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There is a growing literature on design-based methods to estimate averagetreatment effects (ATEs) for randomized controlled trials (RCTs) for fullsample analyses. This article extends these methods to estimate ATEs fordiscrete subgroups defined by pre-treatment variables, with an application toan RCT testing subgroup effects for a school voucher experiment in New YorkCity. We consider ratio estimators for subgroup effects using regressionmethods, allowing for model covariates to improve precision, and prove a finitepopulation central limit theorem. We discuss extensions to blocked andclustered RCT designs, and to other common estimators with randomtreatment-control sample sizes (or weights): post-stratification estimators,weighted estimators that adjust for data nonresponse, and estimators forBernoulli trials. We also develop simple variance estimators that sharefeatures with robust estimators. Simulations show that the design-basedsubgroup estimators yield confidence interval coverage near nominal levels,even for small subgroups.

Design-Based RCT Estimators and Central Limit Theorems for Baseline Subgroup and Related Analyses