
Thank you Thomas,

So you think a t-test is more adequate to use in this case ?

Rad


On Sep 19, 2012, at 8:43 PM, Thomas Lumley <tlumley@uw.edu> wrote:

> On Thu, Sep 20, 2012 at 5:46 AM, Mohamed Radhouane Aniba
> <aradwen@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.
>> 
>> The wilcoxon test is giving me a pvalue of 5.139217e-303 of a over b with the alternative "greater". Now if I make a summary on each of them I have the following
>> 
>>> summary(a)
>>     Min.   1st Qu.    Median      Mean   3rd Qu.      Max.
>> 0.0000000 0.0001411 0.0002381 0.0002671 0.0003623 0.0012910
>>> summary(c)
>>     Min.   1st Qu.    Median      Mean   3rd Qu.      Max.
>> 0.0000000 0.0000000 0.0000000 0.0004947 0.0002972 1.0000000
>> 
>> The mean ratio is then around 0.5399031 which naively goes in opposite direction of the wilcoxon test ( I was expecting to find a ratio >> 1)
>> 
> 
> 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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