# non-parametric post-hoc tests

#### JennJoy

##### New Member
Hi,
Does anyone know what the proper non-parametric post-hoc test to use with multiple groups? (3, 4, 5). We have run the Kruskal-Wallis anova so far, and need to do some post-hoc testing.
Thanks

#### TheEcologist

##### Global Moderator
This is not so easy

Hi,
Does anyone know what the proper non-parametric post-hoc test to use with multiple groups? (3, 4, 5). We have run the Kruskal-Wallis anova so far, and need to do some post-hoc testing.
Thanks
Seeing as opinions vary amongst statisticians about good ways to conduct a post-hoc tests on non-parametric data and of course it depend on the nature of your data this question is not answered easily but here are a few options;

A) Use Man-Whitney/ Wilcoxen tests with a Bonferoni correction (if the # ofgroups are not too big your fine). http://en.wikipedia.org/wiki/Bonferroni_correction
B) Use randomization techniques like the bootstrap to calculate confidence limits for the groups
C) Because it logically also depends on your data, you should try reading up on your options cause there are quite a few. for instance if you have unequal variances Tamhane's T2 is a good one. A place to start reading: http://www.jstor.org/pss/1164855, a journal article on the subject.

OR

(I wonder if he might supply us a digital copy)

#### Dragan

##### Super Moderator
Hi,
Does anyone know what the proper non-parametric post-hoc test to use with multiple groups? (3, 4, 5). We have run the Kruskal-Wallis anova so far, and need to do some post-hoc testing.
Thanks

A test that you can use is:

| RBari - RBarj | >= Z*Sqrt[ (N*(N+1)/12)*(1/ni + 1/nj) ]

where RBari, RBarj, ni, nj are the mean of the ranks and the sample sizes associated with the i-th and j-th groups. N is the total sample size and Z is the critical value from the standard normal curve.

To control for familywise error you would select the critical value as follows:

Z = 2.395 for k=3 groups and where alpha=0.05/(k*(k -1)) = 0.0083333.

#### JohnM

##### TS Contributor
Jenn,

There are several nonparametric post-hocs you can run, analogous to the parametric versions you would run after a 1-way ANOVA.

Mann-Whitney U Test (similar to t-tests) --> lower Type II error, but potentially high Type I error

Nemenyi Test (similar to Tukey) --> "middle of the road" in terms of Type I and II error risk, but sort of weak on power

and a nonparametric version of Bonferroni-Dunn --> overly conservative on Type I error, so it is very weak power

I would go with doing Mann-Whitney U tests.....

#### Dragan

##### Super Moderator
Jenn,

I would go with doing Mann-Whitney U tests.....

John: You can't control familywise error by running a series of tests --if that's what you're implying.

Mkay.

#### JohnM

##### TS Contributor
Not implying anything - just presenting a set of alternatives. In my opinion, however, avoidance of Type I error is a bit over-blown, but I tend to be more liberal.

#### JoyceMarie4ecology

##### New Member
A test that you can use is:

| RBari - RBarj | >= Z*Sqrt[ (N*(N+1)/12)*(1/ni + 1/nj) ]

where RBari, RBarj, ni, nj are the mean of the ranks and the sample sizes associated with the i-th and j-th groups. N is the total sample size and Z is the critical value from the standard normal curve.

To control for familywise error you would select the critical value as follows:

Z = 2.395 for k=3 groups and where alpha=0.05/(k*(k -1)) = 0.0083333.
Dragan - I would like to use this formula for some work I plan to publish. How should I cite it?

#### Dragan

##### Super Moderator
Dragan - I would like to use this formula for some work I plan to publish. How should I cite it?

You can cite:

Siegal, S., & Castellan, N. J. (1988). Nonparametric tests for the behavioral sciences. McGraw-Hill College: ISBN 13: 9780070573574

I don't remember the exact page numbers...but the test you're referring to is in this book and thus, you can look it up if need be.