
Sorry that I did not answer you earlier, I would like to thank you again 
for your advice and the time you dedicated to my problem.
In my case it was not possible to increase the sample size but I would 
take your advice into account for the next sampling and also for 
presenting these results!
Thanks again, have a nice day!
Best wishes,
Chloé


Le 21/08/2010 16:18, Cedric Laczny [via R] a écrit :
> Glad that I could help :)
> Another thing that came to my mind ist that when you simply look at 
> the values
> of the different groups, they differ quite strongly in my opinion. 
> They are
> between two and three times higher in the second group than the ones 
> from the
> first group. Therefore it would be a good idea to increase your sample 
> sizes
> and see if that trend can be observed further. I know that this is not 
> always
> feasible.
> IMHO statistics are nice and can help to gain insight into various 
> things.
> However, for small sample sizes, talking about "statistical 
> significance" is in
> my opinion always a bit tricky.
> If I had to present such results, I would rather refer to the folds by 
> which
> the data differ, rather than talking about statistics. Because 
> "statistical
> significance" and "relevance" are two different "measures" ;)
>
> Best,
>
> Cedric
>
> On Saturday, 21. August 2010 15:58:50 Chloe wrote:
>
> > Hi Cedric,
> > Thanks a lot for your help, after calculating U value using the formula
> > from wikipedia I also found that the W given by R was in fact the U 
> value
> > that I could directly compared to table of critical value.
> > Your advice were really good and useful. I would also be careful 
> with the
> > conclusions of the test due to the limitations you suggested!
> > Have a nice day,
> > ChloÃ©
> >
> > > Hi Chloe,
> > >
> > > first of all, I want to note, that you should be careful using the
> > > WMW-test.
> > > Even though it is often reported to be some sort of a 
> "swiss-army-knife"
> > > for
> > > comparing two distributions, recent research on this test has 
> revelaed
> > > that it
> > > is crucial what hypotheses you consider. Also the assumptions 
> imposed to
> > > the
> > > test are critical. For the assumptions, the test basically is a 
> test on
> > > identical distributions. For your sample sizes, this is in my opinion
> > > quite
> > > problematic, as you can not really know what the population 
> distributions
> > > look
> > > like. Furthermore, the test has shown to be quite strongly 
> influenced by
> > > differing variances in the two groups. All this is more or less 
> valid for
> > > not
> > > necessarily small sample sizes, therefore I am not sure how much 
> it might
> > > affect your results. Therefore, caution should be adressed to the
> > > interpretation of the results.
> > >
> > > On Friday, 20. August 2010 19:41:55 Chloe wrote:
> > >> Dear all,
> > >> I want to compare the efficiency of 2 methods in extracting proteins
> > >> from
> > >> algal samples. I collected 6 independant algal samples and I 
> extracted 3
> > >> by
> > >> the method 1 and 3 others by the method 2.
> > >> So I have 2 groups of 3 samples, that are not paired. I would 
> like to
> > >> know
> > >> if the results obtained by these 2 methods are significantly 
> different,
> > >> I
> > >> hope method 2 to be more efficient than method 1. As I have few 
> data I
> > >> went
> > >> for the Mann-whitney test:
> > >>
> > >> method1=c(35,40,56)
> > >> method2=c(90,110,115)
> > >> wilcox.test(method1,method2,paired=FALSE,alternative="less")
> > >>
> > >>   Wilcoxon rank sum test
> > >>
> > >> data:  method1 and method2
> > >> W = 0, p-value = 0.05
> > >> alternative hypothesis: true location shift is less than 0
> > >>
> > >> As I have a small number of samples, I would prefer to compare the U
> > >> value
> > >> of the Mann-Whitney test to critical value for table rather than 
> to rely
> > >> on
> > >> the p-value.
> > >>
> > >> Is W value correspond to U value ?
> > >>
> > >> >From the help I understand that W=U+m*(m+1)/2, is this true ?
> > >>
> > >> In the case it is, my U values would be U=W-6=-6!! I thought that 
> a U
> > >> value
> > >> could not be neagtive.
> > >
> > > Im a little bit puzzled on this one... I would agree with you. I 
> can't
> > > really
> > > help you with this one right now, but doing the calculation of U 
> manually
> > > is
> > > not really hard for your problem. All the values from method 2 are 
> higher
> > > than
> > > the ones from method 1. So the ranking would be:
> > >
> > > method1 : 1,2,3
> > > method2: 4,5,6
> > > => W(rank sum)_m,n = 1 + 2 + 3 = 6
> > >
> > > If I use the definition of U from
> > > http://de.wikipedia.org/wiki/Mann-Whitney-U-
> > > Test
> > > I would calculate U = 0 , which goes with your formula: U = W - 6 
> = 6 - 6
> > > = 0,
> > > what makes sense because the values of X are never greater than 
> the ones
> > > of Y.
> > > (s. link: the formula for U with the two summations )
> > >
> > > Thinking of that, the usage of W in R might simply be misleading 
> and it
> > > could
> > > indeed represent U.
> > >
> > >> I would be happy to have any information about how to obtain the 
> U value
> > >> from the Mann-Withney test (wilcox.test()) in order to be able to
> > >> compare
> > >> it with table of critical U value commonly found.
> > >> Thanks a lot for your time and help
> > >> Have a nice day,
> > >> ChloÃÂ©
> > >
> > > For your sample sizes you can nicely use the critical value tables 
> that
> > > can be
> > > found easily on the net.
> > >
> > > I hope I could help with your problem, if not, please feel free to 
> ask
> > > further.
> > >
> > > Best,
> > >
> > > Cedric
> > >
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> > >
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