Chiang Mai Journal of Science

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The purpose of this paper is to present and illustrate that parametric statistics, such as ANOVA, multiple regression, and non-parametric cross-tab analysis are all special cases of canonical analysis. Implications of this fact are then noted. It is well known that ANOVA and multiple regression analysis are both special cases of the general linear model, and that nominal variables can be analyzed with a multiple regression program if the categories of the nominal variable are appropriately coded. What is less known is that canonical analysis is the multivariate generalization of GLM, and so ANOVA and regression analysis are special cases of canonical analysis. The chi square statistics for a cross-tab table is also a special case of canonical analysis. This can be done with any canonical program by using the same coding method by which nominal variables are analyzed with a multiple regression program. The nominal independent variable’s categories are “dummy coded” as the “independent variables” and the dependent variable’s categories are “dummy coded” as the “dependent variables”. There are several advantages of this conceptualization. One is that a standard measure of effect size, based in correlations, can be consistently used across all types of analyses. A second is that courses can be taught using just this one model instead of several models, resulting in more material being covered in a standard statistics course. Third is the flexibility to include any variables any place in the analysis, regardless of the level of measurement. Illustrative data are presented showing the same results are found in both tradition analysis and by using canonical analysis in SPSS.

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