1. For the validity of Lemma 9.5.1 it is only required that the probability of rejecting homogeneity of any set containing {μi1 ,..., μiv1

} as a proper subset tends to 1 as the distance between the different groups (9.89) all → ∞, with the analogous condition holding for H

2,..., H

r.

2. The condition of part (i) is satisfied for example if homogeneity of a set S is rejected for large values of |Xi· − X··|, where the sum extends over the subscripts i for which μi ∈ S.