Bayesian Pearson Correlation Analysis

  • Ton J. Cleophas
  • Aeilko H. Zwinderman


In studies with two continuous variables usually named the x-values and y-values a linear relation between the two variables can be assessed with the help of the Pearson correlation coefficient R. R is a measure of strength of association, and varies from −1 to +1. Instead of a traditional Pearson correlation analysis a Bayesian analysis of linear correlation is possible.

A traditional analysis of Pearson linear correlation analysis provided an r-value of 0.483 with an F statistic of 10047, p-value 0.003. A Bayesian Analysis of Pearson linear correlation provided support in favor of the traditional test with a Bayes factor of 0.105.

The maximum of the posterior likelihood distribution was 0.478 with 95% credible interval
$$ 0.183\kern0.5em \mathrm{to}\kern0.5em 0.685. $$

This was less wide than the 95% confidence interval of the traditional Pearson linear correlation which was

$$ {\displaystyle \begin{array}{l}0.483\pm 2\times \left[\left(4.83\times 0.553\right)/0.174\right]=\\ {}0.483\pm 2\times 0.1535=\\ {}\mathrm{between}\ 0.176\ \mathrm{and}\ 0.790.\end{array}} $$

Thus, the Bayesian analysis provided slightly better statistics than did the traditional Pearson correlation analysis.

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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