapStats One-Sample Analysis)

The Analysis Summary displays various summaries of the input data, including:

Summary Statistics – statistics computed from the data.

Histogram – shows the number of observations in non-overlapping intervals.

Box-and-Whisker Plot – a five-number summary of the data with an indication of unusual or outside points.

Confidence Intervals - for the mean and for the standard deviation, assuming that the data are a random sample from a normal distribution.

Diagnostics – Shapiro-Wilks P-value (small values indicate non-normal data) and the lag 1 autocorrelation (large absolute values indicate serially correlated data).

Time Sequence Plot – plot of data values versus row number.

Normal Probability Plot – data from a normal distribution should fall close to a straight line.

For additional information, see One Variable Analysis.


Data Input (SnapStats Two Sample Comparison)

This SnapStat allows you to compare the data values in two independent samples.

The data may be input in either of two ways:

Two Data Columns – specify the names of two columns, one containing each sample.

Data and Code Column – specify the name of the column containing the data values from both samples and the name of a second column containing two unique codes which specify which sample each value belongs to.

The titles of the first two text boxes on this dialog box differ, depending on how you want to enter the data (see Input Options on the dialog box).  If you decide to use data as Two Data Columns (the first option, and the default), the titles are: Sample 1 and Sample 2.  If you decide to use Data and Code Columns (the second option), the titles are: Data and Sample Code.

Sample 1 (Two Data Columns)

Sample 2 (Two Data Columns)

Sample Code (Data and Code Columns)

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Data (Data and Code Columns)

Input

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Analysis Summary (SnapStats Two Sample Comparison)

The Analysis Summary displays various components of a Two Sample Comparison analysis, including:

Summary Statistics – summaries of each sample.

Bihistogram - a double histogram showing the distribution of each sample.

Box-and-Whisker Plot – a five-number summary of each sample with an indication of unusual or outside points.

Confidence Intervals - for the difference of means and ratio of standard deviations, assuming that the data are random samples from normal distributions.

Diagnostics – Shapiro-Wilks P-values (small values indicate non-normal data) and the lag 1 autocorrelations (large absolute values indicate serially correlated data).

Quantile Plot – shows the proportion of data values in each sample which are less than X as a function of X.

Normal Probability Plot – data from a normal distribution should fall close to a straight line.  The slopes of the lines are related to their standard deviations.

For additional information, see the Two-Sample Comparison Analysis.


Data Input (SnapStats Paired Sample Comparison)

The Paired-Sample Comparison analysis is appropriate to use for comparing two sets of data when the observations in the samples are paired.

For example, suppose you are analyzing data that contain information about the miles per gallon ratings achieved by the same automobile during highway driving and city driving.  The data represent two different sets of values for each automobile:  miles per gallon ratings for highway driving and miles per gallon ratings for city driving.

When data are from paired samples, you analyze it by calculating the difference between the values in each pair of observations.  That is, you treat the paired differences as though they were a single sample from a population of differences.

To perform the analysis, enter the names of the two columns containing the paired samples.

Sample 1

Sample 2

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Analysis Summary (SnapStats Paired Sample Comparison)

The Analysis Summary displays various summaries of the input data, including

Summary Statistics – statistics computed from the paired differences.

Histogram – shows the number of paired differences in non-overlapping intervals.

Box-and-Whisker Plot – a five-number summary of the paired differences with an indication of unusual or outside points.

Confidence Intervals - for the mean and for the standard deviation of the paired differences, assuming that the data are a random sample from a normal distribution.

Comparison of Means – a test of the hypothesis that the mean difference equals 0.

Diagnostics – Shapiro-Wilks P-value (small values indicate non-normal data) and the lag 1 autocorrelation (large absolute values indicate serially correlated data).

Time Sequence Plot – plot of paired differences versus row number.

Normal Probability Plot – paired differences from a normal distribution should fall close to a straight line.

For additional information, see the Paired-Sample Comparison Analysis.


Data Input (SnapStats Multiple Sample Comparison)

This analysis allows you to compare several samples, each contained in a separate column.  Enter the names of the columns, which must all be numeric.


Analysis Summary (SnapStats Multiple Sample Comparison)

The Analysis Summary option displays various components of a Multiple-Sample Comparison, including:

Summary Statistics – the size, mean, and standard deviation of each sample.

Scatterplot – a plot of the data in each sample.

Multiple Box-and-Whisker Plot - a five-number summary of each sample with an indication of unusual or outside points.

ANOVA Table – a test of the hypothesis that the means of the populations from which the samples came are all equal.  A small P-value indicates significant differences amongst the means.

Variance Check - a test of the hypothesis that the standard deviations of the populations from which the samples came are all equal.  A small P-value indicates significant differences amongst the standard deviations.  Note: use the SnapStats options dialog box to select the desired test.

Means Plot – a plot of the sample means with uncertainty intervals. Note: use the SnapStats options dialog box to select the type of intervals.

