ABSTRACT
This conclusion presents an overview of key concepts covered in the preceding chapters of this book. A full canonical-correlation analysis generates a sequence of s canonical triplets that characterize the relationship between the two sets of variables. One can treat these components purely descriptively, as a way to measure and represent the association. However, one often wants to determine whether the association that they describe is due to more than chance. Suppose that in an underlying population, the variables measured by the Xj and the Yj are truly unrelatedthe population vectors are orthogonal. Accidents of sampling can only decrease these right angles, so that some evidence of angular agreement appears in the sample. By maximizing the association between uk and vk, canonical correlation captures the accidental variation and the observed Rk is positive. One wants a test to determine whether the magnitudes of the observed canonical correlations are larger than could be attributed to these accidental effects.
