Ordinal association in contingency tables: Some interpretive aspects. (English) Zbl 0644.62065

Gilula, Zvi; Krieger, Abba M.; Ritov, Yaakov

J. Am. Stat. Assoc. 83, No. 402, 540-545 (1988).

Two families of models for ordered contingency tables - Goodman’s association models and canonical correlation models - are investigated and compared with respect to the interpretation of their parameters. We show that the two families of models actually refer to different kinds of ordinal association: stochastic order extremity for correlation models and stochastic order entropy for association models. This difference is related to the way the two models scale interaction. The scale difference is proven to be of substantial consequence, especially under strong association.

MSC:

62H17	Contingency tables
62H20	Measures of association (correlation, canonical correlation, etc.)

Keywords:

ordered contingency tables; Goodman’s association models; canonical correlation models; ordinal association; stochastic order extremity; stochastic order entropy