Analysis of Means Plot – any means beyond the decision limits are significantly different from the grand mean.

For additional information, see the Multiple-Sample Comparison analysis.


Data Input (SnapStats Curve Fitting)

The Simple Regression Analysis estimates a linear or nonlinear regression between two variables.

The model relates one dependent variable to one independent variable by minimizing the sum of the squares of the residuals for the fitted line.  In addition to a straight line, you can also use the analysis to estimate a number of standard nonlinear models

To execute the analysis, you specify the names of the columns containing the dependent (Y) variable and the independent (X) variable.  Both variables must be numeric.

Y (Dependent Variable)

X (Independent Variable)

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Analysis Summary (SnapStats Curve Fitting)

The Analysis Summary displays various components of the Simple Regression Analysis:

Estimated model – the equation of the fitted regression model. Also displayed are standard errors for the estimated coefficients, t-tests of the hypothesis that the coefficients equal 0, and other summary statistics.

Plot of Fitted Model – the fitted model with optional confidence limits and prediction limits.   Note: use the SnapStats Options dialog box to select the desired test.

Residual Plot – a plot of the residuals versus the values of the independent variable.  Note: use the SnapStats Options dialog box to select the type of residuals to be plotted.

Observed versus Predicted Plot – plot of the observed values of the dependent variable versus the values predicted by the fitted model.

Residual Plot – a plot of the residuals versus row number.  Note: use the SnapStats Options dialog box to select the type of residuals to be plotted.

For additional information, see the Simple Regression Analysis.


Data Input (SnapStats Capability Assessment (Individuals))

Process capability studies in STATGRAPHICS Plus estimate process capability for processes that generate data from one of eight distributions: Normal, Exponential, Extreme Value, Gamma, Laplace, Logistic, Lognormal, and Weibull.

To run the analysis, enter the name of the numeric variable containing a sample of data values from your process.  Then enter an upper specification limit, a lower specification limit, or both. You can also enter a nominal or target value.

Data

USL

Nominal

LSL

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See also

Using the Process Capability Analysis

Process Capability Options


Analysis Summary (SnapStats Capability Assessment (Individuals))
Analysis Summary (SnapStats Capability Assessment (Individuals)

The Analysis Summary displays the results of the analysis. It includes:

Sample statistics – the number of data values, sample mean, and sample standard deviation.

Data Beyond Spec. – the percent of observed data values beyond the specification limits.

Z-score – for a normal distribution, the number of standard deviations from the sample mean to the specification limits.  For other distributions, an equivalent measure based on the percentiles of the fitted distribution.

Long-Term Capability – the estimated long-term process standard deviation, long-term capability indices, and estimated defects per million opportunities (DPMO).

Short-Term Capability – the estimated short-term process standard deviation, computed from the moving range chart, short-term capability indices, and estimated defects per million opportunities (DPMO). Note: this is available only when fitting a normal distribution.

X Chart – a plot of the data values with control limits at plus and minus 3 times the short-term sigma.

Capability Histogram – a histogram of the data values with the fitted distribution.  The taller vertical lines show the specification limits, while the shorter vertical lines show the mean plus and minus 3 times the long-term sigma (or equivalent percentiles if not a normal distribution).

Range Chart – a moving range of 2.

Probability Plot – if the assumed distribution is correct, the data values should lie close to the line.

Tolerance Chart – a plot of the data values and the specification limits.

Use Analysis Options to select the distribution for the data.

For additional information, see the Process Capability Analysis.


Data Input (SnapStats Capability Assessment (Grouped Data))

Process capability studies in STATGRAPHICS Plus estimate process capability for processes that generate data from one of eight distributions: Normal, Exponential, Extreme Value, Gamma, Laplace, Logistic, Lognormal, and Weibull.

To run the analysis, enter the name of the numeric variable containing a sample of data values from your process.  Then enter an upper specification limit, a lower specification limit, or both. You can also enter a nominal or target value.

The Subgroup Numbers or Size lets you enter the size of the subgroups, or the column indicating the various sizes of the subgroups.

Data

USL

Nominal

LSL

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See also

Using the Process Capability Analysis

Process Capability Options


Analysis Summary (SnapStats Capability Assessment (Grouped Data))
Analysis Summary (SnapStats Capability Assessment (Grouped Data)

The Analysis Summary displays the results of the analysis. It includes:

Sample statistics – the number of data values, sample mean, sample standard deviation, and average subgroup size.

Data Beyond Spec. – the percent of observed data values beyond the specification limits.

Z-score – for a normal distribution, the number of standard deviations from the sample mean to the specification limits.  For other distributions, an equivalent measure based on the percentiles of the fitted distribution.

Long-Term Capability – the estimated long-term process standard deviation, long-term capability indices, and estimated defects per million opportunities (DPMO).

Short-Term Capability – the estimated short-term process standard deviation, computed from the moving range chart, short-term capability indices, and estimated defects per million opportunities (DPMO). Note: this is available only when fitting a normal distribution.

