A Potential Tale of Two by Two Tables from Completely Randomized Experiments

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

Treatment Effects on Ordinal Outcomes: Causal Estimands and Sharp Bounds

Assessing the causal effects of interventions on ordinal outcomes is an important objective of many educational and behavioral studies. Under the potential outcomes framework, we can define causal effects as comparisons between the potential outcomes under treatment and control. However, unfortunately, the average causal effect, often the parameter of interest, is difficult to interpret for ordinal outcomes. To address this challenge, we propose to use two causal parameters, which are defined as the probabilities that the treatment is beneficial and strictly beneficial for the experimental units. However, although well-defined for any outcomes and of particular interest for ordinal outcomes, the two aforementioned parameters depend on the association between the potential outcomes, and are therefore not identifiable from the observed data without additional assumptions. Echoing recent advances in the econometrics and biostatistics literature, we present the sharp bounds of the aforementioned causal parameters for ordinal outcomes, under fixed marginal distributions of the potential outcomes. Because the causal estimands and their corresponding sharp bounds are based on the potential outcomes themselves, the proposed framework can be flexibly incorporated into any chosen models of the potential outcomes, and are directly applicable to randomized experiments, unconfounded observational studies, and randomized experiments with noncompliance. We illustrate our methodology via numerical examples and three real-life applications related to educational and behavioral research.Comment: Accepted by the Journal of Education and Behavioral Statistic