Sampling-based randomized designs for causal inference under the potential outcomes framework
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We establish the inferential properties of the mean-difference estimator for the average treatment effect in randomized experiments where each unit in a population of interest is randomized to one of two treatments and then units within treatment groups are randomly sampled. The properties of this estimator are well-understood in the experimental design scenario where first units are randomly sampled and then treatment is randomly assigned, but this is not the case for the aforementioned scenario where the sampling and treatment assignment stages are reversed. We find that the mean-difference estimator under this experimental design scenario is more precise than under the sample-first-randomize-second design, but only when there is treatment effect heterogeneity in the population. We also explore to what extent pre-treatment measurements can be used to improve upon the mean-difference estimator for this experimental design.
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