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

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.

Keywords

• equally replicated two-way ANOVA
• generalised correlations
• singular value decomposition theorem