Power Analysis Calculator
Enter effect size, variability, significance level, and sample size to compute statistical power. Optionally, estimate the required sample size for a target power.
Difference between true mean and null hypothesis mean.
Used to estimate minimum n for the specified effect size and α.
Standard error (σ / √n): 1.2649
Non-centrality parameter: 2.7670
Power: 79.0176%
Required n for desired power: 42
How to Use This Calculator
- Specify the true effect size you aim to detect and the population (or estimated) standard deviation.
- Enter the planned sample size and significance level.
- Select a one- or two-tailed hypothesis depending on your alternative.
- Review the computed power and optionally adjust inputs until the desired power level is achieved.
Formula
Z statistic under H₁: Z = (x̄ − μ₀) / (σ / √n) with mean δ = (μ₁ − μ₀) / (σ / √n)
Two-tailed power: 1 − [Φ(zα/2 − δ) − Φ(−zα/2 − δ)]
One-tailed power (upper): 1 − Φ(zα − δ)
Required sample size (two-tailed): n = [(zα/2 + zβ) σ / |μ₁ − μ₀|]²
Full Description
Power analysis quantifies the probability of detecting a true effect. It depends on effect size, variability, sample size, significance level, and test direction. Adequate power (commonly 80%) reduces Type II error risk and informs study planning.
This calculator assumes a one-sample z-test with known σ. For t-tests or more complex designs, use specialized power formulas or software.
Frequently Asked Questions
What if σ is unknown?
Replace σ with an estimate or conduct pilot studies. For small samples, t-distribution adjustments may be needed.
Can I analyze two-sample tests?
This tool covers one-sample z-tests. Extend formulas for two-sample comparisons by using pooled variance and adjusted effect sizes.
Why does power increase with n?
Larger samples reduce standard error, making true deviations from the null easier to detect.
What is β in sample size formulas?
β = 1 − power. For 80% power, β = 0.2 and zβ corresponds to Φ−1(0.8).