Just as there are cases of nonparametric ANOVA there should be nonparametric MANOVA as natural extensions of MANOVA.

Probably your best bet for a nonparametric-type manova is a permutation or randomization approach. And the key is finding an appropriate software implementation.

In R, there is a package nmpv. I haven't used it, but it is specifically written for nonparametric manova by permutation and randomization.

The coin package in R is commonly used and well respected. It conducts permutation and resampling tests. The independence_test function can have multiple dependent variables.

If the five measures all measure the same thing, why don't you map them onto the underlying construct using, say, item response theory or structural equation modelling.

If they measure different aspects of sexism, then a MANOVA will test a hypothesis too vague to do justice to the data, and risk missing differential effects.

Tobias,

This is the first lecture I have found on the subject and I see it is appropriate to answer your question:

Article Nonparametric MANOVA approaches for non-normal multivariate ...

Thank you very much for your answers!

Not sure right now, but take a look at PerMANOVA assumptions as they are different and I recall that they do not require normality

Hi, Tobias,

Here is a non-parametric alternative to MANOVA. The analysis demonstrated in the article linked below identifies the most accurate solution, has no distributional assumptions, and conducts a variety of cross-generalizability analyses.

• https://odajournal.com/2016/11/11/novometric-analysis-vs-manova-mmpi-codetype-gender-setting-and-the-macandrew-alcoholism-scale