Unifying Some Association Criteria Between Partitions by Using Relational Matrices

Julien Ah-Pine , Jean-François Marcotorchino (1)

1 THALES [France]

Association criteria used for measuring the relationship between categorical variables or partitions, are mainly applied and studied using contingency tables. There is another way for representing categorical variables : the Relational Analysis representation which uses binary pairwise comparison matrices and which has many properties. There exist correspondence formulas that allow to get from the contingency representation to the relational representation. By using these formulas, we show in this paper how Relational Analysis allows to unify many association criteria such as Rand, Tchuprow, Belson criteria and others. This unified framework allows also to have a better understanding of the main differences between those association criteria. In that context, we also present different kinds of independence : statistical, geometrical and " logical " .

Mots clés: Relational Analysis; Association criteria; Independence; Nominal categorical variables; Partitions comparison

Domaines: Statistiques [stat]

Julien Ah-Pine, Jean-François Marcotorchino. Unifying Some Association Criteria Between Partitions by Using Relational Matrices. Communications in Statistics - Theory and Methods, 2010, 39 (3), pp.531-542. ⟨10.1080/03610920903140262⟩. ⟨hal-01504571⟩