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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: RE: RE: median equality test for non normal variables |

Date |
Wed, 26 May 2010 15:52:57 +0100 |

Stretching the point a bit wider, it's striking to note how simple fallacies about descriptive statistics persist. Thus in the last week I've come across two texts from reputable publishers including statements of the form "mean, median and mode coincide in unimodal (*) symmetric distributions but not otherwise". 0, 0, 1, 1, 1, 1, 3 : mean, median, mode all 1. Binomial(10, 0.1): same story. (0 .. 10)' , binomial(10, (0 .. 10)', 0.1) 1 2 +-----------------------------+ 1 | 0 .3486784401 | 2 | 1 .7360989291 | 3 | 2 .9298091736 | 4 | 3 .9872048016 | 5 | 4 .9983650626 | 6 | 5 .9998530974 | 7 | 6 .9999908784 | 8 | 7 .9999996264 | 9 | 8 .9999999909 | 10 | 9 .9999999999 | 11 | 10 1 | +-----------------------------+ * Statements omitting "unimodal" are also common. Nick n.j.cox@durham.ac.uk Ronan Conroy On 25 Beal 2010, at 17:04, Feiveson, Alan H. (JSC-SK311) wrote: > Isn't it true that the Wilcoxon rank sum test is designed only for > possibilities of one distribution being a translation of the other? 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. 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. 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. 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. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: median equality test for non normal variables***From:*amatoallah ouchen <at.ouchen@gmail.com>

**st: RE: median equality test for non normal variables***From:*"Nick Cox" <n.j.cox@durham.ac.uk>

**st: RE: RE: median equality test for non normal variables***From:*"Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>

**Re: st: RE: RE: median equality test for non normal variables***From:*Ronan Conroy <rconroy@rcsi.ie>

**RE: st: RE: RE: median equality test for non normal variables***From:*"Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov>

**Re: st: RE: RE: median equality test for non normal variables***From:*Ronan Conroy <rconroy@rcsi.ie>

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