The odds ratio is a measure of association used both for the analysis of a contingency table and an contingency table, where I and J are bigger than 2. Nevertheless, the total number of odds ratios to check grows with I and J and several methods have been developed to summarize them. In the present paper we present a general framework for the analysis of the complete set of log odds ratio. Particularly we propose and connect two different methodologies performed on two different data sets. Moreover starting from these methodologies, we focus our attention on the factorial representation of the log odds ratios
