Definition:Power Function

Definition

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

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

Let $\delta$ be a test procedure for hypotheses about the value of $\theta$.

Let $C$ be the critical region of $\delta$.

Let $T$ be the test statistic of $\delta$.

The power function of $\delta$, written $\map \pi {\theta_0}$, is defined by:

$\map \pi {\theta_0} = \condprob {T \in C} {\theta = \theta_0}$

for all $\theta_0 \in \Omega$.

Sources

• 2011: Morris H. DeGroot and Mark J. Schervish: Probability and Statistics (4th ed.): $9.1$: Problems of Testing Hypotheses: Definition $9.1.6$