Issues like that in this thread can often be resolved by reading the
help page for the relevant function.
From:
?wilcox.test
Note
The literature is not unanimous about the definitions of the Wilcoxon
rank sum and Mann-Whitney tests. The two most common definitions
correspond to the sum of the ranks of the first sample with the
minimum value subtracted or not: R subtracts and S-PLUS does not,
giving a value which is larger by m(m+1)/2 for a first sample of size
m. (It seems Wilcoxon's original paper used the unadjusted sum of the
ranks but subsequent tables subtracted the minimum.)
R's value can also be computed as the number of all pairs (x[i], y[j])
for which y[j] is not greater than x[i], the most common definition of
the Mann-Whitney test.
====
HTH,
Chuck
On Fri, 20 Aug 2010, Cedric Laczny wrote:
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,
Chlo??
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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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
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Charles C. Berry (858) 534-2098
Dept of Family/Preventive Medicine
E mailto:cbe...@tajo.ucsd.edu UC San Diego
http://famprevmed.ucsd.edu/faculty/cberry/ La Jolla, San Diego 92093-0901
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