From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>

Date: Wed 04 Jan 2006 - 20:37:38 EST

Date: Wed 04 Jan 2006 - 20:37:38 EST

Some user error it appears. I googled, got the data file from

http://www3.interscience.wiley.com:8100/legacy/college/davis/0471172758/datafiles/data_index.html

and did

*> temp <- read.table("c:/TEMP/CROATRAD.TXT", header=T)
**> Cs137 <- temp$X137Cs
*

> t.test(Cs137)$conf.int

[1] 5.115488 7.239712

attr(,"conf.level")

[1] 0.95

which agrees with your report

> 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)
*

0.01 0.05 0.1 0.2

4.77 5.12 5.29 5.49

> round(ci.hi <- mu + se.mean * t.vals, 2)

0.01 0.05 0.1 0.2 7.58 7.24 7.07 6.87

> c(ci.low[2], ci.hi[2])

0.05 0.05 5.115488 7.239712

which agrees with t.test and not what you reported you got.

On Wed, 4 Jan 2006, David Rossiter wrote:

> 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_at_itc.nl, Internet: http://www.itc.nl/personal/rossiter
*

-- Brian D. Ripley, ripley@stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595 ______________________________________________ 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.htmlReceived on Wed Jan 04 20:56:19 2006

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