Model-averaged Bayesian t tests.

Area of Science:

• Psychology
• Statistics
• Bayesian Inference

Background:

• Frequentist t-tests are common but do not quantify evidence and require assumption checks.
• Existing Bayesian t-tests quantify evidence but assume equal variances.
• Both methods have limitations in handling real-world data assumptions.

Purpose of the Study:

• To develop a comprehensive t-test framework using Bayesian model averaging as an alternative to frequentist and existing Bayesian methods.
• To integrate assumption checks and inference into a single, robust procedure.
• To provide a more flexible and informative approach to comparing two means in experimental psychology.

Main Methods:

• Bayesian model averaging framework incorporating models with equal and unequal variances.
• Inclusion of t-likelihoods for enhanced robustness against outliers.
• Weighted averaging of model predictions based on their fit to the observed data.

Main Results:

• The proposed Bayesian model-averaged t-test framework simultaneously considers multiple models, including those with equal and unequal variances and t-likelihoods.
• Inference is achieved through a weighted average across an ensemble of models, prioritizing those that best predict the data.
• This approach integrates assumption checking and statistical inference, offering robustness without sequential model selection.

Conclusions:

• The Bayesian model-averaged t-test provides a robust and integrated approach to comparing two means, addressing limitations of frequentist and standard Bayesian methods.
• It offers improved robustness to assumption violations, such as unequal variances and outliers, by averaging across relevant models.
• User-friendly implementations in JASP and R facilitate practical application of this advanced statistical framework.