Comparison via simulation of association coefficients calculated between categorical variables

Abstract

Aim: The aim of this study was to compare the robustness of some association coefficients used to determine the relationships between categorical variables under different experimental conditions.

Material and Methods: A simulation study was conducted where random numbers were generated from a bivariate standard normal distribution with correlations of 0.5 and 0.9. Sample sizes were set at 30, 50, 100, 150 and 200. Random numbers were equally spaced and coded as 3×3, 4×4 and 5×5 cross-tabulations, respectively. The robustness of Pearson’s, Spearman's rank, Kendall's tau-b, Kendall's tau-c, Goodman-Kruskal’s gamma and Somer's d coefficients were compared under different experimental conditions consisting of combinations of specified population correlation degrees, table dimensions and sample sizes.

Results: The Goodman-Kruskal’s gamma coefficient gave the closest result to the relationship levels set at the beginning of the study in all experimental conditions. However, after a certain level, it was negatively affected by the increase in table dimension and sample size. Kendall's tau-b and tau-c coefficients were furthest from the actual degree of the association. Spearman's rank correlation was more robust than Kendall's tau-b, Kendall's tau-c and Somer's d coefficients.

Conclusion: The results of the study showed that the dimension of the contingency tables and sample size were effective factors in the robustness of association coefficients for categorical variables. Therefore, researchers should consider the table dimension and sample size as well as the type of variable when selecting the association coefficient to be calculated.