Also, as far as I know just for historical consistency, the test statistic in R 
is the rank sum of the first group MINUS its minimum possible value: W = 110.5 
- sum(1:13) = 19.5

-pd

> On 21 Apr 2017, at 14:54 , Achim Zeileis <achim.zeil...@uibk.ac.at> wrote:
> 
> On Fri, 21 Apr 2017, Tripoli Massimiliano wrote:
> 
>> Dear R users,
>> Why the result of Wilcoxon sum rank test by R is different from sas
>> 
>> https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_npar1way_sect022.htm
>> 
>> The code is next:
>> 
>> sampleA <- c(1.94, 1.94, 2.92, 2.92, 2.92, 2.92, 3.27, 3.27, 3.27, 3.27,
>>       3.7, 3.7, 3.74)
>> 
>> sampleB <- c(3.27, 3.27, 3.27, 3.7, 3.7, 3.74)
>> wilcox.test(A,B,paired = F)
> 
> There are different ways how to compute or approximate the asymptotic or 
> exact conditional distribution of the test statistic:
> 
> SAS reports an asymptotic normal approximation (apparently without continuity 
> correction along with an asymptotic t approximation and the exact conditional 
> distribution.
> 
> Base R's stats::wilcox.test can either report the exact conditional 
> distribution (but only if there are no ties) or the asymptotic normal 
> distribution (with or without continuity correction). In small samples the 
> default is to use the former but a warning is issued when there are ties (as 
> in your case).
> 
> Furthermore, coin::wilcox_test can report either the asymptotic normal 
> distribution (without continuity correction) or the exact conditional 
> distribution (even in the presence of ties).
> 
> Thus:
> 
> ## collect data in data.frame
> d <- data.frame(
>  y = c(sampleA, sampleB),
>  x = factor(rep(0:1, c(length(sampleA), length(sampleB))))
> )
> 
> ## asymptotic normal distribution without continuity correction
> ## (p = 0.0764)
> stats::wilcox.test(y ~ x, data = d, exact = FALSE, correct = FALSE)
> coin::wilcox_test(y ~ x, data = d, distribution = "asymptotic")
> 
> ## exact conditional distribution (p = 0.1054)
> coin::wilcox_test(y ~ x, data = d, distribution = "exact")
> 
> These match SAS's results. The default result of stats::wilcox.test is 
> different as explained by the warning issued.
> 
> hth,
> Z
> 
> ______________________________________________
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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Office: A 4.23
Email: pd....@cbs.dk  Priv: pda...@gmail.com

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