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Informed Bayesian t-Tests

Author

Listed:
  • Quentin F. Gronau
  • Alexander Ly
  • Eric-Jan Wagenmakers

Abstract

Across the empirical sciences, few statistical procedures rival the popularity of the frequentist t -test. In contrast, the Bayesian versions of the t -test have languished in obscurity. In recent years, however, the theoretical and practical advantages of the Bayesian t -test have become increasingly apparent and various Bayesian t-tests have been proposed, both objective ones (based on general desiderata) and subjective ones (based on expert knowledge). Here, we propose a flexible t-prior for standardized effect size that allows computation of the Bayes factor by evaluating a single numerical integral. This specification contains previous objective and subjective t-test Bayes factors as special cases. Furthermore, we propose two measures for informed prior distributions that quantify the departure from the objective Bayes factor desiderata of predictive matching and information consistency. We illustrate the use of informed prior distributions based on an expert prior elicitation effort. Supplementary materials for this article are available online.

Suggested Citation

  • Quentin F. Gronau & Alexander Ly & Eric-Jan Wagenmakers, 2020. "Informed Bayesian t-Tests," The American Statistician, Taylor & Francis Journals, vol. 74(2), pages 137-143, April.
  • Handle: RePEc:taf:amstat:v:74:y:2020:i:2:p:137-143
    DOI: 10.1080/00031305.2018.1562983
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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. Joaquim Fernando Pinto da Costa & Manuel Cabral, 2022. "Statistical Methods with Applications in Data Mining: A Review of the Most Recent Works," Mathematics, MDPI, vol. 10(6), pages 1-22, March.
    3. 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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