Definition:Simple Hypothesis Test

Definition

Let $\delta$ be a hypothesis test.

Then $\delta$ is a simple hypothesis test if and only if the probability distribution of the population random variable is completely specified.

Examples

Arbitrary Example

Let $\delta$ be a hypothesis test.

Let $H_0$ be the null hypothesis that the probability distribution $X$ of $\delta$ is:

$X \sim \Gaussian 2 9$

where $\Gaussian 2 9$ denotes the normal (Gaussian) distribution.

Then $\delta$ is a simple hypothesis test.

Also see

• Definition:Composite Hypothesis Test

• Results about simple hypothesis tests 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