F Distribution (1 of 3)
The F distribution is the distribution of the ratio of two
estimates of variance.
It is used to
compute probability values
analysis of variance.
The F distribution
has two parameters: degrees of freedom
numerator (dfn) and degrees of freedom denominator (dfd). The dfn is
the number of degrees of freedom that the estimate of variance used
in the numerator is based on. The dfd is the number of degrees of
freedom that the estimate used in the denominator is based on. The
dfd is often called the degrees of freedom error or dfe. In the
simplest case of a one-factor
dfn = a-1
dfd = N-a
where "a" is the number of groups and "N" is the total number
of subjects in the experiment. The shape of the F distribution depends
on dfn and dfd. The lower the degrees of freedom, the larger the
value of F needed to be significant. For instance, if dfn = 4 and dfd
= 12, then an F of 3.26 would be needed to be significant at the
If the dfn were 10 and the dfd
were 100, then an F of 1.93 would be significant at the .05 level.