17. (i) For the validity of Theorem 1 it is only required that the probability of rejecting homogeneity of any set containing {JL; , . ••, JL ; } as a proper , v, subset tends to 1 as the distance between the different groups (26) all -+ 00, with the analogous condition holding for H5., ..., H:. (ii) The condition of part (i) is satisfied for example if homogeneity of a set S is rejected for large values ofEIX;.- X..I, where the sum extends over the subscripts i for which JL; E S.