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Model-averaged Bayesian t tests
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DOI：10.3758/s13423-024-02590-5.png)
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Abstract
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One of the most common statistical analyses in experimental psychology concerns the comparison of two means using the frequentist t test. However, frequentist t tests do not quantify evidence and require various assumption tests. Recently, popularized Bayesian t tests do quantify evidence, but these were developed for scenarios where the two populations are assumed to have the same variance. As an alternative to both methods, we outline a comprehensive t test framework based on Bayesian model averaging. This new t test framework simultaneously takes into account models that assume equal and unequal variances, and models that use t-likelihoods to improve robustness to outliers. The resulting inference is based on a weighted average across the entire model ensemble, with higher weights assigned to models that predicted the observed data well. This new t test framework provides an integrated approach to assumption checks and inference by applying a series of pertinent models to the data simultaneously rather than sequentially. The integrated Bayesian model-averaged t tests achieve robustness without having to commit to a single model following a series of assumption checks. To facilitate practical applications, we provide user-friendly implementations in JASP and via the RoBTT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\texttt {RoBTT}$$\end{document} package in R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\texttt {R}$$\end{document}. A tutorial video is available at https://www.youtube.com/watch?v=EcuzGTIcorQ
Keywords:
Bayesian model-averaging
t test
Bayes factor
t-likelihood
Robust inference
Unequal variances
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