The aggregate association index

Recently (Beh, 2008, JSPI) presented an index that helps to identify how likely two dichotomous categorical variables may be associated given only the aggregate (or marginal) information. Such an index was referred to as the aggregate association index. This paper will further consider some of the issues concerned with that index. These include variations of the original index as well as adaptations for quantifying the possibility that there exists a statistically significant positive or negative association between the two dichotomous variables.