Friday, October 13, 2006

Genetics and IQ and all that

Much ink has been spilled about genes for Intelligence and IQ. A recent article in the New Replublic by Steven Pinker, a Harvard Professor of Pyschology, points out that the appearance of an advantage in intelligent is much easier to establish than its causes. So what exacly is the appearance? Consider Ashkenazic Jews. Pinker writes "though never exceeding 3 percent of the American population, Jews account for 37 percent of the winners of the U.S. National Medal of Science, 25 percent of the American Nobel Prize winners in literature, 40 percent of the American Nobel Prize winners in science and economics, and so on". While the average US Jewish IQ is 8-15 points higher than the average US IQ, this smallish difference in mean translates out into a large difference in the tails- large enough to overcome the population inbalance. Larry Summers in his much chattered about speech on Women in Science, challenged researchers to consider all possible reasons for the underepresentation of women in Math and Science departments. Even the possibility that there is a sex linked genetic advantage. He suggests specifically that the causal factor is the differences in group variances. If two populations are Normally distributed then the group with the higher variance will dominate in the tails. As usual it is easier to establish the appearance of a difference than to establish its causes. Could the difference in variance have a biological basis? That is a legitimate subject of inquiry, which is all that Summers suggested. What was the problem? Dean? Inspired by the statistics, I concocted the following exam question: Suppose for the sake of this problem only, that the average IQ for men is 100 with an SD of 15 and the average IQ for women is 105 with an SD of 10. Both distributions are Normal. Assume that there are equal numbers of men and women in the population. What fraction of men have smaller IQ’s that the median Woman? A person is considered a genius if their IQ is greater than 145. What is the relative proportion of men among the geniuses? Is it too PIC to adiminister?

6 Comments:

At 1:33 PM , Anonymous Anonymous said...

nonsens.

 
At 8:55 AM , Anonymous cg said...

Great first comment.

Assuming your questions are genuine, under your assumptions, the fraction of men below 105 is 63%. Not sure how this fits in your argument though.

The fraction of you "men" above 145 (again, under your assumptions) is given by the cumulative normal distribution at 3 s.d., that is 0.135%. For your "women" you have to go to 4 s.d. of course, so 0.0032% of them are above. Relative ratio: about 43 to 1.

In fact, in your example, the proportion switches above 1 s.d., i.e. at 115 for these conveniently chosen numbers.

Did I pass?

 
At 8:28 AM , Blogger Adi said...

Yes, you did. I administered the question to several classes, with a different scenario but similar numbers. The groups were private school versus public schools and the test score was a made up math test.

 
At 12:16 PM , Anonymous Anonymous said...

here is a related story in Slate which might interest you

http://www.slate.com/id/2178122/entry/2178123/

 
At 11:38 AM , Anonymous Anonymous said...

http://article.nationalreview.com/?q=OGM1ZjEyOWQwNzkwMTZkNGY3NjhiNzBiYWVkNmE4ODg=#more

 
At 8:57 PM , Anonymous Anonymous said...

I'm a female with OCD and minor tourettes syndrome, ... so what part does this information play in my IQ score?(I was recently required to take an IQ test, and I found that I was a so called "genious".)

 

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