Re: [R] significant test

From: Peter Dalgaard <>
Date: Tue 01 Nov 2005 - 04:25:08 EST

Prof Brian Ripley <> writes:

> Sorry, no. The Wilcoxon test does NOT test a difference in means: its
> null hypothesis is that the two samples came from the same continuous
> distribution, a much narrower assumption. (It is sensitive to
> differences in variances, for example, and is probably closer to
> testing a difference in medians than means where the shapes of the two
> samples differ)

Actually, it is quite easy to come up with examples where the median is identical but Wilcoxon still comes out significant, most often if the distribution has more than 50% zeros in both groups -- think "functional impairment" or "alcohol consumption on a weekday". The distribution is not continuous in those cases, but wilcox.test deals with the resulting ties. The test statistic is directly related to the sign of the difference between a random observation from each group, i.e. P(X > Y) / P(X != Y) which can be assumed to be 0.5 under the null.

   O__  ---- Peter Dalgaard             ุster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (                  FAX: (+45) 35327907

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Received on Tue Nov 01 04:30:16 2005

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