Hi Roger,
I sent Margaret a real example, it is in my textbook An Introduction to
Medical Statistics.
Martin
On 18 September 2018 at 17:45, Newson, Roger B <[log in to unmask]>
wrote:
> What Margaret seems to be looking for is something that illustrates the
> difference between a median pairwise difference (which is zero under the
> null hypothesis tested by the Mann-Whitney U-test) and a difference between
> medians (which is equal to the median pairwise difference for some pairs of
> distributions but not others). A counterexample might be comparing 2
> exponential (or shifted exponential) subpopulations. See Newson (2008),
> downloadable from my website, for the mathematical details.
>
> For more about the detailed maths of computing confidence intervals for
> median differences, differences between medians and other parameters behind
> "nonparametric" statistics, Margaret might like to check out Newson (2017),
> also downloadable from my website.
>
> These documents (and a few more) are part of my repository of
> miscellaneous unrefereed mathematical jottings at
>
> http://rogernewsonresources.org.uk/papers.htm#miscellaneous_documents
>
> I hope this helps.
>
> Best wishes
>
> Roger
>
> References
>
> Newson RB. Hodges–Lehmann median differences between exponential
> subpopulations. Uploaded 12 October, 2008. Download from
> http://rogernewsonresources.org.uk/miscdocs/mdexp1.pdf
>
> Newson RB. Asymptotic distributions of two–sample rank statistics for
> continuous outcomes. Uploaded 27 April, 2017. Download from
> http://rogernewsonresources.org.uk/miscdocs/asy2con1.pdf
>
> -------- Forwarded Message --------
> Subject: Re: Mann-Whitney U-test illustrations for special case
> only, please
> Date: Tue, 18 Sep 2018 15:40:09 +0000
> From: Robert Newcombe <[log in to unmask]>
> Reply-To: Robert Newcombe <[log in to unmask]>
> To: [log in to unmask]
>
>
>
> It's best to think of this in ROC terms. The ROC curve has to pass through
> (0, 0) and (1, 1) anyway. Identical medians implies it also passes through
> (0.5, 0.5). But, although constrained by these 3 points, one or both halves
> of the curve must lie substantially above the main diagonal. It is quite
> possible to construcy sets of numbers that satisfy this constraint. But I
> think it would be difficult to find a convincing real example in which such
> a departure from H0 would be plausible.
>
> Robert Newcombe
> Cardiff
>
>
> -----Original Message-----
> From: A UK-based worldwide e-mail broadcast system mailing list [mailto:
> [log in to unmask]] On Behalf Of MACDOUGALL Margaret
> Sent: 29 August 2018 21:34
> To: [log in to unmask]
> Subject: Mann-Whitney U-test illustrations for special case only, please
>
> Hello
>
> I am in search of good illustrations for teaching purposes where for two
> groups, the medians are identical but when the two groups are compared
> using the Mann-Whitney U-test, there is a significant difference between
> these groups.
>
> Thanks in advance
>
> Best wishes
> Margaret
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> Dr Margaret MacDougall
> Medical Statistician and Researcher in Education (Senior Lecturer) Centre
> for Population Health Sciences The Usher Institute of Population Health
> Sciences and Informatics University of Edinburgh Medical Shool Teviot Place
> Edinburgh EH8 9AG
> Tel: +44(0)131 650 3211
> Fax: +44(0)131 650 6909
> Email: [log in to unmask]<mailto:[log in to unmask]>
> https://www.ed.ac.uk/profile/margaret-macdougall
>
>
>
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--
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