In Afex documentation and in “An Introduction to Mixed Models for Experimental Psychology”, effects coding (contr.sum()) are mentioned as an example of orthogonal contrasts coding – which requires that 1) “the sum of each variable across observations is zero”, and 2) “the sum of the product of all variable pairs is also zero”. However, doesn’t contr.sum(>2) violate requirement 2? For example: contrast1 [1 0 -1]; contrast2 [0 1 -1]. Sum of the products: (1*0)+(0*1)+(-1*-1)=1. Did I understand it wrong? If not, what caution should I take in interpreting results when using such non-orthogonal contrasts? I have some experimental data for which contr.sum(3) would indeed make much more sense than, for example, contr.helmert(3). However, only the latter seems to me to satisfy requirement 2. In the ANOVA table, results are almost identical for contr.sum(3) and contr.helmert(3), but I am really interested in the fixed effect coefficients provided by summary(lmer(…)) – including interactions with two other two-level factors.

Kind regards

Daniel