From Torsten.Hothorn at rzmail.uni-erlangen.de  Thu Sep 18 10:03:57 2003
From: Torsten.Hothorn at rzmail.uni-erlangen.de (Torsten Hothorn)
Date: Thu Sep 18 09:03:43 2003
Subject: [Rd] dwilcox (PR#4212)
In-Reply-To: <200309172320.h8HNKJJH008077@pubhealth.ku.dk>
References: <200309172320.h8HNKJJH008077@pubhealth.ku.dk>
Message-ID: <Pine.LNX.4.51.0309180853230.10766@artemis.imbe.med.uni-erlangen.de>


> Full_Name: Mark J. Lamias
> Version: 1.7.0
> OS: Windows 2000 Pro
> Submission from: (NULL) (65.222.84.72)
>
>
> I am running the qwilcox procedure and it is producing incorrect results.  For
> example, dwilcox(.025, 3, 5)

not really:

R> dwilcox(.025, 3, 5)
[1] 0

which is natural since the statistic can take integer values only.

> should equal 6, but it is equal to 1.  Similarly,
> dwilcox(.025, 3, 6) should equal 7, but it equals 2.  The critical values are
> not set being returned with the correct values.  I've verified this with a
> program that performs direct enumeration to determine the appropriate critical
> values for .05 (two- tail):
>
> n1 n2 n crtical_value
> 3 5 8 6


I think you failed to notice what `?qwilcox' tries to tell you:

     This distribution is obtained as follows.  Let 'x' and 'y' be two
     random, independent samples of size 'm' and 'n'. Then the Wilcoxon
     rank sum statistic is the number of all pairs '(x[i], y[j])' for
     which 'y[j]' is not greater than 'x[i]'.  This statistic takes
     values between '0' and 'm * n', and its mean and variance are 'm *
     n / 2' and 'm * n * (m + n + 1) / 12', respectively.

Moreover, it is documented that `probabilities are P[X <= x]' and
therefore

R> qwilcox(.025, 3, 5) + 3*4/2
[1] 7

means "the smallest x with P(W <= x) => 0.025 is 7" which you can check
easily

R> pwilcox(7 - 3*4/2, 3, 5)
[1] 0.03571429

whereas following your calculations

R> pwilcox(6 - 3*4/2, 3, 5)
[1] 0.01785714

Best,

Torsten

> 3 6 9 7
> 3 7 10 7
> 3 8 11 8
> 3 9 12 8
> 3 10 13 9
> 3 11 14 9
> 3 12 15 10
> 3 13 16 10
> 3 14 17 11
> 3 15 18 11
> 3 16 19 12
> 3 17 20 12
> 3 18 21 13
> 3 19 22 13
> 3 20 23 14
> 3 21 24 14
> 3 22 25 15
> 3 23 26 15
> 3 24 27 16
> 3 25 28 16
> 3 26 29 17
> 3 27 30 17
> 3 28 31 18
> 3 29 32 19
> 3 30 33 19
> 4 4 8 10
> 4 5 9 11
> 4 6 10 12
> 4 7 11 13
> 4 8 12 14
> 4 9 13 14
> 4 10 14 15
> 4 11 15 16
> 4 12 16 17
> 4 13 17 18
> 4 14 18 19
> 4 15 19 20
> 4 16 20 21
> 4 17 21 21
> 4 18 22 22
> 4 19 23 23
> 4 20 24 24
> 4 21 25 25
> 4 22 26 26
> 4 23 27 27
> 4 24 28 27
> 4 25 29 28
> 4 26 30 29
> 4 27 31 30
> 4 28 32 31
> 4 29 33 32
> 4 30 34 33
> 5 5 10 17
> 5 6 11 18
> 5 7 12 20
> 5 8 13 21
> 5 9 14 22
>
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>
>


[Rd] dwilcox (PR#4212)
Torsten Hothorn