Familial Inference

Ryan Thompson (), Catherine Forbes (), Steven MacEachern () and Mario Peruggia ()

No 2/22, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

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.

Keywords: Bayesian bootstrap; Dirichlet process; Huber loss; hypothesis testing; pathwise optimization (search for similar items in EconPapers)
Pages: 26
Date: 2022
New Economics Papers: this item is included in nep-ecm and nep-ore
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