Cohen's h for two proportions

8.0%
8.6%
5,000
Arcsine-transformed gap
0 π/4 π/2 3π/4 π h Baseline φ₁ Observed φ₂
φ₁ (radians)
0.583
φ₂ (radians)
0.605
Cohen's h
0.021
p-value (2-prop z)
0.62
negligible
small
medium
large
✓ Negligible practical drift (|h| = 0.02)
Even though the sample size may flag this as statistically significant, the effect size says the gap is not material. Probably safe to keep the assumption.
How to interpret this

Cohen's h measures the distance between two proportions on the arcsine scale: h = 2·arcsin(√p₂) − 2·arcsin(√p₁). Unlike a p-value or a Wilson interval, it does not depend on sample size — it only depends on how far apart the two rates actually are.

|h| < 0.2: negligible — treat as noise, even if "significant."

0.2 ≤ |h| < 0.5: small effect — worth a note, rarely urgent alone.

0.5 ≤ |h| < 0.8: medium effect — usually worth investigating.

|h| ≥ 0.8: large effect — material drift, prioritise recalibration.