Discrepancy and statistics.

Factual Questions
1

I were trying to prove for myself how intelligence is a function not of the mind or even the body, but the environment as well. Take the world’s greatest physicists, as it hardly seems controversial to say that the world’s three, at least, most influential physicists have all been male europeans (and you could even limit it further by adding born within the last millenium, etc). And though I’m not at all qualified to make such an assumption and could be way off, I’d estimate only 1 in 16 of all humans ever have been male europeans, and thus the top three seems far from what you’d expect if all humans had equal ability to excel in physics. (Of course excellence in physics isn’t the same as intelligence, but the example still seems to back up the basic assumption)
But I find myself at loss trying to calculate exactly how big a discrepancy this is. And further, how do you calculate the chance for at least one in a random set of sixteen physicists being a male european? It can’t possibly be 16/16, even though the chance for a single one being a male european is 1/16, for all we know they could all be japanese. And so on, if you know the answers, you probably can figure out the questions I’ve forgotten.

And while we’re fighting ignorance, feel free to supply a better demographic estimate.

2

You seem to recognize that innate intelligence, if there is such a thing, is a different entity than excellence in a subject so you should also recognize that the nature/nurture dispute, of which your question is a subset, cannot be answered by way of statistics.

You can look at this through any number of cultural lenses. Take the heavyweight boxing champion, for example. The crown has moved through a variety of ethnic groupings over the past century or so, from Irish to Jews to Blacks and now to Russians. Is there any reason at all to think that physical strength and agility has shifted like this? Of course not. It is purely a function of routes to success in other fields being limited.

No human accomplishment can be correlated with innate intelligence because routes to success have never been equal in any field at any time in history. And that’s even assuming that there is an entity that can be called innate intelligence, which is hotly disputed.

Your statistical example needs to have weights assigned in some factor according to population, or university attendance, or some other function. It still won’t mean anything, though, any more than it meant anything for Germany to be the home of physics in the early 20th century and the U.S. to be the home of physics in the early 21st century and for China, for all we know, to be the home of physics in the early 22nd century. Cultural factors triumph always.

3

I absolutely recognize the fact that people of any background could excel in any discipline, but my point was really that training is essential to percieved intelligence. I’ve absolutely no agenda to discriminize against people that aren’t, like myself, male europeans (hell, you male americans are catching up:)), but I doubt Einstein would have been of much use to physics had he been born an Aborigine. Cultural factors may shift rapidly enough to prove that the genetics of intelligence are evenly distributed, but actual intelligence seldom (to be strict, I’d say never) arise without cultural stimulation. In a way, I don’t believe in intelligence, but results.
Anyway, my question was regarding statistics. I see the introduction might have been a bit confusing, but I wanted to have it there anyway.

4

I take it your question is equivalent to: “1/16 of the balls in this bag are blue, and the rest are red. What are the chances that 3 balls taken randomly from the bag are all blue”? If so, each time you take a ball, the chance of it being blue is (1/16). The chances of that happening 3 times in a raw is (1/16)^3=0.024%. That’s assuming the total number of balls in the bag is much greater than 3 (i.e. you don’t start to run out of red balls just because you took one on the first try).

Your next question (I think) is what’s the chance of drawing 16 balls and getting at least 1 red ball. That is, the chance of drawing 16 balls and not getting all blue balls. For each draw, the chance of getting a blue ball is (15/16), so the chances of that happening 16 times in a raw is (15/16)^16. So the chance of that not happening is 1-(15/16)^16=64%.

5

You’ve got two questions here, the one you asked, and the one that prompted you to ask. On the one that prompted you, I’ll only point out that Archimedes should probably be one of those top three people, and he wasn’t this most recent millenium.

That said, though, on the statistics: We’re given that only 1 person in 16, historically, has been a European male (I’ll trust your research on that, but it doesn’t seem too unlikely). The first question is “Assuming no correlation between European male-ness and physics success, how likely would it be that the top three were all European males”. The top physicist would have a 1 in 16 chance to be a European male, the #2 one would have a 1 in 16, and the #3 one would also have a 1 in 16 chance. If we were to assume that there were no correlation, the chance that all three would be European males is 1 in 16^3, or 4096. This is, as you recognize, a very small probability, which would tend to support the conclusion that success in physics is, in fact, correlated with being male and/or European.

To your second question, given a set of 16 physicists and assuming no correlation, what is the chance that at least one of them would be a male European? This one is easiest to do by considering the opposite case: What are the chances that none of them is a male European? The first one has a 15/16 chance of not being a male European, the second one has a 15/16 chance, and so on. So the total chance that none of them is a male European is (15/16)^16, or .35607… Incidentally, this number is very close to 1/e, and will get closer as you take larger numbers: (99/100)^100, or (99999/100000)^100000, etc. But anyway, the probability of none of them being a male European is .35607…, so the probability of at least one of them being one is 1 minus that, or .64393…

Finally, a caveat: You have to make sure not to cherry-pick your data. If, before collecting your data, you ask “How many of the top three physicists are European males”, then that’s one thing. But if you look at the data and then say “The top three physicists are all European males”, that’s another. Suppose, for instance, that the top 3 were Europeans, but numbers 4-23 were all from India. In that case, if you wanted to make Europe look like the home of physicists, you could decide after the fact to just focus on those top three, but it would be very deceptive to do so. This probably isn’t a big issue in the specific case you’re asking about (I suspect that any way of analyzing the population of physicists will end up showing a bias towards European males), but it can be in general, in statistical debates, and it’s something to look out for.

6

As said, the introduction was confusing and irrelevant to the statistics question, my bad. I’m actually quite aware of such caveats in regard to statistics and shouldn’t make it look like I’m not. I was thinking about intelligence, the first example that came to mind was physicists (and as even Chronos seems to agree, they have mainly been male europeans), and it just struck me that I couldn’t calculate the statistics. Having read the answers (both of you perfectly interpreted my question), I see now that it’s been too long since I had math at school.
I’m doubly ashamed, now. Anyway, thanks for answers and trying to correct the ignorance I insist (or at least, hope) was only an illusion.