Re: A very small p-value

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]]