[R] significant test

[Peter Dalgaard]

Prof Brian Ripley <ripley at stats.ox.ac.uk> 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             Øster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)                  FAX: (+45) 35327907