Definition:Power Function
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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 $9.1.6$