Definition:Hypothesis Test

Definition

A hypothesis test is a rule that specifies, for a null hypothesis $H_0$ and alternative hypothesis $H_1$:

• For which sample values the decision is made to accept $H_0$
• For which sample values $H_0$ is rejected and $H_1$ is accepted.

Consideration of a suitable test statistic $T$ enables the null hypothesis to be rejected at a given significance level $\alpha$ only if $T$ lies in its critical region for $\alpha$.

Also known as

It is often convenient to refer to the process of hypothesis testing as a verb form meaning performing a hypothesis test.

The terms significance testing and significance test can also be found, which are synonyms of these.

Also found is the term statistical significance.

Also see

• Results about hypothesis testing can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): hypothesis testing
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): test
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): hypothesis testing
• 2002: George C. Casella and Roger L. Berger: Statistical Inference (2nd ed.) ... (previous) ... (next): $8.1$: Introduction: Definition $8.1.3$
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): hypothesis testing
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): hypothesis testing