Traditional and Rank-Based Tests for Ordered Alternatives in a Cluster Correlated Model

Methods for the analysis of one-factor randomized groups designs with ordered treatments are well established, but they do not apply in the case of more complex experiments. This article describes ordered treatment methods based on maximum-likelihood and robust estimation that apply to designs with clustered data, including those with a vector of covariates. The contrast coefficients proposed for the ordered treatment estimates yield higher power than those advocated by Abelson and Tukey; the proposed robust estimation method is shown (using theory and simulation) to yield both high power and robustness to outliers. Extensions for nonmonotonic alternatives are easily obtained.