Using Standard Tools From Finite Population Sampling to Improve Causal Inference for Complex Experiments
本文在有限总体框架下，将因果推断与抽样调查结合，提出适用于多处理组随机实验的推断方法，推导出比严格可加性更弱的无偏方差估计条件，并证明保守方差估计的合理性。
This article considers causal inference for treatment contrasts from a randomized experiment using potential outcomes in a finite population setting. Adopting a Neymanian repeated sampling approach that integrates such causal inference with finite population survey sampling, an inferential framework is developed for general mechanisms of assigning experimental units to multiple treatments. This framework extends classical methods by allowing the possibility of randomization restrictions and unequal replications. Novel conditions that are “milder” than strict additivity of treatment effects, yet permit unbiased estimation of the finite population sampling variance of any treatment contrast estimator, are derived. The consequences of departures from such conditions are also studied under the criterion of minimax bias, and a new justification for using the Neymanian conservative sampling variance estimator in experiments is provided. The proposed approach can readily be extended to the case of treatments with a general factorial structure.