# [R] Wilcoxon nonparametric p-values

Peter Dalgaard p.dalgaard at biostat.ku.dk
Tue May 19 16:33:05 CEST 2009

```Charles Van deZande wrote:
> Thanks Peter,
> There are 8 measurements less than 8.5, so calculating the probability
> (binomial)  of 8, or fewer, happening by chance with n = 20 and p = 0.50
> gives P = 0.25-- the book answer.  I've tried several problems in other
> textbooks and in each case I get vastly different P-values than I get
> with wilcox.test or wilcox.exact.

Ah, but that is NOT a signed-rank test, just a sign test. (Using the
former as a test of the median is BTW not really a good idea unless you
assume symmetry of the distribution.)

It is also still a one-sided test, with two tails you get

> binom.test(8,20)

Exact binomial test

data:  8 and 20
number of successes = 8, number of trials = 20, p-value = 0.5034
alternative hypothesis: true probability of success is not equal to 0.5
95 percent confidence interval:
0.1911901 0.6394574
sample estimates:
probability of success
0.4

(and that is disregarding that one observation is exactly 8.5, so you
should really look at 7 in 19 rather than 8 in 20.)

> However, upon further testing, I've found good agreement when the
> calculated P-values are small, but disagreement when P-values are
> large.  This might mean a problem with wilcox.test and wilcox.exact when
> P-values are large or I might be misinterpreting something.

You need to read some more theory.

The extreme cases (all signs equal) are equally unlikely for the sign
test and the signed-rank test.

> CHV
>  ﻿ ﻿
> Charles H Van deZande
> /-------Original Message-------/
>
> /*From:*/ Peter Dalgaard <mailto:p.dalgaard at biostat.ku.dk>
> /*Date:*/ 5/19/2009 5:35:07 AM
> /*To:*/ cvandy <mailto:cvandy26 at gmail.com>
> /*Cc:*/ r-help at r-project.org <mailto:r-help at r-project.org>
> /*Subject:*/ Re: [R] Wilcoxon nonparametric p-values
>
> cvandy wrote:
>  > When I use wilcox.test, I get vastly different p-values than the problems
>  > from Statistics textbooks.
>  > For example:
>  > The following problem comes from "Applied Statistics and Probability for
>  > Engineers", 2nd Edition, by D. C. Montgomery.  Page736, problem
> 14.7.  The
>  > problem is to compare the sample data with a population median of
> 8.5.  The
>  > book answer is p = 0.25, wilcox.test answer is p = 0.573.
>  > I've tried several other similar problems with similar results.  I've
> copied
>  > the following directly from my workspace.
>
> wilcox.exact (from exactRankTests) gives
>
>   > wilcox.exact(x - 8.5)
>
>   Exact Wilcoxon signed rank test
>
> data:  x - 8.5
> V = 80.5, p-value = 0.5748
>
> so I'd suspect the textbook. One-sided p-value perhaps? or table
> limitation (as in "p > .25"). If you want to dig deeper, you'll probably
> have to check the computations implied by the text.
>
>  > Thanks for any help,
>  > CHV
>  >> x<-c(8.32,8.05,
>  >>
> 8.93,8.65,8.25,8.46,8.52,8.35,8.36,8.41,8.42,8.30,8.71,8.75,8.6,8.83,8.5,8.38,8.29,8.46)
>  >> wilcox.test(x,y=NULL,mu=8.5)
>  >         Wilcoxon signed rank test with continuity correction
>  >  data:  x
>  > V = 80.5, p-value = 0.573
>  > alternative hypothesis: true location is not equal to 8.5
>  >
>  > Warning messages:
>  > 1: In wilcox.test.default(x, y = NULL, mu = 8.5) :
>  >   cannot compute exact p-value with ties
>  > 2: In wilcox.test.default(x, y = NULL, mu = 8.5) :
>  >   cannot compute exact p-value with zeroes
>  > ﻿ ﻿
>  > Charles H Van deZande
>  >
>  >
>  >
>  >
>  >
>  >  ﻿
>
>
> --
>     O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
>    c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
>   (*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45) 35327918
> ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk
> <mailto:p.dalgaard at biostat.ku.dk>)              FAX: (+45) 35327907
>
>

--
O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
(*) \(*) -- University of Copenhagen   Denmark      Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)              FAX: (+45) 35327907

```