Sample Size Planning for Detecting Mediation Effects: A Power Analysis Procedure Considering Uncertainty in Effect Size Estimates

Abstract

When planning mediation studies, researchers are often interested in the sample size needed to achieve adequate power for testing mediation. Power depends on population effect sizes, which are unknown in practice. In conventional power analysis, effect size estimates, however, are often used as population values, which could result in underpowered studies. Uncertainty in effect size estimates has been considered in other sample size planning contexts (e.g., t-test, ANOVA), but has not been handled properly for planning mediation studies. In the current study, we proposed an easy-to-use sample size planning method for testing mediation with uncertainty in effect size estimates considered. We conducted simulation studies to demonstrate the impact of uncertainty in effect size estimates on power of testing mediation, and to provide sample size suggestions under different levels of uncertainty. Empirical examples were provided to illustrate the application of our method. R functions and a web application were developed to facilitate implementation.