In case of MANOVA influencing factors are many. If all these multiple influencing factors can vary independently, it is MANCOVA – e.g. blood pressure, obesity and diabetes; all affecting mutually and samples are multiple from multiple study sites. Kruskal Wallis test is the non-parametric analogue of parametric MANOVA.

Discriminant function analysis is multivariate analysis of variance (MANOVA) reversed.

The non parametric alternative test of manova is the wilcoxon, but in my opinion the pillia's trace test is one of MANOVA tests is used if normality condition is infidelity.

Wilcoxon is the best

Cheers

The Wilcoxon is not equivalent of non-parametric MANOVA.