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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: enter image description here

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.

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You don't want to do the averaging approach.

MANOVA might be an appropriate path. Or conducting anovas on each of the attributes separately.

If you conduct several anovas, you should acquaint yourself with the problem of multiple testing. That is, if you conduct several hypothesis tests, the chances of a false positive result increase above the nominal alpha level (e.g. 0.05). In response to this, you may want to adjust the resulting p values for false discovery rate or familywise error rate. Or you might just accept that you might get a false positive for some attributes, and live with it. It really depends upon the objectives of the analysis.

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