Statistics · Hypothesis testing · A-level

Type I and Type II errors

A test decides from one sample, so it can be wrong in two ways: rejecting a null hypothesis that is true (a Type I error) or not rejecting one that is false (a Type II error). How to describe each error in context, why the probability of a Type I error is the probability of the critical region when H0 is true, how to find the probability of a Type II error for a given true value of the parameter in binomial, Poisson and normal tests, and why making one error less likely makes the other more likely.

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Why it works

Two ways a test can be wrong

Priya lands

60\%

of her first serves in. She buys an expensive new racket and will judge it on her next

30

first serves, testing

H_0: p = 0.6

against

H_1: p > 0.6

. Whatever the test decides, it decides from one sample, so it can be wrong in two different ways.

	$H_0$ is true	$H_0$ is false
Reject $H_0$	Type I error	correct decision
Do not reject $H_0$	correct decision	Type II error

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