Wednesday, October 06, 2010

Some data on regression

See previous discussion here.

I grew up in a university town in the midwest. The population of the town was about 40-50K and that of the university about 30K. There was only one high school with a graduating class of just under 400, and about a quarter to a third of each class were faculty kids or children of administrators or people who worked at the nearby government labs (i.e., generally kids of PhDs).

About 20 kids each year score high enough on the PSAT/SAT to be National Merit Semi-Finalists (top .5 percentile). If our school were typical of the US as a whole, this number would be ten times smaller. Almost all of these 20 kids are children of people associated with the university or the labs. The cutoff for semi-finalist is about +2.5 SD (say, IQ 137), and since about 15% of the faculty kids are above this threshold one can obtain an average for the group of about +1.3 SD (IQ 124). Note I am assuming an SD of 13 for the faculty kids (rough estimate of residual variance given known parental midpoint; see link above), but stating everything in terms of the overall population SD of 15. I think a reasonable parental midpoint one can assign to the parents of this group is just over +2 SD (IQ=130) (e.g., the average of 135 + 125 or 140 + 120; remember -- this is the era before assortative mating). At the most extreme I suppose you could argue for midpoint as high as IQ 135 (e.g., the average of 145 + 125), or as low as 125 (135 + 115). I'd say at 95 percent confidence the parental midpoint is between 125 and 135.

These estimates are consistent with an additive heritability of at least .7, possibly much higher.

You could argue the kids are getting a boost from the environmental effect of being raised by eggheads, but adoption data suggests that shared environmental effects are relatively small. I suppose that environmental effects might reduce the additive heritability by .1 or .2 from the range given above.

Homework problem: how smart is the smartest kid at my high school at any given time? ;-)

If someone knows the figures for other similar places (e.g., Los Alamos has only one high school near the lab), please comment.

If you are from my high school and reading this on FaceBook, please don't be offended :-)

Enry Straker said...

Came across a quote by Alvarez that might interest you, since it talks about cognitive thresholds in different intellectual disciplines.

''The world of mathematics and theoretical physics is hierarchical. That was my first exposure to it. There's a limit beyond which one cannot progress. The differences between the limiting abilities of those on successively higher steps of the pyramid are enormous. I have not seen described anywhere the shock a talented man experiences when he finds, late in his academic life, that there are others enormously more talented than he. I have personally seen more tears shed by grown men and women over this discovery than I would have believed possible. Most of those men and women shift to fields where they can compete on more equal terms .''

David said...

I was one of two national merit semi-finalists in my county [we graduated about 800 kids a year, collectively]. The county was uniformly documented by the census to be 47% white, 47% black, and the rest a mix of asian backgrounds. The other kid was clearly, especially in hindsight, another level above me.

I offer this anecdotally, and by no means as counter evidence [more a testament to variability and along the lines of your study]. The other kid went to Virginia Tech for his bachelor's then followed up with a masters in materials, then moved to Detroit to be a materials engineer. He shipped out to South Carolina right before the car industry melted down, working in business development for less than a year before getting canned. He's been jobless for more than a year now. I nearly flunked out of school [at JoeBob State University] the first time, took a couple years off, then barely graduated from Big Southwestern State University. We were both kids of military parents.

The kid who was maybe in the 5th-10th range by this measure had parents who were [former clergy and] both had Ph.D.s [physics, chemistry; his mom was our high school physics teacher]. He went to MIT, then to Yale, married [then divorced, to the chagrin of his parents] a russian literary scholar, and is not a superconducting, quantum computing researcher at Chalmers.

ABCD said...

Yeah, I do realize you're talking about the expectation here. I'm not familiar with Jensen's work on this - links would be appreciated.

ben g said...

For what it's worth since I'm mentioned in this thread, here are my thoughts:

-The shared environment seems to be small, but significant even within groups. See here: http://www.gnxp.com/blog/2009/11/does-family-matter-for-adult-iq.php
This gives environmental hypotheses more breathing room and less need to rely on complex interactive models.

-On that link, I wrote that the environmental effect is related to SES. But the evidence supporting that claim is not very strong.

-Regarding the restriction of range hypothesis, it's hard for me to get excited about it, because the only empirical examination of it did not support it as significant:

"restriction in range in parent disinhibitory psychopathology and family SES had no effect on adoptive-sibling correlations for delinquency, drug use, and IQ. These data support the use of adoption studies to obtain direct estimates of the importance of shared environmental effects on psychological development."

The math of this study (http://www.springerlink.com/content/w592616nn3874j37/) is over my head, so if Steve or someone else better than me with math could check it out that would be great.

Also, common sense suggests that even with restriction of range (and every other criticism of adoption studies taken into account) you'd see some environmental effect.. Why isn't there one

-I'm open to the idea that group differences on IQ in adulthood are environmental, but there doesn't seem to be any good evidence for that.

-Educational and economic outcomes are influenced by which family you're raised in. And there is adoption literature to support that.. So no one here should be claiming that the adoption literature supports the idea that we live in a completely fair society..

As for core psychological characteristics like personality and intelligence, I'm not sure the same can be said though..

*Note that my entire discussion is limited to differences within modern, first world countries.