- Title
- Extended analysis of at least partially ordered multi-factor ANOVA
- Creator
- Rayner, J. C. W.; Best, D. J.; Thas, O.
- Relation
- Australian and New Zealand Journal of Statistics Vol. 57, Issue 2, p. 211-224
- Publisher Link
- http://dx.doi.org/10.1111/anzs.12113
- Publisher
- Wiley-Blackwell
- Resource Type
- journal article
- Date
- 2015
- Description
- For multifactor experimental designs in which the levels of at least one of the factors are ordered we show how to construct components that provide a deep nonparametric scrutiny of the data. The components assess generalised correlations and the resulting tests include and extend the Page and umbrella tests. Application of the tests described is straightforward. Orthonormal polynomials on the ANOVA responses and the factors are required and the formulae needed are given subsequently. These depend on the moments of the responses and of each factor and are easily calculated. Products of at least two of these orthonormal polynomials are then used as inputs into standard ANOVA routines. For example, using the first order orthonormal polynomial on factor A and the second order orthonormal polynomial on the ANOVA response will assess if, with increasing levels of factor A there is an umbrella response with either an increase and then a decrease or a decrease and then an increase.
- Subject
- randomised designs; factorial designs; generalised correlations; orthonormal polynomials
- Identifier
- http://hdl.handle.net/1959.13/1334343
- Identifier
- uon:27271
- Identifier
- ISSN:1369-1473
- Rights
- This is the peer reviewed version of above article, which has been published in final form at http://dx.doi.org/10.1111/anzs.12113. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.
- Language
- eng
- Full Text
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