Power to Detect Moderated Effects in Studies with Three-Level Partially Nested Data

Abstract

Comprehensive evaluation of treatment effects is aided by considerations for moderated effects. In educational research, the combination of natural hierarchical structures and prevalence of group-administered or shared facilitator treatments often produces three-level partially nested data structures. Literature details planning strategies for a variety of experimental designs when moderation effects are of interest but has yet to establish power formulas for detecting moderation effects in three-level partially nested designs. To address this gap, we derive and assess the accuracy of power formulas for detecting the different types of moderation effects possible in these designs. Using Monte Carlo simulation studies, we probe power rates and adequate sample sizes for detecting the different moderation effects while varying common influential factors including variance in the outcome explained by covariates, magnitude of the moderation effect, and sample sizes. The power formulas developed improve the planning of experimental studies with partial nesting and encourage the inclusion of moderator variables to capture for whom and under what conditions a treatment is effective. Educational researchers also have some initial guidance regarding adequate sample sizes and the factors that influence detecting moderation effects in three-level partially nested designs.