Cohen's d Effect Size
Standardised mean difference (small/medium/large effect).
Overview
The Cohen's d Effect Size calculator quantifies how big the difference is between two group means, expressed in pooled standard deviations rather than raw units. Two groups can differ "significantly" with a tiny effect or non-significantly with a big effect — d separates the two questions.
It is essential for psychology students writing up experiments, A/B testers reporting practical impact and meta-analysts comparing results across studies with different measurement scales. Significance tells you "is this real?"; d tells you "does it matter?"
How it works
For two groups with means m1, m2 and standard deviations s1, s2 (sample sizes n1, n2), the pooled standard deviation is sp = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2)). Cohen's d is (m2 - m1) / sp.
Cohen's original rules of thumb categorise effects as small (|d| ≈ 0.2), medium (|d| ≈ 0.5) and large (|d| ≈ 0.8). The calculator also reports Hedges' g, a small-sample correction that multiplies d by 1 - 3 / (4 * (n1 + n2) - 9).
Examples
m1=100, s1=15, n1=50
m2=105, s2=15, n2=50
→ d ≈ 0.333 (small-to-medium)
m1=70, s1=10, n1=30
m2=85, s2=12, n2=30
→ d ≈ 1.36 (very large)
m1=50, s1=8, n1=200
m2=51, s2=8, n2=200
→ d ≈ 0.125 (very small)
FAQ
Should I use pooled or non-pooled SD?
Pooled is standard when variances are similar. If they differ substantially, Glass's delta (using just the control SD) or Welch-style adjustments may be preferable.
What's the difference between d and g?
Hedges' g applies a small-sample correction. With more than ~20 in each group the two are nearly identical; with smaller samples g is the more honest estimate.
Can d be negative?
Yes. The sign tells you which group has the larger mean. Many writers report |d| and describe direction separately.
Why isn't a big d always a useful effect?
Because the unit is SDs, not the raw quantity. A 5-point IQ difference (d ≈ 0.33) might be substantively important; the same d on a 100-point test might not.
Does d depend on sample size?
The point estimate does not, but its precision (confidence interval) does. Larger samples narrow the interval around the same point estimate.