Definition:One-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 single inequality, for example:

$H_1: \theta > x$

where $x$ is the critical value of $\delta$.

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

Also see

• Definition:One-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