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)