Regression-adjusted average treatment effect estimates in stratified randomized experiments

TL;DR

This paper develops a rigorous statistical framework for regression adjustment in stratified randomized experiments, demonstrating improved efficiency and providing reliable variance estimators for treatment effect inference.

Contribution

It establishes a finite population CLT for stratified experiments and proves the consistency and asymptotic normality of regression-adjusted estimators, with conservative variance estimation methods.

Findings

Regression-adjusted estimators are more efficient than simple difference-in-means.

Asymptotic normality holds under mild conditions.

Conservative variance estimators enable valid confidence intervals.

Abstract

Researchers often use linear regression to analyse randomized experiments to improve treatment effect estimation by adjusting for imbalances of covariates in the treatment and control groups. Our work offers a randomization-based inference framework for regression adjustment in stratified randomized experiments. Under mild conditions, we re-establish the finite population central limit theorem for a stratified experiment. We prove that both the stratified difference-in-means and the regression-adjusted average treatment effect estimators are consistent and asymptotically normal. The asymptotic variance of the latter is no greater and is typically lesser than that of the former. We also provide conservative variance estimators to construct large-sample confidence intervals for the average treatment effect.