The Bayesian Range: Simple Methods for Incorporating Bayesian Reasoning into Psychological Research for Psychologists and Psychology Students Unfamiliar with Bayes' Theorem

Abstract

Bayes' theorem is used to calculate posterior probabilities of an event occurring given that a second event occurs. Advanced Bayesian statistics are now commonly used in psychology, but simpler versions can be adopted by social psychologists and psychology students who have little or no prior experience with Bayes’ Theorem using commonly obtained values. Using the post-hoc statistical power of a study, the selected alpha level for determining significance, and a subjective personal probability for the probability that a null hypothesis is false, it is possible to create a version of Bayes’ Theorem that calculates the probability that a null hypothesis is false given the null hypothesis is rejected. Because the subjective personal probability of the null being false is an estimate, the paper recommends that for novel empirical findings, researchers take one of two approaches to incorporating Bayes’ Theorem. The first is to calculate the posterior probability for a range of probabilities that the null is false. The second is to treat a novel finding as though it is unlikely to be true and give the probability that the null is false a low starting probability. With each replication, the posterior probability can be updated. Such a practice would encourage multiple replications of a novel finding before it can be reported with confidence. The emphasis of the paper is on the ready application of Bayes’ Theorem for non-experts in Bayesian statistics who are more comfortable with traditional significance testing.