Guttman's "rank-reduction" theorem is employed to demonstrate how most of the algebra and computational work for standard correlational and analysis of variance methods can be examined within a single matrix system. Analyses of both correlational and experimental data are illustrated with an easy-to-use computer program. This application and the corresponding discussion emphasize distinctions and qualifications needed for appropriate interpretations of both types of data. Since this theorem was initially presented within the framework of factor analysis, it is intended that this paper will contribute to a better understanding of relationships among factor analytic, general correlational, and experimental design methods. (Author/CK)