There is a growing literature on design-based methods to estimate average treatment effects (ATEs) for randomized controlled trials (RCTs) for full sample analyses. This article extends these methods to estimate ATEs for discrete subgroups defined by pre-treatment variables, with an application to an RCT testing subgroup effects for a school voucher experiment in New York City. We consider ratio estimators for subgroup effects using regression methods, allowing for model covariates to improve precision, and prove a finite population central limit theorem. We discuss extensions to blocked and clustered RCT designs, and to other common estimators with random treatment-control sample sizes (or weights): post-stratification estimators, weighted estimators that adjust for data nonresponse, and estimators for Bernoulli trials. We also develop simple variance estimators that share features with robust estimators. Simulations show that the design-based subgroup estimators yield confidence interval coverage near nominal levels, even for small subgroups.

翻译：关于基于设计的方法估计随机对照试验（RCTs）全样本分析的平均处理效应（ATEs）的文献日益增多。本文将此类方法扩展至估计由预处理变量定义的离散子组的ATEs，并以一项检验纽约市学校代金券实验中子组效应的RCT为例进行应用。我们考虑了使用回归方法的子组效应比率估计量，引入模型协变量以提高精度，并证明了有限总体中心极限定理。我们讨论了向区组化与整群RCT设计的扩展，以及向具有随机处理-对照组样本量（或权重）的其他常见估计量（如事后分层估计量、调整数据无响应的加权估计量、以及伯努利试验估计量）的扩展。我们还开发了与稳健估计量共享特征的简单方差估计量。模拟结果显示，即使是针对小子组，基于设计的子组估计量的置信区间覆盖率仍接近名义水平。