[R] wilcox.test p-value = 0
Marc Schwartz
marc_schwartz at me.com
Wed Sep 16 17:54:36 CEST 2009
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 .Machine at double.xmin, but i'm not
>>> comfortable with reporting p < .Machine at 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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