Um, > pnorm(-405, log=TRUE)/log(10) [1] -35620.58 > qnorm(2.2e-226) [1] -32.10006
and I don’t think that our *norm functions are THAT bad in the tails? -pd > On 28 Oct 2025, at 14.26, Michael Dewey <[email protected]> wrote: > > > > On 28/10/2025 10:13, Peter Dalgaard wrote: >> I suspect this is more like a relic from times when people would do (say) 1 >> - pchisq(x,f) instead of pchisq(x, f, lower=FALSE) and intended to avoid the >> embarrassment of printing 0 for things that weren’t actually impossible. >> People have been known to have unexpected uses for the tiny probabilities >> (one case came from theoretical physics - I think it got recorded as a >> fortune() entry) but rarely as low as 10^-16 in actual significance testing. >> Things like whole genome scans may suggest some hefty Bonferroni >> multipliers, but the numer of tests are not (yet?) in the trillions (US). > > A paper in Nature https://www.nature.com/articles/nature14151 by stensola and > colleagues (sorry there does not seem to be a DOI but it is also vol 518, > pages 207–212 (2015)) reports a p-value of Z = 405, P = 2.2 * 10^{−226} which > is believed to be the current record. To give credit where it is due this was > posted in a comment by user amoeba on CrossValidated. > > Michael > >> - pd >>> On 26 Oct 2025, at 23.34, Ben Bolker <[email protected]> wrote: >>> >>> One possible source of confusion is that the `print.Coefmat` function uses >>> .Machine$double.eps as its threshold for printing "< [minimum value]" >>> rather than the precise computed p-value (presumably on the grounds that a >>> number smaller than this is likely to be unrealistic as an accurate >>> statement of the unlikeliness of an outcome in the real world). >>> >>> On 10/26/25 10:41, Richard O'Keefe wrote: >>>> No, 0 and 5-19 are not "equalled". THey are quite distinct. >>>> As for pt() returning something smaller than double.eps, why wouldn't it? >>>> If I calculate 10^-30, I get 1e-30, which is much smaller than double.eps, >>>> but is still correct. It would be a serious error to return 0 for 10^-30. >>>> Welcome to the wonderful world of floating-point arithmetic. >>>> This really has nothing to do with R. >>>> On Sun, 26 Oct 2025 at 09:38, Christophe Dutang <[email protected]> wrote: >>>>> >>>>> Thanks for your answers. >>>>> >>>>> I was not aware of the R function expm1(). >>>>> >>>>> I’m completely aware that 1 == 1 - 5e-19. But I was wondering why pt() >>>>> returns something smaller than double.eps. >>>>> >>>>> For students who will use this exercise, it is disturbing to find 0 or >>>>> 5e-19 : yet it will be a good exercise to find that these quantities are >>>>> equalled. >>>>> >>>>> Regards, Christophe >>>>> >>>>>> Le 25 oct. 2025 à 12:14, Ivan Krylov <[email protected]> a écrit : >>>>>> >>>>>> В Sat, 25 Oct 2025 11:45:42 +0200 >>>>>> Christophe Dutang <[email protected]> пишет: >>>>>> >>>>>>> Indeed, the p-value is lower than the epsilon machine >>>>>>> >>>>>>>> pt(t_score, df = n-2, lower=FALSE) < .Machine$double.eps >>>>>>> [1] TRUE >>>>>> >>>>>> Which means that for lower=TRUE, there will not be enough digits in R's >>>>>> numeric() type to represent the 5*10^-19 subtracted from 1 and >>>>>> approximately 16 zeroes. >>>>>> >>>>>> Instead, you can verify your answer by asking for the logarithm of the >>>>>> number that is too close to 1, thus retaining more significant digits: >>>>>> >>>>>> print( >>>>>> -expm1(pt(t_score, df = n-2, lower=TRUE, log.p = TRUE)), >>>>>> digits=16 >>>>>> ) >>>>>> # [1] 2.539746620181249e-19 >>>>>> print(pt(t_score, df = n-2, lower=FALSE), digits=16) >>>>>> # [1] 2.539746620181248e-19 >>>>>> >>>>>> expm1(.) computes exp(.)-1 while retaining precision for numbers that >>>>>> are too close to 0, for which exp() would otherwise return 1. >>>>>> >>>>>> See the links in >>>>>> https://cran.r-project.org/doc/FAQ/R-FAQ.html#Why-doesn_0027t-R-think-these-numbers-are-equal_003f >>>>>> for a more detailed explanation. >>>>>> >>>>>> -- >>>>>> Best regards, >>>>>> Ivan >>>>>> (flipping the "days since referring to R FAQ 7.31" sign back to 0) >>>>> >>>>> ______________________________________________ >>>>> [email protected] mailing list -- To UNSUBSCRIBE and more, see >>>>> https://stat.ethz.ch/mailman/listinfo/r-help >>>>> PLEASE do read the posting guide >>>>> https://www.R-project.org/posting-guide.html >>>>> and provide commented, minimal, self-contained, reproducible code. >>>> ______________________________________________ >>>> [email protected] mailing list -- To UNSUBSCRIBE and more, see >>>> https://stat.ethz.ch/mailman/listinfo/r-help >>>> PLEASE do read the posting guide >>>> https://www.R-project.org/posting-guide.html >>>> and provide commented, minimal, self-contained, reproducible code. >>> >>> -- >>> Dr. Benjamin Bolker >>> Professor, Mathematics & Statistics and Biology, McMaster University >>> Associate chair (graduate), Mathematics & Statistics >>> Director, School of Computational Science and Engineering >>> * E-mail is sent at my convenience; I don't expect replies outside of >>> working hours. >>> >>> ______________________________________________ >>> [email protected] mailing list -- To UNSUBSCRIBE and more, see >>> https://stat.ethz.ch/mailman/listinfo/r-help >>> PLEASE do read the posting guide >>> https://www.R-project.org/posting-guide.html >>> and provide commented, minimal, self-contained, reproducible code. >> ______________________________________________ >> [email protected] mailing list -- To UNSUBSCRIBE and more, see >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide https://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. > > -- > Michael Dewey -- Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Office: A 4.23 Email: [email protected] Priv: [email protected] ______________________________________________ [email protected] mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide https://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
