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Chi-squared distribution

Index Chi-squared distribution

No description. [1]

89 relations: Analysis of variance, Annals of Statistics, Approximation, Beta distribution, Binomial test, Central limit theorem, Chi (letter), Chi distribution, Chi-squared test, Cochran's theorem, Cochran–Mantel–Haenszel statistics, Confidence interval, Contingency table, Covariance matrix, Cumulant, Cumulative distribution function, Data analysis, Degrees of freedom (statistics), Differential entropy, Digamma function, Erlang distribution, Exponential distribution, F-distribution, Fisher's exact test, Fisher's method, Friedman test, Friedrich Robert Helmert, Gamma distribution, Gamma function, Generalized chi-squared distribution, Generalized normal distribution, Goodness of fit, Hotelling's T-squared distribution, Idempotent matrix, Incomplete gamma function, Independence (probability theory), Independent and identically distributed random variables, Inverse-chi-squared distribution, Karl Pearson, Kurtosis, Laplace distribution, Likelihood-ratio test, Linear regression, List of statistical packages, Logrank test, Magnetic resonance imaging, MathWorld, Maximum entropy probability distribution, Maxwell–Boltzmann distribution, Multivariate normal distribution, ..., Neyman–Pearson lemma, Noncentral beta distribution, Noncentral chi distribution, Noncentral chi-squared distribution, Noncentral t-distribution, Norm (mathematics), Normal distribution, P-value, Pareto distribution, Particular values of the gamma function, Pearson distribution, Pearson's chi-squared test, Probability density function, Probability distribution, Probability theory, Proceedings of the National Academy of Sciences of the United States of America, Proofs related to chi-squared distribution, Quadratic form, Quantile function, Random variable, Rank (linear algebra), Rayleigh distribution, Reduced chi-squared statistic, Ronald Fisher, Sampling distribution, Skewness, Spreadsheet, Standard deviation, Statistical hypothesis testing, Statistical inference, Statistical significance, Statistics, Student's t-distribution, Symmetric matrix, T-statistic, Uniform distribution (continuous), Variance, Wilks's lambda distribution, Wishart distribution. Expand index (39 more) »

Analysis of variance

Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among group means in a sample.

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Annals of Statistics

The Annals of Statistics is a peer-reviewed statistics journal published by the Institute of Mathematical Statistics.

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Approximation

An approximation is anything that is similar but not exactly equal to something else.

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Beta distribution

In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval parametrized by two positive shape parameters, denoted by α and β, that appear as exponents of the random variable and control the shape of the distribution.

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Binomial test

In statistics, the binomial test is an exact test of the statistical significance of deviations from a theoretically expected distribution of observations into two categories.

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Central limit theorem

In probability theory, the central limit theorem (CLT) establishes that, in some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a "bell curve") even if the original variables themselves are not normally distributed.

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Chi (letter)

Chi (uppercase Χ, lowercase χ; χῖ) is the 22nd letter of the Greek alphabet, pronounced or in English.

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Chi distribution

No description.

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Chi-squared test

A chi-squared test, also written as test, is any statistical hypothesis test where the sampling distribution of the test statistic is a chi-squared distribution when the null hypothesis is true.

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Cochran's theorem

In statistics, Cochran's theorem, devised by William G. Cochran, is a theorem used to justify results relating to the probability distributions of statistics that are used in the analysis of variance.

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Cochran–Mantel–Haenszel statistics

In statistics, the Cochran–Mantel–Haenszel test (CMH) is a test used in the analysis of stratified or matched categorical data.

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Confidence interval

In statistics, a confidence interval (CI) is a type of interval estimate, computed from the statistics of the observed data, that might contain the true value of an unknown population parameter.

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Contingency table

In statistics, a contingency table (also known as a cross tabulation or crosstab) is a type of table in a matrix format that displays the (multivariate) frequency distribution of the variables.

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Covariance matrix

In probability theory and statistics, a covariance matrix (also known as dispersion matrix or variance–covariance matrix) is a matrix whose element in the i, j position is the covariance between the i-th and j-th elements of a random vector.

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Cumulant

In probability theory and statistics, the cumulants of a probability distribution are a set of quantities that provide an alternative to the moments of the distribution.

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Cumulative distribution function

In probability theory and statistics, the cumulative distribution function (CDF, also cumulative density function) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. In the case of a continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables.

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Data analysis

Data analysis is a process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making.

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Degrees of freedom (statistics)

In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.

