# The POWER Procedure

## Overview: POWER Procedure

Power and sample size analysis optimizes the resource usage and design of a study, improving chances of conclusive results with maximum efficiency. The POWER procedure performs prospective power and sample size analyses for a variety of goals, such as the following:

• 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 power analysis for a past study, which is not supported by the procedure.

A variety of statistical analyses are covered:

• t tests, equivalence tests, and confidence intervals for means

• tests, equivalence tests, and confidence intervals for binomial proportions

• multiple regression

• tests of correlation and partial correlation

• one-way analysis of variance

• rank tests for comparing two survival curves

• logistic regression with binary response

• Wilcoxon-Mann-Whitney (rank-sum) test

For more complex linear models, see Chapter 47: The GLMPOWER Procedure.

Input for PROC POWER includes the components considered in study planning:

• design

• statistical model and test

• significance level (alpha)

• surmised effects and variability

• power

• sample size

You designate one of these components by a missing value in the input, in order to identify it as the result parameter. The procedure calculates this result value over one or more scenarios of input values for all other components. Power and sample size are the most common result values, but for some analyses the result can be something else. For example, you can solve for the sample size of a single group for a two-sample t test.

In addition to tabular results, PROC POWER 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 POWER 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 POWER procedure, see the PLOT statement and the section ODS Graphics.

The POWER procedure is one of several tools available in SAS/STAT software for power and sample size analysis. PROC GLMPOWER supports more complex linear models. The Power and Sample Size application provides a user interface and implements many of the analyses supported in the procedures. See Chapter 47: The GLMPOWER Procedure, and Chapter 78: The Power and Sample Size Application, for details.

The following sections of this chapter describe how to use PROC POWER and discuss the underlying statistical methodology. The section Getting Started: POWER Procedure introduces PROC POWER with simple examples of power computation for a one-sample t test and sample size determination for a two-sample t test. The section Syntax: POWER Procedure describes the syntax of the procedure. The section Details: POWER Procedure summarizes the methods employed by PROC POWER and provides details on several special topics. The section Examples: POWER Procedure illustrates the use of the POWER 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, see O’Brien and Castelloe (2007); Castelloe (2000); Castelloe and O’Brien (2001); Muller and Benignus (1992); O’Brien and Muller (1993); Lenth (2001).