I have a diffusion tensor imaging set in which I am running an ancova in order to see if two diagnostic groups differ significantly in diffusivity measures (FA, MD, etc.), while controlling for several factors (specifically: demeaned-age and in-scanner motion), for a set of tracts of interest (TOIs). Out of the models ran, several displayed non-normal residuals or evidence of heteroskedasticity. Therefore, I decided to use permutation anova/ancova (implemented in the "permuco" R package). To clarify, by "differ significantly", I mean whether the two diagnostic groups will show a significant, mean difference in 5 dependent measures: tract Volume, FA, MD, RD, and AD. The latter 4 being measures derived from applying diffusion tensor models to diffusion-weighted images, with each describing microscopic properties of diffusion at the voxel-level, and giving (slightly ambiguous) information on white matter microstructural properties.

I have specific hypotheses for the latter 4 measures, that group A will display "greater FA" compared to group B, and that group B will display "greater MD, RD, and AD" than group A.

I would like to calculate an effect size for these permutation anova/ancovas. Normally I would calculate partial eta squared or omega-squared, however I am unsure if these are appropriate for nonparametric tests. Given that, what would be a more appropriate effect size to show? The effect I am most interested in is the size of the group term (i.e. the one that codes for the mean group difference in Volume, FA, MD, RD, and AD).