New Power Analysis For The Pseudo-Median Procedure For More Than Two Groups - Alsaggaff, Ibtesam Ali (2013)
Comparison of treatment groups is frequently used in practical research in a variety of fields. The parametric ANOVA F test is most widely used to compare groups of treatment, specifically the means of three or more treatment groups. However, the parametric test usually requires normality of the distribution and homogeneity of variances. So, failure in meeting these assumptions leads to distortion of Type I error and substantial reduction in the power of the test. Therefore, the pseudo-median procedure which adopts the pseudo-median as a location parameter was developed for treatment groups comparison. This procedure is a modification of the one-sample nonparametric Wilcoxon procedure developed for more than two groups. The pseudo-median procedure is a summation of multiple paired comparisons between the control group and each of the treatment groups. In this study, the performance of the pseudo-median procedure is examined when the assumptions of normality and heterogeneity are violated. The Type I error is examined and a new power analysis of this procedure is proposed and carried out for more than two groups. Both Type I error and power analysis are performed under various degrees of homogeneity and different shapes of distributions. The bootstrap method is employed to generate a pseudo sampling distribution for the pseudo-median test statistic.