Familial inference: Tests for hypotheses on a family of centers

Steven MacEachern, PhD
Professor of Statistics, Ohio State University

The most basic and widely used statistical tests focus on the centers of the distributions. Yet, scientific hypotheses do not always specify a particular center. This ambiguity leaves a gap between scientific theory and statistical practice that can lead to the rejection of a true null. We propose testing a family of plausible centers. Each center in the family generates a point null hypothesis and the resulting family of hypotheses constitutes a familial null hypothesis. A Bayesian nonparametric procedure is devised to test the familial null. We visit the question of what it means to be the center of a distribution.

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