Variable Importance in Multiple Regression and Canonical Correlation.

This paper explains in user-friendly terms why multivariate statistics are so important in educational research. The basic logic of canonical correlation analysis is presented as a simple or bivariate Pearson "r" procedure. It is noted that all statistical tests implicitly involve the calculation of least squares weights, and that all parametric tests can be conducted using canonical analysis, since canonical analysis subsumes parametric methods as special cases. Canonical analysis is potent because it does not require the researcher to discard variance of any of the variables, and because the analysis honors the complexity of a reality in which variables interact simultaneously. Three major classes of procedures for evaluating the importance of specific variables in canonical correlation analysis were explored. Various procedures in each class were illustrated in a concrete fashion using a single small data set for heuristic purposes. Appended program files for the Statistical Package for the Social Sciences and the Statistical Analysis System may facilitate further exploration of the concepts presented. (A 77-item list of references is included. Seventeen data tables, one graph, and outlines of computer programs used are provided.) (Author)