Hypergeometric? [was Re: GREEK PREHISTORY AND IE (EVIDENCE?)]

[Vidhyanath Rao]

> MAI>What is meant here by "the hypergeometric"?

>  It is too difficult to explain it in a nutshell here.

Given that I teach this stuff occasionally, I can't resist trying :-)

Consider an urn with 8 red balls and 4 black balls. Pull out three at
random, without replacing the balls you draw. Then count the number of
black balls among the three drawn. The hypergeometric distribution
models this kind of thing.

More generally, if you have population of size N (12 in the example
above) and a subgroup of size A (4 in our example) and you take a sample
of n (3 for our example) members at random and count the number of
members from the subgroup in the sample, you get the hypergeomtric.

If both A and N-A are at least an order of magnitude larger than the
sample size n, hypergeometric is hardly distinguishable from the
binomial. As this is the common situation in many applications (so I
don't quite understand Hans's comment about where it is used),
hypergeomtric is usually omitted from courses in the US meant for
general audiences.