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

Abstract

Causal inference in completely randomized treatment-control studies with binary outcomes is discussed from Fisherian, Neymanian, and Bayesian perspectives, using the potential outcomes model. 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.

• Causal inference
• Constant causal effect
• Potential outcome
• Randomization-based inference
• Sensitivity analysis.

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