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Regression Toward The Mean And IQ
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January 28, 2013, 03:24 PM
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A reader sends me an Excel file for calculating expected IQs of children based on their parents` IQs. 

As I`ve been pointing out for a long time, these questions are of particular interest to the infertile and to lesbians. (I coined the term "lesbian eugenics" to summarize the issues that lesbian would-be mothers confront in picking a sperm donor, but it hasn`t caught on. After all, as we all know, lesbians are Good and eugenics is Bad, so ... Does Not Compute!)

I am an avid reader of your site for ~10 years (not even sure since when) and wanted to email you about a Steve Sailer / Steve Hsu inspired analysis I did over the weekend ... The topics are intelligence, heredity and mating (I am 32 year old single male considering the best course of action).


The best course of action is probably to find somebody you like talking to because you are going to be doing that for a long time. But, all this stuff is definitely interesting.

This is is based on a presentation by Steve Hsu entitled "Investigating the genetic basis for intelligence".

On slide 19 of the presentation, with the header "Your kids and regression" Steve writes "Assuming a parental midpoint of n standard deviations above the population average the kids` IQ will be normally distributed about a mean which is around +0.6n with residual standard deviation of about 12 points." He also gives a helpful example immediately below "So, e.g., for n=4 (parental midpoint of 160 - very smart parents!), the mean for the kids would be 136 with only a few percent chance of any kid to surpass 160 (requires +2 standard deviation fluctuation)."


I`ve seen estimates of the "narrow sense heritability" of IQ ranging from 0.34 to 0.86. At the lowest figure, the two 160 IQ parents` children would average 120 and at the highest, 152. But, as my reader points out, for most values in the middle of that range, the implications he draws are still more or less true.

Another thing to keep in mind is that this assumes that the IQs of grandparents and earlier ancestors are unknown. In contrast, the Darwin-Wedgwood-Galton-Keynes-Benn-Vaughan Williams extended family seems to regress toward a higher IQ than 100, as do the Huxley-Arnolds.

Here are some implications the reader draws, assuming a 0.6 figure.

1) Mating insight

Many nerdy or high achieving men bent on reproducing are troubled by the fact that most intelligent women want a career and likely do not want to have children (or want to adopt orphan baby at age 50, once they have “made it”). Women who are slightly less intelligent may want to have families and even to have bigger families. The above Excel file lets one see the impact of say a man with an IQ of 140 marrying a woman with an IQ of 140 and having only one child (whose expected IQ would be 124) vs. that same man marrying a woman with an IQ of 120 and having three children. The second man`s highest IQ child will have an expected mean IQ of 128 which is higher than the man who married the smarter woman but had only one child. Even if the smarter woman chooses to have two children the two smartest children out of the three children that the less intelligent woman had will have approximately the same expected IQ as the two children of the high IQ woman.

Takeaway - twenty IQ points is a lot: 120 vs. 140 is a big difference and it will be by definition much harder to find a woman with an IQ of 140+ (one in 261) vs. one with an IQ of 120+ (one in 11) and it will be much more difficult to persuade your wife to give up IQ 140-career track (Fortune 500 CEO, Ivey League tenured professorship etc.) than IQ 120-career track (nurse, high school teacher etc.) for changing diapers in the middle of the night. If one is concerned about having one or two competent kids to whom one can leave the family business to one might consider finding a slightly less intelligent woman who is willing to have a few kids. Of course there are other factors. Having more children means giving each child less attention but spacing births helps mitigate this and we know that nature dominates over nurture in this matter anyhow. Not to mention that having only one child can result in tragedy if god forbid something was to happen to it.

2) The speed of the regression to the mean.

If one starts with two parents whose IQs are 160 and looks at the average IQs across generations the speed of the regression to the mean is quite fast.

Parents 160, 160

Children average 136 (assume these mate with a 136)

Grandchildren average 122 (assume these mate with a 122)

Greatgrandchildren average 113 (assume these mate with a 113)

There is already a huge drop between the grandparents and the grandchildren. So in just 4 generations the regression to the mean has brought down the Nobel-prize-level grandparents to the pretty much average intelligence. (all this is of course "on average")

This might be a reason why the intellectual elite might want to pay more attention to making America a country where those with IQs of 110-115 can still live satisfying lives with good middle class jobs and publicly funded services. Chances are that most of their descendants will need those jobs and services only century from now; after all “fool and his money are soon parted” – even if dimmer kids inherit billions chances are that they will not have what it takes to keep the wealth in the long run.  

3) "Geniuses belong to the people"

Imagine that with two parents with IQs of 160 set out to produce one child with the same IQ. How many kids we can expect them to have before they succeed? They would have to have 44 kids to have one kid whose IQ would be 160 or higher on average! This is clearly impossible. And if they set standard to IQ 170 - they would require 434 kids!!! Thus geniuses are really borne out of a people and not out of any two particular parents. Having smart parents helps, a lot, but even then, the chances that your little one is going to be the next Newton are small. Very, very small. On the other hand, according to historians none of Newton’s paternal kinsfolk were able to even sign their names. 

4) "The advantage of the rich - buying IQ points through marriage?"

Say you have a family scion with an IQ of 160 who marries a woman with an IQ of 132 (so top 2%). And then their kid perhaps regresses but he leverages family fortune and name to marry a woman with an IQ of 132 and so on and so on. (Sure he might not be the smartest but he`s rich so why not marry him). Assume other generations repeat the same trick. What happens?

In just three generations the IQ falls to 114 and stays there. The 132 woman helps keep it at 114 vs. falling back down but it doesn`t go up.

Thus another conclusion, being multi-generational rich helps, you can buy intelligence and ensure that your kids are one standard deviation higher than the average. That is a lot, but it also allows for a lot of overlap between the populations. (Especially because never dipping under the IQ 132 threshold is an optimistic assumption - it assumes multi-generational saintly resistance to blonde bimbo`s charms). Thus, richer kids are on average smarter but plenty of them are dumber than the average Joe.