The aggregate association index and its extension for the analysis of multiple 2x2 contingency tables

Data aggregation often occurs due to data collection methods or confidentiality laws imposed by government and institutional organisations. This is largely due to confidentiality issues arising from the imposition of government and corporate protection and data collection methods. The availability of only aggregate data makes it difficult to draw conclusions about the association between categorical variables at the individual level. For data analysts, this issue is of growing concern, especially for those dealing with the aggregate analysis of a single 2x2 table, or stratified, 2x2 tables and lies in the field of ecological inference (EI). Currently, there are a number of EI approaches that are available and provide data analysts with tools to analyse aggregated data. Nonetheless, their results are still questionable due to the variety of assumptions that are made about the individual level data, or the models that are developed to analyse them. As an alternative to ecological inference, one may consider the Aggregate Association Index (AAI) proposed by Beh (2008, 2010). This index gives data analysts an indication of the likely association structure between two categorical variables of a single 2x2 contingency table when the individual level, or joint frequency, data are unknown. To date, the AAI has been developed only for the analysis of a single 2x2 table. Hence, the purpose of this thesis is to extend the application of the AAI to the case where aggregated data from multiple 2x2 tables (i.e. stratified 2x2 tables) require analysis.