The Benefits of Sampling Clusters with Probability Proportional to Size in Cluster-Randomized Experiments

• Activity Number: 406
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Survey Research Methods Section
• Author(s): Michael Higgins*+
• Keywords: Cluster-randomized ; experiments ; sampling ; probability proportional to size ; potential outcomes ; estimation

Abstract

In cluster-randomized experiments--commonly used in the social sciences--a subset of clusters is randomly drawn from the population, treatment is assigned randomly across clusters, and individuals are sampled within each cluster. The number of clusters sampled and the number of units sampled within each cluster is typically constrained by a budget allotted for the experiment. We derive estimators for the average treatment effect (ATE) for cluster-randomized experiments with an arbitrary number of treatment categories and an arbitrary pretreatment blocking of clusters under the Neyman-Rubin potential outcomes model for response. We demonstrate that sampling clusters with probability proportional to the number of units with a cluster will allow unbiased, location-invariant estimators of the ATE with smaller variance than those under simple random sampling of clusters. We show that, given a budget allotted for an experiment, choosing the number of clusters and number of units sampled within a cluster to maximize the power of tests can be accomplished by solving an integer programming problem.