The aggregate association index and its links with common measurements of association in a 2x2 table: an analysis of early New Zealand gendered voting data

Abstract

The analysis of aggregate, or marginal, data for contingency tables is an increasingly important area of statistics, especially in political science and epidemiology. Aggregation often exists due to confidentiality issues or by source of the data itself. Aggregate data alone makes drawing conclusions about the true association between categorical variables difficult, especially in dealing with the aggregate analysis of single or stratified 2x2 contingency tables. These tables are the most fundamental of data structures when dealing with cross-classifying categorical variables hence it is not surprising that the analysis of this type of data has received an enormous amount of attention in the statistical, and related, literature. However, the information, from which the aggregate data can provide for the inference of association between the variables, is still a long standing issue. In order to analyse the association that exists between the variables of a 2x2 table, or stratified 2x2 tables, based only on the aggregate data, numerous approaches that lie within the area of Ecological Inference (EI) have been proposed. As an application of this new development, we shall analyse a unique record of New Zealand gendered election data from 1893 when it was the first selfgo verning country in the world allowing women to vote, this trend quickly spread across the globe