Definition:Composite Hypothesis Test

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Definition

Let $\delta$ be a hypothesis test.

Then $\delta$ is a composite hypothesis test if and only if the probability distribution of the population random variable is not 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:

$X$ is normally distributed with an expectation of $2$, but whose variance is unknown.

Then $\delta$ is a composite hypothesis test.

Also see

• Definition:Simple Hypothesis Test

• Results about composite 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