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    Originally Posted by ColinsMum
    ETA: we've talked about this often on this site. Here is a post I wrote last year to explain that "regression to the mean" doesn't work the way people sometimes think. Short version: if you think children's IQ will regress towards the mean of the population, you have to ask yourself "which population?" Humans? Primates? Mammals? PhD scientists?
    Since humans give birth only to humans, the 2nd and 3rd choices are silly. The PhD scientists choice is more plausible, if you are talking about their children, but we know that many children of two PhDs are not smart enough to get PhDs themselves, and that some of the offspring of non-PhD parents are.

    A blog post by Steve Hsu (author of the article that started this thread) on "regression to the mean" is at
    http://infoproc.blogspot.com/2008/10/regression-to-mean.html .


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    Good grief, he should really stick to physics. Sorry, Bostonian, but this guy is not someone to listen to, really.


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    Originally Posted by ColinsMum
    Good grief, he should really stick to physics. Sorry, Bostonian, but this guy is not someone to listen to, really.

    I just reread the blog post on regression to the mean and don't see the problem with it.



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    OK, let me spell out the first problem. (Calling MegMeg for the others!)
    Originally Posted by Hsu
    Consider a trait like height or intelligence that is at least partially heritable. For simplicity, suppose the adult value of the trait X is equally affected by genes G and environment E, so

    X = G + E

    where G and E are, again for simplicity, independent Gaussian random variables (normally distributed) with similar standard deviations (SDs).
    OK, for simplicity let's allow him that, setting aside the total implausibility of genes and environment being independent.
    Originally Posted by Hsu
    Suppose that you meet someone with, say X = +4 SD (i.e., someone with an IQ of 160 or a (male) height of roughly 6 ft 9). What are the likely values of G and E? It's more likely that the +4 SD is obtained from two +2 SD draws from the G and E distributions than, say, a +3 SD and +1 SD draw.
    In fact neither of those situations is even possible. Suppose G ~ N(mu_G, sigma^2) and E ~ N(mu_E, sigma^2) - he said similar SDs, we're giving the distributions identical SDs of sigma. Now given the independence assumption, X = G + E ~ N(mu_G+mu_E, 2sigma^2); that is, the SD of X is sqrt(2)sigma. So two +2SD draws from the G and E distributions correspond to an individual with x = g + e = mu_G + 2sigma + mu_E + 2sigma = (mu_G + mu_E) + 4sigma = (mu_G + mu_E) + 2sqrt(2)(sqrt(2)sigma). In words: in the X distribution, this person isn't a +4SD individual, it's a +2sqrt(2)SD individual.

    Totally basic error. Not the only one, nor even the only one I can see. Not someone I'm going to trust on matters where I might not spot the basic errors!


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    Yes, ColinsMum. Even I, non-mathematically gifted person, thought it was nonsensical to add the standard deviations like that. In addition in the previously linked slides he seems to present the regression to the mean of IQ scores in children as a fact, but in this blog post it's obviously conjecture. I think you've made other good points too, about picking populations for the supposed regression, etc. I'd buy perhaps that some regression happens in children, but not the way it's been presented.


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    Originally Posted by Iucounu
    In addition in the previously linked slides he seems to present the regression to the mean of IQ scores in children as a fact, but in this blog post it's obviously conjecture.
    There will be regression to the mean in IQ as long the correlation between the IQ of children and the average IQ of their parents is less than one. A lot of research has found this to be the case. Hsu is not breaking new ground here. Galton discussed regression to the mean in the 1800s.



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    Originally Posted by Bostonian
    Originally Posted by Iucounu
    In addition in the previously linked slides he seems to present the regression to the mean of IQ scores in children as a fact, but in this blog post it's obviously conjecture.
    There will be regression to the mean in IQ as long the correlation between the IQ of children and the average IQ of their parents is less than one. A lot of research has found this to be the case. Hsu is not breaking new ground here. Galton discussed regression to the mean in the 1800s.
    Really? Galton discussed regression to the mean of IQ scores in children of highly gifted parents that long ago, or did he just discuss height? Does Hsu have some source for his assertions of hard facts, for example the .6 factor etc., or are they just based on fiddlings with numbers in turn based on his assumptions of how it might work, with an admittedly simplified model, while demonstrating lack of knowledge of how the calculations ought to be made, and while allowing that the real world might not be that way? Stating some basic ideas about regression to the mean in general is not enough to convince me in this context.

