To increase statistical efficiency in a randomized experiment, researchers often use stratification (i.e., blocking) in the design stage. However, conventional practices of stratification fail to exploit valuable information about the predictive relationship between covariates and potential outcomes. In this paper, I introduce an adaptive stratification procedure for increasing statistical efficiency when some information is available about the relationship between covariates and potential outcomes. I show that, in a paired design, researchers can rematch observations across different batches. For inference, I propose a stratified estimator that allows for nonparametric covariate adjustment. I then discuss the conditions under which researchers should expect gains in efficiency from stratification. I show that stratification complements rather than substitutes for regression adjustment, insuring against adjustment error even when researchers plan to use covariate adjustment. To evaluate the performance of the method relative to common alternatives, I conduct simulations using both synthetic data and more realistic data derived from a political science experiment. Results demonstrate that the gains in precision and efficiency can be substantial.

翻译：在随机化实验中，为提高统计效率，研究者常在设计阶段采用分层（即区组化）方法。然而，传统的分层实践未能充分利用协变量与潜在结果之间预测关系的有价值信息。本文提出了一种自适应分层程序，用于在已知协变量与潜在结果间部分关系信息时提升统计效率。研究表明，在配对设计中，研究者可以对不同批次的观测进行重新匹配。为进行统计推断，本文提出了一种允许非参数协变量调整的分层估计量。随后，论文讨论了在何种条件下研究者可预期通过分层获得效率提升。研究证明，分层与回归调整形成互补而非替代关系，即使在研究者计划使用协变量调整时，也能防范调整误差。为评估该方法相对于常见替代方案的性能，本文使用合成数据以及源自政治学实验的更现实数据进行了模拟研究。结果表明，该方法在精确性与效率方面均可带来显著提升。