This tool converts between the three effect-size languages researchers meet most: Cohen’s d (standardized mean difference), Pearson’s r (correlation), and the odds ratio (for binary outcomes). Meta-analysts constantly need conversions because primary studies report different metrics, and a reader comparing two papers may find d in one and an odds ratio in the other. You enter any one value and the tool returns all three, using the standard approximations: r = d / √(d² + 4), d = 2r / √(1 − r²), and the logistic conversion between d and the log odds ratio. Effect sizes matter more than p-values for judging importance: a tiny effect can be highly significant in a huge sample, and a large effect can miss significance in a small one.
How to use it
- Choose the effect size you know.
- Enter its value.
- Click Convert.
- Read all three metrics.
- Report the converted value with the original and the conversion used.
Worked example
A study reports d = 0.5, conventionally a medium effect. Converted, that is r = 0.243 and an odds ratio of about 2.48 — the intervention group has roughly two and a half times the odds of the outcome. Another study reports an odds ratio of 6.13, which converts back to d = 1.0, a large effect. Without conversion, comparing “0.5” with “6.13” is meaningless; with it, the two studies speak one language and a meta-analysis can pool them. Always keep the original metric visible next to the converted one, so readers can trace the arithmetic.
Honest limits
Conversions are approximations with assumptions: equal group sizes, roughly normal distributions, and the logistic bridge between d and odds ratios. They break down for extreme values — r near ±1 converts to an enormous d — and for outcomes where the odds ratio itself misleads, such as common outcomes where odds ratios exaggerate relative risks. Converted values inherit every flaw of the original estimate, including publication bias. For a formal meta-analysis, use established conversion tables or software and report the exact formulas; this tool is for quick comparison and reporting, not as the sole basis of a pooled estimate.
Who it is for
This tool is for meta-analysts harmonizing studies, students learning that d, r, and odds ratios are dialects of one idea, and readers translating a reported effect into a scale they understand. It turns three incompatible numbers into one conversation.
Going further
Benchmarks like “0.2 is small, 0.5 medium, 0.8 large” are Cohen’s rough guides, not laws of nature: a d of 0.2 can be enormously important for a cheap, harmless intervention applied to millions, while a d of 0.8 can be trivial for an expensive treatment with side effects. Judge an effect by its practical context — the cost, the risk, the alternatives, and the outcome’s importance — not by which benchmark bin it lands in. When reporting, give the raw difference in original units alongside the standardized effect: “3.2 points higher (d = 0.5)” tells a practitioner something a bare d never can, and it keeps the conversion honest by anchoring it to real-world size. For binary outcomes, prefer reporting both the odds ratio and the absolute risk difference when you can: an odds ratio of 2.5 sounds dramatic, but if the baseline risk is 2 percent, the absolute increase is only 3 percentage points — a very different story for a patient deciding on treatment. Conversions between d and odds ratios cannot recover absolute risks, because they discard baseline rates entirely. Whenever the original study gives event counts, compute risks directly instead of converting; use conversion only when counts are unavailable and say so. When in doubt, show your working in a footnote: the original metric, the formula, and the converted value, so any reader can check the arithmetic in seconds.
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