Canonical correlation and chi-square: Relationships and interpretation

A 2 X 2 chi-square can be computed from a phi coefficient, which is the Pea rson correlation between two binomial variables. Similarly, chi-square for larger contingency tables can be computed from canonical correlation coeffi cients. The authors address the following series of issues involving this r elationship: (a) how to represent a contingency table in terms of a correla tion matrix involving r -1 row and c - 1 column dummy predictors; (b) how t o 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 proced ures integrate chi-square analysis of contingency tables with general corre lational theory and serve as an introduction to some recent methods of anal ysis more widely known by sociologists.