Aligned Rank Transform Techniques for Analysis of Variance and Multiple Comparisons

Abstract

The aligned rank transform (ART) technique for testing linear hypotheses and performing multiple comparisons is known to provide a powerful and robust nonparametric alternative to the usual classical analysis techniques where a normal error distribution is assumed. ART procedures are also known to provide results that are more powerful and robust when compared with other procedures. In this paper, we review the ART testing procedures in linear models. We pay special attention to the two-way layout and multiple comparison techniques, and attempt to show the ease with which the ART methods can be implemented by researchers desiring a nonparametric alternative to the usual least squares methods. Some examples are given for analyzing a two-way layout and performing multiple comparisons. The results of a small-scale simulation study are also presented to show that the ART testing procedures may be quite robust against violations of the assumption of a continuous error distribution.

Key Words:

• Aligned ranking
• Rank transformation
• Analysis of variance
• Multiple comparison
• Simulation

Mathematics Subject Classification:

• Primary 62J, 62G, 62K
• Secondary 62P, 65C