Simultaneous aligned rank transform tests in analysis of covariance based on pairwise ranking

There are two approaches to non-parametric 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 the familywise error rate. However, this method is only available for data involving one-way layouts and randomized complete blocks. Here, the Steel-Dwass pairwise comparisons method is extended to the classical analysis of covariance model and factorial models for one-(and two)-sided comparisons as well as testing for treatment versus control. In addition to the two-sample standardization of test statistics, a weighted estimate of the scale parameter based on the rank scores is proposed and shown to have superior small sample performance while controlling the familywise error rate. The marginal and joint asymptotic distributions are derived, and power comparisons are made with the method of aligned overall rank transformation and the least squares method.