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Differential entropy

Differential entropy (also referred to as continuous entropy) is a concept in information theory that began as an attempt by Shannon to extend the idea of (Shannon) entropy, a measure of average surprisal of a random variable, to continuous probability distributions.

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Digamma function

In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: It is the first of the polygamma functions.

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Erlang distribution

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Exponential distribution

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F-distribution

No description.

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Fisher's exact test

Fisher's exact test is a statistical significance test used in the analysis of contingency tables.

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Fisher's method

In statistics, Fisher's method, also known as Fisher's combined probability test, is a technique for data fusion or "meta-analysis" (analysis of analyses).

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Friedman test

The Friedman test is a non-parametric statistical test developed by Milton Friedman.

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Friedrich Robert Helmert

Friedrich Robert Helmert (July 31, 1843 – June 15, 1917) was a German geodesist and an important writer on the theory of errors.

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Gamma distribution

In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions.

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Gamma function

In mathematics, the gamma function (represented by, the capital Greek alphabet letter gamma) is an extension of the factorial function, with its argument shifted down by 1, to real and complex numbers.

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Generalized chi-squared distribution

In probability theory and statistics, the specific name generalized chi-squared distribution (also generalized chi-square distribution) arises in relation to one particular family of variants of the chi-squared distribution.

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Generalized normal distribution

The generalized normal distribution or generalized Gaussian distribution (GGD) is either of two families of parametric continuous probability distributions on the real line.

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Goodness of fit

The goodness of fit of a statistical model describes how well it fits a set of observations.

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Hotelling's T-squared distribution

In statistics Hotelling's T-squared distribution (T2) is a multivariate distribution proportional to the ''F''-distribution and arises importantly as the distribution of a set of statistics which are natural generalizations of the statistics underlying Student's ''t''-distribution.

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Idempotent matrix

In linear algebra, an idempotent matrix is a matrix which, when multiplied by itself, yields itself.

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Incomplete gamma function

In mathematics, the upper incomplete gamma function and lower incomplete gamma function are types of special functions, which arise as solutions to various mathematical problems such as certain integrals.

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Independence (probability theory)

In probability theory, two events are independent, statistically independent, or stochastically independent if the occurrence of one does not affect the probability of occurrence of the other.

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Independent and identically distributed random variables

In probability theory and statistics, a sequence or other collection of random variables is independent and identically distributed (i.i.d. or iid or IID) if each random variable has the same probability distribution as the others and all are mutually independent.

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Inverse-chi-squared distribution

In probability and statistics, the inverse-chi-squared distribution (or inverted-chi-square distributionBernardo, J.M.; Smith, A.F.M. (1993) Bayesian Theory,Wiley (pages 119, 431)) is a continuous probability distribution of a positive-valued random variable.

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Karl Pearson

Karl Pearson HFRSE LLD (originally named Carl; 27 March 1857 – 27 April 1936) was an English mathematician and biostatistician. He has been credited with establishing the discipline of mathematical statistics. He founded the world's first university statistics department at University College London in 1911, and contributed significantly to the field of biometrics, meteorology, theories of social Darwinism and eugenics. Pearson was also a protégé and biographer of Sir Francis Galton.

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Kurtosis

In probability theory and statistics, kurtosis (from κυρτός, kyrtos or kurtos, meaning "curved, arching") is a measure of the "tailedness" of the probability distribution of a real-valued random variable.

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Laplace distribution

In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace.

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Likelihood-ratio test

In statistics, a likelihood ratio test (LR test) is a statistical test used for comparing the goodness of fit of two statistical models — a null model against an alternative model.

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Linear regression

In statistics, linear regression is a linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables).

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List of statistical packages

Statistical software are specialized computer programs for analysis in statistics and econometrics.

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Logrank test

In statistics, the logrank test is a hypothesis test to compare the survival distributions of two samples.

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Magnetic resonance imaging

Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body in both health and disease.

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MathWorld

MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein.

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Maximum entropy probability distribution

In statistics and information theory, a maximum entropy probability distribution has entropy that is at least as great as that of all other members of a specified class of probability distributions.

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Maxwell–Boltzmann distribution

In physics (in particular in statistical mechanics), the Maxwell–Boltzmann distribution is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann.

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Multivariate normal distribution

In probability theory and statistics, the multivariate normal distribution or multivariate Gaussian distribution is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions.

