Statistical Power For Study Calculator

Work out statistical power for study instantly with clear inputs, formula shown and shareable results.

About Statistical Power For Study Calculator

Power is the probability of detecting a real effect. For d = 0.5 with 64 per group at alpha 0.05, power is about 80% - exactly why 64 per group is the classic textbook figure for a medium effect. The type II error rate of 20% means one study in five would miss a genuine effect of that size.

Formulas

Power

power = P(|Z| > z(alpha/2) | true effect), with non-centrality d x sqrt(n/2)

Sample for 80% power

n per group = 2((z(alpha/2) + z(0.80)) / d)^2

Worked example

With the default values below, Statistical Power For Study Calculator returns Statistical Power of 80.74%. Change any input above and every figure here is recalculated in your browser.

Inputs used

Expected effect size (Cohen's d)minimum 0.01: 0.5
Sample size per groupminimum 2: 64
Significance levelaccepts 0.1–20 %: 5 %

Results

Statistical Power: 80.74%
Sample Per Group For 80% Power: 63
Type II Error Rate: 19.26%
Critical z Value: 1.9600

Step by step

1Values used
2Power
3Sample for 80% power
4Statistical Power= 80.74
5Sample Per Group For 80% Power= 63
6Type II Error Rate= 19.26
7Critical z Value= 1.9600

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why is 80% power the convention?

It balances the cost of a larger sample against the risk of missing an effect. Some fields now expect 90% or 95%.

What happens with underpowered studies?

They miss real effects and, when they do reach significance, overestimate the effect size - a major driver of the replication crisis.