Comparison of a Class of Rank-Score Tests in Two-Factor Designs

Abstract

Rank score functions are known to be versatile and powerful techniques in factorial designs. Researchers have established the theoretical properties of these methods based on nonparametric hypotheses, but only scanty empirical results are available in the literature on these procedures. In this paper, four types of rank score functions Wilcoxon-scores, Mood-scores, normal-scores and expected normal- scores are studied in the context of two¡Vway factorial designs using asymptotic ƒÓ2 (Wald-Type) and modified Box- approximation (ANOVA-Type) tests. The empirical Type I error rate and power of these test statistics on the rank scores were determined using Monte Carlo simulation to investigate the robustness of the tests. The results show that there are problems of inflation in the Type I error rate using asymptotic ƒÓ2 test for all the rank score functions, especially
for small sample sizes and distributions studied. The modified Box- approximation test was found to be robust for both validity and efficiency, especially for Wilcoxon, normal and expected normal score functions. It was concluded that the asymptotic ƒÓ2 test is non-robust for rank score functions in two-factor designs.

Keywords: Rank score functions, Type I error rates, Power, Factorial designs.