Which is the most suitable non-parametric test (and post-hoc)for a heavily umbalanced groups (3, 15 and 11 observations)? I am comparing soil properties among different geological substrates.
I have only 3 observations in one category (karst soils), 15 observations in sedimentary terrains and 11 observations in crystalline terrains. My variables are non-normal, however homocedastic (according to Levene's test). Which would be the most suitable non-parametric and post hoc tests in this situation?
Many thanks

Echoing @Dave, statistical tests are to be avoided in this situation, and in general they fail to answer the "how much effect" question.  Compatibility (aka confidence; credible intervals for a Bayesian analysis) intervals are called for.  These expose the difficulty of the task (i.e., how much you don't know) when N=3 in one of the groups.  You can use the proportional odds model (a generalization of the Kruskal-Wallis test) to get confidence intervals for 3 different odds ratios for the pairwise comparisons.
