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Friday, September 4, 2015

Either I Am Insanely Brilliant or Steve Hsu is Wrong Again

Steve Hsu made the claim that if parents have a mean IQ of n, their children will have a mean IQ of .6n.  Ok, my children have a mean IQ of 2.5 sigma.  That means that their mother and I have a mean IQ of 4.2 sigma.  Their mother has an IQ of 1.8 sigma, so my IQ must be 6.6 sigma.  Of course, that would statistically make me the smartest person in the world.  I think that there may be a different explanation.

The answer is that regression to the mean isn't 40%.  In fact making that assumption leads to other curious conclusions.  The Terman subjects had a mean IQ of 3.25 sigma.  Their children had a mean IQ of 2 sigma.  So, from this we can calculate the mean IQ of the spouses.  It is 3.4 sigma.  In other words, despite the difficulty of finding spouses in the same intellectual range for people with IQs above 2 sigma, the Terman subject managed to find spouses that were even smarter than themselves.

Let's take a more reasonable assumption.  Suppose the Terman subjects managed to find spouses at 2.5 sigma.  That is high and, actually, not very likely.  Still, from this we can conclude that regression to the mean would be about 30%.  This would calculate my IQ at 4.65 sigma.  High but at least not outrageous.

What astonishes me is that we don't KNOW the answer to the regression to the mean.  It is not a hard piece of research.

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