This is a follow up question to "How do I test if two non-normal distributions differ?
I have 13 distributions, . According to the previous question, I should do the following.
- Kruskal-Wallis test with 13 samples.
- Mann-Whitney U pairwise.
I found that all p-values are practically 0. At first, this did not seem right. For example, distributions A and B look very similar. (Subquestion: Should I use
alternative = "greater" in R for example? I would like to roughly argue that D is greater than A.) Now, based on another question, I believe that this is due to the fact that my sample sizes are so large. Based on that same question, it appears that I need to calculate the effect size.
I followed these instructions. I obtained tiny effect sizes, for example, 0.00005. How can I interpret these values? I obtain "tiny" effect sizes even when comparing A and D, which to me, look like very different distributions.
@whuber's comment, I would like to state that D > L > K > J > ... > [A,B,C]. In other words, that those in D are generally larger than those in L. In the case of A,B,C, I would have to say that there is no significant difference. But again, I would like to an argument based on statistics not just visual observation.