Inference for Cluster Randomized Experiments with Nonignorable Cluster Sizes

We consider the problem of inference in randomized experiments where treatment is assigned at the level of a cluster and cluster sizes are nonignorable, in that cluster-level average treatment effects may depend on the cluster sizes. In a novel superpopulation framework in which cluster sizes are modeled as random and allowing for only a subset of the units within each cluster to be sampled, we distinguish between two parameters of interest that differ in how they average the treatment effect across units. For each parameter, we provide methods for inference when treatment is assigned using a covariate-adaptive stratified randomization procedure.