##
Am I getting regression to the mean right?

Posted by teageegeepea under

Blinded by Science,

Blogosphere soap opera
[10] Comments
At EconLog Brad DeLong’s comments about IQ not being able to explain why rich parents have rich kids (prompting Fabio Rojas to say DeLong had discovered sociology) sparked the following from commenter Dr. T

DeLong’s argument shows ignorance of biology and statistics. The reason we do not see regression to the mean with IQ is that human procreation is not random. Few high IQ people have children with partners of below average IQ. If a person with a 140 IQ marries a person of 130 IQ, the likelihood that their child will have a 100 IQ is less than 5% (unless there is premature birth or brain damage).

I’m not an expert, but that sounded wrong to me. I said this in reply:

Even with non-random mating, we should still expect regression to the mean. If Andre Agassi marries Venus Williams, their kids are probably not going to be as good at tennis as they were, even though they will likely be better than average. Both people are flukes, statistically unlikely outliers in the field (by that I mean tennis ability in the general population). In the random pairing of genes that will produce their children, it is unlikely lightning will strike yet again (though I admit that did basically happen with both Venus and Serena giving their folks a perfect batting average).

If people reading this are familiar with the concept, have I given an accurate description of how regression to the mean works?

### Like this:

Like Loading...

*Related*

November 27, 2007 at 7:40 pm

You are correct.

November 27, 2007 at 8:03 pm

As I understand it, regression will occur no matter if both parents are outliers. If heritability is .5, the kids regress halfway to the mean. By equal inheritance(close enough for people) then if mom has an IQ of 140, without assortive mating, her partner has an average IQ of 100, and the kids have an average IQ of(140+100)*.5=120. If there is assortive mating, then her partner will have an IQ of say, 110, and (140+110)*.5 =125.

There is still regression with assortive mating. Assortive mating also increases the standard deviation of the offspring generation.

November 27, 2007 at 9:22 pm

There can also be regression away from the mean if both parents are unusually close to the mean. We can’t predict in advance which way their kids will deviate though. If they are both outliers in the same direction we can more confidently predict that their kids will deviate the other way from the average of the parents.

November 28, 2007 at 8:25 am

And you know, I still got it wrong. The average numbers I gave are the parental generation means from which the offspring regress. So if the parental mean is 120, heritability is .5, and the population mean is 100, the offspring regress to an average 110. If the parental mean is 125, then they regress to an average 112.5.

November 28, 2007 at 10:27 am

Yes, you are correct. After reading the other commenter’s post three times, I realized that he misunderstands “regression to the mean” to mean “regression exactly to the mean”, i.e., an IQ of 100. Maybe it should be renamed “regression towards the mean”.

November 28, 2007 at 3:31 pm

nope, I got it. They offspring regress to the population mean. Average parental IQ=120, 50% heritability, pop mean =100, offspring mean=110

November 30, 2007 at 9:01 am

Rob,

I did not mean you; I meant the commenter that was quoted in the original post.

December 1, 2007 at 12:12 pm

Oh sorry. I kinda gots math anxiety (ie. I’m bad at it, and would rather ascribe my inability to emotion than intelligence. And because I was trying to argue two things at once, what regression to the mean is and what what happens with and without assortive mating, it would be super easy for me to get it totally wrong.

And TGGP, your site rox.

December 13, 2007 at 10:35 pm

So in other words, you have a theory that tennis-ability is preprogrammed into DNA…

Interesting.

If you stuck out your tongue right now, would you taste your colon or your intestines?

If Andre and Serena have kids, they will be, on average, highly athletic, with excellent coordination and reflexes. If they’re incredible at tennis depends entirely on practice.

December 16, 2007 at 5:06 pm

DaCracka, regression to the mean applies to a wide variety of phenomena, not just genetic ones. I believe it was originally discovered with regard to height, which has both genetic and environmental influences. I believe there are genetic factors behind tennis-playing ability, but that it is not wholly genetic.

If they’re incredible at tennis depends entirely on practice.It is always possible they will have a genetic disorder that makes them unable to walk or something, and no matter how much practice they have they won’t be able to overcome it. Try to use the word “entirely” sparingly.

If you stuck out your tongue right now, would you taste your colon or your intestines?That’s not very polite. I asked a question about regression to the mean and I requested that those who had a better grasp of it correct any misconceptions I displayed. Your answer does not give me any indication that you are familiar with RTTM.