# [R] about a p-value < 2.2e-16

Bogdan Tanasa t@n@@@ @end|ng |rom gm@||@com
Fri Mar 19 16:40:10 CET 2021

```Dear Jiefei, and all,

-- bogdan

On Fri, Mar 19, 2021 at 7:52 AM Jiefei Wang <szwjf08 using gmail.com> wrote:

> After digging into the R source, it turns out that the argument `exact`
> has nothing to do with the numeric precision. It only affects the statistic
> model used to compute the p-value. When `exact=TRUE` the true distribution
> of the statistic will be used. Otherwise, a normal approximation will be
> used.
>
> I think the documentation needs to be improved here, you can compute the
> exact p-value *only* when you do not have any ties in your data. If you
> have ties in your data you will get the p-value from the normal
> approximation no matter what value you put in `exact`. This behavior should
> be documented or a warning should be given when `exact=TRUE` and ties
> present.
>
> FYI, if the exact p-value is required, `pwilcox` function will be used to
> compute the p-value. There are no details on how it computes the pvalue but
> its C code seems to compute the probability table, so I assume it computes
> the exact p-value from the true distribution of the statistic, not a
> permutation or MC p-value.
>
> Best,
> Jiefei
>
>
>
> On Fri, Mar 19, 2021 at 10:01 PM Jiefei Wang <szwjf08 using gmail.com> wrote:
>
>> Hey,
>>
>> I just want to point out that the word "exact" has two meanings. It can
>> mean the numerically accurate p-value as Bogdan asked in his first email,
>> or it could mean the p-value calculated from the exact distribution of the
>> statistic(In this case, U stat). These two are actually not related, even
>> though they all called "exact".
>>
>> Best,
>> Jiefei
>>
>> On Fri, Mar 19, 2021 at 9:31 PM Spencer Graves <
>> spencer.graves using effectivedefense.org> wrote:
>>
>>>
>>>
>>> On 2021-3-19 12:54 AM, Bogdan Tanasa wrote:
>>> > thanks a lot, Vivek ! in other words, assuming that we work with 1000
>>> data
>>> > points,
>>> >
>>> > shall we use EXACT = TRUE, it uses the normal approximation,
>>> >
>>> > while if EXACT=FALSE (for these large samples), it does not ?
>>>
>>>
>>>        As David Winsemius noted, the documentation is not clear.
>>> Consider the following:
>>>
>>> > set.seed(1)  > x <- rnorm(100) > y <- rnorm(100, 2) > > wilcox.test(x,
>>> y)\$p.value
>>> [1] 1.172189e-25 > wilcox.test(x, y)\$p.value [1] 1.172189e-25 > >
>>> wilcox.test(x, y, EXACT=TRUE)\$p.value [1] 1.172189e-25 > wilcox.test(x,
>>> y, EXACT=TRUE)\$p.value [1] 1.172189e-25 > wilcox.test(x, y,
>>> exact=TRUE)\$p.value [1] 4.123875e-32 > wilcox.test(x, y,
>>> exact=TRUE)\$p.value [1] 4.123875e-32 > > wilcox.test(x, y,
>>> EXACT=FALSE)\$p.value [1] 1.172189e-25 > wilcox.test(x, y,
>>> EXACT=FALSE)\$p.value [1] 1.172189e-25 > wilcox.test(x, y,
>>> exact=FALSE)\$p.value [1] 1.172189e-25 > wilcox.test(x, y,
>>> exact=FALSE)\$p.value [1] 1.172189e-25 > We get two values here:
>>> 1.172189e-25 and 4.123875e-32. The first one, I think, is the normal
>>> approximation, which is the same as exact=FALSE. I think that with
>>> exact=FALSE, you get a permutation distribution, though I'm not sure.
>>> You might try looking at "wilcox_test in package coin for exact,
>>> asymptotic and Monte Carlo conditional p-values, including in the
>>> presence of ties" to see if it is clearer. NOTE: R is case sensitive, so
>>> "EXACT" is a different variable from "exact". It is interpreted as an
>>> optional argument, which is not recognized and therefore ignored in this
>>> context.
>>>           Hope this helps.
>>>           Spencer
>>>
>>>
>>> > On Thu, Mar 18, 2021 at 10:47 PM Vivek Das <vd4mmind using gmail.com> wrote:
>>> >
>>> >> Hi Bogdan,
>>> >>
>>> >> You can also get the information from the link of the Wilcox.test
>>> function
>>> >> page.
>>> >>
>>> >> “By default (if exact is not specified), an exact p-value is computed
>>> if
>>> >> the samples contain less than 50 finite values and there are no ties.
>>> >> Otherwise, a normal approximation is used.”
>>> >>
>>> >> For more:
>>> >>
>>> >>
>>> https://stat.ethz.ch/R-manual/R-devel/library/stats/html/wilcox.test.html
>>> >>
>>> >> Hope this helps!
