Hereditarianism III: Discussion

In the last post, we have seen that for African-Americans and Hispanics, IQ varies according to ancestry. In this post we will discuss what this actually means and whether there is still leeway for the environmentalist to wriggle about.

The key idea of this kind of admixture study is to show that the differences between ethnic groups can entirely be explained by genetic factors. This is done by showing that the IQ differences within each ethnic group by ancestry extrapolate to the differences between ethnic groups. So it is essential that we only look at IQ and ancestry within each ethnic group.

Without a strict restriction to one ethnic group, it would not be enough to prove that IQ correlates with admixture. We already know that there is an IQ gap and we already know that there is an “admixture gap”. So a correlation is already a given.

But what if the self-identified ethnicity is noisy? For example some of the “Hispanics” might actually identify or be identified as White. In that case the correlation between ethnicity and IQ would bleed over into the IQ-admixture. Of course this assumption borders on paranoia. But the correlations observed are quite small, which means that admixture explains very little of the IQ variance in the data set, which might seem counterintuitive from a hereditarian perspective.

So what kind of correlation should we expect? If the European-Amerindian-gap is 16 points, similar to the Hispanic standard deviation, shouldn’t we expect admixture to explain a very significant part of the variation? Well, actually not. If admixture is uniformly distributed the mean difference in admixture between two Hispanics is only 33.3%. This means the average IQ difference explained by admixture would at most be 5-6 points. But the admixture is not uniformly distributed, Hispanics with less than 40% European admixture are notably rarer. This is why the actual standard deviation of admixture is just 23.3. So we are down to less than 4 points explained by admixture. This would lead to a correlation of 0.50 … given perfect data. But both the admixture data and especially the IQ data invariably contain noise, reducing this correlation further. So it is actually not surprising that we only see correlations between 0.17 (for the very range-restricted African Americans) and 0.41 (for much more uniformly distributed African-European Hispanics).

A better way than looking at correlations to drive home the meaning of the hereditarian hypothesis is to visualize how mean IQ of percentiles change. The hereditarian hypothesis posits, that IQ varies continuously with admixture. This means that the IQ averages of admixture percentiles will more or less linearly increase.

To show this effect for each percentile would require a much larger data set. This data set is almost too small and heterogeneous to show the effect convincingly for quartiles. For example, as we have seen, the Hispanic IQ is slightly depressed compared to the same admixture in African Americans. Because the middle region of European admixture is dominated by Hispanics this results in a depressed middle if we use the whole sample.

Instead we restrict ourselves to the Hispanic sample. Because the mean White and mean Asian IQ in our data is almost identical, we can just pool European and East Asian admixture to create a well-powered Hispanic quartile admixture plot:

n=323, slope=21.56, intercept=75.32, correlation=0.273, p-value=6.217e-07

Here, we see that the average IQ of the admixture quartiles fall pretty nicely on the regression line.
This plot perfectly illustrates the hereditarian hypothesis: The averages vary exactly according to admixture. (Note also, that if we plot a line through the first two quartile averages only, we would overshoot the mean white IQ, presumably because the lowest quartile is slightly environmentally depressed. This might be happening in the African-American sample.)

It is tough to come up with environmental causes for IQ differences that vary according to ancestry. Colorism is one of the best tries. Colorism is the idea that racism is graded by how dark somebodies skin is, which varies according to ancestry, and that this racism somehow reduces IQ. Except when you are NE-Asian … Colorism as the reason for IQ varying with ancestry, is a theory that has a lot to prove before it can be remotely taken seriously.

However, IQ varying by ancestry also doesn’t prove that the gap is fully genetic. Or, to put it differently, even if we could predict IQ perfectly directly from the genome, it remains theoretically possible that there are gene-environment feedback mechanisms involved that allow us to reduce the magnitude of the gap by improving living/learning conditions. Of course the history of intervention studies tells us not to hold our breath.

So, what are the take-aways from this series:

  1. IQ varies by ancestry within ethnic groups with the same country of birth.
  2. This intra-ethnic variation fully explains IQ differences between ethnic groups.
  3. This invalidates most environmental explanations for the IQ gaps.
  4. And strongly suggests a genetic reason for IQ gaps between ethnic groups.
  5. Ancestry nonetheless explains little individual IQ variation – people should be judged as individuals.

Hereditarianism II: Admixture Data and Gaps

In the last post, we have seen, that the environmentalist position about group differences in IQ is mostly based on the idea of x-factors. Factors hard to identify that vary systematically between groups and affect IQ. Given that there are many factors that vary between ethnic groups, this is a difficult theory to disprove.

