• M O Scheinhardt and A Ziegler.
• Institut für Medizinische Biometrie und Statistik, Universität zu Lübeck, Ratzeburger Allee 160, Haus 24, 23562 Lübeck, Germany.
• Methods Inf Med. 2013 Jan 1; 52 (4): 351-9.

BackgroundGene, protein, or metabolite expression levels are often non-normally distributed, heavy tailed and contain outliers. Standard statistical approaches may fail as location tests in this situation.ObjectivesIn three Monte-Carlo simulation studies, we aimed at comparing the type I error levels and empirical power of standard location tests and three adaptive tests [O'Gorman, Can J Stat 1997; 25: 269 -279; Keselman et al., Brit J Math Stat Psychol 2007; 60: 267- 293; Szymczak et al., Stat Med 2013; 32: 524 - 537] for a wide range of distributions.MethodsWe simulated two-sample scenarios using the g-and-k-distribution family to systematically vary tail length and skewness with identical and varying variability between groups.ResultsAll tests kept the type I error level when groups did not vary in their variability. The standard non-parametric U-test performed well in all simulated scenarios. It was outperformed by the two non-parametric adaptive methods in case of heavy tails or large skewness. Most tests did not keep the type I error level for skewed data in the case of heterogeneous variances.ConclusionsThe standard U-test was a powerful and robust location test for most of the simulated scenarios except for very heavy tailed or heavy skewed data, and it is thus to be recommended except for these cases. The non-parametric adaptive tests were powerful for both normal and non-normal distributions under sample variance homogeneity. But when sample variances differed, they did not keep the type I error level. The parametric adaptive test lacks power for skewed and heavy tailed distributions.

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