Tutorial: Power Analyses for Interaction Effects in Cross-Sectional Regressions

Abstract

Interaction analyses (also termed “moderation” analyses or “moderated multiple regression”) are a form of linear regression analysis designed to test whether the association between two variables changes when conditioned on a third variable. It can be challenging to perform a power analysis for interactions with existing software, particularly when variables are correlated and continuous. Moreover, although power is affected by main effects, their correlation, and variable reliability, it can be unclear how to incorporate these effects into a power analysis. The R package InteractionPoweR and associated Shiny apps allow researchers with minimal or no programming experience to perform analytic and simulation-based power analyses for interactions. At minimum, these analyses require the Pearson’s correlation between variables and sample size, and additional parameters, including reliability and the number of discrete levels that a variable takes (e.g., binary or Likert scale), can optionally be specified. In this tutorial, we demonstrate how to perform power analyses using our package and give examples of how power can be affected by main effects, correlations between main effects, reliability, and variable distributions. We also include a brief discussion of how researchers may select an appropriate interaction effect size when performing a power analysis.