e-Statistics > 4480-5480 Probability and Statistics II

F-Distribution

The F distribution has a pair (df1 = , df2 = ) of numbers for the degree of freedom. The shape of the distribution is unimodal with a long right-hand tail. The critical point for the F distribution, denoted by $ F_{\alpha,df1,df2}$, is provided separately for the lower tail and the upper tail.

The critical point $ F_{1-\alpha,df1,df2}$ is related to $ F_{\alpha,df2,df1}$ via the formula $ F_{1-\alpha,df1,df2} = \displaystyle\frac{1}{F_{\alpha,df2,df1}}$. Thus, an lower-tailed region can be found from another upper-tailed region, or vice versa.

Level (p-value) $ \alpha =$
Lower-tailed region $ X < F_{1-\alpha,df1,df2} =$
Upper-tailed region $ X > F_{\alpha,df1,df2} =$

F-distribution table contains the selected critical values in a form of table.