On 06/24/2010 12:40 PM, David Winsemius wrote:
On Jun 23, 2010, at 9:58 PM, Atte Tenkanen wrote:
Thanks. What I have had to ask is that
how do you test that the data is symmetric enough?
If it is not, is it ok to use some data transformation?
when it is said:
"The Wilcoxon signed rank test does not assume that the data are
sampled from a Gaussian distribution. However it does assume that the
data are distributed symmetrically around the median. If the
distribution is asymmetrical, the P value will not tell you much about
whether the median is different than the hypothetical value."
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.
To add to what David and others have said, look at the kernel that the
U-statistic associated with the WSR test uses: the indicator (0/1) of xi
+ xj > 0. So WSR tests H0:p=0.5 where p = the probability that the
average of a randomly chosen pair of values is positive. [If there are
ties this probably needs to be worded as P[xi + xj > 0] = P[xi + xj <
0], i neq j.
Frank
--
Frank E Harrell Jr Professor and Chairman School of Medicine
Department of Biostatistics Vanderbilt University
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