# Estimating Bayes factors from minimal summary statistics in repeated measures analysis of variance designs

## TL;DR

This paper introduces a simple formula to estimate Bayes factors in repeated measures ANOVA using only basic summary statistics, facilitating easier Bayesian analysis for researchers.

## Contribution

The paper presents a minimal BIC-based formula for estimating Bayes factors from limited summary data in repeated measures designs, improving accessibility and efficiency.

## Key findings

- The formula performs well compared to more complex methods.
- It requires only F-statistic, sample size, and number of measurements.
- It enables Bayesian evidence estimation from published summary statistics.

## Abstract

In this paper, I develop a formula for estimating Bayes factors directly from minimal summary statistics produced in repeated measures analysis of variance designs. The formula, which requires knowing only the $F$-statistic, the number of subjects, and the number of repeated measurements per subject, is based on the BIC approximation of the Bayes factor, a common default method for Bayesian computation with linear models. In addition to providing computational examples, I report a simulation study in which I demonstrate that the formula compares favorably to a recently developed, more complex method that accounts for correlation between repeated measurements. The minimal BIC method provides a simple way for researchers to estimate Bayes factors from a minimal set of summary statistics, giving users a powerful index for estimating the evidential value of not only their own data, but also the data reported in published studies.