Type I and Type II error
Type I and Type II error are the two ways a hypothesis test can go wrong. A Type I error rejects a null that is actually true; its probability equals the significance level. A Type II error fails to reject a null that is false.
Also known asfalse positive · false negative
FrameworkHypothesis testing
See it move
A two-by-two matrix crosses the decision (reject or do not reject) against the true state of the null hypothesis (true or false). Rejecting a true null produces a Type I error (false positive) at rate α; correctly rejecting a false null gives power of 1 − β. Failing to reject a false null produces a Type II error (false negative) at rate β; correctly retaining a true null is a true negative. Every hypothesis test trades off these two error rates — reducing α raises β unless the sample size is increased.
The formula
Variables
- Significance level — set by the researcher before the test, commonly 0.05 or 0.01 (decimal)
The probability of falsely rejecting a true null hypothesis equals the significance level; it is a direct consequence of the decision rule chosen.
Variables
- Probability of failing to reject a null hypothesis that is actually false (decimal)
Lowering α to reduce Type I risk tends to raise β; reducing both requires a larger sample size.
The probability of correctly detecting a real effect; higher power is achieved by increasing sample size or effect size.
Check yourself
A bank's fraud-detection model flags a transaction as suspicious and blocks it when the hypothesis 'this transaction is legitimate' is rejected. Which event is a Type I error?