On Jun 24, 2010, at 6:09 PM, Joris Meys wrote:
I do agree that one should not trust solely on sources like wikipedia
and graphpad, although they contain a lot of valuable information.
This said, it is not too difficult to illustrate why, in the case of
the one-sample signed rank test,
That is a key point. I was assuming that you were using the paired
sample version of the WSRT and I may have been misleading the OP. For
the one-sample situation, the assumption of symmetry is needed but for
the paired sampling version of the test, the location shift becomes
the tested hypothesis, and no assumptions about the form of the
hypothesis are made except that they be the same. Any consideration of
median or mean (which will be the same in the case of symmetric
distributions) gets lost in the paired test case.
--
David.
the differences should be not to far
away from symmetrical. It just needs some reflection on how the
statistic is calculated. If you have an asymmetrical distribution, you
have a lot of small differences with a negative sign and a lot of
large differences with a positive sign if you test against the median
or mean. Hence the sum of ranks for one side will be higher than for
the other, leading eventually to a significant result.
An extreme example :
set.seed(100)
y <- rnorm(100,1,2)^2
wilcox.test(y,mu=median(y))
Wilcoxon signed rank test with continuity correction
data: y
V = 3240.5, p-value = 0.01396
alternative hypothesis: true location is not equal to 1.829867
wilcox.test(y,mu=mean(y))
Wilcoxon signed rank test with continuity correction
data: y
V = 1763, p-value = 0.008837
alternative hypothesis: true location is not equal to 5.137409
Which brings us to the question what location is actually tested in
the wilcoxon test. For the measure of location to be the mean (or
median), one has to assume that the distribution of the differences is
rather symmetrical, which implies your data has to be distributed
somewhat symmetrical. The test is robust against violations of this
-implicit- assumption, but in more extreme cases skewness does matter.
Cheers
Joris
On Thu, Jun 24, 2010 at 7:40 PM, David Winsemius <dwinsem...@comcast.net
> wrote:
You are being misled. Simply finding a statement on a statistics
software
website, even one as reputable as Graphpad (???), does not mean
that it is
necessarily true. My understanding (confirmed reviewing
"Nonparametric
statistical methods for complete and censored data" by M. M. Desu,
Damaraju
Raghavarao, is that the Wilcoxon signed-rank test does not require
that the
underlying distributions be symmetric. The above quotation is highly
inaccurate.
--
David.
--
Joris Meys
Statistical consultant
Ghent University
Faculty of Bioscience Engineering
Department of Applied mathematics, biometrics and process control
tel : +32 9 264 59 87
joris.m...@ugent.be
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