Equivalence testing for mean vectors of multivariate normal populations

Abstract

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.