Measures of association in the Fréchet class

When populations are cross-classified with respect to two or more qualitative characters, the question often arise of the degree of association existing between the several polytomies. The main unsolved problem with traditional measures of association is that it is difficult to meaningfully compare their values. Given a particular r x c table T, our approach to association starts from the consideration of its entire Fréchet class T (ni• ; n•j): chosen a particular association ordering for all the bivariate distributions, as defined in Zenga and Greselin 2001, the relative position assumed by T in T (ni• ; n•j) can be a meaningful and sound index of association. Moreover, this family of indexes has several desirable and interesting properties that are shown in detail.