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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 :-)

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