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From |
"Nick Cox" <[email protected]> |

To |
<[email protected]> |

Subject |
RE: st: Mann-whitney U test |

Date |
Sun, 23 Jan 2005 15:46:09 -0000 |

In addition to Roger's routines and remarks, note that the -ranksum- command has a fairly recently added option, -porder-. To underline the view that measuring the magnitude of something is often much more interesting and useful than testing a null hypothesis, I would argue for making it part of the default output. Nick [email protected] Roger Newson > At 01:25 23/01/2005, Ricardo wrote: > >Thank Roger. I am familiar with this program and I > >have used it before. So the test really test both > >hypotheses: that the difference between the median is > >zero, and that the degree of non-overlap of the two > >populations is zero. i.e. whether the degree of > >overlap between the two populations is significantly > >different than would be expected by chance alone. Is > >this correct? > > No and yes. The Wilcoxon ranksum test does indeed test the > hypopthesis that > Somers' D is zero, where Somers' D is the difference between 2 > probabilities, namely the probability that a randomly-chosen > member of > Subpopulation A has a higher outcome value than a > randomly-chosen member of > Subpopulation B and the probability that a randomly-chosen member of > Subpopulation B has a higher outcome value than a > randomly-chosen member of > Subpopulation A. If these 2 probabilities are equal, then you > can argue > that (in Ricardo's words) "the degree of non-overlap of the > two populations > is zero". However, the Hodges-Lehmann median difference is > not always the > difference between the 2 subpopulation medians. The > Hodges-Lehmann median > difference is the median difference between 2 outcome values, > assuming that > the first is sampled at random from Subpopulation A and the second is > sampled at random from Subpopulation B. > > If the 2 sub-population distributions are different only in > location, then > the Hodges-Lehmann median difference is indeed the difference > between the 2 > subpopulation medians, because then the difference between 2 > outcome values > sampled independently from the 2 subpopulations is distributed > symmetrically around the location difference, and the median > difference is > the mean difference, which is the difference between means, > which is the > difference between medians. However, the 2 subpopulations may > differ in > ways other than location, and then the difference between the > 2 medians may > be different from the Hodges-Lehmann median difference. I > often get queries > from users of my program -cendif- (part of the -somersd- > package) asking > why, in their data, the Hodges-Lehmann median difference is not the > difference between the 2 medians. > * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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