# Is there a nonparametric equivalent of Tukey HSD?

I am using JMP to examine differences in vegetation cover in growth form groups (trees, shrubs, forbs, etc.) before and after three treatments with a control. My sample size is small (n=5) and most of my distributions are not normally distributed.

For the normal distributions I used ANOVA to analyze the differences (percent change) between the results of treatments, then used the Tukey HSD to test the significance of differences between pairs of results.

For the non-normally distributed data I used the Wilcoxon/Kruskal-Wallis test. Is there a nonparametric equivalent of Tukey HSD, that I can use to examine the differences between these pairs of results?

I did a little google research because I found the question quite interesting, these tests have been mentioned:

• Nemenyi-Damico-Wolfe-Dunn test (link, there is an r-package for doing the test)
• Dwass-Steel-Chritchlow-Fligner (link, Conover WJ, Practical Nonparametric Statistics (3rd edition). Wiley 1999.
• Conover-Inman test (link, same as above)

I didn't know any of these and I don't know if any of these is available in JMP. If not: There are people doing a standard anova but simply replacing the dependent values by their ranks. Then you could use Tukey's HSD again.

• Just a heads up that the ukph link is dead, some info on dwass-steel can be found here. Mar 1, 2020 at 18:17

There is kruskalmc function in pgirmess package in R. Description of the test:

Multiple comparison test between treatments or treatments versus control after Kruskal-Wallis test.

If you want to test for an effect using many Wilcoxon statistics, You can go about by calculating the range of your statistics, and then simulating the distribution of the range under the "all effect are null" hypothesis. I do not think you will find tables for the distribution of the range of sample from a Wilcoxon distribution.

JMP does Steel-Dwass comparisons. Use 'Fit Y by X' then on the 'Oneway Analysis of ...' menu choose 'Nonparametric' -> 'Nonparametric Multiple Comparisons' -> 'Steel-Dwass All Pairs'