Exact power comparison of three criteria to assess the independence between two sets of variates

Powers of the three criteria are evaluated for testing the hypothesis of the independence between a -set and a q-set of variates in a (p + q) -variate normal population. They are: (1) the likelihood ratio type criterion, Wt (2) the largest root criterion, r1, and (3) criterion of the sum of roots, V. For p= 2, Pillai and Jayachandran, and others have studied for the restricted range of the alternative hypothesis. Recently the power of the largest root was investigated in detail by Sugiyama and %%. In this paper, their power functions are compared in a wide range of the alternative hypotheses. The powers of rl and V are locally optimum, but the W shows a large power in a wide range.