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

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  • Min Wang
  • Guangying Liu

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.

Suggested Citation

  • Min Wang & Guangying Liu, 2016. "A Simple Two-Sample Bayesian t -Test for Hypothesis Testing," The American Statistician, Taylor & Francis Journals, vol. 70(2), pages 195-201, May.
    • Handle: RePEc:taf:amstat:v:70:y:2016:i:2:p:195-201
    DOI: 10.1080/00031305.2015.1093027
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    References listed on IDEAS

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    1. Ruud Wetzels & Raoul P. P. P. Grasman & Eric-Jan Wagenmakers, 2012. "A Default Bayesian Hypothesis Test for ANOVA Designs," The American Statistician, Taylor & Francis Journals, vol. 66(2), pages 104-111, May.
    2. Bruce Western, 1999. "Bayesian Analysis for Sociologists," Sociological Methods & Research, , vol. 28(1), pages 7-34, August.
    3. Fernandez, Carmen & Ley, Eduardo & Steel, Mark F. J., 2001. "Benchmark priors for Bayesian model averaging," Journal of Econometrics, Elsevier, vol. 100(2), pages 381-427, February.
    4. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
    5. Min Wang & Xiaoqian Sun, 2014. "Bayes Factor Consistency for One-way Random Effects Model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(23), pages 5072-5090, December.
    6. Gonen, Mithat & Johnson, Wesley O. & Lu, Yonggang & Westfall, Peter H., 2005. "The Bayesian Two-Sample t Test," The American Statistician, American Statistical Association, vol. 59, pages 252-257, August.
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    Cited by:

    1. Riko Kelter, 2022. "A New Bayesian Two-Sample t Test and Solution to the Behrens–Fisher Problem Based on Gaussian Mixture Modelling with Known Allocations," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 14(3), pages 380-412, December.
    2. Riko Kelter, 2021. "Analysis of type I and II error rates of Bayesian and frequentist parametric and nonparametric two-sample hypothesis tests under preliminary assessment of normality," Computational Statistics, Springer, vol. 36(2), pages 1263-1288, June.
    3. Vo Van Tuan, 2020. "Quality Assurance in Higher Education According to AUN-QA: A Case Study of Private Universities," International Journal of Economics & Business Administration (IJEBA), International Journal of Economics & Business Administration (IJEBA), vol. 0(2), pages 402-419.
    4. Zhu, Yanli & Han, Xiaoyi & Chen, Ying, 2020. "Bayesian estimation and model selection of threshold spatial Durbin model," Economics Letters, Elsevier, vol. 188(C).
    5. Yen-Jung Chen & Robert Li-Wei Hsu, 2021. "Understanding the Difference of Teachers’ TLPACK before and during the COVID-19 Pandemic: Evidence from Two Groups of Teachers," Sustainability, MDPI, vol. 13(16), pages 1-17, August.

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