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Topic: two-sample nonparametric test on quantiles
Replies: 8   Last Post: Feb 3, 2013 12:50 AM

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Richard Ulrich

Posts: 2,860
Registered: 12/13/04
Re: two-sample nonparametric test on quantiles
Posted: Jan 31, 2013 5:30 PM
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On Thu, 31 Jan 2013 00:50:03 -0800 (PST), "Mickey M."
<cz3728@gmail.com> wrote:

>Yes,
>the point was, that the weaker null hypothesis
>H0: P(X>Y) = 0.5 was satisfies for both A and B.
>but the distributions U1 for A and B were different.
>
>This casts some doubt on what is written on e.g. wikipedia:
>
>http://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U
>
>"If one is only interested in stochastic ordering of the two populations (i.e., the concordance probability P(Y > X)), the U test can be used even if the shapes of the distributions are different."
>
>But here is still some chance, that the test can be used "approximately"
>even though the exact distribution of U1 is different than under standard
>null hypothesis (equality of distributions of Xi and Yi).


Yes. Wikip seems to overstate.

By the way -- for years I have been somewhat disparaging
towards rank tests. Now it turns out that I underestimated
how bad they could be.


... <snip, previous, examples>

--
Rich Ulrich




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