It is well known, and without controversy, that in experiments with randomization at the individual or unit level, stratification on covariates is beneficial if these covariates are substantially correlated with the outcome. However, there is less agreement in the literature concerning the benefits of stratification in small samples if this correlation is potentially weak.

The comments regarding the relative merits of complete randomization, stratification, and pairwise randomization can be divided into three strands. The first concerns precision of point estimates. The second argument focuses on statistical power of tests of the null hypothesis of no effects. The third refers to the statistical limitations regarding the analysis of pairwise randomized experiments.

The argument that pairing leads to a reduction in accuracy is somewhat counterintuitive: if one constructs pairs based on a covariate that is completely independent of the potential outcomes, then pairing is for all intents and purposes equivalent to complete randomization.