Closed-form approximations of the two-sample Pearson Bayes factor

Abstract

In this paper, I present three closed-form approximations of the two-sample Pearson Bayes factor, a recently developed index of evidential value for data in two-group designs. The techniques rely on some classical asymptotic results about Gamma functions. These approximations permit simple closed-form calculation of the Pearson Bayes factor in cases where only minimal summary statistics are available (i.e., the t-score and degrees of freedom). Moreover, these approximations vastly outperform the classic BIC method for approximating Bayes factors from experimental designs.

arXiv commentrevised version: January 7, 2026. Accepted for publication in Lithuania Journal of Statistics