# KS Test and Wilcoxon Rank Sum Test, large differences in p values

I am relatively new to non-parametric tests. I wrote the following R code to test 2 sample tests using the KS test and the Wilcoxon Rank Sum test. Drawing 2 samples of various sizes from unit Normal and checking p values under both tests. I see a rather large variation in p-values and no convergence as sample size increases.

The R code I used is as follows:

    results<-data.frame(Picks=numeric(), NoTie1=numeric(), NoTie2=numeric(),  intersect=numeric(), ks.stat=numeric(), ks.pval=numeric(), wx.stat=numeric(), wx.pval=numeric(), pval.diff=numeric())
for(i in (1:100)) {
aa<-round(rnorm(i*10),4)
bb<-round(rnorm(i*10),4)
cc<-intersect(aa,bb)
aa<-setdiff(aa,cc)
bb<-setdiff(bb,cc)
intersect(aa,bb)
kst<-ks.test(aa,bb,alternative="t")
wxt<-wilcox.test(aa,bb,alternative="t")
results[i,]<-list(i*10,length(aa), length(bb), length(cc), kst$statistic, kst$p.value, wxt$statistic, wxt$p.value,round(abs(kst$p.value-wxt$p.value),2))
}


Besides this, although I draw a sample from the unit normal, p-values don't seem to converge as sample size increases.

• Welcome to Cross Validated! I've formatted the code for readability, but it still needs some commenting to explain what you're doing (not everyone speaks R) & why - in particular the rounding of the simulated observation followed by removal of ties across the two samples doesn't have any obvious motivation. It would also help to show the results & clearly explain how they differ from what you expected, as well as why you expected what you expected. – Scortchi May 31 '15 at 11:12
• I rounded for readability. I did run the code without rounding and so no difference. Removed ties since for ks.test an wilcox.test expect no ties. I expected the diff in the p-values of the tests to be larger with small sample sizes and converge to the same value with larger sample size, but didn't see that. – jay May 31 '15 at 23:56
• You introduced ties by rounding - if you want to display results to a different precision use the digits argument to the print function. – Scortchi Jun 1 '15 at 8:43