# [R] Discrepency between confidence intervals from t.test andcomputed manually -- why?

Dimitris Rizopoulos dimitris.rizopoulos at med.kuleuven.be
Wed Jan 4 10:21:07 CET 2006

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

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 at itc.nl>
To: <r-help at 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.
> ------------------
> 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
>
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