Demystifying Parametric Analyses: Illustrating Canonical Correlation Analysis as the Multivariate General Linear Model

Abstract

A review of the research literature suggests that teachers need to provide students with engaging problems, facilitate their discovery of analysis methods, and encourage classroom discussion and presentation of their approaches to solving problems. The present article illustrates how canonical correlation analysis can be employed to implement all the parametric tests that canonical methods subsume as special cases, including multiple regression. The point is heuristic: all analyses are correlational, all apply weights to measured variables to create synthetic variables, and all yield effect sizes analogous to r^2. Knowledge of such relationships helps inform researcher judgement of analysis selection and use.