Transforming Odds Ratios into Correlation Coefficients

Correlation Coefficients as a Replacement of Odds Ratios
  • Ton J. Cleophas
  • Aeilko H. Zwinderman


In order for odds ratios to be suitable for effect size estimation in meta-analysis, a measure of their spread is required. Unfortunately, this is often missing in clinical reports. A tentative solution for the problem is the replacement of odds ratios with regression coefficients and correlation coefficients, for which it is easier to compute a measure of spread. In this chapter the Yule and Ulrich approximations and the tetrachoric correlation coefficients are explained as possible solutions for odds ratios without measure of spread. This subject is pretty new, and possible solutions are, so far, little used in present meta-analyses.


Path Statistic Polychoric Correlation Tetrachoric Correlation Weighted Effect Size Ellipse Type 
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  1. More information about the Yule, Ulrich and tetrachoric approximations of correlation coefficients are given in Yule (J Roy Stat Soc 1912; 75: 579), Ulrich (On the correlation of a naturally and artificially dichotomized variable, Br J Math Stat Psychol 2004; 57: 235–51), and Bonett (Transforming odds ratios into correlations for meta-analytic research, Am Psychologist 2007; 62: 254–55).Google Scholar

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Ton J. Cleophas
    • 1
  • Aeilko H. Zwinderman
    • 2
  1. 1.Department of MedicineAlbert Schweitzer HospitalSliedrechtThe Netherlands
  2. 2.Department of Epidemiology and BiostatisticsAcademic Medical CenterAmsterdamThe Netherlands

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