From: Jose Claudio Faria <joseclaudio.faria_at_terra.com.br>

Date: Sat 05 Aug 2006 - 06:42:37 EST

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R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Sat Aug 05 19:58:35 2006

Date: Sat 05 Aug 2006 - 06:42:37 EST

Dears John, Peter and Sundar,

Many thanks for the quick answers!!!

.. and sorry for all..

[]s

___

Jose Claudio Faria

Brasil/Bahia/Ilheus/UESC/DCET

Estatística Experimental/Prof. Adjunto

mails: joseclaudio.faria@terra.com.br

jc_faria@uesc.br jc_faria@uol.com.br

John Fox escreveu:

> Dear Jose,

*>
**> The problem is that you're using the population standard deviation (sigma)
**> rather than the sample SD of each sample [i.e., t[i] = (mean(amo.i) - mu) /
**> (sd(amo.i) / sqrt(n)) ], so your values should be normally distributed, as
**> they appear to be.
**>
**> A couple of smaller points: (1) Even after this correction, you're sampling
**> from a discrete population (albeit with replacement) and so the values won't
**> be exactly t-distributed. You could draw the samples directly from N(mu,
**> sigma) instead. (2) It would be preferable to make a quantile-comparison
**> plot against the t-distribution, since you'd get a better picture of what's
**> going on in the tails.
**>
**> I hope this helps,
**> John
**>
**> --------------------------------
**> John Fox
**> Department of Sociology
**> McMaster University
**> Hamilton, Ontario
**> Canada L8S 4M4
**> 905-525-9140x23604
**> http://socserv.mcmaster.ca/jfox
**> --------------------------------
**>
*

>> -----Original Message----- >> From: r-help-bounces@stat.math.ethz.ch >> [mailto:r-help-bounces@stat.math.ethz.ch] On Behalf Of Jose >> Claudio Faria >> Sent: Friday, August 04, 2006 3:09 PM >> To: R-help@stat.math.ethz.ch >> Subject: [R] Doubt about Student t distribution simulation >> >> Dear R list, >> >> I would like to illustrate the origin of the Student t >> distribution using R. >> >> So, if (sample.mean - pop.mean) / standard.error(sample.mean) >> has t distribution with (sample.size - 1) degree free, what >> is wrong with the simulation below? I think that the >> theoretical curve should agree with the relative frequencies >> of the t values calculated: >> >> #== begin options===== >> # parameters >> mu = 10 >> sigma = 5 >> >> # size of sample >> n = 3 >> >> # repetitions >> nsim = 10000 >> >> # histogram parameter >> nchist = 150 >> #== end options======= >> >> t = numeric() >> pop = rnorm(10000, mean = mu, sd = sigma) >> >> for (i in 1:nsim) { >> amo.i = sample(pop, n, replace = TRUE) >> t[i] = (mean(amo.i) - mu) / (sigma / sqrt(n)) } >> >> win.graph(w = 5, h = 7) >> split.screen(c(2,1)) >> screen(1) >> hist(t, >> main = "histogram", >> breaks = nchist, >> col = "lightgray", >> xlab = '', ylab = "Fi", >> font.lab = 2, font = 2) >> >> screen(2) >> hist(t, >> probability = T, >> main = 'f.d.p and histogram', >> breaks = nchist, >> col = 'lightgray', >> xlab = 't', ylab = 'f(t)', >> font.lab = 2, font = 2) >> >> x = t >> curve(dt(x, df = n-1), add = T, col = "red", lwd = 2) >> >> Many thanks for any help, >> ___ >> Jose Claudio Faria >> Brasil/Bahia/Ilheus/UESC/DCET >> Estatística Experimental/Prof. Adjunto >> mails: joseclaudio.faria@terra.com.br >> jc_faria@uesc.br >> jc_faria@uol.com.br >> >> ______________________________________________ >> R-help@stat.math.ethz.ch mailing list >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide >> http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code.

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R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Sat Aug 05 19:58:35 2006

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