[R] U value from wilcox.test

[Cedric Laczny]

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