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Type I and type II errors

A type I error is rejecting a true H0H_0; its probability is the significance level α\alpha. A type II error is retaining a false H0H_0, with probability β\beta. The test's power, 1−β1-\beta, is the probability of detecting a real effect when one exists.

α=P(reject H0∣H0 true)\alpha = P(\text{reject } H_0 \mid H_0 \text{ true})type I error
β=P(retain H0∣H0 false)\beta = P(\text{retain } H_0 \mid H_0 \text{ false})type II error

Symbols

α\alphasignificance level
β\betaprobability of a type II error
1−β1-\betathe test's power

Example

Lowering α\alpha (a stricter requirement to reject H0H_0) usually increases β\beta for the same sample size.

Type I and type II are opposite errors — reducing one usually increases the other, unless nn is increased.
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Part of Statistics and Risk Analysis: Inference and risk.