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Effect Size Calculator
Quantify how big the difference between two independent groups really is with Cohen’s d, computed from the pooled standard deviation and reported as an absolute value. See the formula and the reproducible R command, and read a full interpretation guide below. Validated against R 4.3.3.
In Simple Words
An effect size tells you how large a difference is, in a way that does not depend on your sample size. A p-value can tell you a difference is unlikely to be chance, but not whether it is big enough to matter. Effect size fills that gap.
Cohen’s d expresses the gap between two group means in units of pooled standard deviation, so d = 0.5 means the groups differ by half a standard deviation. As a rough guide, 0.2 is small, 0.5 medium, and 0.8 large — but those labels are conventions, not laws, and the clinical meaning depends on your field.
When to Use Effect Size
Report an effect size whenever you report a comparison or an association. For the difference between two group means, Cohen’s d (or the bias-corrected Hedges’ g for small samples) is standard. Reporting guidelines increasingly expect an effect size and its confidence interval alongside the p-value, because together they show both whether an effect exists and how large it plausibly is.
Effect size is also the input you need to plan a study: it drives the sample size calculation and lets results be pooled in meta-analysis. Choose the measure that matches your design — d-family measures for differences between means, r-family measures for strength of association. Not sure which fits your data? Our interactive Test Selector can help.
Expected: 2 columns: Group 1 values | Group 2 values
Drop a CSV here or click to choose. Parsed in your browser: nothing is uploaded.
Expected: 2 columns: Group 1 values | Group 2 values
g1 <- c({g1})
g2 <- c({g2})
library(effsize)
cohen.d(g1, g2)
cohen.d(g1, g2, hedges.correction = TRUE) # Hedges' gUser guide
When to use. Quantify the standardised magnitude of difference between two groups.
Assumptions. Continuous data; pooled SD is meaningful (similar variances).
Common mistakes. Effect size measures magnitude, not statistical significance or clinical importance.
Worked example
Click Load example data above, then Run Analysis to see a fully worked result with figure, formula and interpretation for this test.
References
- Cohen J. Statistical Power Analysis for the Behavioral Sciences. 1988.
Worked Examples
Example 1 — A large effect
Two groups with means of 5.90 and 7.72 and a pooled standard deviation of 0.45 (the ‘Large effect’ example under Load example data) give Cohen’s d = 4.01, a very large effect. Report d with its 95% confidence interval, not the difference in means alone, so readers can judge magnitude on a standardised scale.
Example 2 — Why small samples need Hedges’ g
Cohen’s d slightly overestimates the population effect in small samples. Hedges’ g applies a correction factor and is preferred when each group has fewer than about 20 observations. With large samples the two converge. To get g from your d, enter d and the two group sizes in the effect size converter.
Assumptions to Check
Comparable spread. The pooled standard deviation assumes the two groups have similar variances. When variances differ markedly, use a measure based on the control-group SD (Glass’s delta) instead.
Continuous, roughly normal data. Cohen’s d is built for continuous outcomes. For ranked or skewed data, a rank-based effect size is more appropriate.
Independent observations. The standard formula assumes independent groups. Paired or repeated-measures designs need an effect size that accounts for the within-pair correlation.
Common Mistakes
Treating effect size as significance
A large d is not the same as a small p-value. Effect size measures magnitude; significance measures whether the effect is distinguishable from chance. Report both.
Reading the 0.2/0.5/0.8 labels as absolute
Cohen’s small/medium/large thresholds are rules of thumb. A “small” d can be clinically important, and a “large” one trivial, depending on the outcome.
Omitting the confidence interval
A point estimate of d without its interval hides the uncertainty. Always report the confidence interval around the effect size.
Using d on the wrong design
Independent-groups d does not fit paired data or more than two groups. For several groups, use eta-squared from ANOVA.
Frequently Asked Questions
What is the difference between Cohen’s d and Hedges’ g?
Both express a standardised mean difference. Hedges’ g multiplies d by a small-sample correction factor, so it is slightly smaller and less biased when samples are small.
How do I interpret the size of d?
As a convention, 0.2 is small, 0.5 medium, and 0.8 large — but interpret in the context of your field and report the value with its confidence interval rather than a label alone.
Why report effect size at all?
It communicates practical magnitude, is needed for sample-size planning, and lets studies be combined in meta-analysis — none of which a p-value alone provides.
Does the result match SPSS, R, and Stata?
Yes. The calculator uses the same pooled-SD formula as standard software and shows the exact R command so you can reproduce it.
Related Calculators
References
- Kallogjeri D, Piccirillo JF. A simple guide to effect size measures. JAMA Otolaryngol Head Neck Surg. 2023;149(5):447–451. PMID 36951858.
- Lakens D. Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs. Front Psychol. 2013;4:863. PMID 24324449.
- Cohen J. Statistical Power Analysis for the Behavioral Sciences. 2nd ed. Hillsdale, NJ: Lawrence Erlbaum; 1988.
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