Explain why there are no individual differences in the numer

Explain why there are no individual differences in the numerator and in the denominator of the F ratio

Solution

In repeated measure ANOVA the same individuals are tested in every treatment so there are no individual differences between treatments.

And basically it means that the variability due to individual differences is not a component of the numerator of the F ratio.

Now when there is no treatment effect, the F ratio should maintain a balanced ratio with an expected value of 1 and thus as the numerator does not contain the individual differences part so we also remove individual differences from the denominator as well to make it balanced with expected value 1 under no treatment effect.

These are the reasons why there are no individual differences in the numerator and in the denominator of the F ratio.