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Mann–Whitney U Test
The Mann–Whitney U test (also called the Mann–Whitney–Wilcoxon (MWW/MWU), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a nonparametric statistical test of the null hypothesis that randomly selected values ''X'' and ''Y'' from two populations have the same distribution. Nonparametric tests used on two ''dependent'' samples are the sign test and the Wilcoxon signed-rank test. Assumptions and formal statement of hypotheses Although Henry Mann and Donald Ransom Whitney developed the Mann–Whitney ''U'' test under the assumption of continuous responses with the alternative hypothesis being that one distribution is stochastically greater than the other, there are many other ways to formulate the null and alternative hypotheses such that the Mann–Whitney ''U'' test will give a valid test. A very general formulation is to assume that: # All the observations from both groups are independent of each other, # The responses are at least ordinal (i.e., one ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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., p. 350 The one-sample version serves a purpose similar to that of the one-sample Student's ''t''-test. For two matched samples, it is a paired difference test like the paired Student's ''t''-test (also known as the "''t''-test for matched pairs" or "''t''-test for dependent samples"). The Wilcoxon test is a good alternative to the t-test when the normal distribution of the differences between paired individuals cannot be assumed. Instead, it assumes a weaker hypothesis that the distribution of this difference is symmetric around a central value and it aims to test whether this center value differs significantly from zero. The Wilcoxon test is a more powerful alternative to the sign test because it considers the magnitude of the differ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Nonparametric Statistics
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Independent And Identically Distributed Random Variables
Independent or Independents may refer to: Arts, entertainment, and media Artist groups * Independents (artist group), a group of modernist painters based in Pennsylvania, United States * Independentes (English: Independents), a Portuguese artist group Music Groups, labels, and genres * Independent music, a number of genres associated with independent labels * Independent record label, a record label not associated with a major label * Independent Albums, American albums chart Albums * ''Independent'' (Ai album), 2012 * ''Independent'' (Faze album), 2006 * ''Independent'' (Sacred Reich album), 1993 Songs * "Independent" (song), a 2007 song by Webbie * "Independent", a 2002 song by Ayumi Hamasaki from '' H'' News media organizations * Independent Media Center (also known as Indymedia or IMC), an open publishing network of journalist collectives that report on political and social issues, e.g., in ''The Indypendent'' newspaper of NYC * ITV (TV network) (Independent Televi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Hare
Hares and jackrabbits are mammals belonging to the genus ''Lepus''. They are herbivores and live Solitary animal, solitarily or in pairs. They nest in slight depressions called forms, and their young are precociality, able to fend for themselves shortly after birth. The genus includes the largest Lagomorpha, lagomorphs. Most are fast runners with long, powerful hind legs, and large ears that dissipate body heat. Hare species are native to Africa, Eurasia and North America. A hare less than one year old is called a "leveret". Members of the ''Lepus'' genus are considered true hares, distinguishing them from rabbits which make up the rest of the Leporidae family. However, there are five leporid species with "hare" in their common names which are not considered true hares: the hispid hare (''Caprolagus hispidus''), and four species known as red rock hares (''Pronolagus''). Conversely, several ''Lepus'' species are called "jackrabbits", but classed as hares rather than rabbits. The p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Tortoise
Tortoises ( ) are reptiles of the family Testudinidae of the order Testudines (Latin for "tortoise"). Like other turtles, tortoises have a shell to protect from predation and other threats. The shell in tortoises is generally hard, and like other members of the suborder Cryptodira, they retract their necks and heads directly backward into the shell to protect them. Tortoises can vary in size with some species, such as the Galápagos giant tortoise, growing to more than in length, whereas others like the Speckled cape tortoise have shells that measure only long. Several lineages of tortoises have independently evolved very large body sizes in excess of , including the Galapagos giant tortoise and the Aldabra giant tortoise. They are usually diurnal animals with tendencies to be crepuscular depending on the ambient temperatures. They are generally reclusive animals. Tortoises are the longest-living land animals in the world, although the longest-living species of tortois ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
The Tortoise And The Hare
