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?