Effect size calculator
Unlimited free effect size calculations: Cohen d, Hedges g, paired effects, odds ratios and Pearson r. OR and r intervals; no d or g intervals.
Effect size
Formula and supported method
Independent d=(mean1−mean2)/pooled SD; g=Jd, with exact gamma correction J. Paired dz uses SD of differences; dav uses sqrt((SD1²+SD2²)/2). OR=ad/bc with log-Wald CI; Fisher r interval=tanh(atanh(r) ± z/sqrt(n−3)).
Choose the standardizer explicitly. Positive effects refer to group 1 minus group 2. Pearson uses complete independent pairs. A zero odds-ratio cell triggers 0.5 added to all four cells. d/g confidence intervals are unsupported.
Worked example: Means 10 and 8, SDs 4 and 5, sizes 20 and 30 give d≈0.431959 and g≈0.425169.
Method reference · Implementation 2026-09-14
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How to use effect size calculator
- Choose independent groups, a paired standardizer, an odds-ratio table or Pearson correlation.
- Enter group means/SDs/counts, paired differences, event counts or complete pairs as labelled.
- Calculate the signed effect; intervals are available for odds ratios and Pearson r, not d or g.
- Copy or download the text or CSV result with its assumptions before leaving; the page does not retain it.
Independent Cohen d and exact-correction Hedges g
Enter the two means, sample standard deviations and sample sizes for independent groups. The pooled variance is ((n1−1)SD1² + (n2−1)SD2²)/(n1+n2−2). Cohen d is the group 1 minus group 2 mean difference divided by the square root of that variance. Positive values therefore mean group 1 has a higher mean, regardless of whether a higher score is desirable. The standardizer is the pooled sample SD, not the standard error of the mean difference. Unequal sample sizes affect the weights in the pooled variance; entering only the total sample size would lose that information.
Hedges g multiplies d by J, where df=n1+n2−2 and J=Gamma(df/2)/(sqrt(df/2)Gamma((df−1)/2)). This implementation uses that exact gamma-function correction rather than the common approximation 1−3/(4df−1). The result includes d, g, the pooled SD, degrees of freedom and J so the calculation can be reproduced. Load example uses means 10 and 8, SDs 4 and 5, and group sizes 20 and 30. The calculation is an estimate under the selected standardizer, not a causal claim. No confidence interval for d or g is produced; the correlation and odds-ratio modes provide their separately specified intervals.
Paired effects and conversions use different assumptions
Paired dz divides the mean within-pair difference by the SD of those individual differences. Paired dav divides the same mean difference by sqrt((SD1²+SD2²)/2). Both options are available and explicitly labelled because their denominators answer different standardization questions. A strong within-pair correlation can make the difference SD much smaller than either condition’s SD, so dz can be larger than dav for the same measurements. Do not select the denominator that gives the most impressive result. Choose the definition that matches the analysis and the comparison you plan to make with other studies.
The t conversion also depends on design. A pooled independent-groups t statistic gives d=t sqrt(1/n1+1/n2); a paired or one-sample t statistic gives dz=t/sqrt(n). These formulas preserve the sign of t and assume its contrast matches the group ordering. A Welch t statistic cannot be treated as the pooled independent statistic without further information. The approximate d-to-r conversion uses r=d/sqrt(d²+4), with inverse d=2r/sqrt(1−r²). This equal-group independent approximation is not a universal identity, especially for unequal groups or paired observations. At absolute r=1, the inverse does not produce a finite d and is rejected.
Odds ratios and correlations need their own interpretation
For an odds ratio, label the event and enter group 1 events and non-events followed by group 2 events and non-events. OR=ad/bc compares event odds in group 1 with group 2. If any cell is zero, the Haldane–Anscombe correction adds 0.5 to all four cells and the output states that it did so. With no zero cell, no correction is applied. The confidence interval is the Wald interval on log OR, using standard error sqrt(1/a+1/b+1/c+1/d), then exponentiating the endpoints. Sparse counts can make this asymptotic interval unreliable. An odds ratio is not a risk ratio and does not supply NNT without baseline risks.
Pearson correlation accepts exactly two complete numeric columns, one independent pair per row, or a t statistic with degrees of freedom using r=t/sqrt(t²+df). The Fisher z interval transforms r with atanh, adds and subtracts the normal critical value divided by sqrt(n−3), and transforms back with tanh. It requires more than three pairs. Constant variables are rejected because correlation is undefined. Perfect correlation is shown with a degenerate limiting interval and an explicit warning about the infinite transform. Inspect a scatterplot and potential outliers before interpreting linear association. All methods retain the supplied direction; generic small, medium or large labels are intentionally omitted because scientific importance depends on context. Copy the method and assumptions with the number.
Frequently asked questions
Why are d and g different?
Hedges g applies a small-sample bias correction to Cohen d. This implementation uses the exact gamma-function J and reports it with the pooled SD and degrees of freedom.
Which paired effect should I choose?
Choose dz for standardization by the SD of within-pair differences, or dav for standardization by the average condition variance. They describe different standardizers.
When is the odds-ratio correction applied?
Only when at least one of the four cells is zero. Then 0.5 is added to every cell and the correction is stated in the output.
Are calculations free and unlimited?
Yes. Local calculations have no quota and require no login. External lookups are rate limited to protect provider access; waiting and retrying never requires signup.
Does AnswerThis save or receive my result?
No. Signup opens the AnswerThis app; it does not save or transfer this result. Copy or download your calculation before leaving the page.
How can I reproduce a result?
Keep the supplied inputs, selected method, units, assumptions and implementation date in the text or CSV export. Numerical fixtures are checked against SciPy 1.15.3, statsmodels 0.14.4 and pingouin 0.5.5.
What if a value is missing or invalid?
Required fields show a specific error. Zero-variance and invalid-degree-of-freedom cases are refused. Missing provider metadata is labelled unknown or not reported, and a failed lookup is never replaced by invented data.
Sources and related research tools
Method version: 14 September 2026. Numeric reference validation: SciPy 1.15.3, statsmodels 0.14.4, pingouin 0.5.5. Numeric inputs stay in your browser; these calculations use no AI model or external calculation service.
SciPy statistical distributions; statsmodels statistical methods; OpenAlex access and limits; OpenAlex metric definitions.