effect size calculator
cohen's d, hedges' g with hopkins magnitude thresholds
design
inputs — independent groups
group 1
group 2
inputs — paired (pre–post)
results
cohen's d
—
hedges' g
—
95% CI
—
hopkins magnitude
magnitude
—
00.20.61.22.04.0+
| magnitude | threshold (|d|) |
|---|---|
| trivial | < 0.2 |
| small | 0.2 – 0.6 |
| moderate | 0.6 – 1.2 |
| large | 1.2 – 2.0 |
| very large | 2.0 – 4.0 |
| extremely large | > 4.0 |
method
Independent groups. Cohen's d uses the pooled standard deviation:
pooled_sd = sqrt( ((n1-1)·sd1² + (n2-1)·sd2²) / (n1+n2-2) ) d = (m1 - m2) / pooled_sd
Paired (pre–post). The pooled SD treats pre and post as independent (Cohen's dav):
pooled_sd = sqrt( (sd_pre² + sd_post²) / 2 ) d = (m_post - m_pre) / pooled_sd
Hedges' g. Bias correction for small samples:
g = d · (1 - 3 / (4·df - 1)) where df = n1 + n2 - 2
95% confidence interval. Approximate standard error:
SE = sqrt( (n1+n2) / (n1·n2) + d² / (2·(n1+n2)) ) CI = d ± 1.96 · SE
Magnitude thresholds. Hopkins (2002) sport science convention: trivial < 0.2, small 0.2–0.6, moderate 0.6–1.2, large 1.2–2.0, very large 2.0–4.0, extremely large > 4.0.
- Hopkins WG. A scale of magnitudes for effect statistics. Sportscience, 2002.
- Lakens D. Calculating and reporting effect sizes. Front Psychol, 2013.