Brainy models

I'm going to regret not bringing a TV with me out here, not because I watch much, but the new season of Project Runway begins in a few weeks. I took a look at the models and something jumped out at me: of the 15 models, 3 are pretty bright -- one went to NYU and later got a masters degree in psychology, and two others went to Tufts, one for psych and art history, and another for econ. Given the schools' average SAT scores, I'd say these girls are at least 2 SD above the population mean for IQ.What's the probability of this happening?

If we assume that looks and IQ are sorting independently, we can figure this out as follows. There are about 13 million American females aged 18-25, of whom 130,000 are in the top 1% of the attractiveness distribution for their age group. Assume that the 15 models on the show are random draws from this pool of 130,000, at least with respect to IQ (no SAT scores needed to get on the show). Of the hot girls this age, 2600 will also be in the top 2% of the IQ distribution. (That's what you find at the level of Tufts, NYU, etc.)

Using the hypergeometric distribution, we have a sample of 15 hot girls from a population of 130,000 hot girls. Of them, 2600 will also be brainy, and we draw 3 of these in our sample of 15. The contingency table looks like this:

_______Drawn___Not____Total
Smart____3_____2597____2600
Not_____12____127388__127400
Total____15____129985__130000

Plugging these numbers in, we find the probability of this event occuring is about 0.002584. To really round out a Fisher's Exact Test, we'd have to calculate the probability of all of the more extreme cases -- e.g., where there are 4 smarties, 5 smarties, up to all 15 smarties -- but it's clear that these will be small compared to probability we've already got. And since they're a pain to calculate, I won't do it. So let's say p is less than 0.003.

That's pretty rare. One explanation is that this is just a fluke -- unfortunately, the biographies for the models of the previous three seasons just mention their hometown, so I can't tell. However, I wouldn't be surprised to find out that this pattern is fairly representative. The reason is that looks and IQ are not independent: smart, successful guys marry good-looking women, who may also be smart.

Here I suggested that there is greater assortative mating among hot-and-smart people "back East" compared to the Mountain Time Zone. This region is at least several generations behind the "rest of" the country, meaning the parts where power is concentrated, so it's only a matter of time before it happens here too. And sure enough, the three brainy models are from upstate New York, suburban Philadelphia, and western Massachusetts (where she went to the elite Deerfield Academy boarding school).

The econ degree is something of a red flag, but the other two studied psychology and art history -- very little chance that they're the get-outta-my-way girls who use their big brains to work on Wall Street or for Manhattan law firms. So what's not to love?

Update: A commenter raises the issue of affirmative action and whether these girls are really in the top 1%. As to the latter, think of a small liberal arts school with 5000 undergrads -- the top 1% is 50, and if they're uniform across classes, that makes about 12 or 13 per class. Wouldn't these girls make that cut? I think so, but I've re-done the calculation assuming they're only in the top 5% -- I don't think that's really debateable. It says you expect to have to sample 20 people at random to find a girl who's that attractive.

As for affirmative action, I don't think it's enough to make a difference. Both Blacks went to Tufts, which has an average SAT score of 1390, and so the average person there is between 2 and 3 SD above the pop mean. I used 2 as a lower-bound, but the average White student there is probably 135 or a bit more. Schools like Tufts get to snatch up the limited pool of high-IQ Blacks; once you get into U-Mich territory, where the average score is somewhere in the low 1300s, that's when the pool has been dried up by Harvard et al, and AA plays a larger role.

Let's assume, however, that the average Black student at Tufts has an IQ of 125, and ditto for the White girl who went to NYU. That's in the top 5% of IQ. To really get our priors straight, though, one of the Black girls is Jamaican, and they (and Caribbeans in general) tend to do much better academically than other African-Americans, so she may be on an equal footing with her White peers. The other girl majored in econ -- that's not something a dope can do, since it involves a lot of math and abstraction, so she too could be on par with her White peers.

But just to buffer against these criticisms, conservatively assume all three girls are just in the top 5% for both looks and IQ. Using the same procedure as before, we find that the probability of exactly this pattern showing up is about 0.03073, and adding in the other even smaller probabilities to fill out Fisher's Exact Test likely won't raise that above 0.05, the conventional cut-off for "unlikely." So the result stands as before.