Also, the central limit theory and kurtosis is why the economics associates fought against lockdown during covid.
Because of the central limit theorem, any position on the curve was itself a distribution, and since kurtosis would apply, any attempt to flatten a curve would increase the mean. Said folks were correct. The two statements you identified as indicating incorrectness by the author are actually correct. Nov 5, 2025 11:29:18 AM Robert Knight <[email protected]>: > "The CLT says nothing about the distribution of the raw data." > > The central limit theorem is explicitly about the distribution of the raw > data.(1) > > You also said the law of large numbers did not apply, but does. The law of > large numbers is that as the sample size increases, the mean of the sample > will approach the mean of the population. > > Your two critiques seem out if place. > > The BMJ has an excellent lesson calculating z scores. > > https://www.geeksforgeeks.org/maths/central-limit-theorem/ > > Regards, > > Economist Bob > > Nov 5, 2025 9:04:57 AM Viechtbauer, Wolfgang (NP) via R-help > <[email protected]>: > >> 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 >>>>> >>>>>> … >>>>> [1] 2.539746620181247991746e-19 >>>>>> … >>>>> [1] 2.539746631161970791961e-19 >>>>> >>>>> But if I compute with pt(lower=TRUE), I got 0 >>>>> >>>>>> … >>>>> [1] 0 >>>>> >>>>> Indeed, the p-value is lower than the epsilon machine >>>>> >>>>>> … >>>>> [1] TRUE >>>>> >>>>> Using the square of t statistic which follows a Fisher distribution, I got >>>>> the same issue: >>>>> >>>>>> … >>>>> [1] 5.079493240362495983491e-19 >>>>>> … >>>>> 22) >>>>> [1] 5.079015231299358486828e-19 >>>>>> … >>>>> [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.
