Statistical Power for Randomized Controlled Trials with Clusters of Varying Size

Power in multilevel models remains an area of interest to both methodologists and substantive researchers. In two-level designs, the total sample is a function of both the number of level-2 (e.g., schools) clusters and the average number of level-1 (e.g., classrooms) units per cluster. Traditional multilevel power calculations rely on either the arithmetic average or the harmonic mean when estimating the average number of level-1 units across clusters of unbalanced size. The current study evaluates and contrasts these two approaches with simulation-based power estimates in two-group two-level cluster randomized controlled trial designs with unbalanced cluster sizes. Results from the Monte Carlo study demonstrated the largest differences in simulated versus the two forms of calculated power occurred in study designs with large variability in the number of level-1 units sampled. Overall, power was less sensitive to the level-2 sample size or the effect size, regardless of the imbalance in cluster size. Implications of these findings for the design of cluster randomized trials are discussed. [This paper will be published in "The Journal of Experimental Education."]