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I would like to test the significance difference between two groups by multiple numerical non-normal features to determine the p-value. If we want to test this we may use MANOVA because it could handle multiple features, but the features should be normally distributed within the groups. With wilcoxon.test we could test significance with non-normal features, but I am not sure how to use that with multiple features. So I was wondering if anyone knows which test could be suitable to test the significance between groups using multiple non-normal features to determine the p-value?

Quinten
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  • Significance of what? – Dave Feb 10 '23 at 16:53
  • @Dave, Sorry I mean statistical significance difference, so I would like to determine the p-value. – Quinten Feb 10 '23 at 16:54
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    I think what @Dave hints at is the question of what parameter you want to compare between the groups? A MANOVA tests the mean vector, a Mann-Withney-U test tests if one distribution is stochastically greater than the other. What's your research question/goal? – COOLSerdash Feb 10 '23 at 16:57
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    @COOLSerdash, I would like to compare their means values. The problem I face is that the features I have are non-normal distributed within each group. So I am not sure which test could be used in that situation. Do you understand what I mean? Thanks – Quinten Feb 10 '23 at 17:01
  • The normal/non-normal distinction is not as all or none as it sounds. If your sample size is large and non-normality is modest then ordinary ANOVA will work well enough. Also, if the non-normality is of a simple form then a transformation might make it go away. Logarithmic transformation is helpful (and usual) for many types of data, see here: https://stats.stackexchange.com/questions/27951/when-are-log-scales-appropriate – Michael Lew Feb 10 '23 at 20:58

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