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To: Lane3 who wrote (97019)1/26/2005 3:58:24 PM
From: neolib  Respond to of 793725
 
Yes, but what does that matter?

It matters if you want to understand what it means to say: "These two groups are somewhat different, but are they different enough for me to distinguish between them?"

If the difference (by difference I'm always referring to the set of factors you base your detection methods on, generally more than one!) is so great that there is no or almost no overlap between the two groups then you could reliably distinguish individuals. As an example, Scandinavian vs. Bantu. Skin color alone will do it here, except in the case of rare skin disorders, in which case falling back on other facial features will still allow a successful outcome.

If however, the differences (or perhaps your particular ability to detect them!) are not so great, you must fall back to a statistical methods. Conceptually, the easiest way to do this is to take a random sample size of n from each population, and make the call based on your aggregate impression of each sample.

In statistical language, the first case holds if the population means are much further apart than their variance (in practice say > 3 std deviations apart). If the means are only a fraction of a std deviation apart, then one needs a larger sample size.

So if one can reliably tell group X from group Y, on an individual bases it is an admission that the two groups are far apart (wrt the "difference" used as noted above).