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Permutation Tests
A permutation test (also called re-randomization test) is an exact statistical hypothesis test making use of the proof by contradiction. A permutation test involves two or more samples. The null hypothesis is that all samples come from the same distribution H_0: F=G. Under the null hypothesis, the distribution of the test statistic is obtained by calculating all possible values of the test statistic under possible rearrangements of the observed data. Permutation tests are, therefore, a form of resampling. Permutation tests can be understood as surrogate data testing where the surrogate data under the null hypothesis are obtained through permutations of the original data. In other words, the method by which treatments are allocated to subjects in an experimental design is mirrored in the analysis of that design. If the labels are exchangeable under the null hypothesis, then the resulting tests yield exact significance levels; see also exchangeability. Confidence intervals can th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exact Test
In statistics, an exact (significance) test is a test such that if the null hypothesis is true, then all assumptions made during the derivation of the distribution of the test statistic are met. Using an exact test provides a significance test that maintains the type I error rate of the test (\alpha) at the desired significance level of the test. For example, an exact test at a significance level of \alpha = 5\%, when repeated over many samples where the null hypothesis is true, will reject at most 5\% of the time. This is in contrast to an ''approximate test'' in which the desired type I error rate is only approximately maintained (i.e.: the test might reject > 5% of the time), while this approximation may be made as close to \alpha as desired by making the sample size sufficiently large. Exact tests that are based on discrete test statistics may be conservative, indicating that the actual rejection rate lies below the nominal significance level \alpha. As an example, this is t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
F-test
An ''F''-test is any statistical test in which the test statistic has an ''F''-distribution under the null hypothesis. It is most often used when comparing statistical models that have been fitted to a data set, in order to identify the model that best fits the population from which the data were sampled. Exact "''F''-tests" mainly arise when the models have been fitted to the data using least squares. The name was coined by George W. Snedecor, in honour of Ronald Fisher. Fisher initially developed the statistic as the variance ratio in the 1920s. Common examples Common examples of the use of ''F''-tests include the study of the following cases: * The hypothesis that the means of a given set of normally distributed populations, all having the same standard deviation, are equal. This is perhaps the best-known ''F''-test, and plays an important role in the analysis of variance (ANOVA). * The hypothesis that a proposed regression model fits the data well. See Lack-of-fit sum of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Mathematical Statistics
The ''Annals of Mathematical Statistics'' was a peer-reviewed statistics journal published by the Institute of Mathematical Statistics from 1930 to 1972. It was superseded by the ''Annals of Statistics'' and the ''Annals of Probability''. In 1938, Samuel Wilks became editor-in-chief of the ''Annals'' and recruited a remarkable editorial staff: Fisher, Neyman, Cramér, Hotelling, Egon Pearson, Georges Darmois, Allen T. Craig, Deming, von Mises Mises or von Mises may refer to: * Ludwig von Mises, an Austrian-American economist of the Austrian School, older brother of Richard von Mises ** Mises Institute, or the Ludwig von Mises Institute for Austrian Economics, named after Ludwig von ..., H. L. Rietz, and Shewhart. References {{reflist External links Annals of Mathematical Statistics at Project Euclid Statistics journals Probability journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meyer Dwass
Meyer Dwass (April 9, 1923 – July 15, 1996) was an American mathematical statistician known for his contributions to applied probability. Dwass was a professor of statistics at Northwestern University. Born in New Haven, Connecticut, Dwass attended George Washington University, earning a bachelor's degree in 1948. Under supervision of Wassilij Höffding, he earned a Ph.D. from University of North Carolina at Chapel Hill A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States ... in 1952. References External links * 1923 births 1996 deaths American statisticians George Washington University alumni University of North Carolina at Chapel Hill alumni Northwestern University faculty Scientists from New Haven, Connecticut Mathematical statisticians {{US-mathematician- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frank Yates
Frank Yates FRS (12 May 1902 – 17 June 1994) was one of the pioneers of 20th-century statistics. Biography Yates was born in Manchester, England, the eldest of five children (and only son) of seed merchant Percy Yates and his wife Edith. He attended Wadham House, a private school, before gaining a scholarship to Clifton College in 1916. In 1920 he obtained a scholarship at St John's College, Cambridge, and four years later graduated with a First Class Honours degree. He spent two years teaching mathematics to secondary school pupils at Malvern College before heading to Africa where he was mathematical advisor on the Gold Coast Survey. He returned to England due to ill health and met and married a chemist, Margaret Forsythe Marsden, the daughter of a civil servant. This marriage was dissolved in 1933 and he later married Prascovie (Pauline) Tchitchkine, previously the partner of Alexis Tchitchkine. After her death in 1976, he married Ruth Hunt, his long-time secretary. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Sampling
