# 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**

### 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**

### Statistics

**statisticalstatistical analysisstatistician**

### Null distribution

### Test statistic

**Common test statisticst''-test of test statistics**

### 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 ).