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Statistical hypotheses are translations of scientific hypotheses intostatements about one or more distributions, often concerning their centre.Tests that assess statistical hypotheses of centre implicitly assume a specificcentre, e.g., the mean or median. Yet, scientific hypotheses do not alwaysspecify a particular centre. This ambiguity leaves the possibility for a gapbetween scientific theory and statistical practice that can lead to rejectionof a true null. In the face of replicability crises in many scientificdisciplines, significant results of this kind are concerning. Rather thantesting a single centre, this paper proposes testing a family of plausiblecentres, such as that induced by the Huber loss function (the Huber family).Each centre in the family generates a testing problem, and the resulting familyof hypotheses constitutes a familial hypothesis. A Bayesian nonparametricprocedure is devised to test familial hypotheses, enabled by a novel pathwiseoptimization routine to fit the Huber family. The favourable properties of thenew test are demonstrated theoretically and experimentally. Two examples frompsychology serve as real-world case studies.

Familial inference: Tests for hypotheses on a family of centres