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If you fail on the assumptions, PERMANOVA could be an option:
https://www.youtube.com/watch?v=v7u8lHgoWig
In this video, we will have a look at the multivariate analysis of variance (MANOVA). The video starts with a comparison with ANOVA and points out the differences between ANOVA and MANOVA. Then (02:10) we will see how MANOVA can be applied on a simple example, its assumptions (04:40), and the math behind MANOVA (07:40).