Canonical Correlation and Chi-Square: Relationships and Interpretation
A 2 X 2 chi-square can be computed from a phi coefficient, which is the Pearson correlation between two binomial variables. Similarly, chi-square for larger contingency tables can be computed from canonical correlation coefficients. The authors address the following series of issues involving this relationship: (a) how to represent a contingency table in terms of a correlation matrix involving r -1 row and c - 1 column dummy predictors; (b) how to compute chi-square from canonical correlations solved from this matrix; (c) how to compute loadings for the omitted row and column variables; and (d) the possible interpretive advantage of describing canonical relationships that comprise chi-square, together with some examples. The proposed procedures integrate chi-square analysis of contingency tables with general correlational theory and serve as an introduction to some recent methods of analysis more widely known by sociologists.
Journal of General Psychology
Dunlap, W. P.,
Brody, C. J.,
Greer, T. F.
(2000). Canonical Correlation and Chi-Square: Relationships and Interpretation. Journal of General Psychology, 127(4), 341-353.
Available at: https://aquila.usm.edu/fac_pubs/4087