May I implore that those involved in this discussion/dispute take it off R-Help, as it really seems like the sort of thing that we should avoid here,, as well as being off topic.
On Wed, Nov 5, 2025 at 9:29 AM Robert Knight <[email protected]> wrote: > I have not reviewed the formulas presented, but you err in assertion of > wrong information om that site. The Central Limit Theorem is about the raw > data and the law of large numbers applies to averages obtained from it. > > T if n<30 was the metric I was trained to use. If I recall correctly, z is > more reliable below 30 than t is above it. > > Unless the math formulas are wrong, that site seems useful. I wonder how > far t diverges from z, but do not have time to compare them exactly. > > > > > On Wed, Nov 5, 2025, 9:04 AM Viechtbauer, Wolfgang (NP) via R-help < > [email protected]> wrote: > > > Eik, thanks for posting this. I thought that the page was making the > usual > > (just somewhat flawed) argument that once the dfs are sufficiently large, > > whether one does pnorm(...) or pt(..., df=<>) makes little difference > > (although far out in the tails it still does). > > > > Your post made me look at the page and I hope nobody takes anything > > written there serious. The argument is so utterly wrong. I am absolutely > > flabbergasted how somebody could write so many pages of text based on > such > > a flawed understanding of basic statistical concepts. > > > > Just to give some examples: > > > > "The next issue I have is that I can't see the underlying data. So I > don't > > know what the actual shape of the distribution is, but it's probably fair > > to say it's normally distributed (assuming the Central Limit Theorem > > applies)." The CLT says nothing about the distribution of the raw data. > > > > "As the sample size increases, samples will begin to operate and appear > > more and more like the population they are drawn from. This is the Law of > > Large Numbers." The law of large numbers has nothing to do with this. > > > > And as Eik already pointed out, the 'z-test' the author is describing is > > not a test at all, but essentially just calculates the standardized mean > > difference (and computing a p-value from it makes no sense). > > > > Best, > > Wolfgang > > > > > -----Original Message----- > > > From: R-help <[email protected]> On Behalf Of Eik > Vettorazzi > > via R- > > > help > > > Sent: Tuesday, November 4, 2025 20:44 > > > To: Petr Pikal <[email protected]>; Christophe Dutang < > > [email protected]> > > > Cc: [email protected] > > > Subject: Re: [R] [EXT] Re: A very small p-value > > > > > > 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 > > > > > > > > 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 > > ______________________________________________ > > [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. > [[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.
