- Title
- Extended Anova and rank transform procedures
- Creator
- Rayner, J. C. W.; Best, D. J.
- Relation
- Australian & New Zealand Journal Of Statistics Vol. 55, Issue 3, p. 305-319
- Publisher Link
- http://dx.doi.org/10.1111/anzs.12041
- Publisher
- Wiley-Blackwell
- Resource Type
- journal article
- Date
- 2013
- Description
- The rank transform procedure is often used in the analysis of variance when observations are not consistent with normality. The data are ranked and the analysis of variance is applied to the ranked data. Often the rank residuals will be consistent with normality and a valid analysis results. Here we find that the rank transform procedure is equivalent to applying the intended analysis of variance to first order orthonormal polynomials on the rank proportions. Using higher order orthonormal polynomials extends the analysis to higher order effects, roughly detecting dispersion, skewness etc. differences between treatment ranks. Using orthonormal polynomials on the original observations yields the usual analysis of variance for the first order polynomial, and higher order extensions for subsequent polynomials. Again first order reflects location differences, while higher orders roughly detect dispersion, skewness etc. differences between the treatments.
- Subject
- complete randomised block designs; factorial designs; generalised ranks; orthonormal polynomials; ranks
- Identifier
- http://hdl.handle.net/1959.13/1042931
- Identifier
- uon:14147
- Identifier
- ISSN:1369-1473
- Rights
- This is the accepted version of the following article: Rayner, J. C. W.; Best, D. J. “Extended Anova and rank transform procedures” Australian & New Zealand Journal Of Statistics Vol. 55, Issue 3, p. 305-319 (2013), which has been published in final form at http://dx.doi.org/10.1111/anzs.12041
- Language
- eng
- Full Text
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