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

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  • Peng Ding
  • Tirthankar Dasgupta

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.

Suggested Citation

  • Peng Ding & Tirthankar Dasgupta, 2016. "A Potential Tale of Two-by-Two Tables From Completely Randomized Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 157-168, March.
    • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:513:p:157-168
    DOI: 10.1080/01621459.2014.995796
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    References listed on IDEAS

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    1. Donald B. Rubin, 2005. "Causal Inference Using Potential Outcomes: Design, Modeling, Decisions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 322-331, March.
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    Cited by:

    1. Jiannan Lu & Peng Ding & Tirthankar Dasgupta, 2018. "Treatment Effects on Ordinal Outcomes: Causal Estimands and Sharp Bounds," Journal of Educational and Behavioral Statistics, , vol. 43(5), pages 540-567, October.
    2. Jiannan Lu & Yunshu Zhang & Peng Ding, 2020. "Sharp bounds on the relative treatment effect for ordinal outcomes," Biometrics, The International Biometric Society, vol. 76(2), pages 664-669, June.
    3. Yasutaka Chiba, 2020. "Definition and Estimation of Covariate Effect Types in the Context of Treatment Effectiveness," Mathematics, MDPI, vol. 8(10), pages 1-11, September.

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