Power Function

μG(μ):=Pμ( reject H0)(μH0H1)\mu \mapsto G(\mu):=\mathbb{P}_{\mu}\left(\text { reject } H_{0}\right) \quad\left(\mu \in H_{0} \cup H_{1}\right)

Probability that H0H_0 gets rejected based on some unknown μ\mu.

  • α(μ)\alpha(\mu) is probability of Type 1 Error for μ\mu
  • β(μ)\beta(\mu) is probability of Type 2 Error for μ\mu

Power of the test: 1β(μ)1-\beta(\mu)