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Using orthogonal trend contrasts for testing ranked data with ordered alternatives

(2012) STATISTICA NEERLANDICA. 66(4). p.452-471
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Abstract
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.
Keywords
independent samples layout, balanced incomplete blocks Durbin test Friedman test, location-shift model, page test, Pearson test, probabilistic index, randomized blocks, umbrella test, K-SAMPLE PROBLEMS

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Please use this url to cite or link to this publication:

MLA
Thas, Olivier, D John Best, and John CW Rayner. “Using Orthogonal Trend Contrasts for Testing Ranked Data with Ordered Alternatives.” STATISTICA NEERLANDICA 66.4 (2012): 452–471. Print.
APA
Thas, O., Best, D. J., & Rayner, J. C. (2012). Using orthogonal trend contrasts for testing ranked data with ordered alternatives. STATISTICA NEERLANDICA, 66(4), 452–471.
Chicago author-date
Thas, Olivier, D John Best, and John CW Rayner. 2012. “Using Orthogonal Trend Contrasts for Testing Ranked Data with Ordered Alternatives.” Statistica Neerlandica 66 (4): 452–471.
Chicago author-date (all authors)
Thas, Olivier, D John Best, and John CW Rayner. 2012. “Using Orthogonal Trend Contrasts for Testing Ranked Data with Ordered Alternatives.” Statistica Neerlandica 66 (4): 452–471.
Vancouver
1.
Thas O, Best DJ, Rayner JC. Using orthogonal trend contrasts for testing ranked data with ordered alternatives. STATISTICA NEERLANDICA. 2012;66(4):452–71.
IEEE
[1]
O. Thas, D. J. Best, and J. C. Rayner, “Using orthogonal trend contrasts for testing ranked data with ordered alternatives,” STATISTICA NEERLANDICA, vol. 66, no. 4, pp. 452–471, 2012.
@article{3188536,
  abstract     = {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.},
  author       = {Thas, Olivier and Best, D John and Rayner, John CW},
  issn         = {0039-0402},
  journal      = {STATISTICA NEERLANDICA},
  keywords     = {independent samples layout,balanced incomplete blocks Durbin test Friedman test,location-shift model,page test,Pearson test,probabilistic index,randomized blocks,umbrella test,K-SAMPLE PROBLEMS},
  language     = {eng},
  number       = {4},
  pages        = {452--471},
  title        = {Using orthogonal trend contrasts for testing ranked data with ordered alternatives},
  url          = {http://dx.doi.org/10.1111/j.1467-9574.2012.00525.x},
  volume       = {66},
  year         = {2012},
}

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