Fig. 1

Trial designs that achieve 90% power at the two-sided 5% significance level to detect various effect sizes, δ/σ, for different combinations of ρ (the intracluster correlation for two individuals sampled at the same time from the same cluster) and τ (representing the decay in this correlation over the duration of the trial). Designs assume K = 30 clusters which are arranged down the vertical axis of each schematic, and M = 100 eligible participants presenting in each cluster, arranged along the horizontal axis. Underneath each schematic is the overall sample size. In those instances where even a complete design is not powerful enough to detect the given effect size, we illustrate the most powerful complete design that the algorithm can find