Confusion about Kruskal-Wallis (pairwise) using qiime 2

[hongwei2017 (hongwei liu)]

Dear all,

I am calculating the differences of alpha diversity between three treatments, with 3 replicates in each. With the H and P values obtained, I am confused by the exactly the same values generated. I attached the results in qzv format below, which I cannot interpret. Does anyone know why? Thank you very much!
observed_otus-group-significance.qzv (355.2 KB)

Cheers
Hongwei

[Nicholas_Bokulich]

Hi @hongwei2017,
I think the H and P values obtained here are expected, due to (1) the large level of differences and (2) small sample size. Kruskal-Wallis H stats are calculated based on the rank of values, so large differences between groups and small sample sizes together will mean that groups are always ranked together (as the first 3 or last 3) in the pairwise tests, leading to the identical H results you see here... see the calculation to see what I mean.

Let me know if that makes sense!

[hongwei2017 (hongwei liu)]

@Nicholas_Bokulich

I think the H and P values obtained here are expected, due to (1) the large level of differences and (2) small sample size. Kruskal-Wallis H stats are calculated based on the rank of values, so large differences between groups and small sample sizes together will mean that groups are always ranked together (as the first 3 or last 3) in the pairwise tests, leading to the identical H results you see here… see the calculation to see what I mean.

Thanks Nicholas! Your explanation makes sense to me. I definitely need to read more about this statistical method.

Cheers
Hongwei