On the real possibility of human differences

By Razib Khan | November 26, 2011 1:16 pm

I have discussed the reality that many areas of psychology are susceptible enough to false positives that the ideological preferences of the researchers come to the fore. CBC Radio contacted me after that post, and I asked them to consider that in 1960 psychologists discussed the behavior of homosexuality as if it was a pathology. Is homosexuality no longer a pathology, or have we as a society changed our definitions? In any given discipline when confronted with the specter of false positives which happen to meet statistical significance there is the natural tendency to align the outcome so that it is socially and professionally optimized. That is, the results support your own ideological preferences, and, they reinforce your own career aspirations. Publishing preferred positive results furthers both these ends, even if at the end of the day many researchers may understand on a deep level the likelihood that a specific set of published results are not robust.

This issue is not endemic to social sciences alone. I have already admitted this issue in medical sciences, where there is a lot of money at stake. But it crops up in more theoretical biology as well. In the early 20th century Charles Davenport’s research which suggested the inferiority of hybrids between human races was in keeping with the ideological preferences of the era. In our age Armand Leroi extols the beauty of hybrids, who have masked their genetic load through heterozygosity (a nations like Britain which once had a public norm against ‘mongrelization’ now promote racial intermarriage in the dominant media!). There are a priori biological rationales for both positions, hybrid breakdown and vigor (for humans from what I have heard and seen there seems to be very little evidence overall for either once you control for the deleterious consequences of inbreeding). In 1900 and in 2000 there are very different and opposing social preferences on this issue (as opposed to individual preferences). The empirical distribution of outcomes will vary in any given set of cases, so researchers are incentivized to seek the results which align well with social expectations. (here’s an example of heightened fatality due to mixing genetic backgrounds; it seems the exception rather than the rule).

Thinking about all this made me reread James F. Crow’s Unequal by nature: a geneticist’s perspective on human differences. Crow is arguably the most eminent living population geneticist (see my interview from 2006). Born in 1916, he has seen much come and go. For those of us who wonder how anyone could accept ideas which seem shocking or unbelievable today, I suspect Crow could give an answer. He was there. In any case, on an editorial note I think the essay should have been titled “Different by nature.” Inequality tends to connote a rank order of superiority or inferiority, though in the context of the essay the title is obviously accurate. Here is the most important section:

Two populations may have a large overlap and differ only slightly in their means. Still, the most outstanding individuals will tend to come from the population with the higher mean. The implication, I think, is clear: whenever an institution or society singles out individuals who are exceptional or outstanding in some way, racial differences will become more apparent. That fact may be uncomfortable, but there is no way around it.

The fact that racial differences exist does not, of course, explain their origin. The cause of the observed differences may be genetic. But it may also be environmental, the result of diet, or family structure, or schooling, or any number of other possible biological and social factors.

My conclusion, to repeat, is that whenever a society singles out individuals who are outstanding or unusual in any way, the statistical contrast between means and extremes comes to the fore. I think that recognizing this can eventually only help politicians and social policymakers.

You can, and should, read the whole thing. Let’s make it concrete. Imagine the following trait with two distributions (i.e., two populations):

– Mean = 100 and 105 (average value)
– Standard deviation = 15 (measure of dispersion)
– Let’s assume a normal distribution

Let’s plot the two distributions:

Observe the close overlap between the two distributions. Most of the variance occurs within both sets of populations. Now let’s impose a cut-off of about ~130 on the curves:

Now the similarity between the two curves is not as striking. As you move to the tails of the distribution they begin to diverge. In other words, the average of the two populations is pretty much interchangeable, but the values at the tails differ. Now let’s move the cut-off to 145:

The difference is now even more stark. Let’s compare the ratios of the area under the curve for the two populations as defined by the cut-offs:

Value at 100 = 1.26 (any given individual in the blue population is 1.26 times more likely to be above 100 than in the red population)
Value at 130 = 1.83
Value at 145 = 28

A major caveat: quantitative traits are only approximately normally distributed, and there tends to be a “fat tail” dynamic, where deviation from the normal increases as one moves away from the mean. Concretely, this means that the ratios at the tails are probably not quite as extreme, as there are more individuals in all populations at the tails than you’d expect.

