Goodness of Fit of an Assigned Set of Scores for the Analysis of Association in a Contingency Table

摘要

The problem of association between two attributes in a p x q contingency table can be looked upon as the problem of relationship between two vector variables x and y. If there is only one true non-zero canonical correlation between x and y, the association between the two attributes is of rank 1 and in this case, one set of scores is adequate to describe the association completely; these scores are nothing but the coefficients in the canonical variates corresponding to the true non-zero canonical correlation. Given a set of hypothetical scores for the rows, one is interested in testing their goodness of fit. Tests for this are suggested in this paper. For obtaining these tests, a preliminary result about direction and collinearity factors in discriminant analysis, when S irrelevant variables are eliminated, is needed. This is derived in part one of this paper. (Author)