# Optimal group sizes for testing group mean differences using the Bayes factor

## TL;DR

This paper explores how to best choose group sizes for comparing group averages using Bayesian methods, showing that optimal sizes depend on costs, variances, and group means.

## Contribution

The paper introduces optimal group sizes for Bayes factor hypothesis testing, considering variances, costs, and group means.

## Key findings

- Optimal group sizes depend on variances, costs, and group means in Bayesian hypothesis testing.
- Using conventional optimal design or equal group sizes can reduce the Bayes factor significantly.
- A Shiny app is provided to apply the optimal design methodology in practice.

## Abstract

Determination of group sizes is an important issue when planning a study that aims to compare mean outcomes across groups. Using equal group sizes is not the best choice in the case of heterogeneous costs and/or variances. Conventional optimal design methodology has shown that groups with higher variance and lower costs should include more subjects. However, these results are based on the framework of null hypothesis significance testing, which has received severe criticism over the past decades. The Bayesian approach to hypothesis testing has been proposed as an alternative and uses the Bayes factor to quantify the support of a hypothesis given the data. Group sizes that maximize the Bayes factor are determined, and it is shown how these optimal group sizes depend on the variances, costs and group means. Furthermore, it is shown to what degree the Bayes factor becomes smaller while using conventional optimal design methodology or equal group sizes. The optimal design methodology is illustrated using examples on multidisciplinary pain management and psychological status and asthma outcomes. A Shiny app has been made available to facilitate the use of the optimal design methodology.