Evaluating blocked randomized experiments from a potential outcomes perspective has two primary branches of work. The first focuses on larger blocks, with multiple treatment and control units in each block. The second focuses on matched pairs, with a single treatment and control unit in each block. These literatures not only provide different estimators for the standard errors of the estimated average impact, but they are also built on different sets of assumptions. Neither literature handles cases with blocks of varying size that contain singleton treatment or control units, a case which can occur in a variety of contexts, such as with different forms of matching or poststratification. In this article, we reconcile the literatures by carefully examining the performance of variance estimators under several different frameworks. We then use these insights to derive novel variance estimators for experiments containing blocks of different sizes.

从潜在结果的角度评估封闭的随机实验有两个主要的工作分支。第一个重点是较大的块，每个块中都有多个处理和控制单元。第二个重点是匹配对，每个块中都有一个处理和控制单元。这些文献不仅为估计的平均影响的标准误差提供了不同的估计量，而且还建立在不同的假设集合上。两种文献都没有处理具有包含单例治疗或控制单元的大小不同的块的案例，这种案例可以在多种情况下发生，例如具有不同形式的匹配或后分层。在本文中，我们通过仔细检查几种不同框架下方差估计量的性能来调和文献。