Brothers and IQ, again

Something that's important to keep in mind in all the hoopla over the Norwegian study of conscripts showing a few point higher IQs for oldest brothers, with the New York Times running three articles on the subject over the last week, is that small differences in IQ scores like this can be influenced by methodological issues of specific tests.

Now, big differences in average IQ, such as 15 points (one standard deviation), are test-independent. For decades, the Holy Grail of cognitive test designers has been to invent a test on which blacks and whites would average the same, without losing most real world predictive power. The first psychometrician to accomplish this would be rich and celebrated. Unfortunately, it has turned out to be the equivalent of the perpetual motion machine for engineers and cold fusion for physicists.

But small differences are sensitive to test design trade-offs. For example, the U.S. military's 1979 version of its very heavily g-loaded entrance exam for enlistment applicants, the Armed Forces Qualifying Test, found an anomalously large 18.6 point gap between whites and blacks when it was standardized on the National Longitudinal Study of Youth in 1980 (this is the study that provides much of the new data in The Bell Curve). The average study has found a 16.5 point difference, so this 18.6 point gap was strange because the AFQT is a test the military has spent a fortune developing, and the NLSY sample, with about 13,000 participants including an oversampling of minorities, was the gold standard for a nationally representative data set..

The 1979 AFQT was designed to be highly accurate around IQs of 100. For instance, from 1992-2004, the military took very few applicants with IQs of 90, but would take quite a few 95s.

So, the 1979 AFQT was designed to be extremely thorough for the average person: it was 105 pages long! As Charles Murray pointed out recently, in the 1990s it was finally realized by studying results on a question-by-question basis that the length of the test had a downside that explained the unusually large 18.6 point white-black gap. Low IQ applicants, especially black males, often got discouraged by all the questions they couldn't answer and would give up, either not filling in the rest or bubbling in the rest of the way.

In 1997, the 105 page paper and pencil AFQT was replaced with a computerized test that dynamically changed the test to reflect performance so far. For instance, if you missed a lot of early questions, the computer would serve up easier questions. The white-black gap turned out to be 14.7 points on the 1997 normalization of the computerized AFQT.

Unfortunately, we don't know enough to be able to divvy up this 3.9 point narrowing of the white-black gap from one version of the AFQT to the next between the test methodology change and actual change in the size of the gap.

Somewhat similarly, Half Sigma hypothesizes that the brother result on the Norwegian equivalent of the AFQT is caused by older brothers being more conscientious. Perhaps they study harder in school and thus do better on the parts of the test that are less g-weighted. Or perhaps they just don't give up as easily.

Or this could be a real result.

The point is, however, that it's exactly backward for the media to get all worked up over one study reporting a 3 point difference between demographic groups (older and younger siblings) while ignoring the dozens of studies reporting much larger differences between demographic groups, such as between whites and Hispanics -- especially because the Senate is voting on an immigration bill right now!

The best estimate I've yet seen of Hispanic-American IQs is the 2001 meta-analysis by Roth of 39 studies covering a total 5,696,519 individuals in America (aged 14 and above). It came up with an overall difference of 0.72 standard deviations in g (the "general factor" in cognitive ability) between "Anglo" whites and Hispanics. The 95% confidence range of the studies ran from .60 to .88 standard deviations, so there's not a huge amount of disagreement among the studies.

One standard deviation equals 15 IQ points, so that's a gap of 10.8 IQ points, or an IQ of 89 on the Lynn-Vanhanen scale where white Americans equal 100. That would imply the average Hispanic would fall at the 24th percentile of the white IQ distribution. This inequality gets worse at higher IQs Assuming a normal distribution, 4.8% of whites would fall above 125 IQ versus only 0.9% of Hispanics, which explains why Hispanics are given ethnic preferences in prestige college admissions.

In contrast, 105 studies of 6,246,729 individuals found an overall average white-black gap of 1.10 standard deviations, or 16.5 points. (I typically round this down to 1.0 standard deviation and 15 points). So, the white-Hispanic gap appears to be about 65% as large as the notoriously depressing white-black gap.

So, the white-Hispanic IQ gap is about what you'd guess from observing life around you with your lying eyes: not as big and deleterious as the white-black gap, but not trivial either.

If a 3 point IQ difference between brothers is worth three articles in the New York Times, you might think that an eleven point gap between whites and Hispanics would be worth, oh, say, eleven articles, especially when the immigration bill is up for debate in the Senate. But almost nobody has ever mentioned Roth's finding in the press.