Bayesian Tests for One Sample Continuous Data

  • Ton J. Cleophas
  • Aeilko H. Zwinderman


In studies with one sample continuous data a single outcome per patient is usually compared to zero.

Instead of t-test also a Bayesian one sample normal test is possible. A one sample t-test of a hypertension study provided a result significantly different from zero at t = 2.429, p = 0.038. A Bayesian one sample t-test provided support in favor of the above t-test with a Bayes factor of 0.506. The 95% confidence intervals of (1) the traditional test, (2) the Bayesian test, and (3) the bootstrap t-test were respectively
  • 0.1165–3.2835

  • −0.1769 to 3.5769

  • 0.4000–2.9000.

Therefore, some overfitting cannot be ruled out. We conclude that in this chapter the Bayes factor is a better test statistic than the traditional p-value is.

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. 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

Personalised recommendations