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

David Winsemius dw|n@em|u@ @end|ng |rom comc@@t@net
Fri Mar 19 07:32:45 CET 2021

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> On Mar 18, 2021, at 10:26 PM, Bogdan Tanasa <tanasa using gmail.com> wrote:
>
> ﻿Dear Spencer, thank you very much for your prompt email and help. When
> using :
>
>> wilcox.test(rnorm(100), rnorm(100, 2), exact=TRUE)
> W = 698, p-value < 2.2e-16
>
>> wilcox.test(rnorm(100), rnorm(100, 2), exact=FALSE)
> W = 1443, p-value < 2.2e-16
>
> and in both cases p-value < 2.2e-16. By "exact" p-value, i have meant the
> "precise" p-value ;
>
> If I may ask please, could we write p-value = 0 ?
>
> i have noted a similar conversation on stackexchange, although the answer
> is not very clear (to me).

The reason it wasn’t and couldn’t be “clear” was that the underlying scientific question and the statistical methods were not precisely described.

The same lack of background information still persists in this discussion.

—
David
>
> https://stats.stackexchange.com/questions/78839/how-should-tiny-p-values-be-reported-and-why-does-r-put-a-minimum-on-2-22e-1
>
> thanks again,
>
> bogdan
>
>> 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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