Which non-parametric statistical test should I use for pairwise comparisons: Mann-Whitney U or paired Wilcoxon signed-rank?

Question

[antonioggsousa]

Hi,

I have calculated several diversity indices from a 16S table, that includes in total more than 30 samples/replicates. Samples were collected across two seasons for each of 3 treatments tested.

I checked normality (through density and Q-Q plots as well as through Shapiro-Wilk’s and Kolmogorov-Smirnov tests) for the several alpha-diversity indices calculated and none of them seemed to follow a normal distribution. Thus, I decided to used non-parametric tests to assess if there was difference between means across seasons and also across seasons for each treatment. If I had more than one factor with more than two levels I used the Kruskal-Wallis test.

However, I get confused when I wanted to test differences between seasons and seasons by treatment (pairwise comparisons, ie, Shannon-diversity in Spring vs. Summer). I know that I could use the Wilcoxon test, but there are two versions, ie, paired Wilcoxon signed-rank test, and unpaired Mann-Whitney U. I understand the difference between them, but I'm not sure which one is more appropriate to our study. We have collected microbial environmental samples in the same place over seasons to study the temporal succession of microbial communities. This is not exactly the same sample as there is a lot of environmental variation and noise, but it is like the same entity being sampled. The place sampled was exactly the same (geographic coordinates). Therefore, it makes sense for me, since our aim is to study the temporal succession of microbial communities in the same place, that we have to use the paired Wilcoxon signed-rank test, but I'm not sure.

Can someone with better background in statistics, help me on this.

Thanks in advance,

António

[antonioggsousa]

Thank you @Alex Reynolds!

Answer 1

[Alex Reynolds]

You might use distance correlation to measure dependence. Distance metrics run from 0 (independence) to 1 (dependence). This should give a quantitative measurement that would bolster choice of testing.

If pairs of samples between treatments appear to show dependence, then you might prefer Wilcoxon signed-rank testing. If independence is shown, then you might prefer Mann-Whitney U testing.