Enter the means and standard deviations for two groups to calculate Cohen's d — the standardized effect size measuring how different the groups are. You can also calculate using a t-value and degrees of freedom. Results include Cohen's d, the effect-size correlation r, and an interpretation of the effect magnitude.
Cohen's d
--
Effect-Size Correlation (r)
--
Pooled Standard Deviation
--
Effect Magnitude
--
Cohen's d is a standardized effect size statistic that measures the magnitude of the difference between two group means in units of standard deviation. A value of 0 means no difference, while larger values indicate greater separation between groups. It allows meaningful comparison of effect sizes across different studies and scales.
Jacob Cohen (1988) proposed benchmark thresholds: d = 0.2 is considered a small effect, d = 0.5 is a medium effect, and d = 0.8 is a large effect. Values above 1.0 indicate very large effects where the groups overlap minimally. These are rough guidelines — context and domain always matter when interpreting effect sizes.
Cohen's d = (M1 − M2) / s_pooled, where the pooled standard deviation is s_pooled = √[(SD1² + SD2²) / 2]. This formula assumes the two groups have roughly equal sample sizes. For unequal sample sizes, a weighted pooled SD is more appropriate.
When you have results from an independent samples t-test, Cohen's d = 2t / √(df), where df is the degrees of freedom for the test. This is a convenient conversion when raw group data isn't available but the t-statistic and df are reported in a study.
The effect-size correlation r (also called r_YL) is an alternative effect size measure on a scale of 0 to 1. It is calculated as r = d / √(d² + 4). Values of r ≈ 0.1, 0.3, and 0.5 correspond roughly to small, medium, and large effects. Both d and r convey the same underlying effect — they are mathematically interchangeable.
Statistical significance (p-value) tells you whether an observed difference is likely due to chance, but it depends heavily on sample size. Effect size measures like Cohen's d describe the practical magnitude of the difference, independent of sample size. A large study can produce a statistically significant result with a trivially small effect size, so both measures are important.
A negative Cohen's d simply means Group 2 had a higher mean than Group 1 — it reflects direction, not a qualitatively different result. When reporting effect size magnitude, researchers typically use the absolute value |d|. The sign is only meaningful when interpreting whether the result was in the predicted direction.
Glass's delta uses only the control group's standard deviation in the denominator, rather than a pooled value. It is preferred when the two groups have substantially different variances, or when one group is clearly the control/reference group. Cohen's d with pooled SD assumes roughly equal variances across groups.