Canonical correlation and chi-square: Relationships and interpretation

Citation
Wp. Dunlap et al., Canonical correlation and chi-square: Relationships and interpretation, J GEN PSYCH, 127(4), 2000, pp. 341-353
Citations number
16
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Psycology
Journal title
JOURNAL OF GENERAL PSYCHOLOGY
ISSN journal
0022-1309 → ACNP
Volume
127
Issue
4
Year of publication
2000
Pages
341 - 353
Database
ISI
SICI code
0022-1309(200010)127:4<341:CCACRA>2.0.ZU;2-D
Abstract
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.