F-distribution

F distributionF''-distributionF'' distributionFF statisticF valueF''(''ν'' 1 , ''ν'' 2 ) distributedF''(2,2) distributionF-F-distributed
In probability theory and statistics, the F-distribution, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor) is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA), e.g., F-test.wikipedia
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Ronald Fisher

R.A. FisherR. A. FisherFisher
In probability theory and statistics, the F-distribution, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor) is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA), e.g., F-test.
Fisher's 1924 article On a distribution yielding the error functions of several well known statistics presented Pearson's chi-squared test and William Gosset's Student's t-distribution in the same framework as the Gaussian distribution and is where he developed Fisher's z-distribution a new statistical method, commonly used decades later as the F distribution.

F-test

F''-testF testF-statistic
In probability theory and statistics, the F-distribution, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor) is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA), e.g., F-test.
An F-test is any statistical test in which the test statistic has an F-distribution under the null hypothesis.

George W. Snedecor

SnedecorSnedecor, George W.George Snedecor
In probability theory and statistics, the F-distribution, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor) is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA), e.g., F-test.
Snedecor's F-distribution and the George W. Snedecor Award of the American Statistical Association are named after him.

Analysis of variance

ANOVAanalysis of variance (ANOVA)corrected the means
In probability theory and statistics, the F-distribution, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor) is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA), e.g., F-test. In instances where the F-distribution is used, for example in the analysis of variance, independence of U 1 and U 2 might be demonstrated by applying Cochran's theorem.
to the F-distribution with I - 1, n_T - I degrees of freedom.

Chi-squared distribution

chi-squaredchi-square distributionchi square distribution
A random variate of the F-distribution with parameters d 1 and d 2 arises as the ratio of two appropriately scaled chi-squared variates:
It is also a component of the definition of the t-distribution and the F-distribution used in t-tests, analysis of variance, and regression analysis.

Probability distribution

distributioncontinuous probability distributiondiscrete probability distribution
In probability theory and statistics, the F-distribution, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor) is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA), e.g., F-test.

Hotelling's T-squared distribution

Hotelling's ''T''-squared distributionHotelling's T-square distributionMultivariate hypothesis testing
In statistics Hotelling's T-squared distribution (T 2 ) 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.

Ratio distribution

ratio distributionsComplex normal ratio distributionGaussian ratio distribution
while the F-distribution originates from the ratio of two independent chi-squared distributed random variables.

Beta prime distribution

Beta primecompound gamma distributionGeneralized Beta Prime
The F-distribution is a particular parametrization of the beta prime distribution, which is also called the beta distribution of the second kind.

Degrees of freedom (statistics)

degrees of freedomdegree of freedomEffective degrees of freedom
If there is no difference between population means this ratio follows an F distribution with 2 and 3n − 3 degrees of freedom.

Cochran's theorem

Cochran's QCochran’s theorem
In instances where the F-distribution is used, for example in the analysis of variance, independence of U 1 and U 2 might be demonstrated by applying Cochran's theorem.
where F 1,n − 1 is the F-distribution with 1 and n − 1 degrees of freedom (see also Student's t-distribution).

Noncentral F-distribution

noncentral ''F''-distributionnon-central F-distributionnoncentral ''F''-distributed
In probability theory and statistics, the noncentral F-distribution is a continuous probability distribution that is a generalization of the (ordinary) F-distribution.

Fisher's z-distribution

Fisher's z-distribution is the statistical distribution of half the logarithm of an F-distribution variate:

Beta distribution

beta betabeta of the first kind

Laplace distribution

Laplacedouble exponentialLaplace distributed

Student's t-distribution

Student's ''t''-distributiont-distributiont''-distribution

Pearson distribution

Pearson Type III distributionPearson's system of continuous curvesPearson
The Pearson type VI distribution is a beta prime distribution or F-distribution.

Chow test

The test statistic follows the F distribution with k and N_1+N_2-2k degrees of freedom.

Wilks's lambda distribution

Wilks' lambda distributionlambdaWilk's Lambda range
From the relations between a beta and an F-distribution, Wilks' lambda can be related to the F-distribution when one of the parameters of the Wilks lambda distribution is either 1 or 2, e.g.,

Probability theory

theory of probabilityprobabilityprobability theorist
In probability theory and statistics, the F-distribution, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor) is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA), e.g., F-test.

Statistics

statisticalstatistical analysisstatistician
In probability theory and statistics, the F-distribution, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor) is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA), e.g., F-test.

Null distribution

In probability theory and statistics, the F-distribution, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor) is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA), e.g., F-test.

Test statistic

Common test statisticst''-test of test statistics
In probability theory and statistics, the F-distribution, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor) is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA), e.g., F-test.

Random variable

random variablesrandom variationrandom
If a random variable X has an F-distribution with parameters d 1 and d 2, we write X ~ F(d 1, d 2 ).