Definitions and interpretations

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Explain what the Box's M, the canonical correlation, the Chi-square, standardized canonical discriminant function coefficients, structure matrix, and the classification statistics mean and how they are interpreted?

Box's M test tests the assumption of homogeneity of covariance matrices. This test is very sensitive to meeting the assumption of multivariate normality.
Box's M tests the null hypothesis that the observed covariance matrices of the dependent variables are equal across groups. The Box's M test statistic is transformed to an F statistic with df1 and df2 degrees of freedom. Here, the significance value of the test is less than 0.05, suggesting that the assumptions are not met, and thus the model results are suspect. Box's M is sensitive to large data files, meaning that when there are a large number of cases, it can detect even small departures from homogeneity.
Canonical correlation analysis is used to identify and measure the associations among two sets of variables. Canonical correlation is appropriate in the same situations where multiple regression would be, but where are there are multiple intercorrelated outcome variables. Canonical correlation analysis determines a set of canonical variates, orthogonal linear combinations of the variables within each set that best explain the variability both within and between sets.
Examples of canonical correlation analysis.
Example 1. A researcher has collected data on three psychological variables, four academic variables (standardized test scores) and gender for 600 college freshman. She is interested in how the set ...