2 k contingency tables in ecology

Suppose observations are made on the presence or absence of k different species in N sampling units. Denote by s the number of species per sampling unit and let m₂ and Var(s) respectively be the observed variance of s and its expectation under the null hypothesis that all k species are independent. It is shown that the difference m₂—Var(s) is directly interpretable as a measure of the overall association among the species. Examples using field data are given and it is shown how the proposed measure of association may be used to judge: (i) whether some chosen group of species contributes markedly to the total amount of interdependence within a community; and (ii) whether some chosen group of species may be disregarded without affecting the result when ecological data are to be classified or ordinated.     

Exploring contingency tables with correspondence analysis

An algorithm for correspondence analysis is described and implementedin SAS/IML (SAS Institute, 1985a). The technique is shown, throughthe analysis of several biological examples, to supplement thelog-linear models approach to the analysis of contingency tables,both in the model identification and model interpretation stagesof analysis. A simple two-way contingency table of tumor datais analyzed using correspondence analysis. This example emphasisesthe relationships between the parameters of the log-linear modelfor the table and the graphical correspondence analysis results.The technqiue is also applied to a three-way table of surveydata concerning ulcer patients to demonstrate applications ofsimple correspondence analysis to higher dimensional tableswith fixed margins. Finally, the diets and foraging behaviorsof birds of the Hubbard Brook Forest are each analyzed and thena simultaneous display of the two separate but related tablesis constructed to highlight relationships between the tables. Received on August 29, 1988; accepted on April 25, 1989     

Incorporating prior information into the analysis of contingency tables

Contingency tables are often analyzed using log-linear models and in some situations prior information on the value of parameters in the log-linear model is available. In this article we describe a prior-posterior procedure that incorporates prior information directly into the analysis through a multivariate normal prior for the log-linear parameters. The mode and curvature of the posterior density are proposed as summary statistics.