Understanding Statistical Power in Cluster Randomized Trials: Challenges Posed by Differences in Notation and Terminology

Abstract: Research designs in which clusters are the unit of randomization are quite common in the social sciences. Given the multilevel nature of these studies, the power analyses for these studies are more complex than in a simple individually randomized trial. Tools are now available to help researchers conduct power analyses for cluster randomized trials. A key challenge facing researchers in using the tools is that different tools use different language, notation, and design parameters. This makes it difficult for researchers to communicate about the steps for a power analysis or to evaluate the appropriateness of a power analysis. This article provides explicit connections between the language, notation, and design parameters of two widely used approaches and tools for conducting power analyses, Optimal Design Plus and CRT Power. The formulas for translating design parameters between the two programs are provided and the comparability of the two programs is illustrated.