What does this entail concretely? As Crow noted above if you sample from the tails of the distribution then very modest differences between groups become rather salient. Consider long distance running. To be successful in international competitions one presumably has to be many, many, standard deviations above the norm. One can’t be a 1 out of 100, or 1 out of 1,000. Rather, presumably one should be 1 out of hundreds of thousands, at a minimum. This would be the fastest ~100,000 or so people in the world (out of 7 billion). With this in mind, we should not be surprised a priori at the success of the Kalenjin people of Kenya in this domain. They may have both the biological and social preconditions which allow their distribution of talent to be moderately above that of the human norm. Even a marginal shift can make a huge difference at the tails. 1 out of 100,000 is 4.26 deviation units above the mean. Increasing the mean of a population by half a standard deviation units (e.g., if 100 is the mean, 15 is the standard deviation, then for the population with the higher mean you’d be at 107.5) results in a disproportion in ratio of above 8:1 at 4.26 units (as measured in the first population). This is modest, about 1 order of magnitude, but consider possible gene-environment correlations and synergies that might ensue when you have a critical mass of very fast individuals. This could amplify the effect of a difference in distributions on a single variate (more importantly I suspect, consider that virtuosity in many domains requires an intersection of aptitudes many units deviated from the norm across many traits).

In the early 2000s James F. Crow was responding to the Human Genome Project. As has been thoroughly covered elsewhere human genomics has probably underwhelmed in terms of outcomes 10 years out. But it is often the case that with new technologies we overestimate the short-term change which they will effect and underestimate their long-term consequences. I believe with the rise of mass genomics, a radical increase in population coverage and full genome sequencing, we may finally start to adduce the underpinnings of quantitative traits. We already have indirect methods, but I believe that by 2020 we will have direct means at our disposal. We’ll have a good sense how deeply humans are commensurable on a population genetic level. I doubt it will change much in our values, but it may entail some rhetorical adjustments.


Comments (18)

  1. There’s another related issue that’s very close to this: If one population has a larger standard deviation than the other one will also see similar results when one looks at the extreme.

  2. #1, yes. though this obviously quite sensitive to aggregating distinct populations into one pool. ‘multi-modality.’

  3. jb

    Here is something I have wondered about for a while. For traits that we can’t assign a directly measured number to, intelligence in particular, how do we know that they are even approximately normally distributed? If you give an intelligence test to 100 people, all that any test can ever give you is an ordering, from who did best to who did worst. My understanding is that, in order to come up with an actual measure (i.e., IQ), the people who make intelligence tests just assume a normal distribution.

    So do we have any good reason to believe that that assumption is even remotely right? For example, consider the possibility that “true intelligence” (whatever that might be) actually tails off according to a power law. Are our current test protocols good enough to rule this possibility out, or are we just assuming the possibility away by always fitting our results to a normal curve?

  4. DK

    My understanding is that, in order to come up with an actual measure (i.e., IQ), the people who make intelligence tests just assume a normal distribution.

    All IQ tests are normed – i.e., their scoring is made to conform to normal distribution. A typical norming group has N ~ 1,000-2,000, so other than statistical deviations at the tails, distribution of IQ scores will always be normal. A reason to believe that such norming is a right thing to do is the Central Limit Theorem.

  5. free thinker

    I am sympathetic to the notion that autism may be caused by exposure to a pathogen. Hereditary diseases NEVER erupt as “epidemics.” There may have been some increase in assortive mating in the last generation, but that seems like a feeble explanation for what we are seeing. I believe that there have been some studies that show clustering at the level of daycare centers. Everyone knows that it clusters in communities which have seen a lot of recent immigration from India. Probably it is like polio. Early exposure causes no harm, but there is a critical window of development where the pathogen or the body’s attempt to fight off the pathogen causes the brain to develop abnormally. I think Greg Cochran might agree with me.

  6. observer


    I think that the presumption with regard to whatever it is that IQ is getting at — suppose it’s the g factor, or something highly correlated with the g factor — it should observe the same constraints that apply to any additive genetic trait. For reasons both theoretical and empirical, those traits, in the paradigm cases that we can accurately measure (such as height), do conform quite well to a normal curve, even toward the tails. If there’s a deviation from that curve, there would have to be special circumstances to explain it (i.e,, some significant non-additive feature that crops up at those tails). It’s likely that some of the left tail can be so explained (various kinds of genetic defects, many of which we already know), but not so likely, I think, that there are at the upper end (I don’t think there are known genes that engender great intelligence — one would think that such genes would have already swept through the population if there were).

