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Tests that assess statistical hypotheses of centre implicitly assume a specific centre, e.g., the mean or median. Yet, scientific hypotheses do not always specify a particular centre. 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 centre, this paper proposes testing a family of plausible centres, such as that induced by the Huber loss function. Each centre 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 novel pathwise optimization routine to fit the Huber family. The favourable properties of the new test are demonstrated theoretically and experimentally. Two examples from psychology serve as real-world case studies.<\/jats:p>","DOI":"10.1093\/biomet\/asad074","type":"journal-article","created":{"date-parts":[[2023,11,27]],"date-time":"2023-11-27T17:14:04Z","timestamp":1701105244000},"page":"1029-1045","source":"Crossref","is-referenced-by-count":2,"title":["Familial inference: tests for hypotheses on a family of centres"],"prefix":"10.1093","volume":"111","author":[{"given":"Ryan","family":"Thompson","sequence":"first","affiliation":[{"name":"Department of Econometrics and Business Statistics, Monash University , Wellington Road , Clayton, Victoria 3800, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Catherine S","family":"Forbes","sequence":"additional","affiliation":[{"name":"Department of Econometrics and Business Statistics, Monash University , Wellington Road , Clayton, Victoria 3800, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Steven N","family":"MacEachern","sequence":"additional","affiliation":[{"name":"Department of Statistics, The Ohio State University , 1958 Neil Avenue , Columbus, Ohio 43210, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mario","family":"Peruggia","sequence":"additional","affiliation":[{"name":"Department of Statistics, The Ohio State University , 1958 Neil Avenue , Columbus, Ohio 43210, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,11,28]]},"reference":[{"key":"2024090419241810700_asad074-B1","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1214\/19-BA1155","article-title":"Bayesian bootstraps for massive data","volume":"15","author":"Barrientos","year":"2020","journal-title":"Bayesian Anal."},{"key":"2024090419241810700_asad074-B2","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611974997","volume-title":"First-Order Methods in Optimization","author":"Beck","year":"2017"},{"key":"2024090419241810700_asad074-B3","doi-asserted-by":"crossref","first-page":"1469","DOI":"10.1634\/theoncologist.2019-0175","article-title":"Median survival or mean survival: which measure is the most appropriate for patients, physicians, and policymakers?","volume":"24","author":"Ben-Aharon","year":"2019","journal-title":"Oncologist"},{"key":"2024090419241810700_asad074-B4","first-page":"1","article-title":"Time for a change: a tutorial for comparing multiple classifiers through Bayesian analysis","volume":"18","author":"Benavoli","year":"2017","journal-title":"J. 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