The sample size justification for a cluster randomized trial is messy. It requires the use of an intra-class correlation or something similar (the authors use the term within-cluster correlation). In a review of 300 cluster randomized trials, the authors found that in only about a third of the trials did the authors specify the within-cluster correlation. Even fewer compared this to the observed within-cluster correlation observed in the data. We need to do better.
Rutterforda C, Taljaard M, Dixon S, Copas A, Eldridge S. Reporting and methodological quality of sample size calculations in cluster randomized trials could be improved: a review. Journal of Clinical Epidemiology 68 (2015) 716e723. Available in html format.
You can find an earlier version of this page on my blog.