A1 Refereed original research article in a scientific journal

General formulae for transforming Pearson’s r to the scale of Cohen’s d;




AuthorsMetsämuuronen, Jari

PublisherSAGE

Publication year2026

Journal: Applied Psychological Measurement

ISSN0146-6216

eISSN1552-3497

DOIhttps://doi.org/10.1177/01466216261465015

Publication's open availability at the time of reportingOpen Access

Publication channel's open availability Partially Open Access publication channel

Web address https://doi.org/10.1177/01466216261465015

Self-archived copy’s web addresshttps://research.utu.fi/converis/portal/detail/Publication/527003893

Self-archived copy's licenceCC BY

Self-archived copy's versionPublisher`s PDF


Abstract

The traditional thresholds for product-moment correlation (r) usually condensed in terms of “very small,” “small,” “medium,” “large,” “very large,” and “huge” are derived on the scale of d. Properly transforming an estimate of r to the scale of Cohen’s d is important for qualitatively evaluating the magnitude of the r effect size. A proper formula exists for a transformation between r and d in the binary and dichotomous settings, but not in polytomous or continuous settings. The traditional formula for polytomous settings assumes an equal number of cases in the subpopulations and can lead to a radically misleading transformation if the group sizes are severely imbalanced. Two general formulae are derived for transformations applicable to dichotomous, polytomous, and continuous cases, regardless of the imbalance in the group sizes. Real-life examples are given which illustrate the use of the general forms and difference between the general and the traditional forms.


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Funding information in the publication
The author disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The author declares that no funds, grants, or other support were received during the preparation of this manuscript. The study has been completed as part of the EDUCA Flagship project funded by the Research Council of Finland (#358924, #358947).


Last updated on 11/08/2026 08:39:28 AM