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Abstract:
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While attractive from both intuitive and theoretical perspectives, paired experiments suffer from certain analytical limitations not present in stratified experiments. In short, for the classical estimator of the sample average treatment effect (SATE) in a stratified experiment, the corresponding variance estimator is conservative unless unit-level treatment effects are constant within strata; however, in paired experiments the traditional variance estimator is conservative unless treatment effects are constant across pairs. Using insights from agnostic regression adjustment in randomized experiments, we present an improved estimator for the variance of the classical difference-in-means estimator for the SATE in paired experiments. The variance estimator is still conservative in expectation for the true variance of the sample average treatment effect, but is asymptotically no larger than the classical variance estimator under mild conditions. The improvements stem from exploitation of effect modification, and thus the magnitude of the improvement depends upon on the extent to which effect modification can be explained by observed covariates.
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