ABSTRACT
When we reject the hypothesis of independence in contingency tables we often want to analyse the nature of association. In Section 12.3.2 we considered one aspect of association in tables with ordered row and column categories, recommending the Jonckheere-Terpstra test for monotonic association. We consider further aspects of association in this chapter. Our treatment is indicative rather than comprehensive. Approaches used to assess association range from parametric modelling to distribution-free methods. Parametric or semiparametric approaches are usually formulated to reflect knowledge about the mechanism generating the counts. One such model is the logistic regression model for binary responses such as success and failure where the proportions responding depend upon levels of one or more explanatory variables. General descriptions of this model are given by Agresti (1996, Chapter 5 and 2002, Chapter 5) and a detailed treatment covering many applications is presented in Cox and Snell (1989). We return to this model in Section 15.4.
