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Power and Sample Size Computations with SAS/STAT® Software
Overview
Statistical power analysis characterizes the ability of a study to detect a meaningful effect size such as the difference between two population means. It also determines the sample size required to provide a desired power for an effect of scientific interest. Proper planning reduces the risk of conducting a study that does not produce useful results, and it determines the most sensitive design for the resources available. Power analysis is now integral to the health and behavioral sciences, and its use is steadily increasing wherever empirical studies are performed.
SAS/STAT software enables you to perform power and sample size computations through both procedures and an interface:
The POWER and GLMPOWER procedures perform prospective power and sample size computations. Prospective indicates that the analysis pertains to planning for a future study. This is in contrast to a retrospective analysis for a past study, which is not supported by this software. The POWER procedure covers a variety of statistical analyses, while the GLMPOWER procedure focuses on power analysis for the linear model.
Power and Sample Size (PSS) is a Web application that provides a point-and-click interface to these computations. It provides multiple input parameter options, stores results in a project format, displays power curves, and produces appropriate narratives for the results.
- t tests for means
- equivalence tests for means
- confidence intervals for means
- tests of binomial proportions
- multiple regression
- tests of correlation and partial correlation
- one-way analysis of variance
- rank tests for comparing two survival curves
- design (including subject profiles and their allocation weights)
- statistical model
- contrasts of class effects
- significance level (alpha)
- surmised response means for subject profiles (often called "cell means")
- surmised variability
- power
- sample size
- design (including subject profiles and their allocation weights)
- statistical model
- contrasts of class effects
- significance level (alpha)
- surmised response means for subject profiles (often called "cell means")
- surmised variability
- power
- sample size
The POWER Procedure
The POWER procedure covers a variety of statistical analyses:
Many factors are involved in a power analysis, such as the research objective, design, data analysis method, power, sample size, Type I error, variability, and effect size. By performing a power analysis, you can learn about the relationships between these factors, optimizing those that are under your control and exploring the implications of those that are fixed.
The following input to the POWER procedure include these components of study planning:To identify one of these components as the result parameter, you designate it by a missing value. 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 specify axis ranges, number of plotted points, legend appearance, and mapping of graphical features (such as color, line style, symbol, and panel) to analysis parameters.
The GLMPOWER Procedure
The GLMPOWER procedure performs prospective analyses for linear models. The statistical analyses include Type III tests and contrasts of fixed class effects in univariate linear models, optionally with covariates. The covariates can be continuous or categorical. Tests and contrasts that involve random effects are not supported.
You specify the design and the cell means with an exemplary data set and specify the model and contrasts with MODEL and CONTRAST statements like those in the GLM procedure. You specify the remaining parameters with the POWER statement, which is similar to analysis statements in the POWER procedure.
In addition to tabular results, PROC GLMPOWER also produces graphs that are customizable. The input to the POWER procedure includes the following components of study planning:
The following SAS statements illustrate the syntax of PROC GLMPOWER:
proc glmpower data=Exemplary;
class Variety Exposure;
model Height = Variety |
Exposure;
power
stddev = 5
ntotal = 60
power = .;
run;
These statements request power for a planned data analysis that is a two-way analysis of variance with flower height (measured at two weeks) as the response and a model that consists of the effects of light exposure, flower variety, and their interaction. Requested is the power of each effect test using a balanced design with a total of 60 specimens (10 for each combination of exposure and variety) and alpha = 0.05 for each test.
The Power and Sample Size Application
The Power and Sample Size Application, distributed with SAS/STAT software, is a Web interface that provides access to basic power and sample size computations.
PSS computes power and sample size for the following statistical tasks:
- t tests, confidence intervals, equivalence tests, multiple regression, and correlation
- linear models (analysis of variance, analysis of covariance, fixed-effects) with contrasts
- one-proportion, two-proportion, and McNemar tests rank tests for survival analysis
Enabling you to specify alternate input, write narratives, and save each analysis as a project for later retrieval makes PSS a very convenient tool for both you and your clients. PSS can be run locally on a workstation or laptop or surfaced with a browser from a server that is running SAS® software.
