Hi guys !

I have a quick question :

We don't understand why it is better to consider contrasts (linear combination of parameters $\displaystyle (\beta_j)_{j\in J}$ : $\displaystyle \sum_{j=1}^J c_j \beta_j$, where $\displaystyle \sum_{j=1}^J c_j =0$) in the Scheffé method for simultaneous confidence intervals...

Why do we need the latter sum to be 0 ? I read in a lecture note that if we consider contrasts instead of any linear combination, we're considering a Fisher distribution with a degree of freedom that is J-1 instead of J. But is it really the only reason ?

Thanks for any input, even if it doesn't exactly answer the question... if it casts a light on some point of the Scheffé method, I would also be pleased