A comparison of type I error and power of the aligned rank method using means and medians for alignment - Yates, Heath Landon (Kansas State University, 2011)
A simulation study was done to compare the Type I error and power of standard analysis of variance (ANOVA), the aligned rank transform procedure (ART), and the aligned rank transform procedure where alignment is done using medians (ART + Median). The methods were compared in the context of a balanced two-way factorial design with interaction when errors have a normal distribution and outliers are present in the data and when errors have the Cauchy distribution. The simulation results suggest that the nonparametric methods are more outlier-resistant and valid when errors have heavy tails in comparison to ANOVA. The ART + Median method appears to provide greater resistance to outliers and is less affected by heavy-tailed distributions than the ART method and ANOVA.
Keywords: Nonparametrics; Align Rank Transform; Statistics; ANOVA; Statistics (0463)