X-Bar Chart – a plot of the subgroup averages with control limits at plus and minus 3 times the short-term sigma.

Capability Histogram – a histogram of the data values with the fitted distribution.  The taller vertical lines show the specification limits, while the shorter vertical lines show the mean plus and minus 3 times the long-term sigma (or equivalent percentiles if not a normal distribution).

Range Chart – a chart of the subgroup ranges.

Probability Plot – if the assumed distribution is correct, the data values should lie close to the line.

Tolerance Chart – a plot of the data values and the specification limits.

Use Analysis Options to select the distribution for the data and the type of range chart to create.

For additional information, see the Process Capability Analysis and the X-Bar and R Chart Analysis.


Data Input (SnapStats Gage R&R)

This analysis performs a Gage Repeatability and Reproducibility Analysis.  The goal of the analysis is to quantify the magnitude of the error in a measurement process.

In a typical study, k appraisers measure each of m items n times. To analyze the results, create a data file with one row for every measurement made. Then enter:

Operators – the name of a column indicating which appraiser made each measurement.

Parts – the name of a column indicating which part was measured.

Trials – a column containing numbers from 1 to n indicating the number of each trial.

Measurements - the name of a column containing the measurements.

You can create a data sheet for a Gage R&R study by selecting Special, Quality Control, Gage R&R, Data Setup from the main menu.

Use SnapStats Options to change the terminology used for operators, parts, and trials.


Analysis Summary (SnapStats Gage R&R)

The Analysis Summary includes the following information.

Estimated Sigma – Displays values for the standard deviation associated with repeatability and reproducibility as well as the total measurement error(repeatability and reproducibility).  It also indicates an estimate of the standard deviation between the items or parts.

Estimated Variance – The squares of the estimated sigmas.

%R&R – The percentage of the total measurement error represented by each contribution.

5.15 Sigma – 5.15. times the estimated standard deviations.

% Contribution – The percentage of the total variance (including item-to-item variance) represented by each component.

% Tolerance – The percentage of the tolerance (distance between the high and low specification limits) represented by 5.15 times sigma. Use Analysis Options to enter a value for the tolerance.

The SnapStats also includes:

Gage Measurement by Operator – a plot of the average measurement made by each appraiser on each item.

R&R Plot by Operator – a plot of the deviations of the measurement from the grand average.

P/T Ratio – a display of the precision of the measurement process (5.15 sigma) versus the tolerance.  The triangle decomposes the total variance into measurement error and part-to-part variability.

Range Plot by Part – a range chart with a point for each appraiser-part combination.

Run Chart by Part  - a plot of the measurements grouped by operator and part.

For additional information, see the Gage R&R analyses.


Analysis Summary (SnapStats Automatic Forecasting)

Forecasting is based on fitting a model to past observations in a time series. Automatic Forecasting automatically selects the best model to use, by trying various classical forecasting models and stepwise fitting of ARMA(p,p-1) models.  It automatically selects the best model according to a selected information criterion.

The SnapStats displays:

RMSE, MAE, MAPE, ME, and MPE – statistics computed from the one-ahead forecasting errors, which are the errors made when forecasting each data value based on the information available at the previous time period.

Forecasts – forecasted values with lower and upper limits.

Time Series Plot – a plot of the forecasted data values with forecast limits.  Also displayed are the data and one-ahead forecasts.

Residual Autocorrelations – a plot of the estimated residual autocorrelations with 95% probability limits.  If the selected model fits the data well, no bar should extend beyond the limits.

Residual Plot – a plot of the residuals or one-ahead forecast errors.

Residual Periodogram – a periodogram of the residuals, which shows the frequency of any major periodicities left in the residuals.

Normal Probability Plot – if the residuals follow a normal distribution, the points should lie close to the line.

Use SnapStats Options to specify information about the models to be fit and other forecasting options.

For additional information, see the Automatic Forecasting Analysis or the Forecasting Analysis.


Percentiles (Logistic Regression)

The Percentiles tabular option displays a table of estimated percentiles based on the fitted model, with confidence limits. Percentiles indicate the value of the independent variable at which the estimated value of the dependent variable reaches specified percentages.


Residual Plot Options (Logistic Regression)
Residual Plot Options (Regression)

Allows you to select a residual plot and its options.

Plot (Residuals or Studentized Residuals)

Type (of Residual Plot)

Plot versus:

Direction

Fitted Line

Number of Lags

Confidence Level (for Probability Limits)


Data Input (Probit Analysis)

STATGRAPHICS Plus allows you to enter dichotomous response data in either of two forms:

1.	the dependent variable can consist of individual observations of either a 0 or a 1, representing the actual outcome for each individual case.

2.	the dependent variable can contain probabilities between 0 and 1 that are the proportions of successes for groups of observations, whose sizes can vary.

The independent or explanatory variables can be either categorical or continuous.

