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A randomization-based perspective on analysis of variance: a test statistic robust to treatment effect heterogeneity

Author

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  • Peng Ding
  • Tirthankar Dasgupta

Abstract

Summary Fisher randomization tests for Neyman’s null hypothesis of no average treatment effect are considered in a finite-population setting associated with completely randomized experiments involving more than two treatments. The consequences of using the $F$ statistic to conduct such a test are examined, and we argue that under treatment effect heterogeneity, use of the $F$ statistic in the Fisher randomization test can severely inflate the Type I error under Neyman’s null hypothesis. We propose to use an alternative test statistic, derive its asymptotic distributions under Fisher’s and Neyman’s null hypotheses, and demonstrate its advantages through simulations.

Suggested Citation

  • Peng Ding & Tirthankar Dasgupta, 2018. "A randomization-based perspective on analysis of variance: a test statistic robust to treatment effect heterogeneity," Biometrika, Biometrika Trust, vol. 105(1), pages 45-56.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:1:p:45-56.
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    File URL: http://hdl.handle.net/10.1093/biomet/asx059
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    Citations

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    Cited by:

    1. 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.
    2. Rauf Ahmad & Per Johansson & Mårten Schultzberg, 2024. "Is Fisher inference inferior to Neyman inference for policy analysis?," Statistical Papers, Springer, vol. 65(6), pages 3425-3445, August.
    3. Peter L. Cohen & Colin B. Fogarty, 2022. "Gaussian prepivoting for finite population causal inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 295-320, April.
    4. Xiaokang Luo & Tirthankar Dasgupta & Minge Xie & Regina Y. Liu, 2021. "Leveraging the Fisher randomization test using confidence distributions: Inference, combination and fusion learning," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(4), pages 777-797, September.

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