Thanks for all the comments. I've put the answer below.
Let's play find the fallacy!
An academic at the London School of Economics has published an article called "IQ and the Wealth of States" claiming that the average IQ in, for example, New Jersey is 108.6 and in Iowa is 76.6. He writes:
In order to use the incomplete, truncated data on SAT scores to compute state IQ, however, I make two simplifying assumptions.
1. Students who complete high school are uniformly more intelligent than those who do not.
2. High school seniors who take the SAT are uniformly more intelligent than those who do not.
What idiosyncrasy about American college entrance testing is this Londoner not aware of that led him to come up with such implausible state IQ scores?
(Hint: I didn't choose the states in the examples above randomly.)
UPDATE: The American testing idiosyncrasy is that there are two competing college entrance exams: the SAT, which is devised in Princeton, New Jersey is dominant on the East and West Coasts, while the ACT, which is devised in Iowa City, Iowa (I believe), is dominant in the center of the country. If you are a kid in New Jersey whose dream school is Columbia and whose safety school is Rutgers, you'll take the SAT. If you are a kid in Iowa whose dream school is Northwestern and whose safety school is U. of Iowa, you'll take the ACT.
Thus, the average score for high school students who take the SAT in Iowa is much higher than in New Jersey, but that's because the percentage of high school students who take the SAT in Iowa is much lower than in New Jersey.
Kanazawa attempts to correct for the excessively high average SAT scores in Iowa by assuming that everybody who takes the SAT is "uniformly more intelligent than those who do not." That wouldn't be a terrible assumption if there were only one college entrance exam, but because there are two, and they are regionally based, it's disastrous.
Here's a good faith attempt from 2003 to get around this problem, which comes up with not implausible estimates (both Iowa and NJ do pretty good), although I think somebody could do a better job of combining SAT and ACT scores.