Syntax

The following statements are available in PROC GLMPOWER.

• PROC GLMPOWER < options > ;

  • CLASS variables ;

  • MODEL dependent-variables = effects ;

  • WEIGHT variable ;

  • CONTRAST label effect values <... effect values >< / options > ;

  • POWER < options > ;

  • PLOT < plot-options >< / graph-options > ;

The PROC GLMPOWER statement, the MODEL statement, and the POWER statement are required. If your model contains classification effects, the classification variables must be listed in a CLASS statement, and the CLASS statement must appear before the MODEL statement. In addition, CONTRAST statements must appear after the MODEL statement. PLOT statements must appear after the POWER statement defining the analysis for the plot.

You can use multiple CONTRAST, POWER, and PLOT statements. Each CONTRAST statement defines a separate contrast. Each POWER statement produces a separate analysis and uses the information contained in the CLASS, MODEL, WEIGHT, and all CONTRAST statements. Each PLOT statement refers to the previous POWER statement and generates a separate graph (or set of graphs).

Table 34.3 summarizes the basic functions of each statement in PROC GLMPOWER. The syntax of each statement in Table 34.3 is described in the following pages.

Table 34.3: Statements in the GLMPOWER Procedure

Statement	Description
PROC GLMPOWER	invokes procedure and specifies exemplary data set
CLASS	declares classification variables
CONTRAST	defines linear tests of model parameters
MODEL	defines model and specifies dependent variable(s) used for cell means scenarios
WEIGHT	specifies variable for allocating sample sizes to different subject profiles
POWER	identifies parameter to solve for and provides one or more scenarios for values of other analysis parameters
PLOT	displays graphs for preceding POWER statement

PROC GLMPOWER Statement

• PROC GLMPOWER < options > ;

The PROC GLMPOWER statement invokes the GLMPOWER procedure. You can specify the following options.

DATA = SAS-data-set

• names a SAS data set to be used as the exemplary data set, which is an artificial data set constructed to represent the intended sampling design and the conjectured response means for the underlying population.

PLOTONLY

• specifies that only graphical results from the PLOT statement should be produced.

CLASS Statement

• CLASS variables ;

The CLASS statement names the classification variables to be used in the analysis. Classification variables can be either character or numeric.

CONTRAST Statement

• CONTRAST label effect values <... effect values >< / options > ;

The CONTRAST statement enables you to define custom hypothesis tests by specifying an L vector or matrix for testing the hypothesis L ² = 0. Thus, to use this feature you must be familiar with the details of the model parameterization used in PROC GLM. For more information, see the Parameterization of PROC GLM Models section on page 1787 of Chapter 32, The GLM Procedure. All of the elements of the L vector may be given, or if only certain portions of the L vector are given, the remaining elements are constructed by PROC GLMPOWER from the context (in a manner similar to rule 4 discussed in the Construction of Least-Squares Means section on page 1820 of Chapter 32, The GLM Procedure ).

There is no limit to the number of CONTRAST statements you can specify. Each sample size analysis includes tests for all CONTRAST statements.

In the CONTRAST statement,

label	identifies the contrast on the output. A label is required for every contrast specified. Labels must be enclosed in quotes.
effect	identifies an effect that appears in the MODEL statement, or the INTERCEPT effect. You do not need to include all effects that are in the MODEL statement.
values	are constants that are elements of the L vector associated with the effect.

You can specify the following option in the CONTRAST statement after a slash(/):

SINGULAR= number

• tunes the estimability checking. If ABS( L ˆ’ LH ) > C — number for any row in the contrast, then L is declared nonestimable. H is the ( X ² X ) ˆ’ X ² X matrix, and C is ABS( L ) except for rows where L is zero, and then it is 1. The default value for the SINGULAR= option is 10 ^{ˆ’ 4} . Values for the SINGULAR= option must be between 0 and 1.

• The CONTRAST statement enables you to perform custom hypothesis tests. If the hypothesis is estimable , then the sum of squares due to it, SS( H : L ² =0), is computed as

  

• where b =( X ² X ) ˆ’ X ² y is the estimated solution vector.

• The degrees of freedom associated with the hypothesis is equal to the row rank of L . The sum of squares computed in this situation is equivalent to the sum of squares computed using an L matrix with any row deleted that is a linear combination of previous rows.

• Multiple-degree-of-freedom hypotheses can be specified by separating the rows of the L matrix with commas.

