The Scheffe simultaneous interval procedure actually works for all linear combinations, not just contrasts. Show that under the oneway ANOVA assumptions, if M = ˆškFk,N-k,a (note the change in the numerator degrees of freedom), then the probability is 1 - α that

simultaneously for all a = (a1,..., ak). It is probably easiest to proceed by first establishing, in the spirit of Lemma 11.2.7, that if v1,..., vk are constants and c1,..., ck are positive constants, then

The proof of Theorem 11.2.10 can then be adapted to establish the result.

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