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Détente: A Practical Understanding of P values and Bayesian Posterior Probabilities
Author(s) -
Ruberg Stephen J.
Publication year - 2021
Publication title -
clinical pharmacology and therapeutics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.941
H-Index - 188
eISSN - 1532-6535
pISSN - 0009-9236
DOI - 10.1002/cpt.2004
Subject(s) - frequentist inference , bayesian probability , statistical inference , bayesian inference , frequentist probability , posterior probability , bayesian statistics , inference , p value , statistical hypothesis testing , econometrics , psychology , conditional probability , fiducial inference , statement (logic) , null hypothesis , statistics , epistemology , computer science , mathematics , artificial intelligence , philosophy
Null hypothesis significance testing (NHST) with its benchmark P value < 0.05 has long been a stalwart of scientific reporting and such statistically significant findings have been used to imply scientifically or clinically significant findings. Challenges to this approach have arisen over the past 6 decades, but they have largely been unheeded. There is a growing movement for using Bayesian statistical inference to quantify the probability that a scientific finding is credible. There have been differences of opinion between the frequentist (i.e., NHST) and Bayesian schools of inference, and warnings about the use or misuse of P values have come from both schools of thought spanning many decades. Controversies in this arena have been heightened by the American Statistical Association statement on P values and the further denouncement of the term “statistical significance” by others. My experience has been that many scientists, including many statisticians, do not have a sound conceptual grasp of the fundamental differences in these approaches, thereby creating even greater confusion and acrimony. If we let A represent the observed data, and B represent the hypothesis of interest, then the fundamental distinction between these two approaches can be described as the frequentist approach using the conditional probability pr(A | B) (i.e., the P value), and the Bayesian approach using pr(B | A) (the posterior probability). This paper will further explain the fundamental differences in NHST and Bayesian approaches and demonstrate how they can co‐exist harmoniously to guide clinical trial design and inference.