The F distribution is the distribution of the ratio of two estimates of variance. It is used to compute probability values in the 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 between-subjects ANOVA,

dfn = a-1where "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 .05 level. If the dfn were 10 and the dfd were 100, then an F of 1.93 would be significant at the .05 level.

dfd = N-a