Understanding Power and Rules of Thumb for Determining Sample Sizes

Abstract

This article addresses the definition of power and its relationship to Type I and Type II errors.We discuss the relationship of sample size and power.Finally, we offer statistical rules of thumb guiding the selection of sample sizes large enough for sufficient power to detecting differences, associations, chi-square, and factor analyses.As researchers, it is disheartening to pour time and intellectual energy into a research project, analyze the data, and find that the elusive .05significance level was not met.If the null hypothesis is genuinely true, then the findings are robust.But, what if the null hypothesis is false and the results failed to detect the difference at a high enough level?It is a missed opportunity.Power refers to the probability of rejecting a false null hypothesis.Attending to power during the design phase protect both researchers and respondents.In recent years, some Institutional Review Boards for the protection of human respondents have rejected or altered protocols due to design concerns (Resnick, 2006).They argue that an "underpowered" study may not yield useful results and consequently unnecessarily put respondents at risk.Overall, researchers can and should attend to power.This article defines power in accessible ways, provides guidelines for increasing power, and finally offers "rules-of-thumb" for numbers of respondents needed for common statistical procedures.