Type I And Type II Error Calculator

Work out type i and type ii error instantly with clear inputs, formula shown and shareable results.

About Type I And Type II Error Calculator

A Type I error rejects a true null hypothesis and occurs with probability α. A Type II error fails to reject a false null and occurs with probability β; power is 1 − β and rises with both the effect size and the sample size.

Formulas

Power

power = 1 − β = P(reject | the alternative is true)

Beta

β = Φ(z_crit − δ) − Φ(−z_crit − δ)

Worked example

With the default values below, Type I And Type II Error Calculator returns Statistical power (1 − β) of 0.51600535. Change any input above and every figure here is recalculated in your browser.

Inputs used

Significance level αaccepts 0.01–50 %: 5 %
True effect size in standard errors: 2
Test typeone of Two-tailed, One-tailed: Two-tailed

Results

Statistical power (1 − β): 0.51600535
Type II error rate β: 0.48399465
Type I error rate α: 0.05000000
Critical z value: 1.959964

Step by step

1Values used
2Power
3Beta
4Statistical power (1 − β)= 0.51600535
5Type II error rate β= 0.48399465
6Type I error rate α= 0.05000000
7Critical z value= 1.959964

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 8 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

For α = 5% two-tailed with an effect of 2 standard errors?

The critical z is 1.96, so β ≈ 0.4840 and the power is about 51.6% — a coin flip.

How do I raise power?

Increase the sample size, reduce measurement noise, or accept a larger α. There is always a trade-off with the Type I rate.