  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
post-stratification. In this paper, 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.
