I understand deriving a covariance matrix from phylogenetic data to make $cov(X,Y) = 0$ for two variables you're making a regression on. But what happens if you have one continuous variable, that you've previously shown to be dependent on phylogeny, and one ordinal variable? The latter being ordinal, I'm not sure how to relate this to the way in which phylogenetic dependence results in biased test statistics.
Is it meaningful to calculate Felsenstein's Phylogenetic Independent Contrasts on your continuous variable and use these for your ANOVA?
The PIC value is: $$C_{ij} = \frac{(X_i - X_j)}{\sqrt{d_{ij}}} $$
Where $X_i$ is $X$ for species $i, X_j$ is $X$ for species $j$, and $d_{ij}$ is the pairwise distance between species $i$ and $j$ on the phylogenetic tree.
