Hi,

In Wilcoxon test , we look for medians rather than the means. Ratio of
medians should be more coherent with P value.

On Thu, Sep 20, 2012 at 6:30 PM, Ben Bolker <bbolker@gmail.com> wrote:

> Mohamed Radhouane Aniba <aradwen <at> gmail.com> writes:
>
> >
> >
> > Thank you Thomas,
> >
> > So you think a t-test is more adequate to use in this case ?
> >
> > Rad
>
>   No, because a t-test makes even stronger parametric assumptions.
> You were given more specific advice on stackoverflow
> http://stackoverflow.com/questions/12499687/wilcoxon-test-and-mean-ratios
> If you want to prove that there is *some* difference between the
> distributions, you're done. If you want to test for some specific
> difference, you need to think more about what kind of test you want
> to do.  Permutation tests with various test statistics are a way
> to approach that.
>
>   Ben Bolker
>
>
> >
> > On Sep 19, 2012, at 8:43 PM, Thomas Lumley <tlumley <at> uw.edu> wrote:
> >
> > > On Thu, Sep 20, 2012 at 5:46 AM, Mohamed Radhouane Aniba
> > > <aradwen <at> gmail.com> wrote:
> > >> Hello All,
> > >>
> > >> I am writing to ask your opinion on how to interpret this case. I
> have two
> vectors "a" and "b" that I am trying
> > to compare.
>
>   [snip]
>
> > >
> > > There's nothing conceptually strange about the Wilcoxon test showing a
> > > difference in the opposite direction to the difference in means.  It's
> > > probably easiest to think about this in terms of the Mann-Whitney
> > > version of the same test, which is based on the proportion of pairs of
> > > one observation from each group where the `a' observation is higher.
> > > Your 'c' vector has a lot more zeros, so a randomly chosen observation
> > > from 'c' is likely to be smaller than one from 'a', but the non-zero
> > > observations seem to be larger, so the mean of 'c' is higher.
> > >
> > > The Wilcoxon test probably isn't very useful in a setting like this,
> > > since its results really make sense only under 'stochastic ordering',
> > > where the shift is in the same direction across the whole
> > > distribution.
> > >
> > >  -thomas
> > >
> > > --
> > > Thomas Lumley
> > > Professor of Biostatistics
> > > University of Auckland
>
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-- 
Avinash Barnwal, M.Sc.
Statistics and Informatics
Department of Mathematics
IIT Kharagpur

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