Scipy Wilcoxon test: rejection direction

Question

One-sided test

Lets say I want to compute one-sided wilcoxon test:

R:

> wilcox.test(B,A, alternative="greater", paired=TRUE, correct=FALSE, exact=FALSE)

    Wilcoxon signed rank test

data:  B and A
V = 28, p-value = 0.00898
alternative hypothesis: true location shift is greater than 0

> 
> wilcox.test(A, B, alternative="greater", paired=TRUE, correct=FALSE, exact=FALSE)

    Wilcoxon signed rank test

data:  A and B
V = 0, p-value = 0.991
alternative hypothesis: true location shift is greater than 0

but if I do it in python (I need to divide the p-value by 2): wilcoxon(B, A) and wilcoxon(A, B) give the same statistics, so there is no way how to identify the direction of rejection.

>>> wilcoxon(A,B)
WilcoxonResult(statistic=0.0, pvalue=0.011412036386001651)
>>> wilcoxon(B,A)
WilcoxonResult(statistic=0.0, pvalue=0.011412036386001651)

Is there any alternatives for one-sided Wilcoxon test in python that will give also the direction of rejection?

EDIT, Old question: (answered by Robin Ryder)

I found some differences in test statistics in python and R and I cannot figure out what is the difference.

Python:

from scipy.stats import wilcoxon
A = [0.19826790, 1.36836629, 1.37950911, 1.46951540, 1.48197798, 0.07532846,1]
B = [10,10,10,10,10,10,10]
wilcoxon(B, A)
WilcoxonResult(statistic=0.0, pvalue=0.017960477526078766)

R:

A = c(0.19826790, 1.36836629, 1.37950911, 1.46951540, 1.48197798, 0.07532846,1)
B = c(10,10,10,10,10,10,10)

wilcox.test(B,A, alternative="two.sided", paired=TRUE, correct=FALSE, exact=FALSE)


    Wilcoxon signed rank test

data:  B and A
V = 28, p-value = 0.01796
alternative hypothesis: true location shift is not equal to 0

The p-values are the same but the test statistics are completely different. I checked the script code for it and it wasn't so clear how to resemble R test statistics and why there eis a difference.

Answer 1

A and B play symmetric roles in the Wilcoxon test. The issue is simply which is specified as sample 1, and which is sample 2.

R will give you the same answer as Python if you switch the order of the two samples:

wilcox.test(A,B, alternative="two.sided", paired=TRUE, correct=FALSE, exact=FALSE)

Wilcoxon signed rank test

data:  A and B
V = 0, p-value = 0.01796
alternative hypothesis: true location shift is not equal to 0

Answer 2

As mentioned here the last few lines of def wilcoxon() (~python_directory\site-packages\scipy\stats\morestats.py) are:

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

Also according to the comments of this post the apropriate one-sided hypotesis can be decided by the sign of T -mn hence the sign of z

So spending some hours searching for a solution, I have not found the better way than writing my own version of one-sided Wilcoxon test. It is basicly the same as def wilcoxon() from ~python_directory\site-packages\scipy\stats\morestats.py, just returning proper p-value for one-sided test.

def wilcoxon(x, y=None, zero_method="wilcox", correction=False, alternative="two-sided"):
    ...
    <code from the morestats.py until return statement>
    ...
    if alternative == "two-sided":
        return WilcoxonResult(T, prob)
    elif alternative == "greater":
        return WilcoxonResult(T, prob/2) if z > 0 else WilcoxonResult(T, 1 - prob/2)
    elif alternative == "less":
        return WilcoxonResult(T, prob/2) if z < 0 else WilcoxonResult(T, 1 - prob/2)
    else:
        raise ValueError("Alternative should be either 'two-sided' "
                         "or 'less' or 'greater'")