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

Spencer Graves @pencer@gr@ve@ @end|ng |rom e||ect|vede|en@e@org
Fri Mar 19 14:30:36 CET 2021

```
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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>>>
>>> ______________________________________________
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>> --
>> ----------------------------------------------------------
>>
>> Vivek Das, PhD
>>
> 	[[alternative HTML version deleted]]
>
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