|
Lepage Test
In statistics, the Lepage test is an exactly distribution-free test ( nonparametric test) for jointly monitoring the location (central tendency) and scale ( variability) in two-sample treatment versus control comparisons. This is one of the most famous 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. Dr. Amitava Mukherjee and Dr. Marco Marozzi i ... [...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 "c ... [...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 * M ... [...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 product The rank product is a biologically motivated test for the detection of differentially expressed genes in replicated microarray experiments. It is a simple non-parametric statistical method based on ranks of fold changes. In addition to its use in ...s * 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/10.1007/978-1-4614-48 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
