# How to understand this output from qiime longitudinal pairwise-differences?

Dear QIIME2 Community,

I have some questions regarding this output file that is provided on the q2-longitudinal Tutorial:

Output file: pairwise-differences.qzv

Could anyone clarify please if my understanding of the results is correct?

• The null hypothesis of the W (wilcoxon signed-rank test) is that there is no difference between the median of the difference of Shannon index values of the microbiome of the babies measured in month 0 and that of the babies measured in month 12 for each group, am I right?

• Following up the above, we can see that the P value for the Cesarean group is 0.094238, so we can say that we fail to reject the null hypothesis for this group, right?

• But the P value for the Vaginal group is 0.000072, so we can reject the null hypothesis and we can conclude that there is a significant difference between the median of the difference of Shannon index values of the microbiome of the babies measured in month 0 and that of the babies measured in month 12 in the Vaginal group. Is this correct?

• So can we say that these babies that were delivered vaginally generally had different microbiome profiles by the time they were 12 month old, compared to their microbiome profiles when they were just born, but itâ€™s not the case with those who were born by Cesarean section?

• The Kruskal Wallis test can only tell us whether there is difference between any of the groups or not, but cannot tell us exactly for which groups (between which groups), am I right?

• The Mann Whitney U test is used here to tell whether the 2 groups are likely to derive from the same population or not. Is this correct?

So, basically, the W test is used to tell the difference within each group (pairwise between samples), the Kruskal Wallis test is used to tell the difference among all groups overall, and the Mann Whitney U test is used to tell the difference between one specific group to another (pairwise between groups)?

Please please please kindly correct me if Iâ€™m wrongâ€¦ Iâ€™ve been looking everywhere to understand this but couldnâ€™t find the exact answersâ€¦ I checked the ECAM study paper too, but it seems that the Shannon values there are showed as plot only (Fig. 2.) and not statistically tested like this?

I would truly appreciate your help.
Thank you very, very, very much!

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Hi @fgara,
Sorry for the delay.

not exactly. The null hypothesis is that there is no difference in the mean ranks of your groups.

correct

correct, with the caveats above (mean rank difference, not median difference)

Yes â€” this test is asking whether each infantâ€™s shannon diversity changed between timepoint 0 and timepoint 12 with the null hypothesis that there is no change. there is a significant change in the vaginal but not the c-section group, showing that shannon diversity experiences a positive increase in vaginally delivered infants over the first 12 months, but not in c-section infants.

yes, almost. Shannon diversity is looking at the richness and evenness of species, so it is related to the overall profile, but â€śdifferent microbiome profilesâ€ť sounds to me more like a change in structure that would be better measured with, e.g., beta-diversity.

Yes. KW has the null hypothesis that all groups have the same median:

Correct:

This paper is a better place to look with regard to q2-longitudinalâ€¦ the ECAM data is only being used as a test dataset here and this specific test is not replicating the original analyses from the ECAM paper:

Good luck!

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