However, from a hereditarian perspective, two persons belonging to the same ethnic group can sometimes be differentiated by different amounts of a certain genetic ancestry. So in ethnic groups whose members have varying degrees of admixture of some original founding populations we can put the hereditarian hypothesis to the test. This is the case for African-Americans, who have varying degrees of European ancestry and for Hispanics, who are mostly a mixture of Europeans, Amerindians and Africans.

The hereditarian hypothesis predicts that IQ will vary within these groups with the amount of admixture for any chosen ancestral group. This type of admixture study has the power to rule out the majority of x-factors that systematically vary between ethnic groups, except for those that vary roughly according to ancestry.

A recent paper showed IQ varying by ancestry for Hispanics and African Americans [1]. These are the key figures.

The regression line of the relationship between cognitive ability and European ancestry in African Americans
And the same thing for Hispanics …

Courtesy of Emil Kirkegaard we can reanalyze the underlying data set. This data set contains IQ scores for a couple of hundred self-identified Whites, Blacks, Hispanics, East Asians + other minorities and the percentage of their genome being European, African, Amerindian, Asian etc.

First we translate the cognitive ability measure, here given in whole sample standard deviations above the sample mean, into IQ, with white mean = 100 and white standard deviation = 15.

n=137, slope=23.283, intercept=79.6, correlation=0.176, p-value=0.0392

The slope of 23.283 immediately gives us the gap between 100% European and 100% African, while the intercept provides us with the IQ of a 100% African African-American. The regression line overshoots the mean white IQ. This might be noise, or legitimately smarter white genes in the black population, or Amerindian admixture in the whites reducing the mean, or a slight environmental downward bent of the left part of the plot. But whether we take the estimated gap, or the difference between actual white mean IQ and the 100% African IQ, the result is always strikingly close to Galton’s estimate.

Of course this is just a very small sample. With a very restricted range. However, we can immediately replicate this regression line with those Hispanics that have predominately African and European admixture.

n=79, slope=23.837, intercept=73.33, correlation=0.416475096463478, p-value=0.000134

This gives us a virtually identical gap. But the whole line is shifted down. This vibes well with other results, see for example [2]. The average Hispanic IQ in this sample is only 89.5, compared to a usual US Hispanic IQ of 92-93, so it might still be missing a few points of Flynn effect. Note, however, that this seems to affect the entire IQ range in the same fashion.

The combined sample of African Americans and Euro-African Hispanics of course also validates Galton’s estimate of the gap almost perfectly.

n=257, slope=22.282, intercept=77.979, correlation=0.401 p-value=2.34e-11

For comparison, for Hispanics with predominantly European and Amerindian the admixture plot looks like this.

n=323, slope=16.65, intercept=80.024, correlation=0.233, p-value=2.231e-05

The gap is some 7 points smaller and the percentage of European admixture is generally quite high, which is why despite the missing Flynn effect points, the average Hispanic IQ is 89.5 vs 83.7 for African Americans.

[1] Biogeographic Ancestry, Cognitive Ability and Socioeconomic Outcomes

[2] A study of intelligence of children in Brazil

Hereditarianism I: Galton and Gaps

Hereditarianism is the idea that differences in abilities and character traits are substantially genetic in origin. This has been largely validated for individual differences, especially when it comes to IQ.

Everything is heritable.

“Hereditary genius” by Francis Galton published 1869 can be seen as the founding document of hereditarianism [1]. In “Hereditary genius” Galton observes that human traits are often normally distributed, including intellectual abilities. He then proposes a method to sort people into different grades of “eminence”. The grades A, B, C, D, E, F, G, and X are above the average, getting ever more illustrious and the grades a, b, c, d, e, f, g, and x classify people below average in lifetime achievement. He gives precise frequencies for each grade, so that it is possible to translate his statements into the language of IQ. Although Galton’s “eminence” is based on more than just intelligence (he mentions “zeal” and “working capacity”) it is probably the most important aspect.

His grades correspond to the following IQs:

A >100.0
B >110.39
C >120.88
D >131.33
E >141.78
F >152.24
G >162.60
X >171.30

As we can see, each grade should roughly correspond to a range of 10.5 IQ points.

Using his grading system he then starts to analyse the pedigrees of English judges and other notable men. He finds that “eminence” runs in families, and rules out a decisive role of nuture by looking at the adopted sons of popes.

