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Orthonormal F Contrasts for Factors with Ordered Levels in Two-Factor Fixed-Effects ANOVAs

Author

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  • J. C. W. Rayner

    (National Institute for Applied Statistics Research Australia, University of Wollongong, Wollongong, NSW 2522, Australia
    School of Information and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia)

  • G. C. Livingston

    (School of Information and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia)

Abstract

In multifactor fixed-effects ANOVAs, we show how to construct orthonormal F contrasts for main effects. Our primary focus is the case when the levels of the factor of interest are ordered. Likewise, in multifactor equally replicated fixed-effects ANOVAs, we show how to construct orthonormal F contrasts for interactions. The primary focus here is on interactions when both factors are ordered, although the approach also applies if just one factor is ordered. Interactions with both factors ordered may be interpreted in terms of generalised correlations.

Suggested Citation

  • J. C. W. Rayner & G. C. Livingston, 2023. "Orthonormal F Contrasts for Factors with Ordered Levels in Two-Factor Fixed-Effects ANOVAs," Stats, MDPI, vol. 6(3), pages 1-11, September.
    • Handle: RePEc:gam:jstats:v:6:y:2023:i:3:p:57-930:d:1231264
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    References listed on IDEAS

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    1. O. Thas & D. J. Best & J. C. W. Rayner, 2012. "Using orthogonal trend contrasts for testing ranked data with ordered alternatives," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(4), pages 452-471, November.
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