No, it is not distribution free. Independent random sampling is assumed.
That is a non-trivial assumption, and one that is very often not true or
not
strictly true.
John Maindonald email: john.maindonald at anu.edu.au<mailto:
john.maindonald at anu.edu.au>
On 21/03/2021, at 00:00, r-help-request at r-project.org<mailto:
r-help-request at r-project.org> wrote:
From: Jiefei Wang <szwjf08 at gmail.com<mailto:szwjf08 at gmail.com>>
Subject: Re: [R] about a p-value < 2.2e-16
Date: 20 March 2021 at 04:41:33 NZDT
To: Spencer Graves <spencer.graves at effectivedefense.org<mailto:
spencer.graves at effectivedefense.org>>
Cc: Bogdan Tanasa <tanasa at gmail.com<mailto:tanasa at gmail.com>>, Vivek Das <
vd4mmind at gmail.com<mailto:vd4mmind at gmail.com>>, r-help <
r-help at r-project.org<mailto:r-help at r-project.org>>
Hi Spencer,
Thanks for your test results, I do not know the answer as I haven't
used wilcox.test for many years. I do not know if it is possible to compute
the exact distribution of the Wilcoxon rank sum statistic, but I think it
is very likely, as the document of `Wilcoxon` says:
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.
As a nice feature of the non-parametric statistic, it is usually
distribution-free so you can pick any distribution you like to compute the
same statistic. I wonder if this is the case, but I might be wrong.
Cheers,
Jiefei
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