I have a series of continuous measurements that are not normally distributed (multivariate Shapiro-Wilk test p-value = 0.003818, Anderson-Darling test p-value = 0.0178 or lower for each variable) that are then stratified by several other ordinal data (such as: death Y/N, sex M/F, fever Y/N).
I understand that multivariate analysis can be done only with normally distributed data. The question is: are there not-normal alternatives? As there is the Mann–Whitney U test for the t-test, is there a non-parametric MANOVA?
Alternatively, what would be the procedure to analyze not normally distributed data?
The Kruskal-Wallis test can be used. It is the equivalent of MANOVA in non-parametric tests.