Robustness of Type I Error and Power in Set Correlation Analysis of Contingency Tables

The analysis of contingency tables by means of set correlation makes possible the assessment of sub-hypotheses involving contrast functions of the categories of the nominal scales. This follow-up analysis of the overall association provides greater interpretive yield than do the standard methods, but has the problem that its significance tests violate the assumption of multivariate normality. The robustness of such tests both with regard to Type I error and statistical power was addressed by Monte Carlo experiments. From 31 contingency tables of varying size (2 X 3, 3 X 4, and 4 X 6) and marginal distributions, random samples of 1000 cases of sizes 30, 60, 120, and 240 were drawn. The sample multivariate R(2) y,x of each sample was tested for significance at the .01 and .05 levels using the Rao F-test. By comparing the Monte Carlo and theoretical rates, 232 determinations of bias for Type I error and 100 determinations of power bias were made. Bias was found to be negligible and it was concluded that the procedure is generally robust for both Type I error and power.