From: Dimitris Rizopoulos <dimitris.rizopoulos_at_med.kuleuven.be>

Date: Wed 04 Jan 2006 - 20:21:07 EST

rbind(ci.low, ci.hi)

Dimitris Rizopoulos

Ph.D. Student

Biostatistical Centre

School of Public Health

Catholic University of Leuven

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 Received on Wed Jan 04 20:38:31 2006

Date: Wed 04 Jan 2006 - 20:21:07 EST

for me your code works correctly with simulated data, e.g.,

Cs137 <- rexp(100, 1/6)

mu <- mean(Cs137)

n <- length(Cs137)

se.mean <- sqrt(var(Cs137)/n)

alpha <- c(1, 5, 10, 20)/100

t.vals <- qt(1 -(alpha/2), n-1)

names(t.vals) <- alpha

ci.low <- mu - se.mean * t.vals

ci.hi <- mu + se.mean * t.vals

######################

rbind(ci.low, ci.hi)

t.test(Cs137)

maybe you overwrite somewhere the value of the vector Cs137.

I hope it helps.

Best,

Dimitris

Dimitris Rizopoulos

Ph.D. Student

Biostatistical Centre

School of Public Health

Catholic University of Leuven

Address: Kapucijnenvoer 35, Leuven, Belgium

Tel: +32/(0)16/336899 Fax: +32/(0)16/337015 Web: http://www.med.kuleuven.be/biostat/ http://www.student.kuleuven.be/~m0390867/dimitris.htm

- Original Message ----- From: "David Rossiter" <rossiter@itc.nl> To: <r-help@stat.math.ethz.ch> Sent: Wednesday, January 04, 2006 9:58 AM Subject: [R] Discrepency between confidence intervals from t.test andcomputed manually -- why?

>I am sure there is something simple here I am missing, so please bear

*> with me.
**>
**> It concerns the computation of the confidence interval for a
**> population
**> mean.
**>
**> The data are 125 measurements of Cs137 radation, a sample data set
**> from
**> Davis "Statistics and Data Analysis in Geology" 3rd ed.
**> (CROATRAD.TXT)
**> ------------------
**> method 1: using textbook definitions: mean \pm se_mean * t-value
**>
**> mu <- mean(Cs137); n <- length(Cs137)
**> se.mean <- sqrt(var(Cs137)/n)
**> # two-tail alphas
**> alpha <- c(1, 5, 10, 20)/100
**> # t-values for each tail
**> t.vals <- qt(1-(alpha/2), n-1)
**> # name them for the respective alpha
**> names(t.vals) <- alpha
**> # low and high ends of the confidence interval
**> round(ci.low <- mu - se.mean * t.vals, 2)
**> round(ci.hi <- mu + se.mean * t.vals, 2)
**>
**> Output:
**> 0.01 0.05 0.1 0.2
**> 5.66 5.81 5.90 5.99
**>
**> 0.01 0.05 0.1 0.2
**> 6.69 6.54 6.46 6.36
**>
**> -----------------
**>
**> So for the 95% confidence level I seem to get a CI of 5.81 .. 6.54
**>
**> ------------------
**> method 2: using t.test. I am not really testing for any specific
**> mean,
**> I just want the confidence interval of the mean, which t.test seems
**> to
**> give to me:
**>
**> Input:
**> t.test(Cs137)
**>
**> Output:
**>
**> One Sample t-test
**>
**> data: Cs137
**> t = 11.5122, df = 124, p-value < 2.2e-16 <-- not
**> relevant
**> alternative hypothesis: true mean is not equal to 0 <-- not
**> relevant
**> 95 percent confidence interval:
**> 5.115488 7.239712
**> sample estimates:
**> mean of x
**> 6.1776
**> ------------------------------
**>
**> So with t.test I seem to get a CI of 5.12 .. 7.24 which is
**> considerably
**> wider than the directly computed interval 5.81 .. 6.54. Perhaps I
**> am
**> mis-understanding the CI which t.test is reporting?
**>
**> Any help would be appreciated.
**>
**> Thank you.
**>
**> D G Rossiter
**> Senior University Lecturer
**> Department of Earth Systems Analysis (DESA)
**> International Institute for Geo-Information Science and Earth
**> Observation (ITC)
**> Hengelosestraat 99
**> PO Box 6, 7500 AA Enschede, The Netherlands
**> mailto:rossiter@itc.nl, Internet:
**> http://www.itc.nl/personal/rossiter
**>
**> ______________________________________________
**> 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
**>
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https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Wed Jan 04 20:38:31 2006

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