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. 2013 Nov 26;110(48):19313-7.
doi: 10.1073/pnas.1313476110. Epub 2013 Nov 11.

Revised standards for statistical evidence

Valen E Johnson  1
Affiliations

Revised standards for statistical evidence

Valen E Johnson. Proc Natl Acad Sci U S A. .

Abstract

Recent advances in Bayesian hypothesis testing have led to the development of uniformly most powerful Bayesian tests, which represent an objective, default class of Bayesian hypothesis tests that have the same rejection regions as classical significance tests. Based on the correspondence between these two classes of tests, it is possible to equate the size of classical hypothesis tests with evidence thresholds in Bayesian tests, and to equate P values with Bayes factors. An examination of these connections suggest that recent concerns over the lack of reproducibility of scientific studies can be attributed largely to the conduct of significance tests at unjustifiably high levels of significance. To correct this problem, evidence thresholds required for the declaration of a significant finding should be increased to 25-50:1, and to 100-200:1 for the declaration of a highly significant finding. In terms of classical hypothesis tests, these evidence standards mandate the conduct of tests at the 0.005 or 0.001 level of significance.

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Conflict of interest statement

The author declares no conflict of interest.

Figures

Fig. 1.
Fig. 1.
Evidence thresholds and size of corresponding significance tests. The UMPBT and significance tests used to construct this plot have the same (z, formula image, and binomial tests) or approximately the same (t tests) rejection regions. The smooth curves represent, from Top to Bottom, t tests based on 20, 30, and 60 degrees of freedom, the z test, and the χ2 test on 1 degree of freedom. The discontinuous curves reflect the correspondence between tests of a binomial proportion based on 20, 30, or 60 observations when the null hypothesis is p0 = 0.5.
Fig. 2.
Fig. 2.
P values versus UMPBT Bayes factors. This plot depicts approximate Bayes factors derived from 765 t statistics reported by Wetzels et al. (20). A breakdown of the curvilinear relationship between Bayes factors and P values occurs in the lower right portion of the plot, which corresponds to t statistics that produce Bayes factors that are near their maximum value.
Fig. 3.
Fig. 3.
Histogram of P values that were less than 0.05 and reported in ref. .
See this image and copyright information in PMC

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