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Familial Inference

Author

Listed:
  • Ryan Thompson
  • Catherine S. Forbes
  • Steven N. MacEachern
  • Mario Peruggia

Abstract

Statistical hypotheses are translations of scientific hypotheses into statements about one or more distributions, often concerning their center. Tests that assess statistical hypotheses of center implicitly assume a specific center, e.g., the mean or median. Yet, scientific hypotheses do not always specify a particular center. This ambiguity leaves the possibility for a gap between scientific theory and statistical practice that can lead to rejection of a true null. In the face of replicability crises in many scientific disciplines, "significant results" of this kind are concerning. Rather than testing a single center, this paper proposes testing a family of plausible centers, such as that induced by the Huber loss function (the "Huber family"). Each center in the family generates a testing problem, and the resulting family of hypotheses constitutes a familial hypothesis. A Bayesian nonparametric procedure is devised to test familial hypotheses, enabled by a pathwise optimization routine to fit the Huber family. The favorable properties of the new test are verified through numerical simulation in one- and two-sample settings. Two experiments from psychology serve as real-world case studies.

Suggested Citation

  • Ryan Thompson & Catherine S. Forbes & Steven N. MacEachern & Mario Peruggia, 2022. "Familial Inference," Monash Econometrics and Business Statistics Working Papers 2/22, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2022-2
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    File URL: https://www.monash.edu/business/ebs/research/publications/ebs/wp2-2022.pdf
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    References listed on IDEAS

    as
    1. Dateng Li & Jing Cao & Song Zhang, 2020. "Power analysis for cluster randomized trials with multiple binary co‐primary endpoints," Biometrics, The International Biometric Society, vol. 76(4), pages 1064-1074, December.
    2. Luz Adriana Pereira & Daniel Taylor‐Rodríguez & Luis Gutiérrez, 2020. "A Bayesian nonparametric testing procedure for paired samples," Biometrics, The International Biometric Society, vol. 76(4), pages 1133-1146, December.
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    More about this item

    Keywords

    Bayesian bootstrap; Dirichlet process; Huber loss; hypothesis testing; pathwise optimization;
    All these keywords.

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