[R] small sample size confidence interval by bootstrap

J Dougherty jwd at surewest.net
Sat Apr 1 22:00:14 CEST 2006

On Friday 31 March 2006 18:21, Urania Sun wrote:
> 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,
With a sample that small, it is far safer to simply consider them as four 
examples and leave it at that.  In a population where there is little 
variation (say an archaeological projectile point type with a nech width that 
varies between 3 and 5 mm), the examples are likely to be close to typical, 
and the difference isn't really llikely to be important anyway.  However, in 
a population with considerable variation (for example height in humans) you 
can see that trying to make any generalizations from 4 examples is going to 
be more likely to be misleading than anything else.  

If your sample of four is your entire population, you have all the information 
possible through simple measurements.  But, if the population were 100 the 
number of possible samples of size 4 is, as Gnumeric assures me, about 4 x 
10^306, which, to put it scientifically, is a whole bunch.  It'is better not 
to generalize from small samples.


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