"The Tortoise and the Hare" is one of Aesop's Fables and is numbered 226 in the Perry Index. The account of a race between unequal partners has attracted conflicting interpretations. The fable itself is a variant of a common folktale theme in which ingenuity and trickery (rather than doggedness) are employed to overcome a stronger opponent. An ambiguous story The story concerns a Hare who ridicules a slow-moving Tortoise. Tired of the Hare's arrogant behaviour, the Tortoise challenges him to a race. The hare soon leaves the tortoise behind and, confident of winning, takes a nap midway through the race. When the Hare awakes, however, he finds that his competitor, crawling slowly but steadily, has arrived before him. The later version of the story in La Fontaine's Fables (VI.10), while more long-winded, differs hardly at all from Aesop's. As in several other fables by Aesop, the lesson it is teaching appears ambiguous. In Classical times, it was not the Tortoise's plucky conduct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Aesop
Aesop ( ; , ; c. 620–564 BCE; formerly rendered as Æsop) was a Greeks, Greek wikt:fabulist, fabulist and Oral storytelling, storyteller credited with a number of fables now collectively known as ''Aesop's Fables''. Although his existence remains unclear and no writings by him survive, numerous tales credited to him were gathered across the centuries and in many languages in a storytelling tradition that continues to this day. Many of the tales associated with him are characterized by anthropomorphic animal characters. Scattered details of Aesop's life can be found in ancient sources, including Aristotle, Herodotus, and Plutarch. An ancient literary work called ''The Aesop Romance'' tells an episodic, probably highly fictional version of his life, including the traditional description of him as a strikingly ugly Slavery in Ancient Greece, slave () who by his cleverness acquires freedom and becomes an adviser to kings and city-states. Older spellings of his name have included ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Algebra
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication. Elementary algebra is the main form of algebra taught in schools. It examines mathematical statements using variables for unspecified values and seeks to determine for which values the statements are true. To do so, it uses different methods of transforming equations to isolate variables. Linear algebra is a closely related field that investigates linear equations and combinations of them called '' systems of linear equations''. It provides methods to find the values that solve all equations in the system at the same time, and to study the set of these solutions. Abstract algebra studies algebraic structures, which consist of a set of mathemati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
List Of Statistical Packages
The following is a list of statistical software. Open-source * ADaMSoft – a generalized statistical software with data mining algorithms and methods for data management * ADMB – a software suite for non-linear statistical modeling based on C++ which uses automatic differentiation * Chronux – for neurobiological time series data * DAP (software), DAP – free replacement for SAS * Environment for DeveLoping KDD-Applications Supported by Index-Structures (ELKI) a software framework for developing data mining algorithms in Java (programming language), Java * Epi Info – List of statistical packages, statistical software for epidemiology developed by Centers for Disease Control and Prevention (CDC). Apache 2 licensed * Fityk – nonlinear regression software (GUI and command line) * GNU Octave – programming language very similar to MATLAB with statistical features * gretl – gnu regression, econometrics and time-series library * intrinsic Noise Analyzer (iNA) – For analyzin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Permutation Test
A permutation test (also called re-randomization test or shuffle test) is an exact statistical hypothesis test. A permutation test involves two or more samples. The (possibly counterfactual) 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Normal Distribution
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac e^\,. The parameter is the mean or expectation of the distribution (and also its median and mode), while the parameter \sigma^2 is the variance. The standard deviation of the distribution is (sigma). A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Statistic
A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypothesis. The average (or mean) of sample values is a statistic. The term statistic is used both for the function (e.g., a calculation method of the average) and for the value of the function on a given sample (e.g., the result of the average calculation). When a statistic is being used for a specific purpose, it may be referred to by a name indicating its purpose. When a statistic is used for estimating a population parameter, the statistic is called an '' estimator''. A population parameter is any characteristic of a population under study, but when it is not feasible to directly measure the value of a population parameter, statistical methods are used to infer the likely value of the parameter on the basis of a statistic computed from a s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
