A Potential Tale of Two-by-Two Tables From Completely Randomized Experiments

A randomization-based justification of Fisher’s exact test is provided. Arguing that the crucial assumption of constant causal effect is often unrealistic, and holds only for extreme cases, some new asymptotic and Bayesian inferential procedures are proposed.

The proposed procedures exploit the intrinsic nonadditivity of unit-level causal effects, can be applied to linear and nonlinear estimands, and dominate the existing methods, as verified theoretically and also through simulation studies. Supplementary materials for this article are available online.