  Causal inference in completely randomized treatment-control studies with
binary outcomes is discussed from Fisherian, Neymanian and Bayesian
perspectives, using the potential outcomes framework. 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 non-additivity of
unit-level causal effects, can be applied to linear and non-linear estimands,
and dominate the existing methods, as verified theoretically and also through
simulation studies.