    (Also, is there some independent corroboration, besides from the publisher of the test, about how g-loaded the current version of the SAT is?)

    I do detect a bit of an agenda on the part of Hsu. It's not really based on disagreement with anything he believes; I at least would agree that if racial differences in intelligence exist, and are valuable to discuss, we should do so without fear.


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    Originally Posted by Iucounu
    Originally Posted by Bostonian
    Originally Posted by Iucounu
    In addition in the previously linked slides he seems to present the regression to the mean of IQ scores in children as a fact, but in this blog post it's obviously conjecture.
    There will be regression to the mean in IQ as long the correlation between the IQ of children and the average IQ of their parents is less than one. A lot of research has found this to be the case. Hsu is not breaking new ground here. Galton discussed regression to the mean in the 1800s.

    Really? Galton discussed regression to the mean of IQ scores in children of highly gifted parents that long ago, or did he just discuss height? Does Hsu have some source for his assertions of hard facts, for example the .6 factor etc., or are they just based on fiddlings with numbers in turn based on his assumptions of how it might work, with an admittedly simplified model, while demonstrating lack of knowledge of how the calculations ought to be made, and while allowing that the real world might not be that way? Stating some basic ideas about regression to the mean in general is not enough to convince me in this context.

    Here is what the Wikipedia says about the heritability of IQ
    http://en.wikipedia.org/wiki/Heritability_of_IQ#Estimates_of_the_heritability_of_IQ .

    "Various studies have found the heritability of IQ to be between 0.7 and 0.8 in adults and 0.45 in childhood in the United States.[6][16][17] It may seem reasonable to expect that genetic influences on traits like IQ should become less important as one gains experiences with age. However, that the opposite occurs is well documented. Heritability measures in infancy are as low as 0.2, around 0.4 in middle childhood, and as high as 0.8 in adulthood.[7][18] One proposed explanation is that people with different genes tend to seek out different environments that reinforce the effects of those genes.[6]
    A 1994 review in Behavior Genetics based on identical/fraternal twin studies found that heritability is as high as 0.80 in general cognitive ability but it also varies based on the trait, with .60 for verbal tests, .50 for spatial and speed-of-processing tests, and only .40 for memory tests.[5]
    In 2006, The New York Times Magazine listed about three quarters as a figure held by the majority of studies,[8] while a 2004 meta-analysis of reports in Current Directions in Psychological Science gave an overall estimate of around .85 for 18-year-olds and older.[7]"

    The site has the citations. The level of heritability depends on how "child IQ" is measured. Hsu's 0.6 estimate is not implausible. As long as heritability of IQ is significantly less than one -- and all researchers have found that to be the case -- there will be some regression to the mean in IQ, just as there is in other human traits, such as height and athletic ability.


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    Originally Posted by ColinsMum
    OK, let me spell out the first problem. (Calling MegMeg for the others!)
    [quote=Hsu]

    where G and E are, again for simplicity, independent Gaussian random variables (normally distributed) with similar standard deviations (SDs).


    This seems like an awfully big assumption to make. He gives no justification for why we should assume G & E are independent and normally distributed, with similar standard deviations. Much less how we would or could go about actually measuring these values in the first place.

    In addition, I would also point out that the children would have their own E, thus their "X" is not fully dependent on their parents X anyways. So even if you took his calculations as accurate, if you could calculate the parents' X, at most this could only give you the child's G (and that's being generous) but would not be related to their E, thus their outcome could be significantly different than their parents.

    I agree with Colinsmom, he should stick to physics.


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    Originally Posted by Bostonian
    Hsu's 0.6 estimate is not implausible. As long as heritability of IQ is significantly less than one -- and all researchers have found that to be the case -- there will be some regression to the mean in IQ, just as there is in other human traits, such as height and athletic ability.

    Hsu doesn't present his estimate as an estimate, just asserts it as a fact. Elsewhere he admits there may be confounding factors. I'm simply not convinced, though I would never argue that intelligence cannot be inherited or that it is completely based on the intelligence of the parents.

    ETA: In thinking of ColinsMum's objection regarding which mean to use, I'm thinking now that the mean that makes the most sense is that of biological children of the same parents, raised in the same environment. I'd like to see a plot of the average IQs for children of high-IQ people, if anyone can find some.


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