Definition:Two-Sided Alternative

Definition

Let $\delta$ be a hypothesis test.

Let $H_0$ and $H_1$ be the null hypothesis and alternative hypothesis of $\delta$ respectively.

Let $\theta$ be the test statistic which is being used to determine whether $H_0$ or $H_1$ holds.

Let $H_1$ be such that the critical region of $\delta$ is governed by a (possibly implicit) double inequality, for example:

$H_1: \begin {cases} \theta > x + \epsilon \\ \theta < x - \epsilon \end {cases}$

where $H_0: \theta \in \closedint {x - \epsilon} {x + \epsilon}$ is the null hypothesis of $\delta$.

Then $H_1$ is known as a two-sided alternative.

Also see

• Definition:Two-Tail Test

• Results about the alternative hypothesis can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): hypothesis testing
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): hypothesis testing