e-Statistics

## F-Distribution

The F distribution has a pair (df1 = , df2 = ) of numbers for the degree of freedom. The shape of the distribution is unimodal and skewed to the right, exhibiting a long right-hand tail. The critical point for the F distribution, denoted by , corresponds to the upper tail region of level .

The critical point can be found from via the formula . Thus, an lower-tailed region is related to the upper-tailed region.

 Level (p-value) Upper-tailed region

Suppose that the sample variances  and are obtained respectively from Group 1 and Group 2 with the respective sample size and , and that the two groups are independently observed and both satisfy the normality assumption. Then the statistic with true variances  and from the respective groups has the F distribution with degree of freedom.