Definition:Error of First or Second Type

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