The False Positive Risk: A Proposal Concerning What to Do About p-Values

Abstract

It is widely acknowledged that the biomedical literature suffers from a surfeit of false positive results. Part of the reason for this is the persistence of the myth that observation of p < 0.05 is sufficient justification to claim that you have made a discovery. It is hopeless to expect users to change their reliance on p-values unless they are offered an alternative way of judging the reliability of their conclusions. If the alternative method is to have a chance of being adopted widely, it will have to be easy to understand and to calculate. One such proposal is based on calculation of false positive risk(FPR). It is suggested that p-values and confidence intervals should continue to be given, but that they should be supplemented by a single additional number that conveys the strength of the evidence better than the p-value. This number could be the minimum FPR (that calculated on the assumption of a prior probability of 0.5, the largest value that can be assumed in the absence of hard prior data). Alternatively one could specify the prior probability that it would be necessary to believe in order to achieve an FPR of, say, 0.05.

KEYWORDS:

• Bayes
• False positive
• False positive report probability
• False positive risk
• FPR
• Likelihood ratio
• Point null
• Positive predictive value

Acknowledgments

I am especially grateful to the following people: Dr Leonhard Held Epidemiology, Biostatistics and Prevention Institute, University of Zurich, CH-8001 Zurich, for helpful discussions; Dr R.A.J. Matthews for helpful discussions about his paper (Matthews 2018); Prof. Stephen Senn (Competence Center in Methodology and Statistics, CRP-Santé, Luxembourg); and Prof. D. Spiegelhalter for reading an earlier version of Colquhoun (2017) and suggesting the term “false positive risk.”