MODEL Statement

• MODEL dependent-variables = classification-effects ;

The MODEL statement serves two basic purposes.

• The dependent-variables specify scenarios for the cell means.

• The classification-effects specify the model effects.

The classification-effects specification defines the model effects. You can include main effects and interactions using the effects notation of PROC GLM; see the Specification of Effects section on page 1784 in Chapter 32, The GLM Procedure for further details.

All variables in the classification-effects specification must be contained in the CLASS statement, since power and sample size analyses cover only tests and contrasts of class effects. You can account for covariates in the model by using the NCOVARIATES=, CORRXY=, and PROPVARREDUCTION= options in the POWER statement.

Each dependent variable refers to a set of surmised cell means in the exemplary data set (named by the DATA= option of the PROC GLMPOWER statement). These cell means are response means for all of the subject profiles. Multiple dependent variables correspond to multiple scenarios for these cell means. All models are univariate; the GLMPOWER procedure currently does not support multivariate analyses.

The MODEL statement is required. You can specify only one MODEL statement.

WEIGHT Statement

• WEIGHT variable ;

The WEIGHT statement names a variable that provides a profile weight ( cell weight ) for each observation in the exemplary data set specified by the DATA= option in the PROC GLMPOWER statement.

If the WEIGHT statement is not used, then a balanced design is assumed with default cell weights of 1.

POWER Statement

• POWER < options > ;

The POWER statement performs power and sample size analyses for the Type III test of each effect in the model defined by the MODEL statements and for the contrasts defined by all CONTRAST statements.

Summary of Options

Table 34.4 summarizes categories of options available in the POWER statement.

Table 34.4: Summary of Options in the POWER Statement

Task	Options
Specify significance level	ALPHA=
Specify covariates	CORRXY= NCOVARIATES= PROPVARREDUCTION=
Specify error standard deviation	STDDEV=
Specify sample size	NTOTAL=
Specify power	POWER=
Control sample size rounding	NFRACTIONAL
Control ordering in output	OUTPUTORDER=

Table 34.5 summarizes the valid result parameters.

Table 34.5: Summary of Result Parameters in the POWER Statement

Solve for	Syntax
Power	POWER = .
Sample size	NTOTAL = .

Dictionary of Options

ALPHA= number-list

• specifies the level of significance of each test. The default is 0.05, corresponding to the usual 0.05 — 100% = 5% level of significance. Note that this is a test-wise significance level with the same value for all tests, not incorporating any corrections for multiple testing. See the Specifying Value Lists in the POWER Statement section on page 1945 for information on specifying the number-list .

CORRXY= number-list

• specifies the multiple correlation between all covariates and the response. The error standard deviation given by the STDDEV= option is consequently reduced by multiplying it by a factor of (1 ˆ’ ² ) ^1/2 , provided that the number of covariates (as determined by the NCOVARIATES= option) is greater than zero. You cannot use the CORRXY= and the PROPVARREDUCTION= options simultaneously . See the Specifying Value Lists in the POWER Statement section on page 1945 for information on specifying the number-list .

NCOVARIATES= number-list

NCOVARIATE= number-list

NCOVS= number-list

NCOV= number-list

• specifies the number of additional degrees of freedom to accommodate covariate effects ” both class and continuous ” not listed in the MODEL statement. The error degrees of freedom is consequently reduced by the value of the NCOVARIATES= option, and the error standard deviation (whose unadjusted value is provided with the STDDEV= option) is reduced according to the value of the CORRXY= or PROPVARREDUCTION= option. See the Specifying Value Lists in the POWER Statement section on page 1945 for information on specifying the number-list .

NFRACTIONAL

NFRAC

• enables fractional input and output for sample sizes. See the Sample Size Adjustment Options section on page 1946 for information on the ramifications of the presence (and absence) of the NFRACTIONAL option.

NTOTAL= number-list

• specifies the sample size or requests a solution for the sample size with a missing value (NTOTAL=.). Values for the sample size must be no smaller than the model degrees of freedom (counting the covariates). See the Specifying Value Lists in the POWER Statement section on page 1945 for information on specifying the number- list .

OUTPUTORDER= INTERNAL

OUTPUTORDER= REVERSE

OUTPUTORDER= SYNTAX

• controls how the input and default analysis parameters are ordered in the output. OUTPUTORDER=INTERNAL (the default) produces the following order.

