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Effect-size converter
Pubrica’s free effect-size converter expresses one effect as Cohen’s d, Hedges’ g, a correlation coefficient and an odds ratio. Enter the value you have and the two group sizes to see each equivalent with its confidence interval, which helps when combining studies in a meta-analysis or interpreting published results.
The tool runs in your browser. No registration, email address or file upload is required, and the formula, reference or assessment criteria used are shown with the result.
- Runs in your browser
- Nothing uploaded or stored
- No email asked for
- Method shown with the answer
- Sources dated
The Tool
Convert an Effect Size Between d, g, r and Odds Ratio
Converts an effect between Cohen’s d, Hedges’ g, a correlation and an odds ratio, carrying the confidence interval through each conversion.
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Converts an effect between Cohen’s d, Hedges’ g, a correlation and an odds ratio, carrying the confidence interval through each conversion.
d · g · r · odds ratio0.450
Cohen’s d
0.220
Correlation r
With 40 and 40 per group the standard error of d is 0.226, so this effect is in the range usually called small and the interval excludes zero.
Method. g = d·J with J = 1 − 3/(4N−9); r = d/√(d²+a) with a = N²/(n₁n₂); ln OR = d·π/√3 (Hasselblad–Hedges). The standard error is √(N/(n₁n₂) + d²/2N); the limits are converted through the same monotone transforms as the estimate, which is why the odds-ratio interval is not symmetric.
Limitations
What This Tool Does Not Cover
Use the result as a starting point. These are the situations in which it needs specialist review.
The calculators
Limitations of the calculators
The sample size calculator gives the closed-form answer for two independent groups. Cluster randomisation, interim analyses, a non-inferiority margin, repeated measures and competing risks each change the number materially, and none of them can be handled by inflating the answer afterwards. The same applies to the test chooser: it cannot know that your observations are clustered within clinics, and clustering overrides almost everything else it would tell you.
Method
Methods and Sources
The calculation or reference set behind this tool. The result panel also shows the formula or criteria used.
Effect sizes
Hedges, Hasselblad
Hedges’ small-sample correction for g; the Hasselblad–Hedges transform between d and the log odds ratio; the standard error of d from the two group sizes. Interval limits are converted through the same monotone transforms as the estimate.
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