How to use: pick a statistical test, choose what to solve for (sample size, power, or detectable effect size), enter your parameters, and read the result, the power curve, and the null-vs-alternative distribution below. Use the effect-size helpers to convert raw means or proportions into Cohen's d, f, or h.
Design your study
Cohen's h = 2·asin√p₁ − 2·asin√p₂
1 = equal groups; 2 = group 2 is twice as large.
Inflates the required sample size: enroll = n ÷ (1 − dropout).
Effect-size helpers
Cohen's d from two means and a pooled SD
Cohen's f from group means and within-group SD
Cohen's h from two proportions
Small / medium / large conventions (Cohen 1988): d .2 / .5 / .8 · dz .2 / .5 / .8 · f .10 / .25 / .40 · h .2 / .5 / .8 · r .1 / .3 / .5 · w .1 / .3 / .5
Result
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Power curve
power vs. sample size — hover or tap for valuesNull vs. alternative distribution
α and β regions shadedPower table
| n | Power | β (miss rate) |
|---|
Methods-section sentence
Validation
Every statistic is computed in this page's JavaScript (noncentral t / F / chi-square mixtures, normal approximation, Fisher z). The table below re-runs 32 reference cases — computed with statsmodels 0.15.0 and cross-checked with SciPy 1.14.1, with selected cases transcribed from the G*Power 3.1 manual — and compares this app's own result against each expected value.
| Case | Description | Expected | This app | Status |
|---|
Effect-size benchmarks (Cohen 1988)
| Effect size | Small | Medium | Large |
|---|
Data & sources
Validation values computed with statsmodels 0.15.0 and SciPy 1.14.1 (not copied from published tables); selected cases checked against G*Power 3.1 manual examples (Faul et al., 2007). Effect-size conventions from Cohen (1988), summarized in Cohen (1992).