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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.
In statistics, the Lehmann–Scheffé theorem is a prominent statement, tying together the ideas of completeness, sufficiency, uniqueness, and best unbiased estimation. [1] The theorem states that any estimator that is unbiased for a given unknown quantity and that depends on the data only through a complete , sufficient statistic is the unique ...
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 .
Meta-analysis: Though independent p-values can be combined using Fisher's method, techniques are still being developed to handle the case of dependent p-values. Behrens–Fisher problem: Yuri Linnik showed in 1966 that there is no uniformly most powerful test for the
Statistical tests are used to test the fit between a hypothesis and the data. [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.
Phillip I. Good Freygood (born in 1937) is a Canadian-American mathematical statistician. He was educated at McGill University and the University of California at Berkeley.. His chief contributions to statistics are in the area of small sample statistics, including a uniformly most powerful unbiased (UMPU) permutation test for Type I censored data, [pub 1] an exact test for comparing variances ...
In isolation, the upper tail (less than 1,000 out of 24,000 cities) fits both the log-normal and the Pareto distribution: the uniformly most powerful unbiased test comparing the lognormal to the power law shows that the largest 1000 cities are distinctly in the power law regime. [7]
Exact tests that are based on discrete test statistics may be conservative, indicating that the actual rejection rate lies below the nominal significance level . As an example, this is the case for Fisher's exact test and its more powerful alternative, Boschloo's test. If the test statistic is continuous, it will reach the significance level ...