TY - JOUR

T1 - The Bayesian two-sample t test

AU - Gönen, Mithat

AU - Johnson, Wesley O.

AU - Lu, Yonggang

AU - Westfall, Peter H.

PY - 2005/8

Y1 - 2005/8

N2 - 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.

AB - 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.

KW - Bayes factor

KW - Posterior probability

KW - Prior elicitation

KW - Teaching Bayesian statistics

UR - http://www.scopus.com/inward/record.url?scp=23844462531&partnerID=8YFLogxK

U2 - 10.1198/000313005X55233

DO - 10.1198/000313005X55233

M3 - Article

AN - SCOPUS:23844462531

SN - 0003-1305

VL - 59

SP - 252

EP - 257

JO - American Statistician

JF - American Statistician

IS - 3

ER -