Re: R-help Digest, Vol 217, Issue 20

[John Maindonald]

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: [hidden email]<mailto:[hidden email]>


On 21/03/2021, at 00:00, [hidden email]<mailto:[hidden email]> wrote:

From: Jiefei Wang <[hidden email]<mailto:[hidden email]>>
Subject: Re: [R] about a p-value < 2.2e-16
Date: 20 March 2021 at 04:41:33 NZDT
To: Spencer Graves <[hidden email]<mailto:[hidden email]>>
Cc: Bogdan Tanasa <[hidden email]<mailto:[hidden email]>>, Vivek Das <[hidden email]<mailto:[hidden email]>>, r-help <[hidden email]<mailto:[hidden email]>>


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



        [[alternative HTML version deleted]]

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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
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[Bert Gunter-2]

... or a George Box (I believe) said: The crucial "Declaration of
Independence."


Bert Gunter

"The trouble with having an open mind is that people keep coming along and
sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )


On Sat, Mar 20, 2021 at 4:25 PM John Maindonald <[hidden email]>
wrote:

> 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: [hidden email]<mailto:
> [hidden email]>
>
>
> On 21/03/2021, at 00:00, [hidden email]<mailto:
> [hidden email]> wrote:
>
> From: Jiefei Wang <[hidden email]<mailto:[hidden email]>>
> Subject: Re: [R] about a p-value < 2.2e-16
> Date: 20 March 2021 at 04:41:33 NZDT
> To: Spencer Graves <[hidden email]<mailto:
> [hidden email]>>
> Cc: Bogdan Tanasa <[hidden email]<mailto:[hidden email]>>, Vivek Das <
> [hidden email]<mailto:[hidden email]>>, r-help <
> [hidden email]<mailto:[hidden email]>>
>
>
> 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
>
>
>
>         [[alternative HTML version deleted]]
>
> ______________________________________________
> [hidden email] mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

        [[alternative HTML version deleted]]

______________________________________________
[hidden email] mailing list -- To UNSUBSCRIBE and more, see
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.