Uniformly most powerful test

Summary

A uniformly most powerful test of level $\alpha$ is a hypothesis test of level $\alpha$ with the largest possible power. Its power beats that of every other test of level $\alpha$, at every parameter value of the alternative. For simple hypotheses the Neyman–Pearson lemma gives such a test. For one-sided hypotheses in families with a monotone likelihood ratio, the Karlin–Rubin theorem gives one. For many other problems no such test exists.