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

[Jiefei Wang]

Dear Wolfgang,

Thanks for the documentation, but the document only states the default
behavior, it does not mention what would happen if we tell it to compute
the exact p-value but the data has ties. I think this would be misleading
as people might think their result is exact by specifying `exact=TRUE` but
the truth is that their data contains ties and the result is from the
normal approximation.

Best,
Jiefei

On Fri, Mar 19, 2021 at 11:18 PM Viechtbauer, Wolfgang (SP) <
wolfgang.viechtbauer using maastrichtuniversity.nl> wrote:

> Dear Jiefei,
>
> This behavior is documented. From help(wilcox.test):
>
> "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."
>
> Best,
> Wolfgang
>
> >-----Original Message-----
> >From: R-help [mailto:r-help-bounces using r-project.org] On Behalf Of Jiefei
> Wang
> >Sent: Friday, 19 March, 2021 15:52
> >To: Spencer Graves
> >Cc: r-help; Bogdan Tanasa
> >Subject: Re: [R] about a p-value < 2.2e-16
> >
> >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
>

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