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Ultimately, all analyses such as the t-test, Pearson correlation, ANOVA, and MANOVA are subsumed by correlational analysis, and more specifically canonical correlation analysis. Specifically, all analyses are correlational and produce similar latent variables, however the decision to choose a statistical analysis should not be based on its simplicity, but rather on how the analysis fits with the reality of the data and research model. Frequently, many researchers and graduate students make assertions such as "I would rather use Analysis of Variance (ANOVA) than regression in my study because ANOVA is simpler and it will provide me with all the information I need." Comments such as these are ill-informed and often result in the use of less desirable data analytic tools. Maxwell, Camp, and Arvey (1981) emphasized that "researchers are not well acquainted with the differences among the various measures (of association) or the assumptions that underlie their use" (p. Many graduate students, like the author, often learn statistics with a relatively limited conceptual understanding of the foundations of univariate and multivariate analyses. Paper presented at the annual meeting of the Southwest Educational Research Association, Austin, January, 1997.Ĭanonical Correlation Analysis as a General Linear Model Ultimately it is these synthetic variables are actually analyzed in all statistics and which tend to be of extreme importance to erudite researchers who want to understand the substance of their statistical analysis. Furthermore, the paper illustrates how each of these analyses produce a synthetic variable, like the Yhat variable in regression. Through a heuristic data set how canonical analysis subsumes various multivariate and univariate methods is demonstrated. The present paper illustrates the concept of the general linear model (GLM) and how canonical correlational analysis is the general linear model. Canonical Correlation Analysis as the General Linear Model