In observational causal inference, matched-pairs studies are often analyzed using randomization tests. While intuitively appealing, these tests are not formally justified by the randomness in the treatment assignment process (the "design") unless all matches are exact. This paper asks whether these tests can instead be justified by the random sampling of experimental units. We find that under fairly restrictive sampling assumptions, the paired randomization test based on a regression-adjusted test statistic may be asymptotically valid despite inexact matching. We propose a new randomization test based on matching with replacement that can be justified under weaker sampling assumptions.

翻译：在观察因果推断中,对匹配的随机研究往往使用随机测试来分析。这些测试虽然直观地具有吸引力,但并非由治疗任务分配过程(“设计”)的随机性(除非所有匹配都准确)来正式证明。本文询问这些测试是否可由实验单位随机抽样来证明。我们发现,根据相当限制性的抽样假设,基于回归调整测试统计的对称随机测试尽管不精确匹配,但可能同样有效。我们提议根据较弱的抽样假设,根据与替代的匹配,进行新的随机测试。