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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 .
3.2 Uniformly most powerful tests: The Karlin–Rubin theorem. ... a uniformly most powerful test can easily be determined for the hypothesis ...
Most powerful test: For a given size or significance level, the test with the greatest power (probability of rejection) for a given value of the parameter(s) being tested, contained in the alternative hypothesis. Uniformly most powerful test (UMP)
[1] [2] Choosing the right statistical test is not a trivial task. [1] The choice of the test depends on many properties of the research question. The vast majority of studies can be addressed by 30 of the 100 or so statistical tests in use .
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.
The U.S. Navy test-launched a powerful SM-6 supersonic missile from a container mounted on its smallest type of surface warship: the Littoral Combat Ship (LCS).
The score test is the most powerful test for small deviations from . To see this, consider ... Uniformly most powerful test; Score (statistics) Sup-LM test;