  7. Well, I assume the logical next question would be, so what?

    Answer would be, I assume, that you think this line of argument means that we shouldn’t wonder at racial or sexual skews at the tail ends of social reward bell curves.

    But, I think you will agree, long distance running is a massively oversimplified model if you are looking at much more general social outcomes.

    For instance, practically everyone–say 99.9% of 7 billion–desires certain socio-economic outcomes–enough money to live comfortably, to make choices in ones life, to minimize the suffering on ones children etc. etc. Practically no one cares whether or not they are the world fastest marathon runner. It’d be nice, but it’s not what we’re here for.

    So in terms of scale and stakes, the long-distance running as a metaphor obscures rather than elucidates.

    Let’s look, rather, at the bell curve of the game a great many people are actually involved in and concerned about–making money.

    Would you say that the tail ends of the wealth bell curve directly reflects some sort of genetic “deservingness?”

    I’m skeptical. Why? Because economic rewards are doled out in a far, far more complicated fashion than, say, Boston Marathon winnings. If I want to win the Boston Marathon, what do I have to do? Run and do well in a qualifying race, over a set course of a particular distance with particular rules as to how to how to conduct oneself and a remarkably accurate timing method, thereby qualifying for Boston. Then I must run and win at Boston.

    There are loads and loads of rules and technologies brought to bear that make marathons as pure a measurement of 26.2 mile running speed as we can make it.

    If I want to destroy a company and get a 36 million dollar golden parachute, what do I need to do? Well, truth be told, there is no method by which anyone can do this. It is a privilege reserved for a few of us. How chosen? Well, that’s a complicated question. Orders of magnitude more complicated than the marathon question. And if you do not understand the process, you cannot possibly understand the meaning of the outcome, and relating the outcome to this gene or that becomes . . . meaningless.

  8. Miley Cyrax

    @Oran, #8

    “Answer would be, I assume, that you think this line of argument means that we shouldn’t wonder at racial or sexual skews at the tail ends of social reward bell curves.”

    Wondering is one thing, but resource and opportunity transferring from Asian and whites to blacks and latinos in the name of social justice and fairness is another.

  9. Answer would be, I assume, that you think this line of argument means that we shouldn’t wonder at racial or sexual skews at the tail ends of social reward bell curves.

    don’t assume again, or i’ll ban you (again, i thought i’d banned you?). e.g.,

    Would you say that the tail ends of the wealth bell curve directly reflects some sort of genetic “deservingness?”

    i don’t agree that the extremely wealth are more genetically deserving. that’s what you get out of assuming someone’s views when left unstated, you shadow-box with strawmen of your own liking. DON’T DO THAT!

  10. Justin Loe

    An established empirical connection between intelligence (mental retardation) and biological phenotype in the brain is neuronal structure. In mental retardation (Fragile X syndrome) there are observed distortions in the dendritic trees of those with mental retardation (in a mouse model) in comparison to the normal dendritic trees of unaffected individuals. See here: http://www.ncbi.nlm.nih.gov/pubmed/21371563

    Subregion-specific dendritic spine abnormalities in the hippocampus of Fmr1 KO mice, 2011

    As I recall, I believe there have been some unreplicated findings in intelligence research with respect to a few snps connected to synaptic vesicles. It would seem reasonable that genes connected to synaptic plasticity would be connected to intelligence, but the results have not been confirmed.

    Obviously, confirming dendritic phenotype in human subjects has not been easy, and there have been few volunteer participants for these projects.

  11. jb

    @DK (#5) & observer (#7)

    I’m aware that there are good theoretical reasons to expect that traits like intelligence ought to follow a normal distribution, but that doesn’t necessarily mean they do. Please understand: I’m not arguing that intelligence is not normally distributed, I’m just trying to understand the basis for believing it is. Is this belief based purely on abstract theoretical considerations, like the Central Limit Theorem? Or are there more concrete reasons?

