On Tue, 2007-03-06 at 15:54 +, S Ellison wrote:
Small data sets (6-12 values, or a similarly small number of groups)
which don't look nice and symmetric are quite common in my field
(analytical chemistry and biological variants thereof), and often
contain outliers or at least stragglers that I cannot simply discard.
One of the things I occasionally do when I want to see what different
assumptions do to my confidence intervals is to run a quick
nonparametric bootstrap, just to get a feel for how asymmetric the
distribution of any estimates might be. At the moment, I'm also
interested in doing that on some historical data to evaluate some
proposed estimators for interlab studies.
boot() is pretty good, but it's obvious that with such small sets,
there aren't really many distinct resampled combinations (eg 92378 for
10 data points). So I'm really resampling from quite a small
population of possible bootstrap samples. Its surely more efficient to
generate all the different (resampled) combinations of the data set,
and use those and their frequencies to get things like the bootstrap
variance exactly. At worst, that'll stop us fooling ourselves into
thinking more replicates will get better info.
A lengthy dig around R-help and CRAN turned up a blank on generating
distinct combinations with resampling, so I've written a couple of
routines to generate the distinct combinations and their frequencies.
(They work, though I wouldn't guarantee great efficiency). But if a
chemist (me) can think of it, its pretty certain that a statistician
already has. Before I spend hours polishing code, is there already
something out there I've missed?
Steve Ellison
Steve,
The phrase that you seem to be looking for is permutation test.
If you use the following in R:
RSiteSearch({permutation test}, restrict = functions)
that will lead you to some of the functions available.
One CRAN package specifically, 'coin', has a permutation framework for a
variety of such tests.
HTH,
Marc Schwartz
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