The Pearson Bayes factor: An analytic formula for computing evidential value from minimal summary statistics

In Bayesian hypothesis testing, evidence for a statistical model is quantified by the Bayes factor, which represents the relative likelihood of observed data under that model compared to another competing model. In general, computing Bayes factors is difficult, as computing the marginal likelihood of data under a given model requires integrating over a prior distribution of model parameters. This paper builds on prior work that uses the BIC to compute approximate Bayes factors directly from summary statistics from common experimental designs (i.e., t-test and analysis of variance). Here, I capitalize on a particular choice of prior distribution that allows the Bayes factor to be expressed without integral representation (i.e., an analytic expression), leading to a relatively simple formula (the Pearson Bayes factor) that requires only minimal summary statistics commonly reported in scientific papers, such as the t or F score and the degrees of freedom. This provides applied researchers with the ability to compute exact Bayes factors from minimal summary data, and thus easily assess the evidential value of any data for which these summary statistics are provided, even when the original data is not available.