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In statistical hypothesis testing, a uniformly most powerful (UMP) test is a hypothesis test which has the greatest power among all possible tests of a given size α. For example, according to the Neyman–Pearson lemma , the likelihood-ratio test is UMP for testing simple (point) hypotheses.
Neyman–Pearson lemma [5] — Existence:. If a hypothesis test satisfies condition, then it is a uniformly most powerful (UMP) test in the set of level tests.. Uniqueness: If there exists a hypothesis test that satisfies condition, with >, then every UMP test in the set of level tests satisfies condition with the same .
For a given test, the significance criterion determines the desired degree of rigor, specifying how unlikely it is for the null hypothesis of no effect to be rejected if it is in fact true. The most commonly used threshold is a probability of rejection of 0.05, though smaller values like 0.01 or 0.001 are sometimes used.
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The likelihood-ratio test, also known as Wilks test, [2] is the oldest of the three classical approaches to hypothesis testing, together with the Lagrange multiplier test and the Wald test. [3] In fact, the latter two can be conceptualized as approximations to the likelihood-ratio test, and are asymptotically equivalent.
Medusa is one of the most powerful mythological figures of all time. She had the power to petrify a person with a single glance—and we mean quite literally turn a person to stone.