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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 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 ...
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.
Bowker's test of symmetry; Categorical distribution, general model; Chi-squared test; Cochran–Armitage test for trend; Cochran–Mantel–Haenszel statistics; Correspondence analysis; Cronbach's alpha; Diagnostic odds ratio; G-test; Generalized estimating equations; Generalized linear models; Krichevsky–Trofimov estimator; Kuder ...
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 ...
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, the sample standard deviation is not unbiased for the population standard deviation – see unbiased estimation of standard deviation. Further, for other distributions the sample mean and sample variance are not in general MVUEs – for a uniform distribution with unknown upper and lower bounds, the mid-range is the MVUE for the ...