# [R] Wilcoxon Test

Achim Zeileis Achim.Zeileis at uibk.ac.at
Fri Apr 21 14:54:39 CEST 2017

```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

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

```