One-sided Wilcoxon signed-rank test using scipy

Question

I would like to perform a one-sided wilcoxon rank test to my paired data, as I'm interested if one sample is significantly greater than the other.

Scipy offers

scipy.stats.wilcoxon(x,y)

to perform a two-sided test with paired samples x and y. Since I can't assume a normal (symmetric) distribution, I can't derive the one-sided p-value from the two-sided p-value.

Does anybody now a python way to get the p-values for a one-sided test?

Thanks!

Answer 1

P value returned by scipy.stats.wilcoxon has nothing to do with the distribution of x or y, nor the difference between them. It is determined by the Wilcoxon test statistic (W as it in http://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test, or T as in scipy), which is assumed to follow a normal distribution. If you check the source (in ~python_directory\site-packages\scipy\stats\morestats.py), you will find the last few lines of def wilcoxon():

se = sqrt(se / 24)
z = (T - mn) / se
prob = 2. * distributions.norm.sf(abs(z))
return T, prob

and:

mn = count*(count + 1.) * 0.25
se = count*(count + 1.) * (2. * count + 1.)

Where count is the number of non-zero difference between x and y.

So, to get one-side p value, you just need prob/2. or 1-prob/2.

Examples: In Python:

>>> y1=[125,115,130,140,140,115,140,125,140,135]
>>> y2=[110,122,125,120,140,124,123,137,135,145]
>>> ss.wilcoxon(y1, y2)
(18.0, 0.5936305914425295)

In R:

> wilcox.test(y1, y2, paired=TRUE, exact=FALSE, correct=FALSE)

        Wilcoxon signed rank test

data:  y1 and y2 
V = 27, p-value = 0.5936
alternative hypothesis: true location shift is not equal to 0 

> wilcox.test(y1, y2, paired=TRUE, exact=FALSE, correct=FALSE, alt='greater')

        Wilcoxon signed rank test

data:  y1 and y2 
V = 27, p-value = 0.2968
alternative hypothesis: true location shift is greater than 0

Answer 2

If you have enough observations (and other hypothesis) , I recall that the scipy Mann-Withney test is one-sided : http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.mannwhitneyu.html