(i) For the validity of Lemma 9.3.1 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

(9.48) all → ∞, with the analogous condition holding for H

2,...,H

r.

(ii) 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.