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StatsToDo: Probability of Fisher's F (F Test)
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Introduction
The F-distribution is named after the 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.
Javascript Program
The F-distribution is most commonly used in Analysis of Variance (ANOVA) and the F test (to determine the probability that there is no difference between 2 variances). 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:
https://en.wikipedia.org/wiki/F-distributionWikipedia 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
Calculation are presented in maroon and results produced presented in navy
Tables
R CodesProbability of F
FToP<-function(f,ndf,ddf) #function to calculate probability from F, ndf and ddf
{
return(1 - pf(f,df1=ndf,df2=ddf)) #probability
}
FToP(4.46,3,32) #value of probability
0.009994333
PToF<-function(p,ndf,ddf) #function to calculate F from probability
{
return (qf(1-p, df1=ndf, df2=ddf)) # F
}
PToF(0.01,3,32) #value of F
4.459429 Python CodesHeader and Library import scipy.stats as stProbability of F
def FToP(f,ndf,ddf):
""" Calculate probability from F, ndf, ddf """
return st.f.pdf(f, ndf, ddf)
print(FToP(4.46,3,32))
0.009913499368375918
def PToF(p,ndf,ddf):
""" Calculate F from probability, ndf, ddf """
return st.f.ppf(1 - p, ndf, ddf)
print(PToF(0.01,3,32))
4.4594285285032536 α=0.1
ddf=1:40
α=0.05
ddf=1:40
α=0.01
ddf=1:40
α=0.005
ddf=1:40
α=0.001
ddf=1:40
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