Using epistemic ratios to evaluate hypotheses: an imprecision penalty for imprecise hypotheses.

Abstract

According to Bayesians, the null hypothesis significance-testing procedure is not deductively valid because it involves the retention or rejection of the null hypothesis under conditions where the posterior probability of that hypothesis is not known. Other criticisms are that this procedure is pointless and encourages imprecise hypotheses. However, according to non-Bayesians, there is no way of assigning a prior probability to the null hypothesis, and so Bayesian statistics do not work either. Consequently, no procedure has been accepted by both groups as providing a compelling reason to accept or reject hypotheses. The author aims to provide such a method. In the process, the author distinguishes between probability and epistemic estimation and argues that, although both are important in a science that is not completely deterministic, epistemic estimation is most relevant for hypothesis testing. Based on this analysis, the author proposes that hypotheses be evaluated via epistemic ratios and explores the implications of this proposal. One implication is that it is possible to encourage precise theorizing by imposing a penalty for imprecise hypotheses.