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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 .
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]
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
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 ...
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.
The parametric equivalent of the Kruskal–Wallis test is the one-way analysis of variance (ANOVA). A significant Kruskal–Wallis test indicates that at least one sample stochastically dominates one other sample. The test does not identify where this stochastic dominance occurs or for how many pairs of groups stochastic dominance obtains.
However, in practice, most implementations of non-parametric test software use asymptotical algorithms to obtain the significance value, which renders the test non-exact. Hence, when a result of statistical analysis is termed an “exact test” or specifies an “exact p-value ”, this implies that the test is defined without parametric ...