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Power Analysis Calculator — Power, Sample Size, and Detectable Effect — GetCalcMaster

Power analysis workflow: choose α, desired power, effect size, and compute sample size (or detectable effect). Includes quick approximations and common pitfalls.

Power analysis connects four ideas: significance level (α), power (1−β), effect size, and sample size. Fix three, solve for the fourth. This page gives a practical workflow and common approximations.

Open Statistics Calculator Use Notebook Guides

Important: Educational. Real power analysis is test- and design-specific; use domain standards for confirmatory studies.

What this calculator is

The Statistics Calculator is an interactive tool inside GetCalcMaster. It’s designed to help you explore scenarios, understand formulas, and document assumptions.

Key features

Step-by-step planning checklist (not just a formula)
Links effect sizes to power/sample size
Highlights common approximations and when they break
Connects to multiple comparisons (which changes effective α)

Formula

Common z-approximation (two-sample, standardized mean difference):
n_per_group ≈ 2 * ((z_{1-α/2} + z_{power}) / d)^2

Where d is Cohen's d (standardized mean difference).
For proportions and other tests, formulas differ—use a test-specific guide.

Quick examples

Rule-of-thumb: for d=0.5, α=0.05 (two-tailed), power=0.80 → n per group ≈ 63–64 (z approximation).
If you run many hypotheses, adjust α (e.g., Bonferroni) which increases required n.
Power increases with larger n, larger effect sizes, lower noise, or higher α.

Verification tips

Sanity check direction: if desired power increases, required n should increase.
If effect size shrinks, required n should grow roughly like 1/d².

Common mistakes

Using an unrealistically large effect size (leads to underpowered studies).
Forgetting multiple comparisons (effective α is smaller).
Choosing one-tailed α without a justified directional hypothesis.

How to use it (quick steps)

Define the outcome and hypothesis test (mean, proportion, regression coefficient, etc.).
Choose α (two-tailed vs one-tailed) based on your decision cost.
Pick desired power (often 0.80 or 0.90).
Estimate a realistic effect size (from pilot data or domain benchmarks).
Compute required sample size, then inflate for dropout/missingness and multiple comparisons if needed.