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
- 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