Monday, August 09, 2010

IQ regression from Terman data

A reader sent me a link to some data on regression from Eysenck's book The Structure and Measurement of Intelligence. (I actually own this book but had forgotten about these results!) Eysenck quotes from the Terman study:

1528 California children with IQs of 140 or higher were followed into adulthood in order to assess the importance of IQ in adult success and adjustment. The mean IQ of those that married and had children was 152; that of their spouses, 125. The mean IQ of this whole group of parents was 138.5. The mean IQ of 1571 of their children was 133.2, a little less than the parents and showing some regression to the mean.

These results show very little regression -- less than would be predicted from the estimates given in my earlier post. However, I suspect a correction needs to be applied as the Terman study was done before the Flynn Effect was understood. If the same version of the Stanford Binet was used on the parents and children, without Flynn re-norming, then the children were not as exceptional as implied by the 133 average given above. If we take the Flynn Effect in mid-20th century America to be about 10 points per generation (this is just a rough guess), then the 133 should be corrected to about 123, and is pretty consistent with the estimate I gave of: 100 + .6(38.5) = 123, which assumes narrow sense heritability h^2 = .6.

The discussion by Eysenck uses higher heritability numbers (note the non-negligible V_CE = variance due to common environment). If the Terman study used re-normed tests then their data would be evidence for much less regression than in my estimates.


Yan Shen said...

I've always wondered whether or not people with significant differences in IQs could be intellectually compatible with one another in a long term relationship. I wonder what the distribution for IQ differences between spouses would look like? What would be the average difference in IQ between married couples in society today and the corresponding sigma? The 27 point IQ gap on average between the spouses in the study seems rather significant to me. How large can the IQ gap become before two people have trouble sharing the same kinds of values or intellectual interests? But then again, if your IQ is as high as the 150s, you undoubtedly have access to a relatively low pool of potential mates who possess a similar degree of cognitive aptitude, particularly if you're male and all of those claims about lower variance in the female IQ distribution and possibly even a slightly lower female average IQ turn out to be true. ;)

steve hsu said...

Men in that generation probably did not expect intellectual compatibility with their spouse. If I had to guess I would venture that the gap is significantly smaller now -- these days, you find a lot of Ivy-Ivy, PhD-PhD, Prof-Prof or MD-MD pairings.

In my limited experience the smaller variance in females seems real (well, I guess you can confirm definitively by looking at data from the pre-1995 SAT, which had a high ceiling) and it has consequences for guys in the tail seeking a mate.

Max said...

Look do you seriously believe that Flynn effect actually applies to high IQ individuals? As far as I am aware ( I could be wrong) it was mostly for "general" population. I am seriously skeptical whether it exists at all if you do not take into account large masses of inherently stupid malnutritioned individuals .

I think you making same mistake here you made before with estimating regression to the mean - you apply general population statistics to the 3-4 stddev segment of it

Steve Sailer said...

The 1979 National Longitudinal Study of Youth famously acquired IQ data on young people. Less known is that it has now given IQ tests to quite a few thousand children of women in the study. So, that would be an excellent source of data on mother-child regression. Somebody has probably studied it by now, although I don't know who.

Samh550 said...

Rumor has it that La Griffe is a sociologist (!); yet, the man knows math.

Here I am a lowly, 3rd tier MBA guy, confused by his statistical outputs. :-(

ben g said...

Flynn effect has indeed mainly been focused on the lower part of the bell curve

Yan Shen said...

Steve Sailer, you seem to have a penchant for not putting comments that make you or your readers look bad up on your blog, but you'll let comments slip by that contain explicit racial slurs against non-white minority groups. What's up with that buddy? I would've imagined that someone in your position would be desperate to legitimate the white nationalism that he advocates so heartily. If so, shouldn't you welcome comments that add a certain degree of intellectual rigor to the discourse you engage in, even if those comments can be somewhat confrontational in nature? Instead, you seem mostly content with cultivating masses of fawning acolytes, and even allowing your readers to express explicit racial animus against Jews and other non-white minority groups. That doesn't seem like a very smart thing to do, if what you want to accomplish is to legitimate your ideas with mainstream society at large and to debunk the stereotype that that HBD community is full of dumb white racist rednecks. Instead, not only do you allow this kind of bad behavior to persist on your blog, you even seem to encourage it. I suspect that the reason for this is that you've resigned yourself to the fact that HBD will always be considered a fringe movement within polite society at large, and so you're more or less content to become a cheerleader for the masses of not too bright white guys who want to have their voices heard.

