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

David Rossiter rossiter at itc.nl
Wed Jan 4 10:33:37 CET 2006

Problem solved thanks to Dimitris Rizopoulos. A classic beginner's
mistake -- though I've been using R for four years -- I had a local
variable named Cs137 and then one in an active data frame in the R
Commander (I am testing Rcmdr for possible classroom use); in Rcmdr the
active frame is explicitly named, e.g. t.test(hrrad\$Cs137); at the
command prompt I used t.test(Cs137), with frame hrrad attached, but of
course the local variable took precendence. Dumb of me and sorry to
bother you all.

David Rossiter

> -----Original Message-----
> From: David Rossiter
> Sent: Wednesday, January 04, 2006 9:59
> To: 'r-help at lists.R-project.org'
> Subject: Discrepency between confidence intervals from t.test
> and computed 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 at itc.nl,  Internet:
> http://www.itc.nl/personal/rossiter
>
>