>>> >>
>>> >> Best,
>>> >>
>>> >> VD
>>> >>
>>> >>
>>> >> On Thu, Mar 18, 2021 at 10:36 PM Bogdan Tanasa <tanasa using gmail.com>
>>> wrote:
>>> >>
>>> >>> Dear Peter, thanks a lot. yes, we can see a very precise p-value,
>>> and that
>>> >>> was the request from the journal.
>>> >>>
>>> >>> if I may ask another question please : what is the meaning of
>>> "exact=TRUE"
>>> >>> or "exact=FALSE" in wilcox.test ?
>>> >>>
>>> >>> i can see that the "numerically precise" p-values are different.
>>> thanks a
>>> >>> lot !
>>> >>>
>>> >>> tst = wilcox.test(rnorm(100), rnorm(100, 2), exact=TRUE)
>>> >>> tst\$p.value
>>> >>> [1] 8.535524e-25
>>> >>>
>>> >>> tst = wilcox.test(rnorm(100), rnorm(100, 2), exact=FALSE)
>>> >>> tst\$p.value
>>> >>> [1] 3.448211e-25
>>> >>>
>>> >>> On Thu, Mar 18, 2021 at 10:15 PM Peter Langfelder <
>>> >>> peter.langfelder using gmail.com> wrote:
>>> >>>
>>> >>>> I thinnk the answer is much simpler. The print method for hypothesis
>>> >>>> tests (class htest) truncates the p-values. In the above example,
>>> >>>>
>>> >>>> wilcox.test(rnorm(100), rnorm(100, 2), exact=TRUE)
>>> >>>>
>>> >>>> and copying the output, just print the p-value:
>>> >>>>
>>> >>>> tst = wilcox.test(rnorm(100), rnorm(100, 2), exact=TRUE)
>>> >>>> tst\$p.value
>>> >>>>
>>> >>>> [1] 2.988368e-32
>>> >>>>
>>> >>>>
>>> >>>> I think this value is what the journal asks for.
>>> >>>>
>>> >>>> HTH,
>>> >>>>
>>> >>>> Peter
>>> >>>>
>>> >>>> On Thu, Mar 18, 2021 at 10:05 PM Spencer Graves
>>> >>>> <spencer.graves using effectivedefense.org> wrote:
>>> >>>>>         I would push back on that from two perspectives:
>>> >>>>>
>>> >>>>>
>>> >>>>>               1.  I would study exactly what the journal said very
>>> >>>>> carefully.  If they mandated "wilcox.test", that function has an
>>> >>>>> argument called "exact".  If that's what they are asking, then
>>> using
>>> >>>>> that argument gives the exact p-value, e.g.:
>>> >>>>>
>>> >>>>>
>>> >>>>>   > wilcox.test(rnorm(100), rnorm(100, 2), exact=TRUE)
>>> >>>>>
>>> >>>>>           Wilcoxon rank sum exact test
>>> >>>>>
>>> >>>>> data:  rnorm(100) and rnorm(100, 2)
>>> >>>>> W = 691, p-value < 2.2e-16
>>> >>>>>
>>> >>>>>
>>> >>>>>               2.  If that's NOT what they are asking, then I'm not
>>> >>>>> convinced what they are asking makes sense:  There is is no such
>>> thing
>>> >>>>> as an "exact p value" except to the extent that certain assumptions
>>> >>>>> hold, and all models are wrong (but some are useful), as George Box
>>> >>>>> famously said years ago.[1]  Truth only exists in mathematics, and
>>> >>>>>
>>> >>>>>
>>> >>>>>         Hope this helps.
>>> >>>>>         Spencer Graves
>>> >>>>>
>>> >>>>>
>>> >>>>> [1]
>>> >>>>> https://en.wikipedia.org/wiki/All_models_are_wrong
>>> >>>>>
>>> >>>>>
>>> >>>>> On 2021-3-18 11:12 PM, Bogdan Tanasa wrote:
>>> >>>>>>    <
>>> >>>>
>>> >>>>
>>> >>>>>> Dear all,
>>> >>>>>>
>>> >>>>>>
>>> >>>>>> in R, the wilcox.test() provides "a p-value < 2.2e-16", when we
>>> >>> compare
>>> >>>>>> sets of 1000 genes expression (in the genomics field).
>>> >>>>>>
>>> >>>>>> however, the journal asks us to provide the exact p value ...
>>> >>>>>>
>>> >>>>>> would it be legitimate to write : "p-value = 0" ? thanks a lot,
>>> >>>>>>
>>> >>>>>> -- bogdan
>>> >>>>>>
>>> >>>>>>        [[alternative HTML version deleted]]
>>> >>>>>>
>>> >>>>>> ______________________________________________
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>>> >>>          [[alternative HTML version deleted]]
>>> >>>
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>>> >>>
>>> >> --
>>> >> ----------------------------------------------------------
>>> >>
>>> >> Vivek Das, PhD
>>> >>
>>> >       [[alternative HTML version deleted]]
>>> >
>>> > ______________________________________________
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>>> > https://stat.ethz.ch/mailman/listinfo/r-help
>>> http://www.R-project.org/posting-guide.html
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>>>
>>>
>>>         [[alternative HTML version deleted]]
>>>
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