Measure-Theoretic Musings Cannot Salvage the Full Bayesian Significance Test as a Measure of Evidence

Author:

Ly AlexanderORCID,Wagenmakers Eric-Jan

Abstract

AbstractLy and Wagenmakers (Computational Brain & Behavior:1–8, in press) critiqued the Full Bayesian Significance Test (FBST) and the associated statistic FBST ev: similar to the frequentist p-value, FBST ev cannot quantify evidence for the null hypothesis, allows sampling to a foregone conclusion, and suffers from the Jeffreys-Lindley paradox. In response, Kelter (Computational Brain & Behavior:1–11, 2022) suggested that the critique is based on a measure-theoretic premise that is often inappropriate in practice, namely the assignment of non-zero prior mass to a point-null hypothesis. Here we argue that the key aspects of our initial critique remain intact when the point-null hypothesis is replaced either by a peri-null hypothesis or by an interval-null hypothesis; hence, the discussion on the validity of a point-null hypothesis is a red herring. We suggest that it is tempting yet fallacious to test a hypothesis by estimating a parameter that is part of a different model. By rejecting any null hypothesis before it is tested, FBST is begging the question. Although FBST may be useful as a measure of surprise under a single model, we believe that the concept of evidence is inherently relative; consequently, evidence for competing hypotheses ought to be quantified by examining the relative adequacy of their predictions. This philosophy is fundamentally at odds with the FBST.

Funder

Nederlandse Organisatie voor Wetenschappelijk Onderzoek

HORIZON EUROPE European Research Council

Publisher

Springer Science and Business Media LLC

Subject

Developmental and Educational Psychology,Neuropsychology and Physiological Psychology

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