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Robustness of Multiple Comparison Procedures: Treatment versus Control
Author(s) -
Rudolph P. E.
Publication year - 1988
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710300106
Subject(s) - nonparametric statistics , mathematics , statistics , type i and type ii errors , robustness (evolution) , sample size determination , wilcoxon signed rank test , parametric statistics , homogeneity (statistics) , multiple comparisons problem , normality , analysis of variance , variance (accounting) , biochemistry , chemistry , accounting , business , mann–whitney u test , gene
Computer simulation techniques were used to investigate the Type I and Type II error rates of one parametric (Dunnett) and two nonparametric multiple comparison procedures for comparing treatments with a control under nonnormality and variance homogeneity. It was found that Dunnett's procedure is quite robust with respect to violations of the normality assumption. Power comparisons show that for small sample sizes Dunnett's procedure is superior to the nonparametric procedures also in non‐normal cases, but for larger sample sizes the multiple analogue to Wilcoxon and Kruskal‐Wallis rank statistics are superior to Dunnett's procedure in all considered nonnormal cases. Further investigations under nonnormality and variance heterogeneity show robustness properties with respect to the risks of first kind and power comparisons yield similar results as in the equal variance case.