Which pairwise comparison tests are best to use after the Kruskal-Wallis test (Dunn, Conover-Iman or Steel-Dwass-Critchlow-Fligner test)? I have 3 sampling sites where I took 3 water samples in each site. I chose to do the Kruskal-Wallis test to find out if there is a significant difference in total nitrogen between the sites. I did not choose ANOVA, because normality and homoscedasticity were not always respected and I have a small sample size.
When, there is a significant difference between the sites, Xlstat offers me the option of using the Dunn, the Conover-Iman and the Steel-Dwass-Critchlow-Fligner test as a pairwise comparison test. Also, I can do the Bonferroni correction with the Dunn and Conover-Iman test. I would like to know which test is the most appropriate for my analysis and why?

Use the generalization of the Wilcoxon-Mann-Whitney-Kruskal-Wallis tests: the proportional odds ordinal logistic model.  Once you fit the model with two indicator independent variables representing 3 groups you can test any pairwise contrasts you want.  Contrasts will be on the log odds scale.  This is all easily done with the R rms package orm and contrast.rms functions.  More details may be found in the Nonparametrics chapter in BBR.
