A comparison and normality test of some measures of association via simulation for rectangular doubly ordered cross tables

Abstract

Spearman and Pearson correlation coefficient, Gamma coefficient, Kendall's tau-b, Kendall's tau-c, and Somers'd are the most commonly used measures of association for doubly either square or rectangular ordered contingency tables. So far, there has been no existing study expressing a formal priority on those measures of association. The aim of this study is not only to compare these measures of association for several types and different sample sizes of generated rectangular (or non-squared) doubly ordered contingency tables and determine which measures of association are more efficient, but also, to check whether each test statistics of ordinal measure of associations satisfies normality assumption under the null hypothesis of independence. Meanwhile, this study deals with the empirical errors of the test statistics under the null hypothesis of independence in order to investigate if the ? nominal level is achieved for 12 different rectangular table dimensions and 8 different sample sizes. It is found that both the sample sizes and the dimension of the doubly rectangular ordered contingency tables have a significant effect on these ordinal measures of association. © 2011 Academic Journals.