Dependent Variable

Sample Sizes

Quantitative Factors

Categorical Factors

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To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Probit Analysis

Probit Analysis Options

Goodness-of-Fit Options

Predictions Options

Plot of Fitted Model Options

Histogram Options

Residual Plots Options


Tabular Options Dialog Box (Probit Analysis)

Allows you to select tabular options for the Probit Analysis.

Analysis Summary (Probit Analysis)

Goodness-Of-Fit (Probit Analysis)

Confidence Intervals (Probit Analysis)

Correlation Matrix (Probit Analysis)

Predictions (Probit Analysis)

Unusual Residuals (Probit Analysis)

Percentiles (Probit Analysis)


Graphical Options Dialog Box (Probit Analysis)

Allows you to select graphical options for the Probit Analysis.

Plot of Fitted Model (Probit Analysis)

Probit Plot (Probit Analysis)

Observed versus Predicted (Probit Analysis) Observed versus Log Odds (Probit Analysis)

Prediction Capability (Probit Analysis)

Prediction Histogram (Probit Analysis)

Residual Plots (Probit Analysis)


Analysis Summary (Probit Analysis)

The Analysis Summary tabular option displays the results of fitting a linear probit regression model that describes the relationship between the dependent and independent variables. The results include estimates for each of the coefficients and approximate standard errors.

It also includes an Analysis of Deviance.  If the p-value for the model is less than 0.05, there is a statistically significant relationship among the variables at the 5% significance level. If the p-value for the residuals is greater than 0.05, it indicates that the model is not significantly worse than the best possible model for the data you are currently using at the 5% level.

If the model was fit using least squares, the results include: t-tests with associated p-values; an ANOVA table; summary statistics, such as R-squared; and the type III sums of squares for each of the factors.

If the model was fit using maximum likelihood, the results include an analysis of model deviance and the percentage of deviance the model accounts for. This value is similar to the R-squared statistic. The results also include values for the likelihood ratio tests for each of the factors.


Goodness-Of-Fit (Probit Analysis)

The Goodness-of-Fit tabular option displays a table that divides range of the data into intervals, each of which contains approximately the same number of observations.

The observed versus predicted True and False observations in each interval of the observed data are compared with those predicted by the model to determine if the function adequately fits the observed data. Small p-values indicate a significant lack of fit.


Confidence Intervals (Probit Analysis)

The Confidence Intervals tabular option calculates and displays confidence intervals for the coefficient estimates.


Correlation Matrix (Probit Analysis)

The Correlation Matrix option displays a table of the estimated Pearson correlations between the coefficients in the fitted model


Predictions (Probit Analysis)

The Predictions tabular option displays a summary of the prediction capability of the fitted model. The model is first used to predict the response, working with the information in each row of the file.

If the predicted value is larger than the cutoff value, the response is predicted to be true, else it is predicted to be false. Also shown is the percentage of observed data that were correctly predicted at various cutoff values. Using the cutoff value that maximizes the total percentage of correct predictions may provide a good value to use when additional individuals need to be predicted. Another approach is to predict “Success” for any observations with a predicted probability greater than 0.5.


Unusual Residuals (Probit Analysis)

The Unusual Residuals tabular option creates and displays the observations that have Pearson or Deviance residuals less than –2 or greater than 2. The corresponding row, observed dependent variable, residual, and standardized residual are also displayed.


Percentiles (Probit Analysis)

The Percentiles tabular option displays a table of estimated percentiles based on the fitted model, with confidence limits, corresponding to locations on the probit plot at which the upper and lower confidence bands cross the indicated percentage.


Plot of Fitted Model (Probit Analysis)

The Plot of Fitted Model graphical option displays a plot of the fitted model versus the independent variable you select. A curve is drawn over the range of X, and the fitted model is plotted with selected confidence limits. The data is also plotted if there is only one independent variable. The StatAdvisor shows the equation of the fitted model.


Probit Plot (Probit Analysis)

The Probit Plot graphical option displays a plot in which the vertical axis is converted to a probability scale in which the resulting plot is linear.


Observed versus Predicted (Probit Analysis)

The Observed versus Predicted graphical plot option displays a plot of the original data values plotted against the predicted values of the dependent variable. If the model fits well, the points should lie close to the line.


Observed versus Log Odds (Probit Analysis)

The Observed versus Log Odds Plot graphical option displays a plot of the values of Y versus the values of the log odds as predicted by the fitted model. The StatAdvisor displays the equation for the probit transformation. Use the plot to detect cases in which the variance is not constant or to determine if you need to transform the dependent variables.


Prediction Capability (Probit Analysis)

The Prediction Capability Plot graphical option of the Probit Analysis displays a plot that summarizes the prediction capability of the fitted probit model. It shows the percentage of correct predictions for all data values and for those which were True, or False.

The model is first utilized to first utilized to predict the response using the information in each row of the file. If a predicted value is larger than the cutoff, the response is predicted to be True. If the predicted value is less than or equal to the cutoff, the response is predicted to be False. The plot shows the percentage of the observed data that were correctly predicted at various cutoff values.


