Two multivariate statistical methods, factor analysis and canonical analysis, are compared on selected statistical concepts and an example is presented illustrating differences in interpretation arising from the use of the two methods. Only one factor analytic model is considered, this being the principal factor solution based upon the theory of principal components. A review of the statistical theory reveals that both methods call for the solution of characteristic equations to obtain the coordinate system which exhibits the correlations among multiple variables. They differ in the partitioning of the variables into sets, in the scalar quantity to be maximized in solving the characteristic equations, and in the linear regression models. An empirical example is presented to illustrate possible effects of these statistical differences on the interpretation of data. The illustration suggests that factor analysis may be more appropriate for hypothesis generating and exploratory studies, while canonical analysis should have wider application in research involving hypothesis testing and prediction.