Introduction to Power and Sample Size Analysis


Power and sample size analysis optimizes the resource usage and design of a study, improving chances of conclusive results with maximum efficiency. The standard statistical testing paradigm implicitly assumes that Type I errors (mistakenly concluding significance when there is no true effect) are more costly than Type II errors (missing a truly significant result). This may be appropriate for your situation, or the relative costs of the two types of error may be reversed. For example, in screening experiments for drug development, it is often less damaging to carry a few false positives forward for follow-up testing than to miss potential leads. Power and sample size analysis can help you achieve your desired balance between Type I and Type II errors. With optimal designs and sample sizes, you can improve your chances of detecting effects that might otherwise have been ignored, save money and time, and perhaps minimize risks to subjects.

Relevant tools in SAS/STAT software for power and sample size analysis include the following:

  • the GLMPOWER procedure

  • the POWER procedure

  • the Power and Sample Size application

  • the %POWTABLE macro

  • various procedures, statements, and functions in Base SAS and SAS/STAT for developing customized formulas and simulations

These tools, discussed in detail in the section SAS/STAT Tools for Power and Sample Size Analysis, deal exclusively with prospective analysis—that is, planning for a future study. This is in contrast to retrospective analysis for a past study, which is not supported by the main tools. Although retrospective analysis is more convenient to perform, it is often uninformative or misleading, especially when power is computed directly based on observed data.

The goals of prospective power and sample size analysis include 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

  • computing the probability of achieving the desired precision of a confidence interval, or the sample size required to ensure this probability

  • conducting what-if analyses to assess how sensitive the power or required sample size is to other factors

The phrase power analysis is used for the remainder of this document as a shorthand to represent any or all of these goals. For more information about the GLMPOWER procedure, see Chapter 47: The GLMPOWER Procedure. For more information about the POWER procedure, see Chapter 77: The POWER Procedure. For more information about the Power and Sample Size application, see Chapter 78: The Power and Sample Size Application.