The 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:

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 41, 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 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.

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 41, The GLMPOWER Procedure, and Chapter 69, 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 test and sample size determination for a two-sample 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), and Lenth (2001).

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