This dissertation examines the problem of comparing samples of multivariate normal data from two populations and concluding whether the populations are equivalent; equivalence is defined as the distance between the mean vectors of the two samples being less than a given value. Test statistics are developed for each of two cases using the ratio of the maximized likelihood functions. Case 1 assumes both populations have a common known covariance matrix. Case 2 assumes both populations have a common covariance matrix, but this covariance matrix is a known matrix multiplied by an unknown scalar value. The power function and bias of each of the test statistics is evaluated. Tables of critical values are provided.

Thesis (Ph.D.)--Wichita State University, College of Liberal Arts and Sciences, Dept. of Mathematics and Statistics