L'analyse implicative bayésienne : une méthode pour l'étude des dépendances orientées. 1.Données binaires

摘要

Does success to test A imply, approximately, success to test B ? Among the descriptive indices that were proposed to measure such oriented dependencies, we focus on Loevinger's H which has a simple expression in terms of the association rates between modalities. From this index, we define the notions of quasi-implication, quasi-equivalence and quasi-independence for a 2 by 2 contingency table. However, the corresponding existing inferential frequentist methods, because they are based on asymptotic considerations, do not provide valid statements, neither for small datasets, nor, paradoxically, for cases in which the implication is descriptively almost verified. The Bayesian approach to inference avoids these difficulties and provides inductive statements about the size of quasi-implications and other types of "quasi-" relations. The proposed methods, the Bayesian Implicative Analysis, composed of these two aspects (descriptive and inductive), is illustrated on an experiment from Developmental Psychology about number construction in children.