Prediction Histogram (Probit Analysis)

The Prediction Histogram graphical option displays a plot that demonstrates the ability of the fitted probit model to distinguish between cases when the dependent variable is True or False.

The plot shows the frequency distribution of the True and False cases in the data versus the probability predicted by the fitted model. In an ideal situation, the model will predict a small probability for the False cases and a large probability for the True cases. If the model works well, the larger frequencies above the line will appear to the right; larger frequencies below the line will appear to the left.


Residual Plots (Probit Analysis)

The Residual Plots graphical option displays the following plots for the fitted model: Scatterplots (Residuals versus Predicted, Residuals versus Row Number, Residuals versus X where X indicates each independent variable); Normal Probability Plot, and Autocorrelation Function.

Use the Residual Plot Options dialog box to select a plot and its options.


Analysis Options (Probit Analysis)

The Analysis Options Dialog Box of the Probit Analysis includes:

Method: the default is MLE (Maximum Likelihood Estimation. For aggregated data, weighted least squares may be selected instead, in which case the model is estimated using ordinary weighted least squares, with weights inversely proportional to the corresponding value of the dependent variable.

Fit: you can enter either All variables into the model or use Forward or Backward Stepwise Selection, in a manner similar to the multiple regression procedure. You can also select the p-value below which variables are entered into the model, the p-value above which they are removed from the model, and the maximum number of steps.

Display: when using a stepwise fit, you can elect to display the final model only, or all intermediary models as well.

Model: if first order is selected, only linear terms are included in the model. If second order is selected, quadratic terms for the quantitative factors and two-factor interactions for both quantitative and categorical factors are also included.

Include Constant: a check box which determines whether the fitted model contains a constant term.


Save Results Options (Probit Analysis)

The Save Results Dialog Box allows you to save results in the current data sheet. There are eleven selections:

•	Predicted Values

•	Lower Limits

•	Upper Limits

•	Residuals

•	Pearson Residuals

•	Deviance Residuals

•	Leverages

•	Percentages

•	Percentiles

•	Lower Fiducial Limits

•	Upper Fiducial Limits.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the. You can enter new names or accept the defaults.

Note: To access the Save Results Options dialog box, click on the Save Results Options on the Analysis Toolbar (the fourth button from the left)


Data Input (Poisson Regression)

Standard regression models assume that the dependent variable Y is measured on a continuous scale. Poisson Regression is the appropriate model if Y is a count, and thus discrete.

Enter:

Dependent Variable – the name of the variable containing the counts, which must be non-negative integers.

Sample Sizes: an optional name for the column containing the lengths of the sample periods, the default being 1 for each.

Quantitative Factors: the names of any quantitative factors to be included in the model.

Categorical Factors: the names of any non-quantitative factors to be included in the model.

To select options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left on either Pane Options or Analysis Options.

See also

Using the Poisson Regression

Poisson Regression Options

Predictions Options

Plot of Fitted Model Options

Residual Plots Options


Analysis Summary (Poisson Regression)

The Analysis Summary displays the results fitting a model to describe the relationship between the dependent and independent variables.

The results include estimates for each of the coefficients, approximate standard errors, and the estimated rate ratios.

It also includes an Analysis of Deviance. If the p-value for the model is less than 0.05, there is a statistically significant relationship among the variables at the 5% significance level. If the p-value for the residuals is greater than 0.05, it indicates that the model is not significantly worse than the best possible model for the data you are currently using at the 5% level.

Likelihood ratio tests for each factor are also included.  Small p-values correspond to statistically significant factors.


Tabular Options Dialog Box (Poisson Regression)

Allows you to select tabular options for the Poisson Regression.

Analysis Summary (Poisson Regression)

Confidence Intervals (Poisson Regression)

Correlation Matrix (Poisson Regression)

Predictions (Poisson Regression)

Unusual Residuals (Poisson Regression)

Influential Points (Poisson Regression)


Graphical Options Dialog Box (Poisson Regression)

Allows you to select graphical options for the Poisson Regression.

Plot of Fitted Model (Poisson Regression)

Observed versus Predicted (Poisson Regression)

Residual Plots Options (Poisson Regression)


Confidence Intervals (Poisson Regression)

The Confidence Intervals tabular option calculates and displays confidence intervals for the coefficient estimates.


Correlation Matrix (Poisson Regression)

The Correlation Matrix option displays a table of the estimated Pearson correlations between the coefficients in the fitted model.


Predictions (Poisson Regression)

The Predictions tabular option displays the predicted value for each row in the data file.  To make predictions for combinations of the factors for which data is not available, add additional rows to the bottom of the data sheet, entering settings for the factors but leaving the cells for the dependent variable blank.


Influential Points (Poisson Regression)

The Influential Points option displays the row numbers for the observations with leverage values greater than three times that of an average point, or with unusually large values for the DFITS or Cook’s distance statistics.

