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Title: Regression-adjusted average treatment effect estimates in stratified and sequentially randomized experiments Authors:  Hanzhong Liu - Tsinghua University (China) [presenting]
Abstract: Stratified and sequentially randomized experiments are widely used. Baseline covariates are often collected for each unit. Linear regressions are sometimes used to adjust minor imbalances of covariates in the treatment and control group. Asymptotic properties of regression adjustment in stratified and sequentially randomized experiments are studied under randomization-based inference. We allow both the number of strata and their sizes to be arbitrary, provided the total number of experimental units tends to infinity and each stratum has at least two treated and two control units. Under slightly stronger, we re-establish the finite population CLT for a stratified random sample. We prove that, under mild conditions, both the stratified difference-in-means and the regression-adjusted average treatment effect estimator are consistent and asymptotically normal. The asymptotic variance of the latter is no greater, and is typically lesser than that of the former when the proportion of treated units is asymptotically the same across strata or the number of stratum is bounded. The improvement depends on the extent to which the within-strata variation of the potential outcomes can be explained by the covariates. We also provide conservative variance estimators to construct large-sample confidence intervals for the average treatment effect, which are consistent if and only if the stratum-specific treatment effect is constant. Simulations and empirical illustration are provided.