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Re: st: RE: RE: median equality test for non normal variables

 From Ronan Conroy To "statalist@hsphsun2.harvard.edu" Subject Re: st: RE: RE: median equality test for non normal variables Date Wed, 26 May 2010 13:57:39 +0100

```On 25 Beal 2010, at 17:04, Feiveson, Alan H. (JSC-SK311) wrote:

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Isn't it true that the Wilcoxon rank sum test is designed only for possibilities of one distribution being a translation of the other?
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I don't think that this consideration was built into the design, but clearly if the two distributions are or markedly different shapes (as in the artificial example I gave) then a single statistic will not capture the difference between the two groups which exists in two dimensions: location and shape.
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I think that the underlying null hypothesis of the Wilcoxon is actually one of considerable practical interest: that the probability that a random observation from one group will be greater than or equal to a random observation from the other group is 0.5.
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This hypothesis underlies comparisons of treatment effectiveness, for example. Note that it does not specify scale units, simply probabilities. This is a great advantage when we are measuring outcomes using scales which do not map onto real life measures of effect size, such as depression scales or pain scales.
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Of course, if your data are measured on a scale with real life units (blood pressure, money) then you are better off calculating the Hodges Lehmann median difference, which gives a more meaningful measure of effect size.
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Ronan Conroy
=================================

rconroy@rcsi.ie
Royal College of Surgeons in Ireland
Epidemiology Department,
Beaux Lane House, Dublin 2, Ireland
+353 (0)1 402 2431
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+353 (0)1 402 2764 (Fax - remember them?)

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