[R] U value from wilcox.test

[Cedric Laczny]

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,
> Chloé
> 
> > 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,
> >> Chloé
> > 
> > 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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