What is statistical power?

Power (1 − β) is the probability of correctly rejecting a false null hypothesis. A power of 0.80 means there is an 80% chance of detecting a true effect of the specified size.

Cohen's d measures the standardised difference between two group means: d = (μ₁ − μ₂) / σ_pooled. Conventional benchmarks are 0.2 (small), 0.5 (medium), and 0.8 (large).

What is the allocation ratio?

The allocation ratio k = n₂/n₁ sets how many participants go into group 2 relative to group 1. The default is 1 (equal groups). Unequal allocation reduces efficiency.

One-tailed or two-tailed?

Two-tailed tests are standard in most research because they detect effects in either direction. Use one-tailed only when the direction of the effect is known in advance and specified before data collection.

How accurate is the normal approximation?

For n ≥ 30 per group the normal approximation to the t-distribution is very close to the exact t-based calculation (within 1–2%). For smaller samples consider using exact t-distribution tables.

Statistical Power Analysis Calculator

Name: Statistical Power Analysis Calculator
Availability: InStock
Author: Nham Vu

Enter effect size, alpha, and power to find the required sample size — or enter sample size to find the achievable power.

Inputs

Solve for

Sample Size Power

Effect Size (Cohen's d)

Significance Level (α)

Target Power (1 − β)

Allocation Ratio k = n₂ / n₁

Default 1 = equal group sizes.

Test Tails

Two-tailed One-tailed

Set your inputs and click Calculate.

Summary

Enter effect size, alpha, and power to find the required sample size — or enter sample size to find the achievable power.

How it works

Select the calculation mode: solve for sample size or solve for power.
Enter the effect size as Cohen's d (small ≈ 0.2, medium ≈ 0.5, large ≈ 0.8).
Set the significance level (alpha), typically 0.05 or 0.01.
For sample size mode, enter the desired power (e.g. 0.80 for 80%).
For power mode, enter the available sample size per group.
The calculator applies the normal approximation and displays the result with a power curve.

Use cases

Determine how many participants a clinical trial needs before it begins.
Verify a planned study is adequately powered at α = 0.05, power = 0.80.
Estimate achievable power when budget constrains the maximum sample size.
Compare power across several effect sizes during study design.
Support grant applications that require a formal power justification.
Audit a published study's reported sample size for reproducibility.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu