  There are two general views in causal analysis of experimental data: the
super population view that the units are an independent sample from some
hypothetical infinite populations, and the finite population view that the
potential outcomes of the experimental units are fixed and the randomness comes
solely from the physical randomization of the treatment assignment. These two
views differs conceptually and mathematically, resulting in different sampling
variances of the usual difference-in-means estimator of the average causal
effect. Practically, however, these two views result in identical variance
estimators. By recalling a variance decomposition and exploiting a
completeness-type argument, we establish a connection between these two views
in completely randomized experiments. This alternative formulation could serve
as a template for bridging finite and super population causal inference in
other scenarios.
