Measures of Association and Visualization of Log Odds Ratio Structure for a Two Way Contingency Table

The odds ratio (OR) is a measure of association used for analysing an I × J contingencytable. The total number of ORs to check grows with I and J . Several statistical methodshave been developed for summarising them. These methods begin from two differentstarting points, the I × J contingency table and the two-way table composed by the ORs.In this paper we focus our attention on the relationship between these methods and pointout that, for an exhaustive analysis of association through log ORs, it is necessary toconsider all the outcomes of these methods. We also introduce some new methodologicaland graphical features. In order to illustrate previously used methodologies, we consider adata table of the cross-classification of the colour of eyes and hair of 5387 children fromScotland. We point out how, through the log OR analysis, it is possible to extract usefulinformation about the association between variables.