Leveraging Sampling Costs to Design Cost-Efficient Experiments Investigating Moderation and Main Effects

Sampling costs vary across levels and treatment conditions (Hedges & Borenstein, 2014; Liu, 2003). Sample size allocation plays a critical role in determining the cost-efficiency and effectiveness of a study design (Cox & Kelcey, 2019; Konstantopoulos, 2009, 2011; Raudenbush, 1997; Shen & Kelcey, 2020, 2022a, 2022b). Moderation analyses can answer research questions about where, for whom, and under what conditions intervention effects are most salient, providing the evidence base for effective policy development (Raudenbush & Liu, 2000; Spybrook et al., 2016). Researchers must consider both the average/main and moderation effects when designing experimental studies detecting moderation effects. The present study aims to develop a jointly optimal design framework for multilevel experiments investigating moderation and main effects. Such a framework enables researchers to identify the optimal sampling allocations for both effects using minimum resources to achieve a target power level.