Statistical Power for Randomized Controlled Trials with Clusters of Varying Size

Abstract

In two-level designs, the total sample is a function of both the number of Level 2 clusters and the average number of Level 1 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 compares these two approaches with simulation-based power estimates in cluster randomized controlled trial designs with unbalanced cluster size. Results from the Monte Carlo study demonstrated that the largest differences in simulated and calculated power occurred in study designs with large variability in the number of Level 1 units sampled. We discuss implications of these findings for the design of cluster randomized trials.

Keywords:

• Harmonic mean
• multilevel models
• power
• sample size
• unbalanced clusters

Acknowledgements

The authors thank members of our larger research team including Drs. Elise Pas, Rashelle Musci, and Ji Hoon Ryoo.

Additional information

Funding

The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through Grants R305H150027 and R305A150221 to the University of Virginia. The opinions expressed are those of the authors and do not represent views of the Institute or the U.S. Department of Education.