# [R] Power of t-test in R vs. S-PLUS

Prof Brian D Ripley ripley at stats.ox.ac.uk
Fri Mar 1 11:29:18 CET 2002

```On Fri, 1 Mar 2002 joern.quedenau at metanomics.de wrote:

>
>
> Dear all,
>
> I found a discrepancy while performing a power calculation for a two sample
> t-test in R and S-PLUS, respectively.
> For given values of sample number (5 each), sd (0.2) , significance level
> (0.01), and a desired power (80%) I looked for the difference in means.
> These values differ: 0.5488882 in R and 0.4322771 in S-PLUS (see dump
> below).
>
> Did I overlook any detail or confuse some parameters?

Yes. normal.sample.size is not for a Student's t test, as its name might
suggest (at least, it did to me).  It uses a normal distribution and
assumes the variances are known. On the other hand, power.t.test appears to
be for a conventional equi-variance t-test, and as it needs to estimate the
variances has lower power and hence selects a larger minimum delta.

BTW, the t-test that power.t.test computes the power of is not the default
t-test in R, as I understand the code.  (?power.t.test is silent on which
two-sample t-test but the calculations look right for the one that uses the
pooled variance.  Not that it necessarily matters.)

This is only evident because n1 and n2 are so small: at those sample sizes
you are relying critically on normality of the samples, and for
power.t.test on equal variances.  For n1 = n2 = 25, the difference is much
smaller (0.193 vs 0.200).

>
> Thanks for your help,
> Joern Quedenau
>
> Here are the commands & outputs from both tools:
>
> R 1.4.0
> > power.t.test(n=5, sd=0.2, sig.level=0.01, power=0.8, type="two.sample",
> alternative="two.sided")
>
>      Two-sample t test power calculation
>
>               n = 5
>           delta = 0.5488882
>              sd = 0.2
>       sig.level = 0.01
>           power = 0.8
>     alternative = two.sided
>
>  NOTE: n is number in *each* group
>
> S-PLUS 2000 Professional Release 2:
> > normal.sample.size(n1=5, n2=5, mean=0, sd1=0.2, sd2=0.2, power=0.8,
> alpha=0.01, alternative="two.sided")
>   mean1 sd1     mean2 sd2     delta alpha power n1 n2 prop.n2
> 1     0 0.2 0.4322771 0.2 0.4322771  0.01   0.8  5  5       1
>
> ------------------------------------------
> Dr. Jörn Quedenau
> Coordinator Data Management Bioinformatics
> Metanomics GmbH & Co. KGaA
> Tegeler Weg 33, D-10589 Berlin, Germany
> Tel +49 30 34807 125, Fax +49 30 34807 300
>
>
> -.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
> r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html
> Send "info", "help", or "[un]subscribe"
> (in the "body", not the subject !)  To: r-help-request at stat.math.ethz.ch
> _._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._
>

--
Brian D. Ripley,                  ripley at 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 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html
Send "info", "help", or "[un]subscribe"
(in the "body", not the subject !)  To: r-help-request at stat.math.ethz.ch
_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._

```