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In probability theory and statistics, the F-distribution or F-ratio, 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) and other F-tests.
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The F table serves as a reference guide containing critical F values for the distribution of the F-statistic under the assumption of a true null hypothesis. It is designed to help determine the threshold beyond which the F statistic is expected to exceed a controlled percentage of the time (e.g., 5%) when the null hypothesis is accurate.
In probability theory and statistics, the noncentral F-distribution is a continuous probability distribution that is a noncentral generalization of the (ordinary) F-distribution. It describes the distribution of the quotient ( X / n 1 )/( Y / n 2 ), where the numerator X has a noncentral chi-squared distribution with n 1 degrees of freedom and ...
In statistics, the matrix F distribution (or matrix variate F distribution) is a matrix variate generalization of the F distribution which is defined on real-valued positive-definite matrices. In Bayesian statistics it can be used as the semi conjugate prior for the covariance matrix or precision matrix of multivariate normal distributions, and ...
The uniform distribution or rectangular distribution on [a,b], where all points in a finite interval are equally likely, is a special case of the four-parameter Beta distribution. The Irwin–Hall distribution is the distribution of the sum of n independent random variables, each of which having the uniform distribution on [0,1].
Fisher distribution may refer to any of several probability distributions named after Ronald Fisher: Behrens–Fisher distribution; Fisher's noncentral hypergeometric distribution; Fisher's z-distribution; Fisher's fiducial distribution; Fisher–Bingham distribution; F-distribution, also called Fisher–Snedecor distribution or Fisher F ...
In order to create the studentized range distribution for normal data, we first switch from the generic f X and F X to the distribution functions φ and Φ for the standard normal distribution, and change the variable r to s·q, where q is a fixed factor that re-scales r by scaling factor s: