Simultaneous Rank Tests in Analysis of Covariance Based on Pairwise Ranking

TL;DR

This paper extends nonparametric pairwise comparison methods to analysis of covariance and factorial models, combining aligned ranks and pairwise ranking to improve error control and power in small samples.

Contribution

It introduces a new weighted scale estimate for ranks and extends Steel-Dwass comparisons to more complex models, enhancing robustness and accuracy.

Findings

Weighted scale estimate improves small sample performance

Method controls familywise error rate at nominal level

Enhanced large sample approximation for Steel-Dwass method

Abstract

Nonparametric tests provide robust and powerful alternatives to the corresponding least squares methods. There are two approaches to nonparametric pairwise comparisons of treatment effects, the method based on pairwise rankings and the method based on overall ranking. The former is generally recommended in the literature because of its strong control of familywise error rate. However, this method is developed only for one-way layouts and randomized complete blocks. By combining the method of aligned ranks and pairwise ranking, we extend the Steel-Dwass pairwise comparisons to the analysis of covariance and factorial models for both one-sided and two-sided comparisons as well as testing for treatment versus control. Unlike the traditional two-sample standardization of test statistics, we propose a weighted estimate of the scale parameter for ranks and show through simulation that it has superior small sample performance by controlling the familywise error rate at nominal level. This method provides an improvement for large sample approximation of Steel-Dwass method for one-way layouts. The marginal and joint asymptotic distributions are derived and power comparisons are made with the method of aligned rank transformation and the least squares method.