Type I and type II errors

Definition taught in Hypothesis tests, part of Statistical inference

Type I and type II errors

Left: a two-sided z test of size 0.05. From Hypothesis tests.
Type Definition
Taught in Hypothesis tests
Part Statistical inference

A type I error rejects H_0 when H_0 is true. A type II error accepts H_0 when H_1 is true. The size, or significance level, is the probability of a type I error. The power at a particular alternative is the probability of rejecting H_0 there, which is one minus the type II error at that alternative.

Figures

Power curves for two tests of H_0:p=0.6 against p>0.6 from 15 serves. Rejecting at 13 or more keeps the size at 0.027, but has power only 0.40 even at p=0.8. Rejecting at 12 or more gains power everywhere, and its size rises to 0.091, above the 5% level. From Hypothesis tests.

Used in

See also

Neyman–Pearson approach · Power function · Null and alternative hypotheses · Critical region · p-value · One-sample t test · Two-sample t test · F test for equal variances

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