Frequency Distribution or Variance Ratio Distribution
This was developed by R. A Fisher in 1924 and is normally defined in terms of the ratio of the variances of two usually distributed populations. This is utilized to test the hypothesis that the two generally distributed populations have two equal variances. F distribution ratio of the variances between two generally distributed population may be expressed like: (s_{1}^{2}/d_{1}^{2})/(s_{2}^{2}/d_{2}^{2})
Along with Ω^{-1}1 = n1-1 and Ω^{-1}2 = n2-1 degrees of freedom
Whereas general population means are unknown
n_{1} - sample size of independent random 1
n_{2} - sample size of independent random 2
s_{1}^{2} - Sample variance of 1
s_{2}^{2} - sample variance of 2
d_{1}^{2} - Population variance of 1?
d_{2}^{2} - Population variance of 2
s_{1}^{2 }and s_{2}^{2} are described by
s_{1}^{2} = (Σ(x_{1} - x¯_{1})^{2})/(n_{1} - 1) as the unbiased estimator of d_{1}^{2}
s_{2}^{2} = (Σ(x_{2} - x¯_{2})^{2})/(n_{1} - 1) as the unbiased estimator of d_{2}^{2}
if d_{1}^{2} = d_{2}^{2} then the statistic F = s_{1}^{2}/s_{2}^{2}
= larger estimate of variance/smaller estimate of variance
F - Distribution along with n_{1}-1 and n_{2}-1 degrees of freedom. F distribution depends on the degrees of freedom Ω^{-1}1 for the numerator and Ω^{-1}2 for the denominator. This has parameters Ω^{-1}1 and Ω^{-1}2 such that for various values of Ω^{-1}1 and Ω^{-1}2 will have various distributions.