Definition:Error of First or Second Type
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Definition
Type $\text I$ Error
A type $\text I$ error is the rejection of a true null hypothesis as the result of a hypothesis test.
The probability of a type $\text I$ error is controlled by fixing the significance level $\alpha$.
Type $\text {II}$ Error
A type $\text {II}$ error is the failure to reject a false null hypothesis as the result of a hypothesis test.
The probability of a type $\text {II}$ error depends on the alternative hypothesis $H_1$, and for a particular $H_1$ is often denoted $\beta$.
Also known as
An error of the first or second type is also known as an error of the first or second kind.
Also see
- Results about errors of the first or second type can be found here.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): error: 2.
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Type I or II error
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Type I or II error