Statistically comparison between n sets of data which have non Gaussian distribution

Hello, I have three groups of data resulted from a feature extraction. I want to see if the feature I selected has the comparison significance or not. Actually, I want to see if I can use this feature, or this doesn't have any discriminating value, so i n this case to ignore it. For this, I should do the statistics to understand weather there is any relation between groups for this feature or not. The resulted histogram of distributions of each class are as follow:

According to my search these distributions aren't Gaussian and so I use Mann-Whitney test to see if there is a correlation between the groups. There are two values h and p:

h shows to reject the null hypotheses or not (h=1 rejection, h=0 a failure for rejection)

P-value also shows the evidence against the null hypotheses.

My question is first, did I go correct for using this test? Also how should I interpret these values?

The result for instance for the first two groups were as follow:

        p =

        1.5170e-09

        h =

       logical

        1

      stats = 

      struct with fields:

         zval: -6.0425
       ranksum: 1648

Thank you for reading my post.

Answer 1

[Star Strider]

The Mann-Whitney (the ranksum function) is for two-sample comparisons only. If you want to do multiple comparisons, the kruskalwallis (link) or friedman (link) (and multcompare (link)) functions might be more appropriate.

You need to decide, based on your knowledge of your data.

As with everything in statistics, this is not trivial. For a reference, I suggest: Hollander, et al., Nonparametric Statistical Methods, 3e, Section 6.5 (ISBN 978-0-470-38737-5).

[Shaya s]

I see. Actually I would compare each two. I will read those links. Thank you

[Star Strider]

My pleasure.

Doing pairwise comparisons is not an approach I would agree with. If you want to do multiple comparisons with any statistical validity, you have to do simultaneous multiple comparisons.

[Shaya s]

I understand, the pairwise comparison will be less powerful. I should compare the groups all together.

[Star Strider]

Yes, definitely.

There are ‘corrections’ for multiple comparisons for t-tests. I’m not sure if there are any for nonparametric tests.

[Shaya s]

what about kruskal wallis test:

[p,tbl,stats] = kruskalwallis(X);

Actually I used this too but couldn't understand how to interpret it!

[Star Strider]

The stats structure as an argument to the multcompare (link) function will (largely) interpret it for you.

See the documentation for it and the other functions I linked to in this thread for details.

[Shaya s]

Yes I understand, thank you.

[Star Strider]

My pleasure.