Quick Power Estimates for Comparing Proportions

Abstract

Power estimates prior to data collection are an essential part of good research planning. The procedures for estimating power when comparing proportions or percentages are more complex than they are when comparing means. Current procedures for estimating power when comparing two independent proportions are found in sources with limited availability and are confusing to many researchers. Procedures for estimating the power for detecting a difference between two independent proportions require the arcsine transformation of proportions. This transformation is intimidating to many researchers who lack confidence in their mathematical skills. These factors no doubt account, in part, for the fact that power estimates are even less common when comparing proportions than they are when comparing means. In addition, the arcsine transformation robs the "effect size" of some of its intuitive appeal because this metric is unfamiliar and does not consistently correspond to differences in percentages or proportions; it has ambiguous direct meaning. Quick power estimates for detecting a difference in two population proportions are expedient during the early phases of research planning; these estimates are tabled and graphed in this article and facilitate the determination of quick power estimates for various differences between two independent proportions. These estimates are shown to be conservative but quite accurate for most research situations (i.e., when the proportions fall in the range of .25 to .75).

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