

Duy Tran will present his PhD confirmation seminar.
PhD supervisors: A/Prof. Eric Beh, Prof. Irene Hudson, A/Prof. Rosaria Lombardo.
The analysis of aggregate data, or marginal information, for contingency tables is an increasingly important area of statistics. This is, in part, due to confidentiality issues concerned with the study, and the way the data is presented or collected. As a result, the availability of only aggregate data makes it difficult to draw conclusions about the quantification and graphical representation of the association between categorical variables. For categorical data analysts, this issue is of growing concern, especially for those concerned with the aggregate analysis of a single, or multiple 2x2 tables.
In order to analyse the association that exists between the variables of a 2x2 table, or multiple 2x2 tables, based only on the aggregate data, numerous approaches that lie within the area of Ecological Inference (EI) have dealt with this problem to varying degrees. However, current EI techniques still suffer from major shortfalls in the assumptions that are required Hudson, Moore, Beh and Steel (2010, JRSSA). In addition, visualising the association in a single 2x2 table, or multiple 2x2 tables, using Correspondence Analysis (CA; Greenacre, 1984; Beh, 2004, ISR) is an issue when only aggregate data are available.
An approach that does not require ensuring the integrity of the untestable EI assumptions and provides a foundation to extend the traditional CA for a single 2x2 table, given only aggregate data are available, is Aggregate Association Index (AAI). This technique was proposed by Beh (2008, JSPI).
The objective of this research is to broaden the AAI and to expand this new theory for building upon Beh’s (2008, JSPI) CA of aggregate data. Specifically, this research will be built upon the earlier work of Beh (2008, JSPI) and Beh (2010, CSDA) to understand the AAI’s conception, applicability and limitations in comparison to the CA. Another aspect of this research is to consider the AAI technique with the Ecological Inference techniques in Hudson, Moore, Beh and Steel (2010, JRSSA) which was the first New Zealand study of gendered voting data using foundational methods of Ecological Inference. Consequently, the aims of my search are:
 Extending the AAI and its application to simultaneously analyse multiple, or stratified, 2x2 tables.
 Generalising the AAI to consider any of the popular measures of association commonly adopted in the statistical and allied disciplines.
 Establishing a formal connection between the AAI and the EI.
 Generalising the CA approach to incorporate the above advances.
Keywords: Aggregate data, 2x2 tables, Aggregate Association Index, Correspondence Analysis, Ecological Inference.
