<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Bayes factors are an increasingly popular tool for indexing evidence from experiments. For two competing population models, the Bayes factor reflects the relative likelihood of observing some data under one model compared to the other. Computing Bayes factors can be difficult, requiring one to integrate the product of the likelihood and a prior distribution on the population parameter(s) for both competing models. Previous work has obviated this difficulty for independent-groups designs. In this paper, we develop a new analytic formula for computing Bayes factors directly from minimal summary statistics in repeated-measures designs. This work is an improvement on previous methods for computing Bayes factors from summary statistics (e.g., the BIC method), which produce Bayes factors that violate the Sellke upper bound of evidence for smaller sample sizes. The new approach taken in this paper requires knowing only the <italic>F</italic> -statistic and degrees of freedom, both of which are commonly reported in most empirical work. In addition to providing computational examples, we report a simulation study that benchmarks the new formula against other methods for computing Bayes factors in repeated-measures designs. Our new method provides an easy way for researchers to compute Bayes factors directly from a minimal set of summary statistics, allowing users to index the evidential value of their own data, as well as data reported in published studies.</p>
</abstract>

Bayes factors are an increasingly popular tool for indexing evidence from experiments. For two competing population models, the Bayes factor reflects the relative likelihood of observing some data under one model compared to the other. Computing Bayes factors can be difficult, requiring one to integrate the product of the likelihood and a prior distribution on the population parameter(s) for both competing models. Previous work has obviated this difficulty for independent-groups designs. In this paper, we develop a new analytic formula for computing Bayes factors directly from minimal summary statistics in repeated-measures designs. This work is an improvement on previous methods for computing Bayes factors from summary statistics (e.g., the BIC method), which produce Bayes factors that violate the Sellke upper bound of evidence for smaller sample sizes. The new approach taken in this paper requires knowing only the F -statistic and degrees of freedom, both of which are commonly reported in most empirical work. In addition to providing computational examples, we report a simulation study that benchmarks the new formula against other methods for computing Bayes factors in repeated-measures designs. Our new method provides an easy way for researchers to compute Bayes factors directly from a minimal set of summary statistics, allowing users to index the evidential value of their own data, as well as data reported in published studies.

Computing analytic Bayes factors from summary statistics in repeated-measures designs

Biometrical Letters

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Bayes factors are an increasingly popular tool for indexing evidence from experiments. For two competing population models, the Bayes factor reflects the...

Computing analytic Bayes factors from summary statistics in repeated-measures designs

Publicado en línea: 28 jun 2023

Páginas: 1 - 21

DOI: https://doi.org/10.2478/bile-2023-0001

Palabras clave
Bayes factor, Pearson Type VI distribution, summary statistics, repeated measures

© 2023 Thomas J. Faulkenberry et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Computing analytic Bayes factors from summary statistics in repeated-measures designs

Publicado en línea: 28 jun 2023

Páginas: 1 - 21

DOI: https://doi.org/10.2478/bile-2023-0001

Palabras claveBayes factor, Pearson Type VI distribution, summary statistics, repeated measures

© 2023 Thomas J. Faulkenberry et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Palabras clave
Bayes factor, Pearson Type VI distribution, summary statistics, repeated measures