Question

Find the correct CV for a two-tailed F test with α=0.05, dfN is 20, and dfD is 11.

Answer 1

Solution:

Given:  α = 0.05, df_N is 20, and df_D is 11.

We have to find F critical values for two tailed test.

Area in left tail = α / 2 = 0.05 / 2 = 0.025 and area in right tail = 0.025

Use following Excel command:

For left tail CV, use command:

=F.INV(probability , df_N , df_D )

where probability = Area in left tail = 0.025

=F.INV(0.025,20,11)

=0.3675

=0.37

Thus Left tail F_CV = 0.37

and for right tail CV, use command:

=F.INV.RT(probability , df_N , df_D )

where

probability = Area in right tail = 0.025

thus

=F.INV.RT(0.025,20,11)

=3.2261

=3.23

Thud Reft tail F_CV = 3.23

Thus we get critical values: ( 0.37 , 3.23 )

We can use F table also.

Look in F table for dfN = 20 and dfD = 11 and for right tail area = 0.025

Right tail F critical value = 3.23

For left tail F critical value , we use following steps:

Left F critical value = 1 / F_{(0.025,11,20)}

We alter df for this step. That is Numerator df becomes denominator df and denominator df becomes Numerator df.

Thus

F_{(0.025,11,20)} = 2.730867

thus

Left F critical value = 1 / F_{(0.025,11,20)}

Left F critical value = 1 / 2.730867

Left F critical value = 0.366

Left F critical value = 0.37

Thus we get F critical values: ( 0.37 , 3.23 )