Set Correlation and Contingency Tables

Abstract

Set correlation is a realization of the general multi variate linear model, can be viewed as a multivariate generalization of multiple correlation analysis, and may be employed in the analysis of multivariate data in any form. Set correlation supplements the four methods for analyzing two-way contingency tables de scribed by Zwick and Cramer (1986), and its applica tion to their example is illustrated. It gives the same results for the overall association, and in addition, by the use of nominal scale coding and partialling, it as sesses specific hypotheses about the details of the as sociation. Set correlation includes measures of strength of association (including correlations and proportions of variance), significance tests and estimation, power analysis, and computer programs to implement the calculations. Index terms: canonical analysis, con tingency table analysis, correspondence analysis, gen eral multivariate linear model, multivariate analysis of variance, Pearson chi-square, set correlation.