ON AN OPTIMUM PROPERTY OF TWO IMPORTANT STATISTICAL TESTS

P. L. Hsu (1940) has shown that for any linear hypothesis the E2-test is the uniformly most powerful of all the tests whose power function depends on a certain function, A, of the population parameters. Two other tests of importance, namely, those associated with the multiple correlation coefficient and Hotelling's T2 (Hotelling, 1931), have the similar property of being uniformly more powerful than all other tests whose power functions depend on the respective functions of population parameters involved in the distributions of R and T2. It is the purpose of this paper to establish such an optimum property of these two tests. We shall consider them separately.