A nonparametric two-sample comparison for skewed data with unequal variances.
OBJECTIVE
The aim of the study was to recommend a statistical test for the situation in which unequal variances are accompanied by skewed distributions. A previous publication in this journal could not recommend any test; instead, transformations were suggested.


METHODS
A recently introduced generalized Wilcoxon test is presented, which can be applied when variances may be unequal and the distribution may be skewed. This test examines the null hypothesis that the relative effect is 0.5. Its type I error rate was investigated in a simulation study.


RESULTS
The generalized Wilcoxon test was already recommended for various areas of life sciences and, very recently, it was shown that a permutation test could be performed with the generalized test statistic. Simulation results indicate an acceptable control of the type I error rate even for extreme variance ratios.


CONCLUSIONS
The generalized Wilcoxon test should be applied when it cannot be assumed that variances are equal and that the distribution is symmetric. This test is preferable to a transformation, because the use of transformations can be problematic, in particular when sample sizes are small.
Neuhäuser
Markus
M
Department of Mathematics and Technique, RheinAhrCampus, Koblenz University of Applied Sciences, Remagen, Germany. neuhaeuser@rheinahrcampus.de
D000465:Algorithms; D000704:Analysis of Variance; D006801:Humans; D015203:Reproducibility of Results; D018401:Sample Size; D018709:Statistics, Nonparametric