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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.

Détente: A Practical Understanding of P values and Bayesian Posterior Probabilities