Collaborative Research: Power Analyses for Moderator and Mediator Effects in Cluster Randomized Trials

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Cluster randomized experiments are considered the gold standards by which the impact of educational treatments and interventions can be determined. One of the most important design decisions that must be made is determining the size of the sample of classrooms or teachers or schools that must be studied in order to determine a statistically significant effect of the treatment on the outcomes under study. However, currently it is common for a cluster randomized trial to be designed to detect only the main effect of a treatment with adequate power. These studies miss out on being able to provide valid assessments of for whom a treatment might have an impact (mediation) and the conditions under which a treatment is effective (moderation). This study will advance our understanding of cluster randomized trials by developing power formulas and software for tests of multi-level moderation and mediation, as well as the combination of the two.This project will have three components as follows: 1). development of new formulas for estimating the statistical power to deter multilevel moderation, mediation, moderated-mediation and mediated-moderation in cluster randomized trials; 2). assess and validate the formulas through simulations; and, 3). Implement the formulas in two existing software programs, Optimal Design Plus and PowerUp!. The project will develop training materials for the use of the new analyses and develop and conduct workshops in order to disseminate the tool widely to the field.