Bayesian Paired T-Test

  • Ton J. Cleophas
  • Aeilko H. Zwinderman


In studies with paired samples of continuous data the mean difference is usually compared to zero. Instead of a paired t-test also a Bayesian analysis on the mean difference is possible. A traditional paired t-test of two treatment modalities on hours of sleep provided a significant difference with t = 3.184, p-value = 0.011. A Bayesian paired t-test provided support in favor of the traditional test with a Bayes factor of 0.178. The 95% confidence intervals of (1) traditional, (2) Bayesian and (3) bootstrap tests were respectively:
  • between 0.51517 and 3.04483,

  • between 0.2809 and 3.2791,

  • between 0.76025 and 2.8400.

The traditional t-test confidence interval was wider than the bootstraps t-test confidence interval, while the Bayesian 95% credible interval is the widest. Some overfitting in the traditional and Bayesian intervals can not be ruled out, and, in the Bayesian, this may be more so than in the traditional. Nonetheless, the amount of overfitting is limited with confidence intervals between ≈2.3 and ≈2.8.

Suggested Reading1,2

  1. Statistics applied to clinical studies 5th edition, 2012Google Scholar
  2. Machine learning in medicine a complete overview, 2015Google Scholar
  3. SPSS for starters and 2nd levelers 2nd edition, 2015Google Scholar
  4. Clinical data analysis on a pocket calculator 2nd edition, 2016Google Scholar
  5. Understanding clinical data analysis from published research, 2016Google Scholar
  6. Modern Meta-analysis, 2017Google Scholar
  7. Regression Analysis in Clinical Research, 2018Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Ton J. Cleophas
    • 1
  • Aeilko H. Zwinderman
    • 2
  1. 1.Department Medicine Albert Schweitzer HospitalAlbert Schweitzer HospitalSliedrechtThe Netherlands
  2. 2.Department Biostatistics and EpidemiologyAcademic Medical Center Department Biostatistics and EpidemiologyAmsterdamThe Netherlands

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