Computing Bayes factors to measure evidence from experiments: An extension of the BIC approximation

TL;DR

This paper introduces an extended formula for computing Bayes factors directly from common ANOVA statistics, making Bayesian hypothesis testing more accessible and comparable to existing methods.

Contribution

It develops a new approximation for Bayes factors using typical ANOVA outputs, facilitating easier Bayesian analysis without specialized software.

Findings

Approximate Bayes factors align closely with existing software results.

The method requires minimal input data from ANOVA reports.

Simulations demonstrate the approximation's reliability across scenarios.

Abstract

Bayesian inference affords scientists with powerful tools for testing hypotheses. One of these tools is the Bayes factor, which indexes the extent to which support for one hypothesis over another is updated after seeing the data. Part of the hesitance to adopt this approach may stem from an unfamiliarity with the computational tools necessary for computing Bayes factors. Previous work has shown that closed form approximations of Bayes factors are relatively easy to obtain for between- groups methods, such as an analysis of variance or t-test. In this paper, I extend this approximation to develop a formula for the Bayes factor that directly uses information that is typically reported for ANOVAs (e.g., the F ratio and degrees of freedom). After giving two examples of its use, I report the results of simulations which show that even with minimal input, this approximate Bayes factor produces similar results to existing software solutions.