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution. In physics-related problems, Monte Carlo methods are useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model, interacting particle systems, McKean–Vlasov processes, kinetic models of gases). Other examples include modeling phenomena with significant uncertainty in inputs such as the calculation of risk ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equivalence Test
Equivalence tests are a variety of hypothesis tests used to draw statistical inferences from observed data. In these tests, the null hypothesis is defined as an effect large enough to be deemed interesting, specified by an equivalence bound. The alternative hypothesis is any effect that is less extreme than said equivalence bound. The observed data are statistically compared against the equivalence bounds. If the statistical test indicates the observed data is surprising, assuming that true effects are at least as extreme as the equivalence bounds, a Neyman-Pearson approach to statistical inferences can be used to reject effect sizes larger than the equivalence bounds with a pre-specified Type 1 error rate. Equivalence testing originates from the field of clinical trials. One application, known as a non-inferiority trial, is used to show that a new drug that is cheaper than available alternatives works as well as an existing drug. In essence, equivalence tests consist of calculat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Annals Of Statistics
The ''Annals of Statistics'' is a peer-reviewed statistics journal published by the Institute of Mathematical Statistics. It was started in 1973 as a continuation in part of the ''Annals of Mathematical Statistics (1930)'', which was split into the ''Annals of Statistics'' and the ''Annals of Probability''. The journal CiteScore is 5.8, and its SCImago Journal Rank is 5.877, both from 2020. Articles older than 3 years are available on JSTOR, and all articles since 2004 are freely available on the arXiv. Editorial board The following persons have been editors of the journal: * Ingram Olkin (1972–1973) * I. Richard Savage (1974–1976) * Rupert Miller (1977–1979) * David V. Hinkley (1980–1982) * Michael D. Perlman (1983–1985) * Willem van Zwet (1986–1988) * Arthur Cohen (1988–1991) * Michael Woodroofe (1992–1994) * Larry Brown and John Rice (1995–1997) * Hans-Rudolf Künsch and James O. Berger (1998–2000) * John Marden and Jon A. Wellner (2001–2003) * Mor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Behrens–Fisher Problem
In statistics, the Behrens–Fisher problem, named after Walter Behrens and Ronald Fisher, is the problem of interval estimation and hypothesis testing concerning the difference between the means of two normally distributed populations when the variances of the two populations are not assumed to be equal, based on two independent samples. Specification One difficulty with discussing the Behrens–Fisher problem and proposed solutions, is that there are many different interpretations of what is meant by "the Behrens–Fisher problem". These differences involve not only what is counted as being a relevant solution, but even the basic statement of the context being considered. Context Let ''X''1, ..., ''X''''n'' and ''Y''1, ..., ''Y''''m'' be i.i.d. samples from two populations which both come from the same location–scale family of distributions. The scale parameters are assumed to be unknown and not necessarily equal, and the problem is to assess whether t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PERMANOVA
Permutational multivariate analysis of variance (PERMANOVA), is a non-parametric multivariate statistical permutation test. PERMANOVA is used to compare groups of objects and test the null hypothesis that the centroids and dispersion of the groups as defined by measure space are equivalent for all groups. A rejection of the null hypothesis means that either the centroid and/or the spread of the objects is different between the groups. Hence the test is based on the prior calculation of the distance between any two objects included in the experiment. PERMANOVA shares some resemblance to ANOVA where they both measure the sum-of-squares within and between group and make use of F test to compare within-group to between-group variance. However, while ANOVA bases the significance of the result on assumption of normality, PERMANOVA draws tests for significance by comparing the actual F test result to that gained from random permutations of the objects between the groups. Moreover, whilst P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Modern Applied Statistical Methods
The ''Journal of Modern Applied Statistical Methods'' is a biannual peer-reviewed open access journal. It was established in 2002 by Shlomo Sawilowsky, and is currently published by the Wayne State University Library System in Detroit, MI. The ''Current Index to Statistics'' classifies it as one of over 160 core statistics journals. The journal originally appeared as a print and electronic journal through volume 8(1) in 2009, and subsequently as an electronic journal only. It publishes peer-reviewed work pertaining to new statistical tests and the comparison of existing statistical tests; bootstrap, Jackknife, and resampling methods; nonparametric, robust, permutation, exact, and approximate randomization methods; and statistical algorithms, pseudorandom number generators, and simulation techniques. The journal is indexed in the Elsevier Bibliographic Database, EMBASE, Compendex, Geobase, PsycINFO, ScienceDirect, and Scopus. It is also listed in the ''Encyclopedia of Measurement ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
