1. Let Xi j (j = 1,... n;i = 1,...,s) be independent N(i, 2), 2 unknown. Then...

1. Let Xi j (j = 1,... n;i = 1,...,s) be independent N(ξi, σ2), σ2 unknown. Then the problem of obtaining simultaneous confidence intervals for all differences ξ j − ξi is invariant under G

0, G2, and the scale changes G3.

2. The only equivariant confidence bounds based on the sufficient statistics Xi· and S2 = (Xi j − Xi·)2 and satisfying the condition corresponding to (9.146) are those given by S(x) = x : x j· − xi· − 
√n − s S ≤ ξ j − ξi (9.151)
≤ x j· − xi· +

√n − s S for all i = j with  determined by the null distribution of the Studentized range P0 max |X j· − Xi·|
S/
√n − s < 
= γ. (9.152)
3. Extend the results of