Randomization of clusters versus randomization of persons within clusters: Which is preferable?

Many experiments aim at populations with persons nested within clusters. Randomization to treatment conditions can be done at the cluster level or at the person level within each cluster. The latter may result in control group contamination, and cluster randomization is therefore often preferred in practice. This article models the control group contamination, calculates the required sample sizes for both levels of randomization, and gives the degree of contamination for which cluster randomization is preferable above randomization of persons within clusters. Moreover, it provides examples of situations where one has to make a choice between both levels of randomization.