Statistical hypotheses are translations of scientific hypotheses into statements about one or more distributions, often concerning their centre. 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 (the Huber family). 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.

翻译：统计假设是将科学假设转化为关于一个或多个分布的陈述，通常涉及这些分布的中心。检验统计中心假设的方法通常隐含地假定一个特定的中心，例如均值或中位数。然而，科学假设并不总是指定某个特定的中心。这种模糊性可能导致科学理论与统计实践之间存在差距，从而可能拒绝真实的原假设。面对多个学科中出现的可重复性危机，这类显著性结果令人担忧。本文不检验单一中心，而是提出检验一个合理的中心族，例如由Huber损失函数导出的Huber族。族中的每个中心都会生成一个检验问题，由此产生的假设族构成一个族假设。我们设计了一种贝叶斯非参数方法来检验族假设，该方法通过一种新颖的路径优化例程来拟合Huber族。新方法在理论和实验上均展现出优越性质。来自心理学的两个实例被用作实际案例研究。