Wilcoxon test p value with one decimal place

Dear list,

Let's say I have data

?a=c(37.961,38.214,57.68)
?b=c(77.56,61.875,67.683)

wilcox.test(a,b)

the wilcoxon test only gives me a p value with one decimal place. Is this
normal?

No, it's discrete  :-)

(Actually, that's the answer. Read up on the Mann-Whitney test to see why).

-- Bert

Thanks.

Jun

? ? ? ?[[alternative HTML version deleted]]

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On Thu, Feb 16, 2012 at 10:15 AM, Jun Shen <jun.shen.ut at gmail.com> wrote:

Dear list,

Let's say I have data

_a=c(37.961,38.214,57.68)
_b=c(77.56,61.875,67.683)



the wilcoxon test only gives me a p value with one decimal place. Is this
normal?

No, it's discrete  :-)

(Actually, that's the answer. Read up on the Mann-Whitney test to see why).

-- Bert

Thanks.

Jun

To expand on Bert's reply:

Given two sets of 3 numbers (x,y,z), (X,Y,Z) with x < y < z
and X < Y < Z, there are exactly 20 ways to merge them together
(according to possible relationships between the values in the
first and the second):

  x < y < z < X < Y < Z
  x < y < X < z < Y < Z
  x < y < X < Y < z < Z
  x < y < X < Y < Z < z
  [and so on until]
  X < Y < x < Z < y < z
  X < Y < Z < x < y < z

Your example  is the first of these so has probability 1/20.
Since the default for wilcox.test is "two.sided", the result
takes into account also arrangements which are at least as
extreme as the one given, of which the only case is the last
one in the above list, which also has probability 1/20.

Hence the 2-sided P-value is 1/20 + 1/20 = 1/10, which is
exactly 0.1, as returned by wilcox.test(). It would be possible
to display the result as 0.10000, say, but there is no point!

If you do

  wilcox.test(a,b, alternative="less")

then you will get 0.05 as P-value -- again exactly right.

Ted.

-------------------------------------------------
E-Mail: (Ted Harding) <Ted.Harding at wlandres.net>
Date: 16-Feb-2012  Time: 18:57:08
This message was sent by XFMail

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
project.org] On Behalf Of Jun Shen
Sent: Thursday, February 16, 2012 10:16 AM
To: R-help
Subject: [R] Wilcoxon test p value with one decimal place

Dear list,

Let's say I have data

 a=c(37.961,38.214,57.68)
 b=c(77.56,61.875,67.683)

wilcox.test(a,b)

the wilcoxon test only gives me a p value with one decimal place. Is
this
normal? Thanks.

Jun

Well, it depends on what your p-value is.  If you try

w <- wilcox.test(a,b)
print(w$p.value, digits=20)

you will see that it is a rounding / printing issue


Hope this is helpful,

Dan

Daniel J. Nordlund
Washington State Department of Social and Health Services
Planning, Performance, and Accountability
Research and Data Analysis Division
Olympia, WA 98504-5204