Kruskal-Wallis, Dunn's Test, Multiple Mann-Whitney-U Test

#1
Hello everyone,

I am studying immue cell distribution in different types of nontomourous (n=66), precancerous (n=67) and malignant tissues (n=48) in a single patient cohort. As you can see in the violin plot attached below, I started out by applying the K-W test to compare the distribution in the 3 groups (normal versus precancerous vs invasive) [p value seen on graph] and now I want to do a pairwise comparisions to find out where the difference actually relies.

if I tried both Dunn's post hoc test and mutliple Mann-Whitney-U tests between the groups, and obviously ended up with different significant results... The results on the graph are those of the pairwise MWU tests...

Is it appropriate to apply multiple MWU tests after K-W in this particular setting? I obviously "planned" to compare the 3 different groups all along, so my p-values weren't really meant to be post hoc...

My supervisor says it's fine to use multiple MWU tests in this case, but I want to have other opinions.

Thank you very much for you help! (and yes, I'm definitely a stat newbie)
 

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obh

Well-Known Member
#2
The Kruskal-Walis with two groups is the same as Mann-Whitney-U (maybe only a different approximation for the result or not)
If you use multiple testing you should consider reducing the significance level.
Yes, it is okay to apply multiple MWU tests after K-W, as you ask a different question ...

PS why not ANOVA, with n=48 usually, the ANOVA test will be good.
 
#3
The Kruskal-Walis with two groups is the same as Mann-Whitney-U (maybe only a different approximation for the result or not)
If you use multiple testing you should consider reducing the significance level.
Yes, it is okay to apply multiple MWU tests after K-W, as you ask a different question ...

PS why not ANOVA, with n=48 usually, the ANOVA test will be good.

Hi obh,

thanks for the fast and helpful reply! I really appreciate it!

As for the ANOVA, I can only state the following, again as a newbie:
-my data isn't normally distributed
-I've never seen parametric tests being applied when it comes to immue cell distribution in tissue
-the group has already published a similar study (n=375!) using K-W and MWU and it work out fine...

Thanks again! :)
 

obh

Well-Known Member
#4
Hi AC,

I don't have the knowledge about the distribution of the immune cells ...
The one way ANOVA considered to be robust to the deviation from the normality assumption
I would try to draw the histogram of the data, and if it is reasonably symmetrical I would use the ANOVA.

You may use the KW on normal data and the results will be correct, but the test's power will be a bit weaker.
So a border insignificance result might be significant in the ANOVA.

The fact that somebody did something in statistics doesn't always say it is correct...
 
#5
Thank you so much for the input, I will bring this point out to the group.

If I may ask another question:

I did out of curiosity the "two-stage linear step-up procedure of Benjamini, Krieger and Yekutieli" multiple comparison test for false discovery rate after the K-W and found out that the p-values are in the same range as those generated with the multiple pairwise MWUs. Is it appropriate to use this test in this setting to compare the pairwise distribution in these 3 groups?

Thanks!