If you multiply this proportion by the proportion of variance extracted, you arrive at a measure of redundancy , that is, of how redundant one set of variables is, given the other set of variables. The measure of redundancy is also useful for assessing the practical significance of canonical roots. Of course, the final assessment of what does and does not constitute a finding of practical significance is subjective by nature. The following discussion provides only a list of the most important assumptions of canonical correlation analysis, and the major threats to the reliability and validity of results. Little is known about the effects of violations of the multivariate normality assumption.
Outliers can greatly affect the magnitudes of correlation coefficients.
Of course, the larger the sample size, the smaller is the impact of one or two outliers. See also Confidence Ellipse . One assumption is that the variables in the two sets should not be completely redundant. For example, if you included the same variable twice in one of the sets, then it is not clear how to assign different weights to each of them. Such correlation matrices are said to be ill-conditioned .