Statistical Power Calculator
Power of a two-sample test from the sample size per group, effect size and alpha — for means (Cohen’s d) or two proportions, one- or two-sided.
How it works
power = 1 − Φ(z₁₋α/s − δ) [+ Φ(−z₁₋α/s − δ) if two-sided]; δ = d·√(n/2) for means, |p₁−p₂| ÷ √(2p̄(1−p̄)/n) for proportions
Power is the probability of detecting an effect that really exists. It rises with sample size and effect size and falls as alpha is tightened. Under-powered studies waste effort and produce inflated, unreplicable estimates when they do reach significance. The normal approximation used here matches exact t-test power to within a percentage point for groups of 20 or more.
Worked example
64 per group, d = 0.5, two-sided α = 5%: power = 80% — the textbook benchmark. Detecting 10% vs 15% conversion with the same n gives only 13% power.
Frequently asked questions
What power should I aim for?
80% is the conventional minimum; 90% is common in clinical trials where a missed effect is costly.
Why is one-sided power higher?
The whole alpha sits in one tail, so the critical value is lower — but you forfeit the ability to detect an effect in the other direction.
Related calculators
For education — check assumptions (sample size, distribution, independence) before using a test result in a real decision.