Thanks all for your answers. It seems most of my students understand that the way to compute a small probability may impact the result.
Regards, CD > Le 4 nov. 2025 à 20:43, Eik Vettorazzi <[email protected]> a écrit : > > Hi, > Stepping briefly outside the R context, I noticed a statistical point in the > text you linked that, in my opinion, isn't quite right. I believe there's a > key misunderstanding here: The statement that the z-test does not depend on > the number of cases is incorrect. The p-value of the z-test is —just like > other tests— very much dependent on the sample size, assuming the same mean > difference and standard deviation. > The text you linked is actually calculating an Effect Size, which is > (largely) independent of the sample size. Effect Size answers the question of > how "relevant" or "large" the difference between groups is. This is > fundamentally different from testing for "significant" differences. > Specifically, the crucial 1/\sqrt{n} term, which is necessary for calculating > the standard error of the mean difference, seems to be missing from the > presented formula for the z-score. I just wanted to quickly point this out. > > Best regards > > Am 27.10.2025 um 14:12 schrieb Petr Pikal: >> Hallo >> The t test is probably not the best option in your case. With 95 >> observations your data behave more like a population and you may get >> better insight using z-test. See >> https://toxictruthblog.com/avoiding-little-known-problems-with-the-t-test/ >> Best regards. >> Petr >> <https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail> >> Neobsahuje >> žádné viry.www.avast.com >> <https://www.avast.com/sig-email?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail> >> <#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2> >> so 25. 10. 2025 v 11:46 odesílatel Christophe Dutang <[email protected]> >> napsal: >>> Dear list, >>> >>> I'm computing a p-value for the Student test and discover some >>> inconsistencies with the cdf pt(). >>> >>> The observed statistic is 11.23995 for 95 observations, so the p-value is >>> very small >>> >>>> t_score <- 11.23995 >>>> n <- 95 >>>> print(pt(t_score, df = n-2, lower=FALSE), digits=22) >>> [1] 2.539746620181247991746e-19 >>>> print(integrate(dt, lower=t_score, upper=Inf, df=n-2)$value, digits = 22) >>> [1] 2.539746631161970791961e-19 >>> >>> But if I compute with pt(lower=TRUE), I got 0 >>> >>>> print(1-pt(t_score, df = n-2, lower=TRUE), digits=22) >>> [1] 0 >>> >>> Indeed, the p-value is lower than the epsilon machine >>> >>>> pt(t_score, df = n-2, lower=FALSE) < .Machine$double.eps >>> [1] TRUE >>> >>> Using the square of t statistic which follows a Fisher distribution, I got >>> the same issue: >>> >>>> print(pf(z, 1, n-2, lower=FALSE), digits=22) >>> [1] 5.079493240362495983491e-19 >>>> print(integrate(df, lower=z, upper=Inf, df1=1, df2=n-2)$value, digits = >>> 22) >>> [1] 5.079015231299358486828e-19 >>>> print(1-pf(z, 1, n-2, lower=TRUE), digits=22) >>> [1] 0 >>> >>> When using the t.test() function, the p-value is naturally printed : >>> p-value < 2.2e-16. >>> >>> Any comment is welcome. >>> >>> Christophe >>> >>>> R.version >>> _ >>> platform aarch64-apple-darwin20 >>> arch aarch64 >>> os darwin20 >>> system aarch64, darwin20 >>> status >>> major 4 >>> minor 5.1 >>> year 2025 >>> month 06 >>> day 13 >>> svn rev 88306 >>> language R >>> version.string R version 4.5.1 (2025-06-13) >>> nickname Great Square Root >>> ------------------------------------------------- >>> Christophe DUTANG >>> LJK, Ensimag, Grenoble INP, UGA, France >>> ILB research fellow >>> Web: http://dutangc.free.fr >>> ------------------------------------------------- >>> >>> >>> [[alternative HTML version deleted]] >>> >>> ______________________________________________ >>> [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. >>> >> [[alternative HTML version deleted]] >> ______________________________________________ >> [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. > > -- > Eik Vettorazzi > > Universitätsklinikum Hamburg-Eppendorf > Institut für Medizinische Biometrie und Epidemiologie > > Christoph-Probst-Weg 1 > 4. Obergeschoss, Raum 04.1.021.1 > > 20246 Hamburg > > Telefon: +49 (0) 40 7410 - 58243 > Fax: +49 (0) 40 7410 - 57790 > > Web: www.uke.de/imbe > > > > -- > > _____________________________________________________________________ > > Universitätsklinikum Hamburg-Eppendorf; Körperschaft des öffentlichen Rechts; > Gerichtsstand: Hamburg | www.uke.de > Vorstandsmitglieder: Prof. Dr. Christian Gerloff (Vorsitzender), Joachim > Prölß, Prof. Dr. Blanche Schwappach-Pignataro, Corinna Wriedt > _____________________________________________________________________ ______________________________________________ [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.
