*Nassim Taleb recently wrote some thoughts about Richard Dawkins' poor use of stats. It came in three separate facebook posts, so I figured I'd compile them to make sharing easier. Source is here.*

Richard Dawkins, in his statement about the number of Nobels granted to Moslems, showed a total ignorance of probability. A primitive violation. You never get an idea about the mean from measuring the tail (number of Nobels per capita). The "tail", the extreme, depends mostly on the variance and is very sensitive in the mean. Small differences in education, less than 1% can produce 100x changes in the number of persons in the tails. To compare 2 populations, you compare THE MEANS, not the extrema, STATISTICS 101!
It is an intellectual violation of the worst order. I wonder why the press never picked up on this. And why in the world does anyone call Richard Dawkins a scientist?
Please note that I am not a Moslem, but Greek Orthodox Levantine.
(I set aside the notion that had some Medieval moslem compared his population to that of Northern, the difference would have much, much more striking, and to say the least *not predictive*. Also ignore his use of a Western metric on a non Western population).

(continued) Mr Dawkins you cannot compare Nobels per capita as a metric for intelligence because of nonlinearities. If a naive "scientist" (fooled by randomness) like you compared Ashkenazis Jews, representing ~5 million, with 50% of scientific Nobel Prizes, to the rest of the world's population of 7 bil, he would have assumed that Ashkenazis have IQs of 7000 times the average! Mr Dawkins I can send you my book Fooled by Randomness that might help you try to think a bit harder about these problems. Also the error (misunderstanding convexity) is discussed 2x in Antifragile.

(continued) my comment used IQ as an example, but we can use educational level, any metric: the response for the population of the super-super-elite is vastly nonlinear and depends mostly on variance.

this is 100% true, but doesn't mean that comparing the extremes is always inherently unscientific. Yes, using extremes (very low probability events with very far-from-mean values) to identify trends and make predictions is indefensible (as per Pinker's case on wars). But one can legitimately ask: which one of these two distributions produces more extremes? Or "which one has fatter tails?", or, as Dawkins implied, "Does anyone have an idea of why this distribution has a much, much thinner right tail?". And of course the answer has to do with variances and not the means.

In short, I disagree with Taleb on this one. Dawkins was talking about variances, or if you prefer, the right tails, I've followed the debate and can't recall anything that suggested that he was interested in mean values. Having said that, I'm the first to say that his point was delivered poorly and was unhelpful in many ways, for discussion of the non-statistical side of this please see:

http://aveilandadarkplace.com/2013/08/14/how-can-we-discuss-islam-in-better-ways-a-response-to-alex-gabriel-on-dawkins-and-islam/

and my own reply:

http://sergiograziosi.wordpress.com/2013/08/18/a-response-to-marwa-on-dawkins-tweets/

I do think that Taleb would be right if the focus was on inferring the mean (any metric), then looking at Nobel Prizes makes no sense at all. That's agreed and not contested. I am saying that Dawkins was talking about the differences that two populations show in producing extreme values (far from the mean), i.e. differences in variance. This is a measured value, and yes, it would be wrong to use it to make a prediction. But the difference in the measures is there, and it is wrong to say that the difference means nothing at all. More wrong is to assert that Dawkins suggested that a difference on average intelligence (or other metric) can be estimated by the number of Nobel Prizes, he wasn't. Also: how do we know that both populations have fat tails? Or, where is Taleb mentioning this, his post on the Ashkenazis indicates that he's talking about mean values...

So in short, I think we agree on the maths, but disagree on what Dawkins was attempting to do. And since we can't ask him, we'll never get to the bottom of it.

Thanks for the clarification!