Date: Dec 22, 2012 8:11 PM
Author: Gruppa
Subject: kolmogov-smirnov, wilcoxon and kruskal tests

Hi Everybody,

I'm trying to do some hypotheses testing in R and I have problems with interpretation of results.

I have two data sets:
  > x<-c(2,1,1,2,2,3,2,2,1,2,2,4,1,2,4,1,1,5,2,1,4,2,2,1,1,2,2,1)
  > y<-c(2,2,1,1,2,2,1,4,1,4,2,4,4,4,3,2,4,4,3,2,4,5)

according to the KS test they come from the same distribution:
  > ks.test(x,y)

If they come from the same distribution all the characteristics (mean, median, ... ) should be the same.
However,  Wicoxon and Kruskal tests indicate that their null hypothesis should be rejected:
  > wilcox.test(x,y)
  > kruskal.test(list(x,y))

Now, I am puzzled with the outcome of the test.
I can simply imagine a situation when Wilcox and Kruskal tests indicate that their null hypothesis should be accepted but the KS test can indicate that samples comes from different distributions. Here, it is the other way round. Does any one has some hints what causes the problems?

Best,
Gruppo