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Effect Size Converter (d, r, OR, Hedges’ g)
Convert between common effect-size metrics — Cohen’s d, Pearson’s r, the odds ratio, and Hedges’ g — with the exact R command behind the result. A full interpretation guide follows below. Validated against R 4.3.3.
In Simple Words
Different studies report effects in different units: a trial may give Cohen’s d, a survey Pearson’s r, and an epidemiological study an odds ratio. To compare or pool them you first put them on a common scale. This converter applies the standard formulae that translate one metric into another.
Hedges’ g is a small-sample correction to Cohen’s d, and the conversions among d, r, and the log odds ratio follow well-established algebra. The key caution is that conversion preserves the point estimate’s relationship but assumes the original measure was appropriate for the design — a poor metric choice cannot be fixed by converting it.
When to Use Effect-Size Conversion
Convert effect sizes when you are synthesising studies that reported different metrics, most often before a meta-analysis, or when a journal asks for a standardised measure your software did not produce. Converting to a single scale lets you place all studies on one forest plot.
Always carry the uncertainty through the conversion, not just the point estimate: convert the confidence-interval limits too, and report the result with its confidence interval. Choose the target metric to match your audience — r for correlational fields, d or g for group comparisons, the odds ratio for binary outcomes. If you have not yet computed a base effect size, start with our effect size calculator.
n1 and n2 are only needed to convert to/from r and Hedges’ g (via a = (n1+n2)²/(n1·n2) and df = n1+n2−2). They do not affect the d↔OR conversion.
User guide
When to use. Put effect sizes reported on different scales (d, r, g, OR) onto one common metric before pooling them in a meta-analysis, or when a journal requests a specific standardised measure.
Assumptions. The d↔r and d↔OR conversions assume the underlying trait is continuous and approximately normal/logistic — standard textbook assumptions behind these formulas (Cohen 1988; Hedges & Olkin 1985).
Common mistakes. Converting a point estimate without also converting its confidence interval; forgetting the small-sample correction when pooling small studies (use Hedges’ g, not raw d).
Worked example
Click one of the example buttons above, then Run Analysis, to see a fully worked conversion with formulas and the R command.
References
- Cohen J. Statistical Power Analysis for the Behavioral Sciences. 2nd ed. Hillsdale, NJ: Erlbaum; 1988.
- Hedges LV. Distribution theory for Glass’s estimator of effect size and related estimators. J Educ Stat. 1981;6(2):107–128.
- Borenstein M, Hedges LV, Higgins JPT, Rothstein HR. Introduction to Meta-Analysis. Chichester: Wiley; 2009.
Worked Examples
Example 1 — Cohen’s d to r
A study reports Cohen’s d = 0.50 for a two-group comparison. Using the standard relationship, this converts to a Pearson r of about 0.24. The two now sit on the same scale, so this study can be combined with correlational studies reporting r directly.
Example 2 — d to Hedges’ g
With a small sample (n = 20), Cohen’s d slightly overstates the population effect. Applying the small-sample correction turns d = 0.80 into Hedges’ g of roughly 0.77. The corrected value is the one to pool, since unadjusted d is biased upward in small studies.
Assumptions to Check
The original metric suited the design. Conversion assumes the source effect size was appropriate for how the study was conducted. Converting an inappropriate measure simply carries the problem to the new scale.
Conversions are approximate, not exact equivalences. The d-to-r and d-to-odds-ratio formulae rest on distributional assumptions (for example, an underlying normal or logistic model). Treat converted values as good approximations, not identities.
Uncertainty must travel with the estimate. Converting only the point estimate discards its precision. Convert the confidence limits as well so the pooled analysis reflects each study’s true weight.
Common Mistakes
Converting the point estimate but not the interval
A converted effect size without a converted confidence interval cannot be weighted correctly in a meta-analysis. Always transform the limits too.
Forgetting the small-sample correction
For small studies, Cohen’s d is biased upward. Use Hedges’ g when pooling small samples rather than the uncorrected d.
Treating converted values as exact
Conversions rely on modelling assumptions. Quoting a converted odds ratio to three decimals as if it were measured directly overstates its precision.
Mixing metrics on one forest plot without converting
Plotting raw d, r, and odds ratios together is meaningless. Bring every study to one common metric before pooling or displaying.
Frequently Asked Questions
What is the difference between Cohen’s d and Hedges’ g?
They estimate the same standardised mean difference, but Hedges’ g applies a correction that removes the upward bias of d in small samples.
How do I convert d to r?
A standard formula links the two through the group sizes; for equal groups, d = 0.5 corresponds to r near 0.24. The calculator applies the exact expression.
Can I convert an odds ratio to Cohen’s d?
Yes, via the log odds ratio and a scaling constant from the logistic distribution. The result assumes an underlying continuous trait and should be read as an approximation.
Does the result match R packages?
Yes. The conversions follow the formulae used in standard meta-analysis packages, and the calculator shows the R command so you can reproduce each value.
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References
- Lininger M, Riemann BL. Statistical primer for athletic trainers: using confidence intervals and effect sizes to evaluate clinical meaningfulness. J Athl Train. 2017;51(12):1045–1048. PMID 28107049.
- Pautz N, Olivier B, Steyn F. The use of parametric effect sizes in single study musculoskeletal physiotherapy research: a practical primer. Phys Ther Sport. 2018;32:87–97. PMID 29778828.
- Borenstein M, Hedges LV, Higgins JPT, Rothstein HR. Introduction to Meta-Analysis. Chichester: Wiley; 2009.
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