Leverage is a statistic that measures the amount of influence each observation has when determining the coefficients for the estimated model.

DFITS is a statistic that measures the amount each estimated coefficient would change if each observation was removed from the data.

Cook’s distance measures the distance between the estimated coefficients with and without each observation.


Plot of Fitted Model (Poisson Regression)

The Plot of Fitted Model graphical option displays a plot of the fitted model versus the independent variable you select.  A curve is drawn over the range of X, and the fitted model is plotted with selected confidence limits. The data is also plotted if there is only one independent variable.

The StatAdvisor shows the equation of the fitted model.


Observed versus Predicted (Poisson Regression)

The Observed versus Predicted graphical plot option displays a plot of the original data values plotted against the predicted values of the dependent variable. If the model fits well, the points should lie close to the line.


Observed versus Predicted (Life Data Regression)

The Observed versus Predicted graphical plot option displays a plot of the original data values plotted against the predicted values of the dependent variable. If the model fits well, the points should lie close to the line.


Residual Plots (Poisson Regression)

The Residual Plots graphical option displays the following plots for the fitted model:

Scatterplots (Residuals versus Predicted, Residuals versus Row Number, Residuals versus X where X is any independent variable)

Normal Probability Plot

Autocorrelation Function.

Use the Residual Plot Options dialog box to select a plot and its options.


Analysis Options (Poisson Regression)

The Analysis Options Dialog Box of the Poisson Regression includes:

Method: the default is MLE (Maximum Likelihood Estimation.  Weighted least squares may be selected instead, in which case the model is estimated using ordinary weighted least squares, with weights determined by the corresponding value of the dependent variable.

Fit: you can enter either All variables into the model or use Forward or Backward Stepwise Selection, in a manner similar to the multiple regression procedure. You can also select the p-value below which variables are entered into the model, the p-value above which they are removed from the model, and the maximum number of steps.

Display: when using a stepwise fit, you can elect to display the final model only, or all intermediary models as well.

Model: if first order is selected, only linear terms are included in the model. If second order is selected, quadratic terms for the quantitative factors and two-factor interactions for both quantitative and categorical factors are also included.

Include Constant: a check box which determines whether the fitted model contains a constant term.


Residual Plots Options (Poisson Regression)

Choose the type of residuals to plot and the type of plot desired.

You may plot ordinary residuals, Pearson residuals (which are similar to standardized residuals in multiple regression), and Deviance Residuals (their sum of squares sum to the residual deviance).


Save Results Options (Poisson Regression)

The Save Results Dialog Box allows you to save results to columns of the current data sheet. There are seven selections:

• Predicted Values: for the count corresponding to each row in the data file

• Lower Limits: for the mean count corresponding to each row in the data file.

• Upper Limits: for the mean count corresponding to each row in the data file.

• Residuals: the ordinary residuals.

• Pearson Residuals: the residuals divided by their standard errors.

• Deviance Residuals: the residuals scaled so that their sum of squares equals the residual deviance.

• Leverages: leverage values corresponding to each row in the data file.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the values. You can enter new names or accept the defaults.

Note: To access the Save Results Options dialog box, click on the Save Results Options on the Analysis Toolbar (the fourth button from the left)


Data Input (Life Data Regression)Data Input (Life Data Rregression)
Data Input (Life Data Regression)

Life Data Regression builds regression models in which the response variable is time to failure. Since some observations may not have failed yet, the data may be censored. Since failure times are not normal, usually being highly skewed, this regression is done on the logarithm of the response variable.

The Data Input dialog box includes:

Dependent Variable – the column name or STATGRAPHICS expression containing the failure times (for uncensored data) or censoring times (for censored data).

(Censored) – an optional column indicating whether each data value has been censored. Enter 0 if the value of the dependent variable represents an uncensored failure time. Enter a value other than 0 (usually 1) if the value has been right-censored (true failure time exceeds the value entered).

Quantitative Factors – the names of any quantitative factors to be included in the model.

Categorical Factors – the names of any non-quantitative factors to be included in the model.

(Select) –an optional row selection.


Tabular Options Dialog Box (Life Data Regression)

Allows you to select tabular options for the Life Data Regression Analysis.

Analysis Summary (Life Data Regression)

Correlation Matrix (Life Data Regression)

Predictions (Life Data Regression)

Unusual Residuals (Life Data Regression)

Percentiles (Life Data Regression)


Graphical Options Dialog Box (Life Data Regression)

Allows you to select graphical options for the Life Data Regression.

