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.
Dunlap
W P
WP
Department of Psychology, Tulane University, New Orleans, LA 70118, USA.
Brody
C J
CJ
Greer
T
T
D016009:Chi-Square Distribution; D002648:Child; D005127:Eye Color; D006801:Humans; D001523:Mental Disorders / Q000175:diagnosis; D012720:Severity of Illness Index; D012959:Socioeconomic Factors