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Lepage Test
In statistics, the Lepage test is an exact distribution-free test (nonparametric test) for jointly monitoring the location (central tendency) and scale ( variability) in two-sample treatment versus control comparisons. It is a rank test for the two-sample location-scale problem. The Lepage test statistic is the squared Euclidean distance of the standardized Wilcoxon rank-sum test for location and the standardized Ansari–Bradley test for scale. The Lepage test was first introduced by Yves Lepage in 1971 in a paper in ''Biometrika''. A large number of Lepage-type tests exists in statistical literature for simultaneously testing location and scale shifts in case-control studies. The details may be found in the book: ''Nonparametric statistical tests: A computational approach''. Wolfgang Kössler in 2006 also introduced various Lepage type tests using some alternative score functions optimal for various distributions. Amitava Mukherjee and Marco Marozzi introduced a class of perce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonparametric Test
Nonparametric statistics is a type of statistical analysis that makes minimal assumptions about the underlying distribution of the data being studied. Often these models are infinite-dimensional, rather than finite dimensional, as in parametric statistics. Nonparametric statistics can be used for descriptive statistics or statistical inference. Nonparametric tests are often used when the assumptions of parametric tests are evidently violated. Definitions The term "nonparametric statistics" has been defined imprecisely in the following two ways, among others: The first meaning of ''nonparametric'' involves techniques that do not rely on data belonging to any particular parametric family of probability distributions. These include, among others: * Methods which are ''distribution-free'', which do not rely on assumptions that the data are drawn from a given parametric family of probability distributions. * Statistics defined to be a function on a sample, without dependency on a pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Central Tendency
In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution.Weisberg H.F (1992) ''Central Tendency and Variability'', Sage University Paper Series on Quantitative Applications in the Social Sciences, p.2 Colloquially, measures of central tendency are often called '' averages.'' The term ''central tendency'' dates from the late 1920s. The most common measures of central tendency are the arithmetic mean, the median, and the mode. A middle tendency can be calculated for either a finite set of values or for a theoretical distribution, such as the normal distribution. Occasionally authors use central tendency to denote "the tendency of quantitative data to cluster around some central value."Upton, G.; Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP (entry for "central tendency")Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP for International Statistical Institute. (entry for "cent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Variability
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered. On the other hand, when the variance is small, the data in the set is clustered. Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions. Measures of statistical dispersion A measure of statistical dispersion is a nonnegative real number that is zero if all the data are the same and increases as the data become more diverse. Most measures of dispersion have the same units as the quantity being measured. In other words, if the measurements are in metres or seconds, so is the measure of dispersion. Examples of dispersion measures include: * Standard deviation * Interquartile r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rank Test (other)
{{Short description, Type of statistical test In statistics, a rank test is any Statistical hypothesis testing, test involving ranking, ranks. Rank tests are related to permutation tests. Motivation The motivation to test differences between samples is that ranks are in some sense maximally Invariant (mathematics), invariant to monotone transformations. This may be important when there is outliers or when dealing with ordinal data. Examples *Wilcoxon signed-rank test *Kruskal–Wallis one-way analysis of variance **Mann–Whitney U (special case) *Page's trend test *Friedman test *Rank products *Cucconi test *Lepage test Literature * Boos, D.D., Stefanski, L.A. (2013). Permutation and Rank Tests. In: Essential Statistical Inference. Springer Texts in Statistics, vol 120. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4818-1_12 Statistical tests ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Distance
In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance. These names come from the ancient Greek mathematicians Euclid and Pythagoras. In the Greek deductive geometry exemplified by Euclid's ''Elements'', distances were not represented as numbers but line segments of the same length, which were considered "equal". The notion of distance is inherent in the compass tool used to draw a circle, whose points all have the same distance from a common center point. The connection from the Pythagorean theorem to distance calculation was not made until the 18th century. The distance between two objects that are not points is usually defined to be the smallest distance among pairs of points from the two objects. Formulas are known for computing distances b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilcoxon Rank-sum
Wilcoxon is a surname, and may refer to: * Charles Wilcoxon, drum educator * Henry Wilcoxon, an actor * Frank Wilcoxon, chemist and statistician, inventor of two non-parametric tests for statistical significance: ** The Wilcoxon signed-rank test The Wilcoxon signed-rank test is a non-parametric rank test for statistical hypothesis testing used either to test the location of a population based on a sample of data, or to compare the locations of two populations using two matched samples., ... (also known as the Wilcoxon T test) ** The Wilcoxon rank-sum test (also known as the Mann–Whitney U test). See also * Wilcox (surname) {{surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yves Lepage
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Yves may refer to: * Yves, Charente-Maritime, a commune of the Charente-Maritime department in France * ''Yves'' (single album), a single album by Loona * ''Yves'' (film), a 2019 French film People * Yves (given name), including a list of people with the name * Yves Tumor, U.S. musician * Yves (singer), South Korean singer and producer See also * Eve (other) * Evette (other) * Yvette (other) * Yvon (other) * Yvonne (other) Yvonne is a female given name. Yvonne may also refer to: * Yvonne (band), a 1993—2002 Swedish group featuring Henric de la Cour * Yvonne (cow) a German cow that escaped and was missing for several weeks in 2011 * ''Yvonne'' (musical), a 1926 Wes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cucconi Test
In statistics, the Cucconi test is a nonparametric test for jointly comparing central tendency and variability (detecting location and scale changes) in two samples. Many rank tests have been proposed for the two-sample location-scale problem. Nearly all of them are Lepage-type tests, that is a combination of a location test and a scale test. The Cucconi test was first proposed by Odoardo Cucconi in 1968. The Cucconi test is not as familiar as other location-scale tests but it is of interest for several reasons. First, from a historical point of view, it was proposed some years before the Lepage test, the standard rank test for the two-sample location-scale problem. Secondly, as opposed to other location-scale tests, the Cucconi test is not a combination of location and scale tests. Thirdly, it compares favorably with Lepage type tests in terms of power and type-one error probability and very importantly it is easier to be computed because it requires only the ranks of one sampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
R (programming Language)
R is a programming language for statistical computing and Data and information visualization, data visualization. It has been widely adopted in the fields of data mining, bioinformatics, data analysis, and data science. The core R language is extended by a large number of R package, software packages, which contain Reusability, reusable code, documentation, and sample data. Some of the most popular R packages are in the tidyverse collection, which enhances functionality for visualizing, transforming, and modelling data, as well as improves the ease of programming (according to the authors and users). R is free and open-source software distributed under the GNU General Public License. The language is implemented primarily in C (programming language), C, Fortran, and Self-hosting (compilers), R itself. Preprocessor, Precompiled executables are available for the major operating systems (including Linux, MacOS, and Microsoft Windows). Its core is an interpreted language with a na ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Walter A
Walter may refer to: People and fictional characters * Walter (name), including a list of people and fictional and mythical characters with the given name or surname * Little Walter, American blues harmonica player Marion Walter Jacobs (1930–1968) * Gunther (wrestler), Austrian professional wrestler and trainer Walter Hahn (born 1987), who previously wrestled as "Walter" * Walter, standard author abbreviation for Thomas Walter (botanist) ( – 1789) * "Agent Walter", an early codename of Josip Broz Tito * Walter, pseudonym of the anonymous writer of '' My Secret Life'' * Walter Plinge, British theatre pseudonym used when the original actor's name is unknown or not wished to be included * John Walter (businessman), Canadian business entrepreneur Companies * American Chocolate, later called Walter, an American automobile manufactured from 1902 to 1906 * Walter Energy, a metallurgical coal producer for the global steel industry * Walter Aircraft Engines, Czech manufacturer of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
