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I have one IV (faculty) and multiple continuous DVs and wanted to do a one-way MANOVA. As MANOVA requires normal-distributed data, I plotted the DVs and saw that they are heavily long-tailed (keep in mind y-axis is already log-scaled): enter image description here

Now, I was reading a lot about possible solutions to this. These include

  • data transformation

I couldn't find any information though on how to transform long-tailed data such that an approximate normal distribution would result.

  • Non-parametric MANOVA

The most common non-parametric test I found is the multivariate Kruskal-Wallis test but there seems to be no implementation in both Python or R to do this. I have also seen some people probably doing this manually but I don't know if this is the same as an MKW: https://stackoverflow.com/questions/70419691/kruskal-wallis-test-for-multiple-comparison-using-python

  • Semi-parametric MANOVA

I found this package during one discussion on researchgate that could be helpful: https://cran.r-project.org/web/packages/MANOVA.RM/MANOVA.RM.pdf

What would you suggest me to do in this situation? I'm a bit overwhelmed with possibilities and don't know what would be best in this situation.

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  • $\begingroup$ If I am understanding this correctly, you want to pool several outcome variables on quite different scales (some measured, some counted) and throw them into some single procedure. That seems quite wrong to me. What is the statistical question you are trying to answer? $\endgroup$
    – Nick Cox
    Commented Aug 24, 2022 at 12:43
  • $\begingroup$ I want to see if there are different characteristics between these variables for the different categories (faculty). Characteristics refers to all the continuous variables. I don't really understand the remark about the different scales, sorry $\endgroup$
    – beld
    Commented Aug 24, 2022 at 12:47
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    $\begingroup$ That goal requires separate analyses for each outcome. You can't lump together variables that aren't measured on the same scale. If you measured lifespan in year or size in GB you would get different numbers and neither would be comparable with anything counted. $\endgroup$
    – Nick Cox
    Commented Aug 24, 2022 at 12:50
  • $\begingroup$ Thanks, that sounds like the best approach then would be to do a kruskal wallis test for each dependent variable and analyze each result separately. It seems that I have misunderstood the purpose of a MANOVA. $\endgroup$
    – beld
    Commented Aug 24, 2022 at 12:59
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    $\begingroup$ You could be interested in stats.stackexchange.com/questions/190156/… $\endgroup$ Commented Aug 27, 2022 at 4:37

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I spent a lot of time on a very similar issue, and the relatively novel Nonparametric Comparison of Multivariate Samples (npmv package in R) seemed to check all the boxes for me.

It also stands up to, what the authors refer to as, "multivariate data which usually involve different, typically dependent characteristics measured in rather different units." See here.

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