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Abstract:
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Cluster randomized experiments (CREs) have three defining features: (i) treatments are randomized to clusters of units rather than units themselves, (ii) clusters are formed a priori to experimentation and without researcher intervention, and (iii) the research objective and analysis are still centered on units. Conventionally, clusters in CREs are sampled using simple random sampling, but the inherent disparity between the experimental and observational units in CREs can lead to some analytical and design challenges. Stratifying or blocking on clusters based on important covariates can improve precision on estimation. However, we propose utilizing a different sampling scheme: sampling with probability proportional to size without replacement. Under the Neyman-Rubin potential outcomes framework, this modification leads to an unbiased Horvitz-Thompson estimator of the population average treatment effect, which we called HT-PPS, that can accommodate the clustering structure in CREs without having to compromise on desirable statistical properties. We then discuss how our estimator and sampling scheme can be incorporated into best practices for designing CREs.
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