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StatsToDo : Probability of F
Explanations, Calculations, Codes and Tables

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Introduction Calculations Codes Tables
The F-distribution is named after the famous statistician R. A. Fisher.  It is also sometimes known as the Fisher F distribution or the Snecedor-Fisher F distribution. F is the ratio of two variances.

The F-distribution is most commonly used in Analysis of Variance (ANOVA) and the F test (to determine if two variances are equal).  The F-distribution is the ratio of two chi-square distributions, and hence is right skewed. It has a minimum of 0, but no maximum value (all values are positive).  The peak of the distribution is not far from 0, as can be seen in the following diagram

A specific F-distribution is denoted by the numerator degrees of freedom (ndf) for the chi-square and and the degrees of freedom for the denominator chi-square (ddf), written as F(ndf,ddf).  It is important to note that when referencing the F-distribution the numerator degrees of freedom are always given first, and switching the degrees of freedom changes the distribution (ie. F(10,12) does not equal F(12,10)).

Interestingly, the three most famous distributions (normal, t and chi-square) can all be seen as "special" cases of the F-distribution:

  • normal distribution = F(1, infinite)
  • t-distribution = F(1, ddf)
  • chi-square distribution = F(ndf, infinite)
The other panels on this page are
  • Calculations: Javascript program to calculate the probability of t
  • Codes: R and Python codes to calculate the probability of t
  • Tables: Tables for probability of t
References on F

Javascript algorithm adapted from Press WH, Flannery BP, Teukolsky SA, and Vetterling WT. (1994) Numerical recipes in Pascal. Cambridge University Press ISBN 0-521-37516-9. p.189