Plot of Fitted Model Options (Life Data Regression)

Percentile Plot (Life Data Regression)

Observed versus Predicted (Life Data Regression)

Residual Probability Plot (Life Data Regression)

Residual Plots (Life Data Regression)


Analysis Summary (Life Data Regression)

The Analysis Summary pane generated by the Life Data Regression Analysis shows details of the fitted model.   Included are

1. Variable names.

2. Number of uncensored and censored data values.

3. Estimates of the coefficients in the model with standard errors and approximate confidence limits.

4. Likelihood ratio tests for each factor. Small p-values correspond to statistically significant factors.

Use Analysis Options to select the distribution assumed for the data, and to specify the order of the fitted model


Correlation Matrix (Life Data Regression)

The Correlation Matrix option displays a table of the estimated Pearson correlations between the coefficients in the fitted model


Predictions (Life Data Regression)

The Predictions tabular option displays the predicted value for each row in the data file.  To make predictions for combinations of the factors for which data is not available, add additional rows to the bottom of the data sheet, entering settings for the factors but leaving the cells for the dependent variable blank.


Unusual Residuals (Life Data Regression)

The Unusual Residuals tabular option creates and displays the observations that have Standardized residuals less than –2 or greater than 2. The corresponding row, observed dependent variable, residual, and standardized residual and Pearson residual are also displayed.


Percentiles (Life Data Regression)

The Percentiles tabular option displays a table of estimated percentiles based on the fitted model, with confidence limits.


Plot of Fitted Model (Life Data Regression)

The Plot of Fitted Model graphical option displays a plot of the fitted model versus the independent variable you select.  A curve is drawn over the range of X, and the fitted model is plotted with selected confidence limits. The data is also plotted if there is only one independent variable.

The StatAdvisor shows the equation of the fitted model.


Probability Plot (Life Data Regression)

This plots shows the estimated failure probabilities as a function of a selected factor, plotted on a graph with a probability scale along the vertical axis.  Confidence limits for the percentiles are also included.


Residual Plots (Life Data Regression)

The Residual Plots graphical option displays the following plots for the fitted model:

Scatterplots (Residuals versus Predicted, Residuals versus Row Number, Residuals versus X where X indicates any independent variable)

Normal Probability Plot

Autocorrelation Function

Use the Residual Plot Options dialog box to select a plot and its options.


Analysis Options (Life Data Regression)

The Analysis Options Dialog Box of the Life Data Regression Analysis include:

Model: if first order is selected, only linear terms are included in the model. If second order is selected, quadratic terms for the quantitative factors and two-factor interactions for both quantitative and categorical factors are also included.

Distribution: the distribution used to model the dependent variable. The choices are Exponential, Extreme Value, Logistic, Loglogistic, Lognormal, Normal, and Weibull.

Confidence Level: the confidence level for all limits; defaults to 95%.


Percentiles Options (Life Data Regression)

The Percentiles Options dialog box allows you to select the factors and their corresponding levels at which you want to estimate the percentiles of the dependent variable.  You may also select the confidence level.


Plot of Fitted Model Options (Life Data Regression)

The Plot of Fitted Model Options allows you to select the variable over which the Plot of Fitted Model is constructed. It lets you set the low and high values of that variable, the value at which the other variables, if any, are held, up to 5 percentiles at which bounds will be drawn, and whether the mean should also be plotted.


Residual Plots Options (Life Data Regression)

Choose the type of residuals to plot and the type of plot desired.

You may plot ordinary residuals or standardized residuals (which divide each residual by its estimated standard error).


Save Results Options (Life Data Regression)

The Save Results Dialog Box allows you to results to columns of the data sheet. There are thirteen selections:

•	Predicted Values

•	Standard Errors of Means

•	Lower Limits for Forecast Means

•	Upper Limits for Forecast Means

•	Residuals

•	Standardized Residuals

•	Cox-Snell Residuals

•	Coefficients

•	Percentages

•	Percentiles

•	Standard Errors of Percentiles

•	Lower Percentile Confidence Limits

•	Upper Percentile Confidence Limits.

You can also use the Target Variables text boxes to enter the names of the variables in which you want to save the. You can enter new names or accept the defaults.

Note: To access the Save Results Options dialog box, click on the Save Results Options on the Analysis Toolbar (the fourth button from the left)


Matrix Plot Options (Matrix Plot)

The Matrix Plot Options dialog box specifies how missing values are treated in the plot.  If you select Complete Cases Only, only rows for which none of the specified variables has a missing value will be displayed in any of the plots.  If All Data is specified, all values will be used wherever possible in each plot, regardless of whether any of the other variables is missing.


Confidence Intervals Options (One-Variable Analysis)

The Confidence Intervals Options of the One-Variable Analysis sets:

1.	The confidence level for the intervals.

2.	The type of interval or bound desired.

3.	The number of subsamples in optional bootstrap intervals. Bootstrap intervals are based on samples generated from the data values and do not depend on the data coming from a normal distribution. 500 subsamples is usually considered to be sufficient.


Rank Correlations Option (Multiple Variable Analysis)

Select either Spearman or Kendall rank correlations.


Multiple Sample Comparison Input Data Type

The Multiple Sample Comparison Input Data Type dialog box lets you specify whether your data are in separate columns, or all in one column together with another column which contains identifying codes.


