Inference in Experiments With Matched Pairs

• 成果类型: Article
• 署名作者: Bai, Yuehao; Romano, Joseph P.; Shaikh, Azeem M.
• 署名单位: University of Michigan System; University of Michigan; Stanford University; Stanford University; University of Chicago
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.1883437
• 发表日期: 2022
• 页码: 1726-1737
• 关键词: randomized experiments; MULTIVARIATE; balance

摘要

This article studies inference for the average treatment effect in randomized controlled trials where treatment status is determined according to a matched pairs design. By a matched pairs design, we mean that units are sampled iid from the population of interest, paired according to observed, baseline covariates and finally, within each pair, one unit is selected at random for treatment. This type of design is used routinely throughout the sciences, but fundamental questions about its implications for inference about the average treatment effect remain. The main requirement underlying our analysis is that pairs are formed so that units within pairs are suitably close in terms of the baseline covariates, and we develop novel results to ensure that pairs are formed in a way that satisfies this condition. Under this assumption, we show that, for the problem of testing the null hypothesis that the average treatment effect equals a prespecified value in such settings, the commonly used two-sample t-test and matched pairs t-test are conservative in the sense that these tests have limiting rejection probability under the null hypothesis no greater than and typically strictly less than the nominal level. We show, however, that a simple adjustment to the standard errors of these tests leads to a test that is asymptotically exact in the sense that its limiting rejection probability under the null hypothesis equals the nominal level. We also study the behavior of randomization tests that arise naturally in these types of settings. When implemented appropriately, we show that this approach also leads to a test that is asymptotically exact in the sense described previously, but additionally has finite-sample rejection probability no greater than the nominal level for certain distributions satisfying the null hypothesis. A simulation study and empirical application confirm the practical relevance of our theoretical results.