Statistics / Unit 9: Hypothesis Testing Basics
9.5 Type I and Type II Errors
Notes
Decisions based on samples can be wrong in two ways.
- Type I error: rejecting $H_0$ when it is actually true (a false positive). Its probability is $\alpha$.
- Type II error: failing to reject $H_0$ when it is actually false (a false negative).
- Lowering $\alpha$ makes a Type I error less likely but a Type II error more likely. A larger sample size can reduce both.
- Example: A medical test with $H_0$: the patient is healthy. A Type I error tells a healthy patient they are sick.
| $H_0$ true | $H_0$ false | |
|---|---|---|
| Reject $H_0$ | Type I error | Correct |
| Fail to reject $H_0$ | Correct | Type II error |
Practice
In a medical test with $H_0$: the patient is healthy, a Type I error is:
A Type I error rejects a true $H_0$.
A test is changed from $\alpha = 0.05$ to $\alpha = 0.01$ with the same sample size. What happens?
A stricter standard makes it harder to reject $H_0$, which trades one error for the other.
A factory tests $H_0$: the machine fills bottles correctly. A Type II error means:
A Type II error fails to reject a false $H_0$.
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