# small sample size confidence interval by bootstrap

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## small sample size confidence interval by bootstrap

 Hi, All: I only have 4 samples. I wish to get a confidence interval around the mean. Is it reasonable? If not, is there a way to compute a confidence interval for such small sample size's mean? Many thanks, U         [[alternative HTML version deleted]] ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
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## Re: small sample size confidence interval by bootstrap

 On Fri, 31 Mar 2006, Urania Sun wrote: > I only have 4 samples. I wish to get a confidence interval around the mean. > Is it reasonable? If not, is there a way to compute a confidence interval > for such small sample size's mean? (BTW, the CI is for the population mean, not the sample mean.  I'll also assume that you are prepared to assume that you have a single random sample of size 4 from a location family.) For a confidence interval, you need to make some assumptions about the distribution.  If you assume normality, you can use t.test, but the estimate of the standard deviation (on just 3 df) will be very variable and this will be reflected in the length of the CI. Your subject line mentions the bootstrap.  You could use one of several different types of bootstrap CI but they also make assumptions, weaker assumptions that lead to even more variability.  For a sample of size 4 there are (at most) 36 distinct means of bootstrap resamples, so none of the methods I know of will work adequately (and most not at all). As an example to ponder, the Cauchy distribution does not even have a mean, but from small samples you will have no idea that is very long-tailed.  And getting a CI for a location parameter is often better done from a robust estimator of location than from the sample mean. Alternatively, your true distribution might be a discrete distribution on 5 points, and you have no idea at all about the 5th value. -- Brian D. Ripley,                  [hidden email] 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 ______________________________________________ [hidden email] mailing list https://stat.ethz.ch/mailman/listinfo/r-helpPLEASE do read the posting guide! http://www.R-project.org/posting-guide.html