SnapStats Histogram Tab

The SnapStats Histogram Tab lets you choose among different rules for determining the number of intervals k into which the data is grouped.  You may select:

Sturges’ Rule – 1 + 3.322 * log10(n)

10log10(n) – 10 * log10(n)

Scott’s Rule – range of data divided by 3.5*s/n^(1/3)

Freedman-Diaconis – range of data divided by 2*IQR/n^(1/3)

Fixed number


Percentage Options (Gage Linearity and Accuracy Analysis)

The Percentage Options of the Gage Linearity and Accuracy Analysis lets you select the number of decimals places to be displayed for percentages shown on the Analysis Summary.


Automatic Forecasting Analysis Dialog Box

Forecasting is based on fitting a model to past observations in a time series. Automatic Forecasting automatically selects the best model to use, by trying various classical forecasting models and ARMA(p,p-1) models.. For the ARMA models, a stepwise approach is used beginning with p=0. As long as the selected information criterion continues to improve, the model order is increased. When the information criterion starts to rise, searching stops and the best model is chosen.

You may also request that the analysis find the optimal Box-Cox transformation while fitting each model.

Data

Once Every

Starting At

(Seasonality)

Trading Days Adjustment

Select

Sort

Number of Forecasts

Withhold for Validation

To choose options for this analysis, use the Options dialog boxes.  To access the Options dialog boxes, click the right mouse button on a text or graphics pane, then click the left mouse button on either Pane Options or Analysis Options.

See also

Using the Forecasting Analysis

Model Specification Options

Autocorrelation Function Options

Partial Autocorrelation Function Options

Periodogram Table Options

Forecast Limits Options

Forecasting Residual Plots Options

Periodogram Options


Model Comparisons (Automatic Forecasting Analysis)

The Model Comparison tabular option of the Automatic Forecasting Analysis shows the results of fitting each forecasting model.  It displays a table containing:

RMSE (Root Mean Squared Error) – a measure of forecasting precision computed by squaring the individual one-ahead forecasting error for each item in the data, then finding the square root of the average or mean value of those squares. If the result is a small value, you can predict performance more precisely; if the result is a large value, you can predict it less precisely.

MAE (Mean Absolute Error) – the average of the absolute values of the one-ahead forecasting errors. .

MAPE (Mean Absolute Percentage Error) – the mean or average of the absolute percentage errors.

ME (Mean Error) – the average of the one-ahead forecast errors. The closer the ME is to 0, the less biased, or more accurate, the prediction.

MPE (Mean Percentage Error) – the average of the absolute values of the one-ahead forecast errors divided by the corresponding data values.

AIC (Akaike Information Criterion), HQC (Hannan-Quinn Information Criterion), or SBIC (Schwarz Bayesian Information Crfiterion) – the value of the information criterion used to select the model.  The smaller the value, the better the model.

RUNS, RUNM, AUTO, MEAN, VAR – the results of various tests of model adequacy.  OK indicates that the test was passed at the 5% significance level.  Otherwise, the number of asterisks indicates how significant the failure of the test was.


STATGRAPHICS Expression Evaluator

The STATGRAPHICS Expression Evaluator allows you to evaluate any STATGRAPHICS expression.  Enter the Expression and press the Enter key to display the result.


Unusual Residuals (Poisson Regression)

The Unusual Residuals tabular option displays a table that lists all the observations that have Pearson residuals with values greater than 2.0 in absolute value.  Pearson residuals, the residuals divided by their estimated standard errors, measure the number of standard deviations that each observed value of the dependent variable deviates from the model. The Deviance Residuals are the residuals scaled so that their sum of squares equals the residual deviance.


Percentile Plot (Life Data Regression)

The Percentile Plot graphical option displays the cumulative distribution of the response variable at fixed values of the explanatory variables. Use Pane Options to modify this plot.


Factor Level Options (Life Data Regression)

The Factor Level Options of the Life Data Regression allow you to select the type of plot, either a Cumulative Distribution function (F(x)) of the response variable, or a Survivor curve (1-F(x)).  You may also select levels of the explanatory variables.


Residual Probability Plot (Life Data Regression)

The Residual Plots graphical option displays the following plots for the fitted model:

Scatterplot (Residuals versus Predicted, Residuals versus Row Number, and Residuals versus X where X indicates any independent variable).

Normal Probability Plot.

Autocorrelation Function.

Use the Residual Plots Options dialog box to select a plot and its options.


Suppress Ticmark Gap
Suppress Tickmark Gap

The Suppress Tickmark Gap option allows you to eliminate the gap between the intersection of the axes and the first tickmark.


3D Effects

The 3D Effects option makes features appear to have depth, thus enhancing the visual aspect of the plots.


Save Results Options Dialog Box (Logistic Regression)

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SnapStats Multiple Sample Comparison Data Input (Data and Code Column)

Use the Multiple-Sample Comparison Analysis to compare several sets of data.  The observations in the samples are assumed to be independent. The samples do not have to be of equal sizes.

Enter the names of the columns containing the data and code variables.

Samples

Select

Sort