Why does the F-ratio follow an F-distribution when the null hypothesis of equal grouped means is satisfied?
I'm really stuck on this.
I know that an F distribution is:
And the F-Ratio is:
MST= mean squares for treatment
MSE= mean squares for error
From here I'm totally stuck.
I think it all boils down to me not understanding why
Only when all of the group means equal each other.
It seems that
is always a chi squared distribution.