How to test the distribution of (site frequency spectrum) SFS?

Question

[wang.yiguan]

I have the SFS of synonymous sties and non-synonymous sites. It seems more non-synonymous sites are located at low frequency spectrum, which might indicate purifying selection. But how can I test the difference of the two distributions. I noticed some papers using Mann-Whitney U Test. But I am questioning of the application. For example,

x <- c(1,3,5,7,9)

z <- c(9,7,5,3,1)

x and z are clearly different distributions, but the U test gives:

wilcox.test(x,z)

Wilcoxon rank sum test with continuity correction

data: x and z

W = 12.5, p-value = 1

alternative hypothesis: true location shift is not equal to 0

p = 1, no difference! Where is the problem?

Thanks!

[WangYinan]

Hi! Would Kolmogorov-Smirnov test be helpful? I'm facing the same problem, and wandering if I could know your suggestion about this problem. Thanks a lot!