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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] |
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] |
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] |
Odoardo Cucconi
Odoardo is a given name. Notable people with the name include: *Odoardo Barri (1844–1920), the pseudonym of Edward Slater *Odoardo Beccari (1843–1920), Italian naturalist, discovered the titan arum in Sumatra in 1878 *Odoardo Borrani (1833–1905), Italian painter associated with the Macchiaioli group * Juan Manuel Cajigal y Odoardo (1803–1856), Venezuelan mathematician, engineer and statesman *Odoardo Farnese (cardinal) (1573–1626), Italian nobleman, son of Alessandro Farnese, Duke of Parma and Maria of Portugal * Alessandro di Odoardo Farnese, Prince of Parma (1635–1689), Italian military leader, Governor of the Habsburg Netherlands from 1678 to 1682 *Odoardo Farnese, Duke of Parma (1612–1646), also known as Odoardo I Farnese, Duke of Parma, Piacenza and Castro from 1622 to 1646 *Odoardo Farnese, Hereditary Prince of Parma (1666–1693), the son and heir of Duke Ranuccio II Farnese, Duke of Parma and Piacenza * Odoardo Fialetti (1573–1638), Italian painter and printma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation Test
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 then ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
