Coherent Power Analysis in Multilevel Studies Using Parameters From Surveys

Researchers designing multisite and cluster randomized trials of educational interventions will usually conduct a power analysis in the planning stage of the study. To conduct the power analysis, researchers often use estimates of intracluster correlation coefficients and effect sizes derived from an analysis of survey data. When there is heterogeneity in treatment effects across the clusters in the study, these parameters will need to be adjusted to produce an accurate power analysis for a hierarchical trial design. The relevant adjustment factors are derived and presented in the current article. The adjustment factors depend upon the covariance between treatment effects and cluster-specific average values of the outcome variable, illustrating the need for better information about this parameter. The results in the article also facilitate understanding of the relative power of multisite and cluster randomized studies conducted on the same population by showing how the parameters necessary to compute power in the two types of designs are related. This is accomplished by relating parameters defined by linear mixed model specifications to parameters defined in terms of potential outcomes.