[R] about a p-value < 2.2e-16
Bert Gunter
bgunter@4567 @end|ng |rom gm@||@com
Fri Mar 19 17:04:51 CET 2021
I **believe** -- if my old memory still serves-- that the "exact"
specification uses a home grown version of the algorithm to calculate
exact, or close approximations to the exact, permutation distribution
originally developed by Cyrus Mehta, founder of StatXact software. Of
course, examining the C code source would determine this, but I don't care
to attempt this.
If this is (no longer?) correct, please point this out.
Best,
Bert Gunter
"The trouble with having an open mind is that people keep coming along and
sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
On Fri, Mar 19, 2021 at 8:42 AM Jiefei Wang <szwjf08 using gmail.com> wrote:
> Hi Spencer,
>
> Thanks for your test results, I do not know the answer as I haven't
> used wilcox.test for many years. I do not know if it is possible to compute
> the exact distribution of the Wilcoxon rank sum statistic, but I think it
> is very likely, as the document of `Wilcoxon` says:
>
> This distribution is obtained as follows. Let x and y be two random,
> independent samples of size m and n. Then the Wilcoxon rank sum statistic
> is the number of all pairs (x[i], y[j]) for which y[j] is not greater than
> x[i]. This statistic takes values between 0 and m * n, and its mean and
> variance are m * n / 2 and m * n * (m + n + 1) / 12, respectively.
>
> As a nice feature of the non-parametric statistic, it is usually
> distribution-free so you can pick any distribution you like to compute the
> same statistic. I wonder if this is the case, but I might be wrong.
>
> Cheers,
> Jiefei
>
>
> On Fri, Mar 19, 2021 at 10:57 PM Spencer Graves <
> spencer.graves using effectivedefense.org> wrote:
>
> >
> >
> > On 2021-3-19 9:52 AM, Jiefei Wang 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.
> >
> >
> > My example shows that it does NOT use Monte Carlo, because
> > otherwise it uses some distribution. I believe the term "exact" means
> > that it uses the permutation distribution, though I could be mistaken.
> > If it's NOT a permutation distribution, I don't know what it is.
> >
> >
> > Spencer
> > >
> > > 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,
> > >>>>>>> instead of using
> > >>>>>>>
> > >>>>>>> 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
> > >>>>>>>> that's because it's a fiction to start with ;-)
> > >>>>>>>>
> > >>>>>>>>
> > >>>>>>>> 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:
> > >>>>>>>>> <
> > >>>
> > https://meta.stackexchange.com/questions/362285/about-a-p-value-2-2e-16
> > >>>>>>>>> Dear all,
> > >>>>>>>>>
> > >>>>>>>>> i would appreciate having your advice on the following please :
> > >>>>>>>>>
> > >>>>>>>>> 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]]
> > >>>>>>>>>
> > >>>>>>>>> ______________________________________________
> > >>>>>>>>> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more,
> > see
> > >>>>>>>>> https://stat.ethz.ch/mailman/listinfo/r-help
> > >>>>>>>>> PLEASE do read the posting guide
> > >>>>>>> http://www.R-project.org/posting-guide.html
> > >>>>>>>>> and provide commented, minimal, self-contained, reproducible
> > code.
> > >>>>>>>> ______________________________________________
> > >>>>>>>> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more,
> see
> > >>>>>>>> https://stat.ethz.ch/mailman/listinfo/r-help
> > >>>>>>>> PLEASE do read the posting guide
> > >>>>>>> http://www.R-project.org/posting-guide.html
> > >>>>>>>> and provide commented, minimal, self-contained, reproducible
> code.
> > >>>>>> [[alternative HTML version deleted]]
> > >>>>>>
> > >>>>>> ______________________________________________
> > >>>>>> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > >>>>>> https://stat.ethz.ch/mailman/listinfo/r-help
> > >>>>>> PLEASE do read the posting guide
> > >>>>>> http://www.R-project.org/posting-guide.html
> > >>>>>> and provide commented, minimal, self-contained, reproducible code.
> > >>>>>>
> > >>>>> --
> > >>>>> ----------------------------------------------------------
> > >>>>>
> > >>>>> Vivek Das, PhD
> > >>>>>
> > >>>> [[alternative HTML version deleted]]
> > >>>>
> > >>>> ______________________________________________
> > >>>> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > >>>> https://stat.ethz.ch/mailman/listinfo/r-help
> > >>>> PLEASE do read the posting guide
> > >>> http://www.R-project.org/posting-guide.html
> > >>>> and provide commented, minimal, self-contained, reproducible code.
> > >>>
> > >>> [[alternative HTML version deleted]]
> > >>>
> > >>> ______________________________________________
> > >>> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > >>> https://stat.ethz.ch/mailman/listinfo/r-help
> > >>> PLEASE do read the posting guide
> > >>> http://www.R-project.org/posting-guide.html
> > >>> and provide commented, minimal, self-contained, reproducible code.
> > >>>
> >
> >
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
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