Statistical inference concerning the parameters of k multivariate normal populations is considered. Several models in which the parameters have certain hierarchical relationships are discussed. In particular as related to testing the hypothesis that k psychological tests are parallel forms of the same test. The report contains the following sections: Introduction: The Underlying Structure: Maximum Likelihood Estimation: Tests of Hypotheses; and An Application. An appendix is titled "Derivation of the Maximum Likelihood Estimators." References are provided. (DB) (81pp.)