Assumption of F- Test

The  theoretical assumption on which  F test  is based are:

1.The populations for  each sample must  be normally  distributed  with  identical  mean  and variance.

2.All sample observation must be  randomly selected and independent.

3. The ration of  αa2 to α22 should  be equal to or greater than. This is the  reason that  larger variance is divided by the  smaller  variance.

4. Since  the F distribution  is always formed by a ratio of squared values it  can never be a negative number. All F distribution  are unmoral and are  skewed to the right. They tend to  become  more  nearly symmetrical as V₁ and v₂ increase.

5.The total  variance  of the  various sources of  variance  should be additive.

Total sum of squares = sum of squares between  the groups  + sum of  squares within  the groups.