IngentaConnect The Bayesian Two-Sample t Test

Authors: Gönen, Mithat¹; Johnson, Wesley O.²; Lu, Yonggang³; Westfall, Peter H.³

Source: The American Statistician, Volume 59, Number 3, August 2005 , pp. 252-257(6)

Publisher: American Statistical Association

Abstract:

This article shows how the pooled-variance two-sample t statistic arises from a Bayesian formulation of the two-sided point null testing problem, with emphasis on teaching. We identify a reasonable and useful prior giving a closed-form Bayes factor that can be written in terms of the distribution of the two-sample t statistic under the null and alternative hypotheses, respectively. This provides a Bayesian motivation for the two-sample t statistic, which has heretofore been buried as a special case of more complex linear models, or given only roughly via analytic or Monte Carlo approximations. The resulting formulation of the Bayesian test is easy to apply in practice, and also easy to teach in an introductory course that emphasizes Bayesian methods. The priors are easy to use and simple to elicit, and the posterior probabilities are easily computed using available software, in some cases using spreadsheets.

Keywords: BAYES FACTOR; POSTERIOR PROBABILITY; PRIOR ELICITATION; TEACHING BAYESIAN STATISTICS

Document Type: Regular paper

DOI: 10.1198/000313005X55233

Affiliations: 1: Department of Epidemiology and Biostatistics, Memorial Sloan-Kettering Cancer Center, New York, NY 10021 2: Department of Statistics, University of California at Irvine, Irvine, CA 92697 3: Department of Information Systems and Quantitative Sciences, Texas Tech University, Lubbock, TX 79409

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