# The GLMPOWER Procedure

## Overview: GLMPOWER Procedure

Power and sample size analysis optimizes the resource usage and design of a study, improving chances of conclusive results with maximum efficiency. The GLMPOWER procedure performs prospective power and sample size analysis for linear models, with a variety of goals:

• determining the sample size required to get a significant result with adequate probability (power)

• characterizing the power of a study to detect a meaningful effect

• conducting what-if analyses to assess sensitivity of the power or required sample size to other factors

Here prospective indicates that the analysis pertains to planning for a future study. This is in contrast to retrospective analysis for a past study, which is not supported by this procedure.

The statistical analyses that are covered include Type III F tests and contrasts of fixed effects in univariate and multivariate linear models. For univariate models, you can specify covariates, which can be continuous or categorical. For multivariate models, you can choose among Wilks’ likelihood ratio, Hotelling-Lawley trace, and Pillai’s trace F tests for multivariate analysis of variance (MANOVA) and among uncorrected, Greenhouse-Geisser, Huynh-Feldt, and Box conservative F tests for the univariate approach to repeated measures. Tests and contrasts that involve random effects are not supported. For power and sample size analyses in a variety of other statistical situations, see Chapter 89: The POWER Procedure.

Input for PROC GLMPOWER includes the following components, which are considered in study planning:

• design (including subject profiles and their allocation weights)

• statistical model and test

• between-subject contrasts of class effects

• within-subject contrasts (for multivariate models)

• significance level (alpha)

• surmised response means for subject profiles (often called "cell means")

• surmised variability (and correlation for multivariate models)

• power

• sample size

In order to identify power or sample size as the result parameter, you designate it by a missing value in the input. The procedure calculates this result value over one or more scenarios of input values for all other components.

You specify the design and the cell means by using an exemplary data set, a data set of artificial values that is constructed to represent the intended sampling design and the surmised response means in the underlying population. You specify the model and between-subject contrasts by using MODEL and CONTRAST statements similar to those in the GLM, ANOVA, and MIXED procedures. For multivariate models, you specify the within-subject contrasts by using MANOVA and REPEATED statements similar to those in the GLM and MIXED procedures. You specify the remaining parameters by using the POWER statement, which is similar to analysis statements in the POWER procedure.

In addition to tabular results, PROC GLMPOWER produces graphs. You can produce the most common types of plots easily with default settings and use a variety of options for more customized graphics. For example, you can control the choice of axis variables, axis ranges, number of plotted points, mapping of graphical features (such as color, line style, symbol, and panel) to analysis parameters, and legend appearance.

If ODS Graphics is enabled, then PROC GLMPOWER uses ODS Graphics to create graphs; otherwise, traditional graphs are produced.

For more information about enabling and disabling ODS Graphics, see the section Enabling and Disabling ODS Graphics in Chapter 21: Statistical Graphics Using ODS.

For specific information about the statistical graphics and options available with the GLMPOWER procedure, see the PLOT statement and the section ODS Graphics.

The GLMPOWER procedure is one of several tools available in SAS/STAT software for power and sample size analysis. PROC POWER covers a variety of other analyses such as t tests, equivalence tests, confidence intervals, binomial proportions, multiple regression, one-way ANOVA, survival analysis, logistic regression, and the Wilcoxon rank-sum test. The Power and Sample Size application provides a user interface and implements many of the analyses supported in the procedures. For more information, see Chapter 89: The POWER Procedure, and Chapter 90: The Power and Sample Size Application.

The following sections of this chapter describe how to use PROC GLMPOWER and discuss the underlying statistical methodology. The section Getting Started: GLMPOWER Procedure introduces PROC GLMPOWER with examples of power computation for a two-way analysis of variance. The section Syntax: GLMPOWER Procedure describes the syntax of the procedure. The section Details: GLMPOWER Procedure summarizes the methods employed by PROC GLMPOWER and provides details on several special topics. The section Examples: GLMPOWER Procedure illustrates the use of the GLMPOWER procedure with several applications.

For an overview of methodology and SAS tools for power and sample size analysis, see Chapter 18: Introduction to Power and Sample Size Analysis. For more discussion and examples for linear models, see Castelloe and O’Brien (2001); O’Brien and Shieh (1992); Muller and Benignus (1992); O’Brien and Muller (1993). For additional discussion of general power and sample size concepts, see O’Brien and Castelloe (2007); Castelloe (2000); Muller and Benignus (1992); Lenth (2001).