Calculate Cohen's d effect size between two groups using their means and standard deviations. Enter Mean 1, SD 1, Mean 2, and SD 2 — and you'll get back Cohen's d, the effect-size correlation r, and an interpretation (small, medium, or large). You can also calculate using t-value and degrees of freedom from an independent groups t-test.
Cohen's d
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Effect-Size Correlation (r)
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Pooled Standard Deviation
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Effect Size Interpretation
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Cohen's d is a standardized measure of the difference between two group means, expressed in units of the pooled standard deviation. It tells you how large the difference is, independent of sample size. A d of 0 means no difference, while larger values indicate stronger effects.
Cohen's d = (M1 − M2) / s_pooled, where s_pooled = √[(SD1² + SD2²) / 2]. The pooled standard deviation combines the variability of both groups, giving a common scale for comparison.
Jacob Cohen (1988) proposed that d = 0.2 is a small effect, d = 0.5 is a medium effect, and d = 0.8 is a large effect. These are rough guidelines — what counts as meaningful depends on your field and research context.
The effect-size correlation r (also called r_YL) is another way to express effect magnitude on a −1 to +1 scale, similar to a Pearson correlation. It's calculated as r = d / √(d² + 4). Values of 0.1, 0.3, and 0.5 correspond roughly to small, medium, and large effects.
If you ran an independent-samples t-test, you can compute Cohen's d as d = 2t / √(df), where t is your t-statistic and df is the degrees of freedom. The corresponding r is calculated as r = √(t² / (t² + df)).
Unlike p-values, Cohen's d is not directly influenced by sample size — it measures the magnitude of the difference, not its statistical significance. However, with small samples the estimate of d can be unstable. A correction (Hedges' g) applies a small-sample bias adjustment.
Cohen's d is appropriate when comparing the means of two groups on a continuous outcome. For correlational analyses, use Pearson's r. For categorical outcomes or contingency tables, consider Cramér's V or phi. For ANOVA, eta-squared or omega-squared are more appropriate.
Yes. If the mean of Group 2 is larger than Group 1, Cohen's d will be negative. The absolute value of d represents the magnitude, while the sign indicates direction. Many researchers report the absolute value and specify the direction separately.