Yan Shen said...

Let me add two more things to the post below. For someone who's half Jewish himself(your biological father was Jewish by your own account), you seem to express a startling degree of anti-Jewish animus in some of your posts. This behavior immediately recalls to mind that of Bobby Fischer, another person with Jewish ancestry who in real life didn't always say the nicest things about the Jewish people. Are you so desperate to be accepted by gentile white society that you would turn your back on an important part of your own heritage?

And for someone who enjoys writing about HBD issues and who likes focusing on the salience of IQ, you seem to be remarkably sympathetic to the white underclass(some of whom no doubt are prolific readers of your blog, though I doubt they understand everything that you write, most of them just relish any opportunity to bash non-whites). Shouldn't a cognitive elitist privilege high IQ individuals over low IQ individuals regardless of race? In your debates with Jared Taylor, you've taken great pains to assert that you embrace "citizenism" as opposed to "white nationalism", but your behavior often seems to reflect the latter mentality, as opposed to the former. Isn't it highly contradictory to claim that you're advocating "citizenism", but then to engage in behavior that clearly panders to the masses of whites, ahead of other American ethnic groups? Clearly you've adopted this mentality that white Americans are "real" Americans in a way that non-white American citizens aren't, though you don't explicitly state this. You perpetuate this us versus them mentality that's painfully obvious to any clear-headed reader of your blog. In effect, you relegate non-white American citizens to the status of "perpetual foreigner". How does that parochial tribalism accord with the principles of "citizenism" which you've espoused? Are you advocating a universal set of principles applicable to everyone, such as the right to self-preservation, or are you merely pursuing the narrow self-interest of whites ahead of all other people. And if you embrace the latter, why do you excoriate other minority groups, such as the Jews, for doing the same thing that you're doing? Wouldn't a mentality of empathetic understanding be more appropriate in that case?

I've tried bringing these points up in the comments section of your blog in the past, but I noticed that the relevant posts conveniently failed to show up. :) Shame on you Steve, shame on you.

steve hsu said...


Imagine that the bottom fraction (whether it is 1/2 or 2/3 or 4/5) of the distribution gets a 1 SD boost in score between 1930 and 1970. If the 1930 distribution was normal, then the 1970 would not be, and vice versa.

I've never seen any broad psychometric study (using, e.g., army recruits) that had large deviations from normality. So I don't see how gains could be concentrated in the lower part of the curve. The psychometricians of 1930 or 1970 would have noticed something funny! Perhaps they just missed it, but I've never seen this discussed in the literature. To the contrary, everyone assumes a normal distribution and even that the variance stays constant over time. The only way this can happen is if the FE is fairly uniform over the whole distribution.

It is possible that the FE didn't affect the tiny upper tail (e.g., above +(2-3) SD), but then we'd see a secular increase in the "fat tail". However, due to small statistics, this isn't as well studied.

Pincher Martin said...

Don't you have to first identify the ethnicity and race of the parents before you can make an accurate prediction as to what kind of regression to the mean you should see in their kids' IQs? For example, if those 1500+ children who were followed into adulthood were all Jewish, shouldn't we expect a much different regression to the mean than if they were all non-Jewish whites?

Catperson said...

Failure to norm for the Flynn Effect is an excellent explanationand who knows how much other research is invalid for this same reason. The Stanford Binet is notorious for having gone 70 years without being renormed causing a generation of kids to mistake themselves for geniuses. And yes the Flynn Effect does apply to the gifted because it's caused by the same improvements in nutrition that makes us taller (and the secular rise in height impacts has not just eliminated most short people, but created more super tall people). On the other hand I think most people exaggerate how large the Flynn Effect is (especially on a mostly verbal/knowledge based test like the Binet since nutition mostly impacts non-verbal ability and a lot of verbal items become harder as tests become obsolete). Also, do we know how old the kids and parents were when tested. Even though IQ becomes more herritable with age, is it possible that the parent-offspring correlation decreases with age? Perhaps gifted parents provide extremely good environments but as the importants of environment decreases, the kids regress more. It would be interesting to see a similar study on children raised by retarded parents. I suspect their IQ's would increase with age as they spent less and less time at home.

