About the Cohen's h
Cohen's h Calculator produces a standardized effect size for comparing two proportions or percentages, correcting for the fact that a fixed percentage-point gap doesn't mean the same thing everywhere on the 0 to 100% scale. It's commonly used in meta-analyses, A/B testing, and study design when comparing rates such as conversion rates, pass rates, or prevalence between two groups.
How It Works
Enter proportion 1 and proportion 2 as percentages. The calculator converts each one into a transformed value using an arcsine function, twice the arcsine of the square root of the proportion, then subtracts the two transformed values to get h. It then classifies the absolute size of h as negligible, small, medium, or large.
Formula & Methodology
The arcsine transformation stretches out proportions near 0% and 100%, where a given percentage-point gap represents a much bigger practical shift than the same size gap near 50%. Moving from 2% to 7% and moving from 47% to 52% are both 5-point gaps in raw terms, but the arcsine transform assigns them different weight, which is what lets h compare gaps fairly no matter where on the scale they occur.
Examples
Landing Page Redesign
Click-through rate rises from 45% to 60% after a redesign. Cohen's h works out to about 0.30, which the calculator classifies as a 'Small' effect size.
Manufacturing Process Change
A new production process yields 95% defect-free units, compared to 50% for the old process. Cohen's h comes out to about 1.12, a 'Large' effect size, even though it's the same underlying comparison a raw percentage-point subtraction would just call '45 points.'
Advantages
- Puts proportion comparisons on a common, standardized scale, so a gap near the extremes can be compared fairly to a similar-sized gap near 50%.
- Gives a single number suitable for comparing effect sizes across different studies, samples, or A/B tests.
- Classifies the result into a labeled magnitude (negligible to large), removing the guesswork of interpreting a raw h value on its own.
Common Mistakes
- Comparing two raw percentage-point gaps directly across different baseline proportions, without realizing the same point gap can represent very different practical effect sizes.
- Confusing Cohen's h with Cohen's d, which is the equivalent standardized effect size for comparing two means, not two proportions.
- Entering proportions as decimals (like 0.6) instead of percentages (like 60) in a field that expects a percentage input.
Edge Cases to Watch For
- Both proportions must fall between 0% and 100%; anything outside that range returns an error.
- Near the extremes, proportions close to 0% or 100%, the arcsine transform approaches its boundary values, so h stops growing as fast even if the raw percentage gap keeps increasing.
- The sign of h shows direction, positive means proportion 1 is higher, but the negligible/small/medium/large classification is based on the absolute value of h.
- Because h is built from two separate arcsine transforms rather than a single combined formula, it doesn't reference either group's sample size directly; it describes the standardized size of the gap between the two rates, separate from how statistically certain that gap is.
Common Use Cases
- Researchers and meta-analysts comparing the size of an effect on a proportion outcome across multiple studies with different sample sizes and baseline rates.
- Product and growth teams sizing up how meaningful an A/B test's lift in conversion rate really is, beyond just statistical significance.
- Public health analysts comparing prevalence, screening, or recovery rates between two populations or interventions.