What d = 0.83 looks like
The curves overlap by 68%. 80% of the higher group scores above the average of the lower group (Cohen's U₃), and a random person from the higher group beats a random person from the lower group 72% of the time. Drag to feel how big “medium” really is:
Why report an effect size?
A p-value tells you whether an effect is distinguishable from zero; an effect size tells you how big it is. With 5,000 participants a trivial d = 0.06 can be “highly significant”. APA 7 asks for effect sizes with confidence intervals for all primary results.
Conversion formulas
- d from t (independent groups): d = t√(1/n₁ + 1/n₂)
- r from d (equal n): r = d/√(d² + 4); d from r: d = 2r/√(1 − r²)
- f from d (two groups): f = d/2; η² = f²/(1 + f²)
- d from odds ratio: d = ln(OR)·√3/π
Frequently asked questions
How do I calculate Cohen's d?
d = (M₁ − M₂) / SD_pooled, where SD_pooled = √(((n₁ − 1)s₁² + (n₂ − 1)s₂²)/(n₁ + n₂ − 2)). For means 28.2 and 24.6 with SDs 4.1 and 4.6 (n = 20 each), d = 0.83.
What is the difference between Cohen's d and Hedges' g?
Hedges' g multiplies d by a small-sample correction J = 1 − 3/(4(n₁ + n₂) − 9). With 20 per group g is about 2% smaller than d; above 50 per group the difference is negligible.
How do I convert d to r?
For equal groups r = d / √(d² + 4). d = 0.5 corresponds to r ≈ .24. The calculator also converts from r, t, F and odds ratios.
What are small, medium and large effects?
Cohen's (1988) guides: d = 0.2, 0.5, 0.8; r = .10, .30, .50; η² = .01, .06, .14; f = .10, .25, .40. Cohen himself called them a last resort; compare with effects in your own field where possible.