Using orthogonal trend contrasts for testing ranked data with ordered alternatives

• Published in: Statistica Neerlandica Vol. 66; no. 4; pp. 452 - 471
• Main Authors: Thas, O., Best, D. J., Rayner, J. C. W.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01-11-2012
• Subjects: balanced incomplete blocks Durbin test Friedman test; independent samples layout; location-shift model; Orthography; page test; Pearson test; probabilistic index; randomized blocks; Statistical analysis; Studies; umbrella test; Variance analysis
• ISSN: 0039-0402; 1467-9574
• DOI: 10.1111/j.1467-9574.2012.00525.x

In the analysis of variance (Anova) the use of orthogonal contrasts is quite common and is a traditional topic in many basic Anova courses. Similar ideas apply to rank tests. In this paper we present a simple and general method that allows an orthogonal contrast decomposition of rank test statistics such as the Kruskal‐Wallis, Friedman and Durbin statistics. The components of the test statistics are informative, particularly when ordered alternatives are of interest. The method can handle ties, and null distributions are readily available. Most of the methods are not new, but the way we present them is. Moreover, our formulation makes it easier to better understand and interpret the tests when the traditional location‐shift assumption does not hold. The methods are illustrated using several data sets.