Abstract
Researchers often apply moderation analyses to examine whether the effects of an intervention differ conditional on individual or cluster moderator variables such as gender, pretest, or school size. This study develops formulas for power analyses to detect moderator effects in two-level cluster randomized trials (CRTs) using hierarchical linear models. We derive the formulas for estimating statistical power, minimum detectable effect size difference and 95% confidence intervals for cluster- and individual-level moderators. Our framework accommodates binary or continuous moderators, designs with or without covariates, and effects of individual-level moderators that vary randomly or nonrandomly across clusters. A small Monte Carlo simulation confirms the accuracy of our formulas. We also compare power between main effect analysis and moderation analysis, discuss the effects of mis-specification of the moderator slope (randomly vs. non-randomly varying), and conclude with directions for future research. We provide software for conducting a power analysis of moderator effects in CRTs.
Highlights
Researchers often apply moderation analyses to examine whether the effects of an intervention differ conditional on individual or cluster moderator variables such as gender, pretest, or school size
Because a team planning a cluster randomized trials (CRTs) may be interested in the power for a moderator effect of a given magnitude or the minimum detectable effect size difference (MDESD) given sample size and the desired power, we provide the power formulas as well as the MDESD calculations and their corresponding confi dence intervals
We present the formulas for statistical power and the MDESD and its confidence intervals for the moderator variable at level 2 and subsequently for a moderator at Level 1
Summary
Researchers often apply moderation analyses to examine whether the effects of an intervention differ conditional on individual or cluster moderator variables such as gender, pretest, or school size. This study develops formulas for power analyses to detect moderator effects in two-level cluster randomized trials (CRTs) using hierarchical linear models. We derive the formulas for estimating statistical power, minimum detectable effect size difference and 95% confidence intervals for cluster- and individual-level moderators. Our framework accommodates binary or continuous moderators, designs with or without covariates, and effects of individual-level moderators that vary randomly or nonrandomly across clusters. We compare power between main effect analysis and moderation analysis, discuss the effects of mis-specification of the moderator slope (randomly vs non-randomly varying), and conclude with directions for future research. We provide software for conducting a power analysis of moderator effects in CRT
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