How Many Cases per Cluster? Operationalizing the Number of Units per Cluster Relative to Minimum Detectable Effects in Two-Level Cluster Randomized Evaluations with Linear Outcomes

In cluster randomized evaluations, a treatment or intervention is randomly assigned to a set of clusters each with constituent individual units of observations (e.g., student units that attend schools, which are assigned to treatment). One consideration of these designs is how many units are needed per cluster to achieve adequate statistical power. Typically, researchers state that “about 30 units per cluster” is the most that will yield benefit towards statistical precision. To avoid rules of thumb not grounded in statistical theory and practical considerations, and instead provide guidance for this question, the ratio of the minimum detectable effect size (MDES) to the larger MDES with one less unit per cluster is related to the key parameters of the cluster randomized design. Formulas for this subsequent difference effect size ratio (SDESR) at a given number of units are provided, as are formulas for finding the number of units for an assumed SDESR. In general, the point of diminishing returns occurs with smaller numbers of units for larger values of the intraclass correlation.