Canonical Correlation and Chi-Square: Relationships and Interpretation
Document Type
Article
Publication Date
10-1-2000
Department
Psychology
Abstract
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.
Publication Title
Journal of General Psychology
Volume
127
Issue
4
First Page
341
Last Page
353
Recommended Citation
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