  • weight variable (from the WEIGHT statement)

  • source (contrasts from CONTRAST statements, and model effects)

  • ALPHA

  • dependent variable (from the MODEL statement, representing scenarios for cell means)

  • NCOVARIATES

  • CORRXY

  • PROPVARREDUCTION

  • STDDEV

  • NTOTAL

  • POWER

• The OUTPUTORDER=SYNTAX option arranges the parameters in the output in the same order that their corresponding options are specified in the POWER statement. The OUTPUTORDER=REVERSE option arranges the parameters in the output in the reverse of the order that their corresponding options are specified in the POWER statement.

POWER= number-list

• specifies the desired power of each test or requests a solution for the power with a missing value (POWER=.). The power is expressed as a probability (for example, 0.9) rather than a percentage. Note that this is a test-wise power with the same value for all tests, without any correction for multiple testing. See the Specifying Value Lists in the POWER Statement section on page 1945 for information on specifying the number-list .

PROPVARREDUCTION= number-list

PVRED= number-list

• specifies the proportional reduction ( ) in total R ² incurred by the covariates; in other words, the amount of additional variation explained by the covariates. The error standard deviation given by the STDDEV= option is consequently reduced by multiplying it by a factor of (1 ˆ’ ) ^1/2 , provided that the number of covariates (as determined by the NCOVARIATES= option) is greater than zero. You cannot use the PROPVARREDUCTION= and the CORRXY= options simultaneously. See the Specifying Value Lists in the POWER Statement section on page 1945 for information on specifying the number-list .

STDDEV= number-list

• specifies the error standard deviation, or root MSE. If covariates are specified using the NCOVARIATES= option, then the STDDEV= option denotes the error standard deviation before accounting for these covariates. See the Specifying Value Lists in the POWER Statement section on page 1945 for information on specifying the number-list .

Restrictions on Option Combinations

For the relationship between covariates and response, specify either the multiple correlation (using the CORRXY= option) or the proportional reduction in total R ² (using the PROPVARREDUCTION= option).

PLOT Statement

• PLOT < plot-options >< / graph-options > ;

The PLOT statement produces a graph or set of graphs for the sample size analysis defined by the previous POWER statement. The plot-options define the plot characteristics, and the graph-options are SAS/GRAPH-style options.

Options

You can specify the following plot-options in the PLOT statement.

INTERPOL= JOIN

INTERPOL= NONE

• specifies the type of curve to draw through the computed points. The INTERPOL=JOIN option connects computed points by straight lines. The INTERPOL=NONE option leaves computed points unconnected.

KEY= BYCURVE < ( bycurve-options ) >

KEY= BYFEATURE < ( byfeature-options ) >

KEY= ONCURVES

• specifies the style of key (or legend ) for the plot. The default is KEY=BYFEATURE, which specifies a key with a column of entries for each plot feature (line style, color , and/or symbol). Each entry shows the mapping between a value of the feature and the value(s) of the analysis parameter(s) linked to that feature. The KEY=BYCURVE option specifies a key with each row identifying a distinct curve in the plot. The KEY=ONCURVES option places a curve-specific label adjacent to each curve.

• You can specify the following byfeature-options in parentheses after the KEY=BYCURVE option.

  NUMBERS =OFF
  NUMBERS=ON	specifies how the key should identify curves. If NUMBERS=OFF, then the key includes symbol, color, and line style samples to identify the curves. If NUMBERS=ON, then the key includes numbers matching numeric labels placed adjacent to the curves. The default is NUMBERS=ON.
  POS=BOTTOM
  POS=INSET	specifies the position of the key. The POS=BOTTOM option places the key below the x-axis. The POS=INSET option places the key inside the plotting region and attempts to choose the least crowded corner. The default is POS=BOTTOM.

• You can specify the following byfeature-options in parentheses after KEY=BYFEATURE option.

  POS=BOTTOM
  POS=INSET	specifies the position of the key. The POS=BOTTOM option places the key below the x-axis. The POS=INSET option places the key inside the plotting region and attempts to choose the least crowded corner. The default is POS=BOTTOM.

MARKERS= ANALYSIS

MARKERS= COMPUTED

MARKERS= NICE

MARKERS= NONE

• specifies the locations for plotting symbols.

• The MARKERS=ANALYSIS option places plotting symbols at locations corresponding to the values of the relevant input parameter from the POWER statement preceding the PLOT statement.

• The MARKERS=COMPUTED option (the default) places plotting symbols at the locations of actual computed points from the sample size analysis.

