= Most powerful test
At level $\alpha$, a most powerful test against a specified simple alternative maximises <statistical power> among <statistical tests> whose <size of a statistical test> is at most $\alpha$. The <Neyman-Pearson lemma> constructs it by a <likelihood ratio> threshold. A <uniformly most powerful test> is most powerful simultaneously against every member of the specified alternative family; maximising power at one alternative alone need not give uniform optimality.
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