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Neyman–Pearson lemma

In statistics, the Neyman–Pearson lemma was introduced by Jerzy Neyman and Egon Pearson in a paper in 1933.

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Noncentral beta distribution

In probability theory and statistics, the noncentral beta distribution is a continuous probability distribution that is a generalization of the (central) beta distribution.

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Noncentral chi distribution

No description.

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Noncentral chi-squared distribution

No description.

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Noncentral t-distribution

As with other probability distributions with noncentrality parameters, the noncentral t-distribution generalizes a probability distribution – Student's ''t''-distribution – using a noncentrality parameter.

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Norm (mathematics)

In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.

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Normal distribution

In probability theory, the normal (or Gaussian or Gauss or Laplace–Gauss) distribution is a very common continuous probability distribution.

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P-value

In statistical hypothesis testing, the p-value or probability value or asymptotic significance is the probability for a given statistical model that, when the null hypothesis is true, the statistical summary (such as the sample mean difference between two compared groups) would be the same as or of greater magnitude than the actual observed results.

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Pareto distribution

No description.

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Particular values of the gamma function

The gamma function is an important special function in mathematics.

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Pearson distribution

The Pearson distribution is a family of continuous probability distributions.

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Pearson's chi-squared test

Pearson's chi-squared test (χ) is a statistical test applied to sets of categorical data to evaluate how likely it is that any observed difference between the sets arose by chance.

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Probability density function

In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function, whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a relative likelihood that the value of the random variable would equal that sample.

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Probability distribution

In probability theory and statistics, a probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

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Probability theory

Probability theory is the branch of mathematics concerned with probability.

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Proceedings of the National Academy of Sciences of the United States of America

Proceedings of the National Academy of Sciences of the United States of America (PNAS) is the official scientific journal of the National Academy of Sciences, published since 1915.

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Proofs related to chi-squared distribution

The following are proofs of several characteristics related to the chi-squared distribution.

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Quadratic form

In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.

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Quantile function

In probability and statistics, the quantile function specifies, for a given probability in the probability distribution of a random variable, the value at which the probability of the random variable is less than or equal to the given probability.

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Random variable

In probability and statistics, a random variable, random quantity, aleatory variable, or stochastic variable is a variable whose possible values are outcomes of a random phenomenon.

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Rank (linear algebra)

In linear algebra, the rank of a matrix A is the dimension of the vector space generated (or spanned) by its columns.

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Rayleigh distribution

No description.

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Reduced chi-squared statistic

In statistics, the reduced chi-squared statistic is used extensively in goodness of fit testing.

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Ronald Fisher

Sir Ronald Aylmer Fisher (17 February 1890 – 29 July 1962), who published as R. A. Fisher, was a British statistician and geneticist.

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Sampling distribution

In statistics, a sampling distribution or finite-sample distribution is the probability distribution of a given random-sample-based statistic.

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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.

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Spreadsheet

A spreadsheet is an interactive computer application for organization, analysis and storage of data in tabular form.

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Standard deviation

In statistics, the standard deviation (SD, also represented by the Greek letter sigma σ or the Latin letter s) is a measure that is used to quantify the amount of variation or dispersion of a set of data values.

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Statistical hypothesis testing

A statistical hypothesis, sometimes called confirmatory data analysis, is a hypothesis that is testable on the basis of observing a process that is modeled via a set of random variables.

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Statistical inference

Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution.

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Statistical significance

In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given the null hypothesis.

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Statistics

Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.

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Student's t-distribution

In probability and statistics, Student's t-distribution (or simply the t-distribution) is any member of a family of continuous probability distributions that arises when estimating the mean of a normally distributed population in situations where the sample size is small and population standard deviation is unknown.

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Symmetric matrix

In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose.

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T-statistic

In statistics, the t-statistic is the ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error.

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Uniform distribution (continuous)

In probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions such that for each member of the family, all intervals of the same length on the distribution's support are equally probable.

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Variance

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.

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Wilks's lambda distribution

In statistics, Wilks's lambda distribution (named for Samuel S. Wilks), is a probability distribution used in multivariate hypothesis testing, especially with regard to the likelihood-ratio test and multivariate analysis of variance (MANOVA).

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Wishart distribution

In statistics, the Wishart distribution is a generalization to multiple dimensions of the chi-squared distribution, or, in the case of non-integer degrees of freedom, of the gamma distribution.

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References

[1] https://en.wikipedia.org/wiki/Chi-squared_distribution

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