Catperson said...

Another possibility is that the parents (especially the spouses) were tested as adults, while the kids were tested as children. For example according to the WISC-R manual, a 10 year old with the vocabulary of a 13 year old, is in the 90%ile among 10 year olds and the 90%ile is IQ 120 on the deviation IQ scale, however on older versions of the Binet, a 10 year old who performs like a 13 year old has an IQ of (13/10 = 1.3 )* 100 = 130. Thus if we assume the IQ's of the kids was inflated by 10 points because of the way it was calculated, then their IQ's really were 123.

Michael Ferguson said...

Steve, I think you are stretching here. Terman renormed his tests, first the CMTU-A, then the CMTU-T. I assume that at all times, given the general rigor of the study, modern tests were given to subjects. I believe that the implied 15% regression to the mean is appropriate.

Michael Ferguson said...

Also, I have conceptual problems with notion of 40% regression. I took one IQ test and exceeded the ceiling. However, I have, somewhat in jest, suggested that my children and their mother inferentially give me an IQ. My children have a mean IQ of +2.87. Their mother has an IQ of 1.85. (2.87/.85)*2-1.85 = 4.89 or about 181 (15 point), which is a plausible result. However, if one assumes (2.87/.6)*2-1.85 = 7.72 or about 227, which is not plausible. Clearly, this is not to be taken overly seriously, since I only have three children and that does not constitute a valid statistical sampling. However, some of my ceiling busting friends have also done the calculation for themselves and ended up with the same situation, plausible at 15% regression, not plausible at 40%.

I can look at it the other way around. If I were to assume that my raw score was accurate, which Grady Towers suggested it may be, my IQ test score would have been at +4.077. With your 40% regression, my children should have a mean IQ at +1.78 instead of 2.87. That is a pretty big variance even for a small population. None of my high IQ friends have experienced that level of regression, either. I don't believe that anecdotal evidence trumps well constructed experimental evidence. However, in this case, I am simply saying that I am inclined to accept Terman's study at face value, sans a Flynn Effect adjustment.

Also, not to quibble, but a 7.5 years per generation would probably be more centrist.

Michael Ferguson said...

Using Eysenck's 4 point gender difference and the relative frequency of males and females at various IQ levels, Paul Cooijmans estimated for women mean IQ 98, SD 13.7, men mean IQ 102 SD 16.3 I use these for all my gender related IQ calculations as 'better than nothing.'

As to the speculation on assortative mating with respect to IQ, it is the highest assortive factor at .4. Funny, this is twice in one day, I did have a citation that suggested that the higher the mean IQ the greater the assortive mating. But, of course, I can't find it.

Michael Ferguson said...

Steve, the second link is dead. However, I did find it by reproducing your google search. Heritability measures do not directly relate to regression to the mean. If we assume that the environmental factors are random as to IQ, then an expected regression would be 50%. However, clearly, they are not random. Two things. First, the heritability found in this study is on the low side. A conservative midpoint would be 60%. The study you quote claims to have calculated a r^2 for environment of .16. If we used these numbers we would expect a regression of 34%.

There are some interesting data suggesting that most of the 'enviromental' influences of IQ are prenatal. This would seem to argue against such a low environmental component. However, if it is due primarily to differences in actual ontogeny, which would be indistinguishable, statistically, from prenatal environment, then near randomness would be expected.

If I were to approach this theoretically, I would use a heritability factor of .7 (about what was found in the U of Minnesota twin study) and an environmental factor of .5, I will get regression expectation of 15% or what was found by Terman. For all these reasons, and those mentioned in other posts, I am disinclined to be argued down too far from 15%. Certainly, I consider 50% as absolute maximum.

steve hsu said...


Thanks for your comments. I would be pleased if my estimates of regression to the mean were too high :-)
When I have some time I will alert James Lee (Pinker's student) to your comments as perhaps they will change his mind as to what the best central values are for these estimates.

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