The R help page of the quantile function lists 9 types of quantiles, i.e. 9 methods to calculate sample quantiles. Which method suits small sample sizes best? Which method will give the most similar quantile estimates if I take samples of sizes 6, 7, 8 of the same population? The distribution looks similar to log-normal; I'm most interested in percentiles 5, 50 and 95.
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3$\begingroup$ I don't know the answer to this question, but simulation might give you at least an idea of which method is the "best" (whatever you mean by best). $\endgroup$– boscovichCommented May 3, 2013 at 14:33
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It sounds as if you want to estimate a particular quantile rather than report a quantile as a descriptive statistic. For that purpose, consider a tailored estimation method such as that proposed by Harrell and Davis. As Frank Harrell is an enthusiastic R user, there's an implementation in R.
All that said, trying to get at the 5% and 95% percentiles from samples of sizes 6 to 8 is a really big stretch: more ESP than statistics, some might say. Essentially, you are extrapolating wildly, whatever you do.
Note that being "similar" to lognormal does not get you very far, as being slightly wrong about the distribution could get you very wrong answers about quantiles in the tails. But it does suggest to me that you should take logarithms first, and more broadly try at least two different methods, perhaps one assuming (log)normal parent and one not.
Why are you obliged to treat these samples separately? Can you pool them?
