Accession Number : AD0668147

Title :   TESTING FOR EQUALITY OF MEANS, EQUALITY OF VARIANCES AND EQUALITY OF COVARIANCES UNDER RESTRICTIONS UPON THE PARAMETER SPACE (PRELIMINARY REPORT).

Descriptive Note : Technical rept.,

Corporate Author : JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF STATISTICS

Personal Author(s) : Gleser,Leon Jay ; Olkin,Ingram

Report Date : JUL 1967

Pagination or Media Count : 27

Abstract : 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 = eta(1, 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-rho)I + 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.

Descriptors :   (*STATISTICAL ANALYSIS, PROBLEM SOLVING), (*PSYCHOLOGICAL TESTS, STATISTICAL TESTS), ANALYSIS OF VARIANCE, MULTIVARIATE ANALYSIS, STATISTICAL DISTRIBUTIONS, TRANSCENDENTAL FUNCTIONS, MATRICES(MATHEMATICS), INEQUALITIES, VECTOR SPACES, CONVERGENCE, THEOREMS

Subject Categories : Psychology
      Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE