Revised standards for statistical evidence
Valen E. Johnson 1
Author Affiliations
Department of Statistics, Texas A&M University, College Station, TX 77843-3143
Edited by Adrian E. Raftery, University of Washington, Seattle, WA, and approved October 9, 2013 (received for review July 18, 2013)
Significance
The lack of reproducibility of scientific research undermines public confidence in science and leads to the misuse of resources when researchers attempt to replicate and extend fallacious research findings. Using recent developments in Bayesian hypothesis testing, a root cause of nonreproducibility is traced to the conduct of significance tests at inappropriately high levels of significance. Modifications of common standards of evidence are proposed to reduce the rate of nonreproducibility of scientific research by a factor of 5 or greater.
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.
Footnotes
1E-mail: vjohnson@stat.tamu.edu.
Author contributions: V.E.J. designed research, performed research, contributed new reagents/analytic tools, analyzed data, and wrote the paper.
The author declares no conflict of interest.
This article is a PNAS Direct Submission.
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