Statistical Power for Detecting Moderation in Partially Nested Designs

Abstract

Analysis of the differential treatment effects across targeted subgroups and contexts is a critical objective in many evaluations because it delineates for whom and under what conditions particular programs, therapies or treatments are effective. Unfortunately, it is unclear how to plan efficient and effective evaluations that include these moderated effects when the design includes partial nesting (i.e., disparate grouping structures across treatment conditions). In this study, we develop statistical power formulas to identify requisite sample sizes and guide the planning of evaluations probing moderation under two-level partially nested designs. The results suggest that the power to detect moderation effects in partially nested designs is substantially influenced by sample size, moderation effect size, and moderator variance structure (i.e., varies within groups only or within and between groups). We implement the power formulas in the R-Shiny application PowerUpRShiny and demonstrate their use to plan evaluations.