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.
