# Definition:Test Statistic

## Definition

Let $\theta$ be a population parameter of some population $P$.

Let $\Omega$ be the parameter space of $\theta$.

Let $\mathbf X$ be a random sample from $P$.

Let $T = \map f {\mathbf X}$ be a sample statistic.

Let $\delta$ be a test procedure of the form:

reject $H_0$ if $T \in C$

for some null hypothesis $H_0$ and some $C \subset \Omega$.

We refer to $T$ as the test statistic of $\delta$.