Correlation coefficients in medical research: from product moment correlation to the odds ratio

Abstract

Objective: Presentation of effect sizes that can be interpreted in terms of clinical or practical significance is currently urged whenever statistical significance (a ‘ p-value’) is reported in research journals. However, which effect size and how to interpret it are not yet clearly delineated. The present focus is on effect sizes indicating strength of correlation, that is, effect sizes that describe the strength of monotonic association between two random variables X and Y in a population. Methods: A logical structure of measures of association is traced, showing the interrelationships among the many measures of association. Advantages and disadvantages of each are discussed. Conclusions: Suggestions are made for the future use of measures of association in research to facilitate considerations of clinical significance, emphasizing distribution-free effect sizes such as the Spearman correlation coefficient and Kendall’s coefficient of concordance for ordinal versus ordinal associations, weighted and intraclass kappa for binary versus binary associations and risk difference (RD) for binary versus ordinal association.