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Testing for Level–Degree Interaction Effects in Two-Factor Fixed-Effects ANOVA When the Levels of Only One Factor Are Ordered

Author

Listed:
  • 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, Newcastle, NSW 2308, Australia)

  • G. C. Livingston

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

Abstract

In testing for main effects, the use of orthogonal contrasts for balanced designs with the factor levels not ordered is well known. Here, we consider two-factor fixed-effects ANOVA with the levels of one factor ordered and one not ordered. The objective is to extend the idea of decomposing the main effect to decomposing the interaction. This is achieved by defining level–degree coefficients and testing if they are zero using permutation testing. These tests give clear insights into what may be causing a significant interaction, even for the unbalanced model.

Suggested Citation

  • J. C. W. Rayner & G. C. Livingston, 2024. "Testing for Level–Degree Interaction Effects in Two-Factor Fixed-Effects ANOVA When the Levels of Only One Factor Are Ordered," Stats, MDPI, vol. 7(2), pages 1-11, May.
    • Handle: RePEc:gam:jstats:v:7:y:2024:i:2:p:29-491:d:1394748
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