A reformulation of the aggregate association index using the odds ratio
Since its inception in the 1950s the odds ratio has become one of the most simple and popular measures available for analysing the association between two dichotomous variables. Since the direction and magnitude of the association can be captured in such a simple measure, its impact has been felt throughout much of scientific research, in particular in epidemiology and clinical trials. Despite this, its applicability for analysing aggregate data has rarely been considered. In this paper we shall express a new measure of association (the aggregate association index, or AAI), in terms of the classic odds ratio. The advantage of doing so is that we are able to explore the use of the odds ratio in a context for which it was not originally intended, and that is for the analysis of a 22 table where only the aggregate data is known.
22 contingency table aggregate association index (aai) chi-squared statistic fishers criminal twin data new zealand voting data (18831919)