Statistical, geometrical and logical independences between categorical variables

International audienceClassical association criteria, used for measuring statistical independence between categorical variables, are initially defined using contingency tables. There is another way for representing categorical variables : Relational Analysis which uses binary pairwise comparison matrices formalism. There exists corre-spondance formulas that enable to get from one representation to the other. By using these formulas, and these two representations, we can have a better understanding of the main differences between some famous association criteria. In fact, several types of independence, namely statistical, geometrical and logical, appear using one representation or the other. The aim of this paper is to present in a unified framework, these different kinds of independence and their relationships by studying the expression of the following association criteria in the two different representations : Belson, Lerman, χ 2 of Tchuprow, Jordan, Rand and Janson and Vegelius. This paper is based upon previous results obtained in [Marcotorchino, 1984], [Messatfa, 1989], [Marcotorchino and El Ayoubi, 1991], [Najah Idrissi, 2000