TESTING FOR EQUALITY OF MEANS, EQUALITY OF VARIANCES AND EQUALITY OF COVARIANCES UNDER RESTRICTIONS UPON THE PARAMETER SPACE (PRELIMINARY REPORT).
JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF STATISTICS
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Suppose that the p-dimensional random row vector x has a multivariate normal distribution with mean mu and covariance matrix Sigma. Wilks Ann. Math. Statist. 17 1946 has derived likelihood-ratio tests of the hypothesis H sub mvc and H sub vc against general alternatives H. Here H sub mvc is the hypothesis that the components of the mean vector mu are equal mu eta1, 1, ..., 1 is identical with eta e, where eta is an unknown constant and that Sigma has the intraclass correlational form Sigma sigma squared 1-rhoI rho e e prime. H sub vc is the hypothesis that Sigma has the intraclass correlational form, mu unrestricted H is the hypothesis that mu is unrestricted and Sigma is unrestricted, positive definite. In the present paper, we consider likelihood ratio tests of the hypotheses Hr sub mvc and Hr sub vc against general alternatives H, where Hr sub mvc and Hr sub vc differ from H sub mvc and H sub vc, respectively, by constricting the common correlation to lie in an interval rho sub 0 or rho 1. Such tests have practical importance in psychological testing theory, in the analysis of growth curves, and in other contexts.
- Statistics and Probability