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Mann–Whitney U Test
In statistics, 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 test of the null hypothesis that, for randomly selected values ''X'' and ''Y'' from two populations, the probability of ''X'' being greater than ''Y'' is equal to the probability of ''Y'' being greater than ''X''. Nonparametric tests used on two ''dependent'' samples are the Sign test and the Wilcoxon signed-rank test. Assumptions and formal statement of hypotheses Although Mann and 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 a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilcoxon Signed-rank Test
The Wilcoxon signed-rank test is a non-parametric statistical hypothesis test 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 can be a good alternative to the ''t''-test when population means are not of interest; for example, when one wishes to test whether a population's median is nonzero, or whether there is a better than 50% chance that a sample from one population is greater than a sample from another population. History The test is named for Frank Wilcoxon (1892–1965) who, in a single paper, proposed both it and the rank-sum test for two independent samples. The test was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Receiver Operating Characteristic
A receiver operating characteristic curve, or ROC curve, is a graphical plot that illustrates the diagnostic ability of a binary classifier system as its discrimination threshold is varied. The method was originally developed for operators of military radar receivers starting in 1941, which led to its name. The ROC curve is created by plotting the true positive rate (TPR) against the false positive rate (FPR) at various threshold settings. The true-positive rate is also known as sensitivity, recall or ''probability of detection''. The false-positive rate is also known as ''probability of false alarm'' and can be calculated as (1 − specificity). The ROC can also be thought of as a plot of the power as a function of the Type I Error of the decision rule (when the performance is calculated from just a sample of the population, it can be thought of as estimators of these quantities). The ROC curve is thus the sensitivity or recall as a function of fall-out. In general, if the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Common Language Effect Size
In statistics, an effect size is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a statistic calculated from a sample of data, the value of a parameter for a hypothetical population, or to the equation that operationalizes how statistics or parameters lead to the effect size value. Examples of effect sizes include the correlation between two variables, the regression coefficient in a regression, the mean difference, or the risk of a particular event (such as a heart attack) happening. Effect sizes complement statistical hypothesis testing, and play an important role in power analyses, sample size planning, and in meta-analyses. The cluster of data-analysis methods concerning effect sizes is referred to as estimation statistics. Effect size is an essential component when evaluating the strength of a statistical claim, and it is the first item (magnitude) in the M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skewness
In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, zero, negative, or undefined. For a unimodal distribution, negative skew commonly indicates that the ''tail'' is on the left side of the distribution, and positive skew indicates that the tail is on the right. In cases where one tail is long but the other tail is fat, skewness does not obey a simple rule. For example, a zero value means that the tails on both sides of the mean balance out overall; this is the case for a symmetric distribution, but can also be true for an asymmetric distribution where one tail is long and thin, and the other is short but fat. Introduction Consider the two distributions in the figure just below. Within each graph, the values on the right side of the distribution taper differently from the values on the left side. These tapering sides are called ''tai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. Variance has a central role in statistics, where some ideas that use it include descriptive statistics, statistical inference, hypothesis testing, goodness of fit, and Monte Carlo sampling. Variance is an important tool in the sciences, where statistical analysis of data is common. The variance is the square of the standard deviation, the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by \sigma^2, s^2, \operatorname(X), V(X), or \mathbb(X). An advantage of variance as a measure of dispersion is that it is more amenable to algebraic manipulation than other measures of dispersion such as the expected absolute deviatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hare
Hares and jackrabbits are mammals belonging to the genus ''Lepus''. They are herbivores, and live solitarily or in pairs. They nest in slight depressions called forms, and their young are able to fend for themselves shortly after birth. The genus includes the largest lagomorphs. Most are fast runners with long, powerful hind legs, and large ears to dissipate body heat. Hare species are native to Africa, Eurasia and North America. A hare less than one year old is called a "leveret". A group of hares is called a "husk", a "down" or a "drove". 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 (comprising ''Pronolagus''). Conversely, several ''Lepus'' species are called "jackrabbits", but classed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tortoise
Tortoises () are reptiles of the family Testudinidae of the order Testudines (Latin: ''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 100 kg, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aesop
Aesop ( or ; , ; c. 620–564 BCE) was a Greek fabulist and 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 slave () who by his cleverness acquires freedom and becomes an adviser to kings and city-states. Older spellings of his name have included ''Esop(e)'' and ''Isope''. Depictions of Aesop in popular culture over the last 2,500 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables (commonly represented by Roman letters) as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given, mostly in education, to the study of algebraic structures such as groups, rings, and fields (the term is no more in common use outside educational context). Linear algebra, which deals with linear equations and linear mappings, is used for modern presentations of geometry, and has many practical applications (in weather forecasting, for example). There are many areas of mathematics that belong to algebra, some having "algebra" in their name, such as commutative algebra, and some not, such as Galois theory. The word ''alge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Statistical Packages
Statistical software are specialized computer programs for analysis in statistics and econometrics. 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 – free replacement for SAS * Environment for DeveLoping KDD-Applications Supported by Index-Structures (ELKI) a software framework for developing data mining algorithms in Java * Epi Info – 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 analyzing intrinsic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
