Test to compare difference between median value in two discrete samples

#1
Hi, I have two collection of ordinal samples for a discrete variable related to two administration of an experiment.
Using Kolmogorov-Smirnov, I checked that I can't reject the Ho Hypothesis that the two distribution are the same.
Now I would like to check if the median of these two collection of samples are the same or not, under a statistical point of view.
I can't use 1 way Anova because the variable is discrete, for the same reason I can't use Friedman test.
What test should I use, if I could use Wilcoxon or Mann Whitney U test, could you tell me where I can find the theoretical bases of that?
 

hlsmith

Omega Contributor
#2
Many may use Wilcoxon rank sum test, based on medians.

You will find many articles of people who feel this is acceptable and others who have abhorrence at the idea. Can you tell us more about your data (e.g., distribution, sample sizes, etc). I believe for this test you want the same distributions, just that one is shifted to the left or right by some constant (or at least it appears to be).