a robust procedure for comparing multiple means under heteroscedasticity in unbalanced designs一个健壮的程序比较多意味着在不平衡的异方差性的设计.pdfVIP

A Robust Procedure for Comparing Multiple Means under Heteroscedasticity in Unbalanced Designs 1 2 1 Esther Herberich , Johannes Sikorski , Torsten Hothorn * ¨ ¨ ¨ 1 Institut fur Statistik, Ludwig-Maximilians-Universitat, Munchen, Germany, 2 Deutsche Sammlung von Mikroorganismen und Zellkulturen GmbH, Braunschweig, Germany Abstract Investigating differences between means of more than two groups or experimental conditions is a routine research question addressed in biology. In order to assess differences statistically, multiple comparison procedures are applied. The most prominent procedures of this type, the Dunnett and Tukey-Kramer test, control the probability of reporting at least one false positive result when the data are normally distributed and when the sample sizes and variances do not differ between groups. All three assumptions are non-realistic in biological research and any violation leads to an increased number of reported false positive results. Based on a general statistical framework for simultaneous inference and robust covariance estimators we propose a new statistical multiple comparison procedure for assessing multiple means. In contrast to the Dunnett or Tukey-Kramer tests, no assumptions regarding the distribution, sample sizes or variance homogeneity are necessary. The performance of the new procedure is assessed by means of its familywise error rate and power under different distributions. The practical merits are demonstrated by a reanalysis of fatty acid phenotypes of the bacterium Bacillus simplex from the ‘‘Evolution Canyons’’ I and II in Israel. The simulation results show that even under severely varying variances, the procedure controls th