Cohen's d Effect Size Calculator
Calculate Cohen's d to quantify the standardized difference between two independent group means.
Group Statistics Input
Formula
Cohen's d (independent samples)
d = (M₁ − M₂) / SD_pooled SD_pooled = √[((n₁−1)·SD₁² + (n₂−1)·SD₂²) / (n₁ + n₂ − 2)]
The pooled standard deviation weights each group's variance by its degrees of freedom, providing an estimate of the common population standard deviation.
Hedges' g (bias correction)
g = d × (1 − 3 / (4·df − 1)) Where df = n₁ + n₂ − 2
This correction factor (approximately 1 for large samples) reduces the slight upward bias in Cohen's d that occurs with small samples.
How to Interpret Cohen's d
| |d| Value | Interpretation |
|---|---|
| < 0.20 | Negligible |
| 0.20 | Small |
| 0.50 | Medium |
| 0.80 | Large |
Context Matters
Cohen himself emphasized that these benchmarks are arbitrary and should be used cautiously. In some fields (e.g., education), a d of 0.20 may represent a meaningful improvement, while in others (e.g., drug trials with active comparators), a d of 0.50 may be typical. Always interpret effect sizes in the context of your specific research area and practical significance.
Worked Example
A researcher compares test scores between two teaching methods:
Group 1 (Method A): M = 78, SD = 10, n = 30
Group 2 (Method B): M = 72, SD = 12, n = 30
SD_pooled = √[((29)(100) + (29)(144)) / 58]
= √[2900 + 4176) / 58]
= √[7076 / 58]
= √122.0
= 11.045
d = (78 − 72) / 11.045
= 6 / 11.045
= 0.543Cohen's d = 0.543, indicating a medium effect. Group 1 (Method A) scored about half a standard deviation higher than Group 2.
Assumptions
- Both groups are independent (no paired or matched design).
- The outcome variable is continuous (or treated as continuous).
- The population variances are approximately equal (homogeneity of variance). If variances differ substantially, Glass's Δ may be more appropriate.
- Data are approximately normally distributed in each group, especially for small samples.
- Cohen's d uses a pooled standard deviation, which assumes equal population variances.