Bayesian Tests for One Sample Binary Data

  • Ton J. Cleophas
  • Aeilko H. Zwinderman


In studies with one sample of binomial data (yes no data) the z-test is pretty much traditionally used for analysis.

Instead of a z-test also a Bayesian one sample binomial test is possible. A one sample z-test of a hypertension study provided a z-value of 5.5545 and a p-value < 0.001.

A Bayesian one sample binomial test provided less support in favor of the above z-test with a Bayes factor (BF) of only 1.0. Nonetheless, as BFs run from ∞ to 0.0 and p-values run from 1.0 to 0.0, the Bayesian and traditional statistics are very well compatible with one another.

The 95% confidence intervals of the Bayesian and traditional tests of
  • [0.256–0.499], and

  • [0.2327–0.4945]

were pretty similar, although the Bayesian interval was a bit wider. Therefore, some overfitting of the Bayesian statistics could not be ruled out.

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

Personalised recommendations