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Using Standard Tools From Finite Population Sampling to Improve Causal Inference for Complex Experiments

Author

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  • Rahul Mukerjee
  • Tirthankar Dasgupta
  • Donald B. Rubin
Abstract
This article considers causal inference for treatment contrasts from a randomized experiment using potential outcomes in a finite population setting. Adopting a Neymanian repeated sampling approach that integrates such causal inference with finite population survey sampling, an inferential framework is developed for general mechanisms of assigning experimental units to multiple treatments. This framework extends classical methods by allowing the possibility of randomization restrictions and unequal replications. Novel conditions that are “milder” than strict additivity of treatment effects, yet permit unbiased estimation of the finite population sampling variance of any treatment contrast estimator, are derived. The consequences of departures from such conditions are also studied under the criterion of minimax bias, and a new justification for using the Neymanian conservative sampling variance estimator in experiments is provided. The proposed approach can readily be extended to the case of treatments with a general factorial structure.

Suggested Citation

  • Rahul Mukerjee & Tirthankar Dasgupta & Donald B. Rubin, 2018. "Using Standard Tools From Finite Population Sampling to Improve Causal Inference for Complex Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 868-881, April.
    • Handle: RePEc:taf:jnlasa:v:113:y:2018:i:522:p:868-881
    DOI: 10.1080/01621459.2017.1294076
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    Citations

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    Cited by:

    1. Fangzhou Su & Peng Ding, 2021. "Model‐assisted analyses of cluster‐randomized experiments," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(5), pages 994-1015, November.
    2. Zhichao Jiang & Kosuke Imai & Anup Malani, 2023. "Statistical inference and power analysis for direct and spillover effects in two‐stage randomized experiments," Biometrics, The International Biometric Society, vol. 79(3), pages 2370-2381, September.
    3. Zhao, Anqi & Ding, Peng, 2021. "Covariate-adjusted Fisher randomization tests for the average treatment effect," Journal of Econometrics, Elsevier, vol. 225(2), pages 278-294.
    4. Nicole E. Pashley & Luke W. Miratrix, 2021. "Insights on Variance Estimation for Blocked and Matched Pairs Designs," Journal of Educational and Behavioral Statistics, , vol. 46(3), pages 271-296, June.
    5. Alqallaf, Fatemah A. & Huda, S. & Mukerjee, Rahul, 2019. "Causal inference from strip-plot designs in a potential outcomes framework," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 55-62.
    6. Zach Branson & Tirthankar Dasgupta, 2020. "Sampling‐based Randomised Designs for Causal Inference under the Potential Outcomes Framework," International Statistical Review, International Statistical Institute, vol. 88(1), pages 101-121, April.
    7. Jiafeng Chen, 2021. "Nonparametric Treatment Effect Identification in School Choice," Papers 2112.03872, arXiv.org, revised Oct 2023.
    8. Haoge Chang, 2023. "Design-based Estimation Theory for Complex Experiments," Papers 2311.06891, arXiv.org.

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