# ANOVA/Kruskal Wallis on groups with several attributes

I was requested to do an ANOVA test (or a Kruskal Wallis one) on unpaired groups where each subject in a groups has several attributes/features.

For example, I have groups 1,2,3... etc. Where each group $$i$$ has a sample of size $$n_i$$. Each individual/objects in a sample has a fixed amount of attributes. For example, let's say our object is a cell, then it has center of mass, velocity etc. Another example is a patient and their expression level of their genes (the attributes/features are the genes).

A visual explanation:

Now, I wonder what should I do?

Should I average on all the objects in a sample? I.e., $$\sum_{j=1}^{n_i}\frac{x_{ijk}}{n_i}$$ where $$x_{ijk}$$ is the attribute/feature $$k$$ for object $$j$$ in group $$i$$.

Eventually I'll get something like:

group 1: average(attribute1), average(attribute2),...

group 2: average(attribue1), average(attribute2),...

Should I then do ANOVA? By averaging I feel like I'm missing something.

Another approach is to do an ANOVA analysis (or Kruskal Wallis) for each attribute (i.e. no averaging, just doing ANOVA analysis k times for k features).

Is there a statistics test I am not aware of?

The only thing that I found is this post: https://www.researchgate.net/post/How_to_compare_two_groups_with_multiple_measurements but alas no good answer.

Edit: Wait, should I use MANOVA? Just found about it.