Comparison of the Power of Robust F* and Non-Parametric Kruskal-Wallis Tests in the One-Way Analysis of the Variance Model

Abstract

Observations obtained from agriculture, biology and other applied sciences do not generally follow normal distribution. Moreover, outliers may exist in observed data. In these situations, parametric normal theory tests, based on least squares (LS) estimators, have low power and are not robust against these situations. In general, nonparametric test procedures are used to analyze non-normal data. In the context of one-way analysis of variance, the nonparametric Kruskal-Wallis test, based on ranks is a well-accepted reference test for comparison of three or more groups of observations in cases of violation of the normality assumption. On the other hand, the performance of these tests has been discussed in the literature for cases of censored data. In this paper, we firstly derive the F* test, developed by Şenoğlu and Tiku (2004), when the distribution of error terms are type II censored generalized logistic and we then compare this with the Kruskal-Wallis test in terms of power and robustness properties when the distribution of error terms are type II censored generalized logistic. Simulation results show that the F* test is more powerful and robust in general. A real data set from the literature is analyzed using the F* test. A Compaq Visual Fortran program is used for calculations and the executable program is available from the author on request.