Statistical Power Calculator (Two-Sample Test)
Estimate the statistical power of a two-sample z-test — the probability of correctly detecting a real difference between two group means — given the expected effect size, sample size and significance level.
About the Statistical Power Calculator (Two-Sample Test)
Statistical power is the probability that a test correctly detects a real effect when one truly exists — equivalently, 1 minus the chance of a false negative (Type II error, β). Low-powered studies routinely miss real differences simply because the sample was too small.
Formula: Effect size (Cohen's d) = |μ₁ − μ₂| ÷ σ · Standard error = σ × √(2/n) · Power = Φ(|μ₁ − μ₂| ÷ SE − zᶜₓₓℎ₀₂), using the standard normal CDF Φ
Enter the means you expect for each group, a common standard deviation, the planned sample size per group, and your significance level to estimate power before running a study. As a rule of thumb, researchers aim for at least 80% power; if the estimate falls short, use the sample size calculator to find how many observations per group would be needed to reach a target power for the same effect size. This calculator uses a simplified equal-variance, two-sided z-test approximation, which is a close and commonly used stand-in for the more elaborate t-distribution-based power calculations found in dedicated statistical software.