Hello,
Thanks for the correction, sorry Murat I was mistaken. Actually your
answers solved me a problem I was having using multiple fisher.test() on
nucleic acid sequences, where we come up with hundreds of thousands of p
values, a lot of which are 0's. Since we have to correct for multiple
tests, even very, very small p's might end up not being significant, i
had assumed the 0's were tied p values, but now I know I can use the
numerator and the denominator to rank the 0's, even if I don't have the
exact p value.
Best,
Keo.
Marc Schwartz escribió:
Once one gets past the issue of the p value being extremely small,
irrespective of the test being used, the OP has asked the question of
how to report it.
Most communities will have standards for how to report p values,
covering things like how many significant digits and a minimum p value
threshold to report.
For example, in medicine, it is common to report 'small' p values as
'p < 0.001' or 'p < 0.0001'.
Thus, below those numbers, the precision is largely irrelevant and one
need not report the actual p value.
I just wanted to be sure that we don't lose sight of the forest for
the trees... :-)
The OP should consult a relevant guidance document or an experienced
author in the domain of interest.
HTH,
Marc Schwartz
On Sep 16, 2009, at 9:54 AM, Bryan Keller wrote:
That's right, if the test is exact it is not possible to get a
p-value of zero. wilcox.test does not provide an exact p-value in
the presence of ties so if there are any ties in your data you are
getting a normal approximation. Incidentally, if there are any ties
in your data set I would strongly recommend computing the *exact*
p-value because using the normal approximation on tied data sets will
either inflate type I error rate or reduce power depending on how the
ties are distributed. Depending on the pattern of ties this can
result in gross under or over estimation of the p-value.
I guess this is all by way of saying that you should always compute
the exact p-value if possible.
The package exactRankTests uses the algorithm by Mehta Patel and
Tsiatis (1984). If your sample sizes are larger, there is a freely
available .exe by Cheung and Klotz (1995) that will do exact p-values
for sample sizes larger than 100 in each group!
You can find it at http://pages.cs.wisc.edu/~klotz/
Bryan
Hi Murat,
I am not an expert in either statistics nor R, but I can imagine
that since the
default is exact=TRUE, It numerically computes the probability, and
it may
indeed be 0. if you use wilcox.test(x, y, exact=FALSE) it will give
you a
normal aproximation, which will most likely be different from zero.
No, the exact p-value can't be zero for a discrete distribution. The
smallest possible value in this case would, I think, be
1/choose(length(x)+length(y),length(x)), or perhaps twice that.
More generally, the approach used by format.pvalue() is to display
very small p-values as <2e-16, where 2e-16 is machine epsilon. I
wouldn't want to claim optimality for this choice, but it seems a
reasonable way to represent "very small".
-thomas
Hope this helps.
Keo.
Murat Tasan escribi?:
hi, folks,
how have you gone about reporting a p-value from a test when the
returned value from a test (in this case a rank-sum test) is
numerically equal to 0 according to the machine?
the next lowest value greater than zero that is distinct from zero on
the machine is likely algorithm-dependent (the algorithm of the test
itself), but without knowing the explicit steps of the algorithm
implementation, it is difficult to provide any non-zero value. i
initially thought to look at .mach...@double.xmin, but i'm not
comfortable with reporting p < .mach...@double.xmin, since without
knowing the specifics of the implementation, this may not be true!
to be clear, if i have data x, and i run the following line, the
returned value is TRUE.
wilcox.test(x)$p.value == 0
thanks for any help on this!
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