A Simple Two-Sample Bayesian t-Test for Hypothesis Testing

Abstract

In this article, we propose an explicit closed-form Bayes factor for the problem of two-sample hypothesis testing. The proposed approach can be regarded as a Bayesian version of the pooled-variance t-statistic and has various appealing properties in practical applications. It relies on data only through the t-statistic and can thus be calculated by using an Excel spreadsheet or a pocket calculator. It avoids several undesirable paradoxes, which may be encountered by the previous Bayesian approach in the literature. Specifically, the proposed approach can be easily taught in an introductory statistics course with an emphasis on Bayesian thinking. Simulated and real data examples are provided for illustrative purposes.

keywords:

• Bayes factor
• Pooled-variance t-statistic
• Posterior probability
• Prior elicitation
• Teaching elementary statistics

Acknowledgment

The authors thank the editor, associate editor, and the two reviewers for their corrections and suggestions that have led to a significant improvement of the manuscript.

Funding

The first author was partially supported by the New Faculty Start-Up Fund at Michigan Technological University. The second author was supported by NSF of China Grant 11501503, NSF of Jiangsu Province of China Grant BK20131340, Social Science Foundation of Chinese Ministry of Education Grant 12YJCZH128, China Postdoctoral Science Foundation Grant 2014M560471, and Postdoctoral Science Foundation of Zhejiang Province of China Grant BSH1402026.