I recently discussed whether races exist and claimed that we should ignore apparent differences between people in the name of morality. A comment about IQ differences made me realise that the main reason that we should ignore these differences is because there is a feedback between how we see the world, and how it is. This probably applies to lots of social phenomena, but I’m thinking about observed differences in IQ.
I was fairly ignorant about IQ research; it is not very evenly discussed in the media. So it came as a shock to me to discover that social scientists have observed large differences in IQ between different groups of people. After accounting for all the variables the scientists could think of, it still turns out that black people lag white (and white lag asians) by an appreciable amount. The widespread conclusion is that this must have a genetic explanation.
On matters on measuring IQ, and what it means, I bow to the expertise of the experts. However, a brief examination of their statistical methods I became concerned about the definition of “accounting for variables”. Accounting for, say income, means looking at whether income correlates with IQ, and subtracting some multiple of income from IQ so that there is no longer any correlation. (There are also more sophisticated methods trying to achieve a similar aim.)
The correction above works when the effects are “linear”. But IQ is not at all linear. The IQ of a parent affects the IQ of a child, via poor nutrition in the womb, lower access to education, larger family sizes, different childhood priorities, amongst other things. This makes it much harder to understand in IQ (although the more sophisticated methods mentioned above are designed to correct for these, to some extent).
But much worse than this is social feedback. We know that perceived IQ can affect peoples actual IQ; if the world considers them stupid (say, relative to the average IQ), then this can make a person consider themselves stupid. If someone considers themselves stupid then they are unlikely to persue an intellectual lifestyle. This leads to a low measured IQ, which is passed onto children in a “viscious circle”. On top of that, genuine discrimination can act and make the problem dramatically worse.
Can the model above “correct” for this sort of bias too? It depends how the bias works in reality; but for a broad range of possibilities the answer is “No”. It could even be mathematically impossible.
Lets assume from now on there is no genetic difference in IQ between two groups – which could be “black” and “white”. We will also assume that investment in IQ is the same for both groups, and there is no unfair discrimination. But IQ changes slowly; the IQ of a person’s parents affects their own IQ.
Without any investment IQ is at some minimum level Imin. The initial IQ of the two groups is above this. The investment level is called r, which controls the rate that IQ grows towards Imax, where it stops. This is described by the following equation for “Change in IQ” (per generation) for group i :
This says that the change in IQ increases at rate r towards Imax (if r is positive) or towards Imin (if r is negative). A genetic difference in IQ would mean that Imax was different between the two groups. The standard methods would correctly calculate Imax in this case, and so determine if there were an innate difference in IQ.
Now we introduce social bias, which acts to change the rate r that IQ changes. The bias b is proportional to how far IQ is from the average over all groups. The bias parameter b controls how much a 1 point difference from the average IQ (over both groups) slows growth by. Now the equation looks like this:
This is the same equation when b=0, but the growth rate is lower for IQ less than the average IQ (I with a line over it) when b>0. Even with bias, things might not be too bad. Here is what happens when we start the two populations close to each other:
Without social bias, both IQs increase towards the same Imax. With the social bias, the group with the lower initial intelligence increases less rapidly, but still goes to the same Imax. The above methods would struggle, but eventually get the correct answer for Imax in this case.
Now consider what happens when the initial difference is a bit larger.
In this case with social bias, the IQ of the population that starts lower goes down! The social bias leads to a growing difference in IQ between the two groups, and so the lower group “gives up” – perhaps surviving by focussing on avenues that don’t require a high IQ, or a high perceived IQ.
The above “correction” method fails entirely in this scenario. Its extremely difficult to detect whether an observed difference in IQs is due to this sort of social feedback with the same Imax, or due to a real difference in Imax between the two populations.
Of course, this model is wrong. Its far too simple and only captures some rough features of the truth about IQ. But a huge class of models exhibit this sort of behaviour – called bistability – that can lead to two “genetically” identical populations ending up with different observed IQs, and we certainly don’t know enough to rule them out at the moment. I found very little work trying to look into models for how IQ might change. Until this possibility is ruled out, observed IQ differences should (scientifically!) be attributed to social feedback acting on historical differences. If scientists don’t address the problem of social feedback, we can’t expect the world to! Instead, if we assume that the observed difference is probably a genetic difference, this will increase the overall bias b and we may never know the truth.
Notes: I did a very brief literature search, detailed in comment number 2 of this post. For completeness, this is repeated below.
The mathematical model is entirely arbitrary and comes from the simplest model that is bistable (which fortunately is a plausible first model in this case). I don’t have any good references for models although Turchins 2002 book “Historical Dynamics” contains a nice summary of what level of complexity is required to produce which features. “Accounting for variables” above means performing a linear regression (sometimes twice), which is a standard statistical procedure detailed in any statistics book. Clearly for this criticism to be watertight, I need to establish that nobody has tried to fit dynamical models such as the one above to IQ data. I don’t know whether anything like that exists in the literature (I bet it does somewhere) but it is not a standard feature of IQ studies. I’ve seen it in other contexts, such as IQ of individuals over time, but not for social groups. To be convincing, the above model would have to be replaced by one in which different individuals have different IQs, and real decision processes are used to establish how the bias behaves. This sounds like a difficult, but not impossible task.
My IQ literature search: Nature recently featured a two-sided discussion on whether science should even study IQ in the context of race at all (http://www.nature.com/nature/journal/v457/n7231/full/457786a.html). As you point out, twin studies show remarkable correlation between genetics and IQ. This is no surprise – we all believe that intelligence is inherited to some degree within families. Additionally, there is a consistent IQ difference of 4-5 points between the sexes (Lynn, Personality and Individual Differences
February 1998, 24:289-290; Blinkhorn, Nature 438:31-32 2005). There are huge continental differences of tens of points (nicely illustrated by http://alfin2100.blogspot.com/2009/04/iq-by-nation-iq-by-race-us-iq-inherited.html), and large (10 point) geographical differences between areas of the single country of Italy (Lynn 2010, Intelligence 38:93-100). A summary of such results is given by (Rushton and Jensen 2005, Psychology, Public Policy, and Law 11:235–294).
These researchers look for differences and find them. The problem is the circular nature of intelligence: low IQ in parents leads to poor nutrition, low childhood support, poor education, and hence low IQ in children (this is called the “self-fulfilment hypothesis”). Again, the evidence that such a cycle exists is uncontroversial – whether it explains the whole distribution of Iq’s is strongly disputed. Much apparently “genetic” variation in IQ is explained by conditions in the womb (Devlin et al. . 1997, Nature 31;388(6641):468-71). Perceptions of IQ change behaviour and hence lifelong learning potential (The Confounding of Perception of I.Q. on a Measure of Adaptive
Behavior, Bobner, Ronald F et al – sorry this is a conference proceeding; also Sutherland and Goldschmid 1974, Child Development, 45:852-856). Early parenting factors are important for long term academic achievement (Englund et al. Journal of Educational Psychology, 2004), which means that family size and social class are going to be important too.
The consensus in the literature is that self-fulfilment does occur but nobody has modelled it in such a way that it accounts for all observed IQ differences (Jussim and Harber 2005, Personality and Social Psychology Review, 9:131-155; also http://psychology.uwo.ca/faculty/rushtonpdfs/PPPL1.pdf).