A classical measure of evidence for general null hypotheses

Details A classical measure of evidence for general null hypotheses A classical measure of evidence for general null hypotheses

2012-01-01

arxiv.org/abs/1201.0400v1

Mathematics

Statistics Theory

20 pages, one figure and one table

Scientific paper

In science, the most widespread statistical quantities are perhaps $p$-values. A general advice is to reject the null hypothesis $H_0$ if the corresponding $p$-value is sufficiently small (usually smaller than 0.05). Many criticisms regarding $p$-values have arisen in the scientific literature. In this paper, we present two examples where $p$-values lead to conflicting conclusions for nested hypotheses. To overcome these problems, we propose a frequentist measure of evidence for very general null hypotheses that satisfies logical requirements not met by $p$-values (e.g., the proposed measure is also a possibilistic measure). Based on its properties, we strongly recommend this measure as an additional summary of significance tests. At the end of the paper we give a short listing of open problems.

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