The Analysis of Multidimensional Contingency Tables

Abstract

Ecological data often come in the form of multidimensional tables of counts, referred to as contingency tables. During the last decade several new methods of analyzing such tables have been proposed. Here, a class of models analogous to those used in the analysis of variance is discussed, and a method for computing the expected cell counts for the different models is presented. Two differenet tests for checking the goodness—of—fit of a particular model are then examined. The first is the simple generalization of the Pearson chi—square test statistic, while the second is referred to as the likelihood—ratio chi—square test statistic. Both have the same asympototic g 2 distribution. The likelihood—ratio statistic can be used in the selection of a suitable model, via the technique of partitioning. All of the methods presented are illustrated using data collected by Schoener on lizards from the West Indies.