    One motivation for my question is what has happened in the financial markets. People assumed, based on what they considered good theoretical reasons, that certain risks could be modeled by normal distributions, and they made huge bets based on that assumption. But as reasonable as that assumption was, in retrospect it’s looking like it might have been wrong. So how confident should we be that we are not also wrong about the way intelligence is distributed? In his post Razib noted the possibility that traits might have “fat tails.” What I’m wondering is to what degree fat (or thin?) tails would be obscured by the assumption of a normal distribution, and just how nonstandard a tail would have to be before we would be forced to notice that there was something wrong with our assumption.

  12. #12, to my knowledge they do have fat tails. it’s not a possibility. i assume the issue is what DK noted above, that the sample sizes are on the order of 1,000, and you’re not getting too many people who are many many sigmas above the norm. the key would be to look at height and see if it fat tails….

  13. DK

    @jb: No doubt the fat tails are suppressed by norming. With larger norming sizes, it would be possible to further reduce them – it would obscure real distribution but increase analytical power at >3SD. AFAIK, it’s never thin tails, always fat – which, I think, hints at the underlying multimodal distribution rather than just statistical flukes. This can be expected if the ‘general’ sample is already relatively stratified (extreme case: take 1000 Pygmies and 1000 Han – the real distribution will be bimodal).

    I am curious about your financial analogy. Could you perhaps give an example of bets going wrong because they incorrectly assumed Gaussian?

  14. observer


    I wouldn’t call the appeal to genetic additivity as grounding an assumption of a normal curve for IQ (or g) as as being an abstract one based on purely mathematical theorem (the central limit theorem). The normality of the curve depends on certain assumptions made in the well established Mendelian model, along with assumptions as to the approximate number and size of effects of individual genes related to the trait in question. The Central Limit theorem merely shows how a normal curve arises from this model.

    Now it may be that not all of those assumptions are satisfied. In particular, there may be genes whose effects are NOT additive — Downs Syndrome is one deviation from this model on the left tail. I’m not, though, aware of any such established deviation on the right side — there is nothing that corresponds to Gigantism in height, so far as I know.

    And, so far as I know, the standard empirical finding for traits considered to be additive (excepting known genetic abnormalities), and measurable in a fully precise and non-controversial manner (unlike IQ or g), is that they follow a normal curve, well out into the tails. Height, as I had said, would seem to be a pretty good test case — though, again, there are some known genetic abnormalities that might be removed to assess the fit to the curve for the genes more correctly conceived of as additive.

    My guess is that a test might be devised to determine whether IQ at the upper end really fits a normal curve. But even if in principle such a test might be devised and implemented, it will not come to pass, because the numbers are so scarce at this tail, the selection process so difficult, and the precise measurement of g so difficult, that it will be very hard to figure out whether such a deviation exists.

    In the meantime, an assumption of a normal curve seems a very reasonable assumption; we should deviate from that assumption only if we have clear reasons to do so (discovery of non-additive genes of substantial effect would be one such).

  15. observer

    Just to add to my comment, one way to demonstrate non-normality at the tails might be to show that traits that are heavily selected for DON’T fit normal curves very well at the tails. Obviously, I should think, IQ would be a trait which would be heavily selected for.

    I don’t know enough of the theory here to know what is generally believed about the distribution of such heavily selected traits.

  16. #14, i’m pretty sure he’s talking about tail risk



    (a lot of taleb’s stuff seems to fall into this category, though benoit mandelbrot is the original source of the more general issue)

  17. Dob Bole

    Steven Pinker – Jews, Genes and Intelligence

    Bio: Steven Arthur Pinker is a Canadian-American experimental psychologist, cognitive scientist, linguist and popular science author. He is a Harvard College Professor and the Johnstone Family Professor in the Department of Psychology at Harvard University and is known for his advocacy of evolutionary psychology and the computational theory of mind.


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About Razib Khan

I have degrees in biology and biochemistry, a passion for genetics, history, and philosophy, and shrimp is my favorite food. In relation to nationality I'm a American Northwesterner, in politics I'm a reactionary, and as for religion I have none (I'm an atheist). If you want to know more, see the links at http://www.razib.com


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