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Lepage Test
In statistics, the Lepage test is an exactly distribution-free test (nonparametric test) for jointly monitoring the location (central tendency) and scale (Statistical variability, variability) in two-sample treatment versus control comparisons. This is one of the most famous Rank test (other), rank tests for the two-sample location-scale problem. The Lepage test statistic is the squared Euclidean distance of 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''. Kössler, W. in 2006 also introduced various Lepage type tests using some alternative score functions optimal for various distributions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonparametric Test
Nonparametric statistics is the branch of statistics that is not based solely on parametrized families of probability distributions (common examples of parameters are the mean and variance). Nonparametric statistics is based on either being distribution-free or having a specified distribution but with the distribution's parameters unspecified. Nonparametric statistics includes both descriptive statistics and statistical inference. Nonparametric tests are often used when the assumptions of parametric tests are violated. Definitions The term "nonparametric statistics" has been imprecisely defined in the following two ways, among others: Applications and purpose Non-parametric methods are widely used for studying populations that take on a ranked order (such as movie reviews receiving one to four stars). The use of non-parametric methods may be necessary when data have a ranking but no clear numerical interpretation, such as when assessing preferences. In terms of levels of me ... [...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 "ce ... [...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 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 range (IQR) * Range * Mean ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rank Test (other)
In statistics, a rank test is any test involving 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 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 In statistics, the Lepage test is an exactly distribution-free test (nonparametric test) for jointly monitoring the location (central tendency) and scale (Statistical variability, variability) in two-sample treatment versus control comparisons. This ... 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 ... [...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 a line segment between the two points. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefore occasionally being called the Pythagorean distance. These names come from the ancient Greek mathematicians Euclid and Pythagoras, although Euclid did not represent distances as numbers, and 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 between different types of objects, such as the distance from a point to a line. In advanced mathematics, the concept of distance has been generalized to abstract metric spaces, and other distances than Euclidean have been studied. In some applications in statistic ... [...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 (also known as the Wilcoxon T test) ** The Wilcoxon rank-sum test (also known as the Mann–Whitney U test). See also *Wilcox (surname) Wilcox is a surname. Notable people with the surname include: * Adam Wilcox (other), multiple people * Albert Spencer Wilcox (1844–1919), businessman and politician in the Kingdom of Hawaii * Alex Wilcox, airline executive and entrepren ... {{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 (given name), including a list of people with the name * ''Yves'' (single album), a single album by Loona * ''Yves'' (film), a 2019 French film See also * Yves Tumor, U.S. musician * * 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 We ... [...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 samp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Walter A
Walter may refer to: People * Walter (name), both a surname and a given name * 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) 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 aero-engines Films and television * ''Walter'' (1982 film), a British television drama film * Walter Vetrivel, a 1993 Tamil crime drama film * ''Walter'' (2014 film), a British television crime drama * ''Walter'' (2015 film), an American comedy-drama film * ''Walter'' (2020 film), an Indian crime drama film * ''W*A*L*T*E*R'', a 1984 pilot for a spin-off of the TV series ''M*A*S*H'' * ''W ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Control Chart
Control charts is a graph used in production control to determine whether quality and manufacturing processes are being controlled under stable conditions. (ISO 7870-1) The hourly status is arranged on the graph, and the occurrence of abnormalities is judged based on the presence of data that differs from the conventional trend or deviates from the control limit line. Control charts are classified into Shewhart individuals control chart (ISO 7870-2) and CUSUM(CUsUM)(or cumulative sum control chart)(ISO 7870-4). Control charts, also known as Shewhart charts (after Walter A. Shewhart) or process-behavior charts, are a statistical process control tool used to determine if a manufacturing or business process is in a state of control. It is more appropriate to say that the control charts are the graphical device for Statistical Process Monitoring (SPM). Traditional control charts are mostly designed to monitor process parameters when the underlying form of the process distributions ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