• The MARKERS=NICE option places plotting symbols at tick mark locations (corresponding to the argument axis).

• The MARKERS=NONE option disables plotting symbols.

MAX= number

• specifies the maximum of the range of values for the parameter associated with the argument axis (the axis that is not representing the parameter being solved for). The default is the maximum value occurring for this parameter in the POWER statement preceding the PLOT statement.

MIN= number

• specifies the minimum of the range of values for the parameter associated with the argument axis (the axis that is not representing the parameter being solved for). The default is the minimum value occurring for this parameter in the POWER statement preceding the PLOT statement.

NPOINTS= number

NPTS= number

• specifies the number of values for the parameter associated with the argument axis (the axis that is not representing the parameter being solved for). You cannot use the NPOINTS= and STEP= options simultaneously. The default value for typical situations is 20.

STEP= number

• specifies the increment between values of the parameter associated with the argument axis (the axis that is not representing the parameter being solved for). You cannot use the STEP= and NPOINTS= options simultaneously. By default, the NPOINTS= option is used instead of the STEP= option.

VARY ( feature < BY parameter-list > ... feature < BY parameter-list > )

• specifies how plot features should be linked to varying analysis parameters. Available plot features are COLOR, LINESTYLE, PANEL, and SYMBOL. A panel refers to a separate plot with a heading identifying the subset of values represented in the plot.

  The parameter-list is a list of one or more names separated by spaces. Each name must match the name of an analysis option used in the POWER statement preceding the PLOT statement, or one of the following keywords: SOURCE (for the tests) and DEPENDENT (for the cell means scenarios). Also, the name must be the primary name for the analysis option, that is, the one listed first in the syntax description.

  If you omit the < BY parameter-list > portion for a feature, then one or more multivalued parameters from the analysis will be automatically selected for you.

X= N

X= POWER

• specifies a plot with the requested type of parameter on the x-axis and the parameter being solved for on the y-axis. When X=N, sample size is assigned to the x-axis. When X=POWER, power is assigned to the x-axis. You cannot use the X= and Y= options simultaneously. The default is X=POWER, unless the result parameter is power, in which case the default is X=N.

XOPTS= ( x-options )

• specifies plot characteristics pertaining to the x-axis.

• You can specify the following x-options in parentheses.

  CROSSREF=NO
  CROSSREF=YES	specifies whether the reference lines defined by the REF= x- option should be crossed with a reference line on the y-axis that indicates the solution point on the curve.
  REF= number-list	specifies locations for reference lines extending from the x-axis across the entire plotting region. See the Specifying Value Lists in the POWER Statement section on page 1945 for information on specifying the number-list .

Y= N

Y= POWER

• specifies a plot with the requested type of parameter on the y-axis and the parameter being solved for on the x-axis. When Y=N, sample size is assigned to the y-axis. When Y=POWER, power is assigned to the y-axis. You cannot use the Y= and X= options simultaneously. By default, the X= option is used instead of the Y= option.

YOPTS= ( y-options )

• specifies plot characteristics pertaining to the y-axis.

• You can specify the following y-options in parentheses.

  CROSSREF=NO
  CROSSREF=YES	specifies whether the reference lines defined by the REF= y- option should be crossed with a reference line on the x-axis that indicates the solution point on the curve.
  REF= number-list	specifies locations for reference lines extending from the y-axis across the entire plotting region. See the Specifying Value Lists in the POWER Statement section on page 1945 for information on specifying the number-list .

• You can specify the following graph-options in the PLOT statement after a slash (/).

DESCRIPTION= string

• specifies a descriptive string of up to 40 characters that appears in the Description field of the graphics catalog. The description does not appear on the plots. By default, PROC GLMPOWER assigns a description either of the form Y versus X (for a single-panel plot) or of the form Y versus X ( S ), where Y is the parameter on the y-axis, X is the parameter on the x-axis, and S is a description of the subset represented on the current panel of a multipanel plot.

NAME= string

• specifies a name of up to eight characters for the catalog entry for the plot. The default name is PLOT n , where n is the number of the plot statement within the current invocation of PROC GLMPOWER. If the name duplicates the name of an existing entry, SAS/GRAPH software adds a number to the duplicate name to create a unique entry, for example, PLOT11 and PLOT12 for the second and third panels of a multipanel plot generated in the first PLOT statement in an invocation of PROC GLMPOWER.