# How to do a stratified nonparametric test?

I'm trying to use the "coin" (conditional inference) package to perform a stratified nonparametric test for difference in distribution (for count data).

I tried a stratified Mann-Whitney-Wilcoxon rank sum test, which I think is called the van Elteren test:

wilcox_test(count ~ factor_of_interest | confounding_factor)


I also tried to do a stratified permutation test:

oneway_test(count ~ factor_of_interest | confounding_factor, distribution=approximate(B=10000))


The problem is I can't find anywhere how the stratified version of these tests are performed, even in theory. Does anyone know? For example, is a p-value calculated for each stratum and then the p-values combined (say, using Fisher's method)?

By the way, the wilcox_test gave the following result:

Asymptotic Wilcoxon-Mann-Whitney Test
data:  count by factor_of_interest
stratified by confounding_factor
Z = 2.1462, p-value = 0.03186
alternative hypothesis: true mu is not equal to 0


Why would a nonparametric test like the Wilcoxon give a Z score?

• With respect to your final (minor) question - the asymptotic distribution of the Wilcoxon test statistic is Normal, and the Z score is calculated on the basis of that asymptotic distribution. – jbowman Sep 26 '17 at 1:04

## 1 Answer

The test in itself is described in the online supplement to https://www.ahajournals.org/doi/suppl/10.1161/CIRCULATIONAHA.106.613638 by well-renowned statisticans Lisa LaVange and Gary Koch. You can download it in a word document.

Hope this is helpful.

/Magnus