Testing for Level–Degree Interaction Effects in Two-Factor Fixed-Effects ANOVA When the Levels of Only One Factor Are Ordered-Reference-Cited by-同舟云学术

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

Published:2024-05-15 Issue:2 Volume:7 Page:481-491
ISSN:2571-905X
Container-title:Stats
language:en
Short-container-title:Stats

Author:

Rayner J. C. W.¹²^ORCID,Livingston G. C.²^ORCID

Affiliation:

1. National Institute for Applied Statistics Research Australia, University of Wollongong, Wollongong, NSW 2522, Australia

2. 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.

Publisher

MDPI AG

Link

https://www.mdpi.com/2571-905X/7/2/29/pdf

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