He finally goes on to assess the difference between Africans and Europeans, in essence relying on several observations of tail effects. He diagnoses an average intellectual ability gap of 2 grades, which would translate to 21 IQ points.

First, the negro race has occasionally, but very rarely, produced such men as Toussaint l’Ouverture, who are of our class F; that is to say, its X, or its total classes above G, appear to correspond with our F, showing a difference of not less than two grades between the black and white races, and it may be more.

Hereditary Genius

To Galton group differences are obviously innate, but he does see moderating environmental influences. On the Africans in Africa he says:

Thirdly, we may compare, but with much caution, the relative position of negroes in their native country with that of the travellers who visit them. … [A]n average actual difference of three grades, of which one may be due to the relative demerits of native education, and the remaining two to a difference in natural gifts.

Hereditary Genius

However, the currently existing results about the heritability of IQ differences between individuals do not automatically transfer to group differences. If there are systematic environmental differences between groups, in-group heritability could be high, but the between-group differences would be environmental. And of course there are many actual and potential systematic differences between groups. Enough, that as soon as hereditarians have disproven one potential environmental cause for group differences, two new ideas are lined up by the environmentalists. These potential causes include socio-economic status of the parents, lead exposure, number of words heard in early childhood, peer groups, stereotype threat, many aspects of education, prenatal and postnatal nutrition, breast feeding, systemic racism and many more.

Although there is no clear-cut argument for predominantly environmental IQ gaps between ethnic groups, the environmental position is the current consensus.

“Hereditary genius” is a great read, because, while his methods are pretty dodgy, Galton is basically some hundred years ahead of the curve. A true founder of the field. In the next post we are going to analyze a data set to see how well Galton’s assessment of group differences holds up or whether the current environmentalist consensus is still in decent shape.

[1] Hereditary Genius

IQ-GDP VIII: Linear g theory

The second idea of how to interpret the GDP-IQ relationship is based on several different results of IQ research.

As you might know, there is a general factor of intelligence, that can be extracted from any battery of cognitive tests. The so-called g-factor explains a big part of the results on any IQ-test. The essential thing is that it explains the predictive part [1]. That means if you factor out the g-factor, IQ tests do no tell you much about educational attainment, income, criminality or performance in other cognitive domains.

As you might further know, there has been a steady rise of IQ scores, called the Flynn effect [2]. However, the Flynn effect has not been on the g-factor. I.e. the Flynn effect has been anti-correlated with the g-loadings of different IQ tests. This explains why our grandparent’s generation does not seem to be morons, despite scoring 30 points lower on Raven’s matrices. The Flynn effect doesn’t really increase cognitive ability, rather it increases the additional factors that unfortunately do not generalize.

As the Flynn effect is still ongoing in many countries and has stopped in the most developed countries, it is obviously playing a role in the differences in national mean IQ. If one day all countries have reached the end of the Flynn effect, we would expect the differences in mean IQ to have decreased substantially.

But here comes the rub: If the differences decrease due to the Flynn effect, and the Flynn effect is not on g, and only g is predictive of performance in the real world … why would we expect the shrinking IQ gap to be accompanied by a shrinking performance gap in GDP and co?

The linear g theory says that if we could compare nations by g-factor instead of IQ, we would see a linear relationship between g and GDP. The exponential relationship observed between IQ and GDP is just an artifact of poorer countries having still a lot of Flynn left to go.

This figure illustrates the linear g theory: The developed countries have IQs close to their g-factor, everybody else is still catching up. The relationship between g and GDP is linear.

I do not endorse a strong version of the linear g theory. But given the results of IQ research cited above, the hollowness of the Flynn effect must play some role in distorting the IQ-GDP relationship.

[1] g-factor

[2]Flynn effect

IQ-GDP VII: Three section theory

I also want to put another two competing theories out there. Both are based on the idea, that despite all appearances, the relationship between GDP and national IQ is a linear one.

The first theory decomposes the data into three sections: The pre-industrial section with IQs below 80. The middle income trap with IQs between 80 and 95 and the developed world with IQs above 95.

The idea is that each of these sections has it’s own specific IQ-GDP relationship. In pre-industrial countries this relationship is quite weak, a linear fit with minimal slope. Then the relationship becomes very robust in countries that have the ability to adopt some of the innovations created by the developed world. As we have seen, a reason for this robustness might be that here the reverse causality is strongest. Again, this can be fitted by a linear function, maybe with a short transition phase. In the developed world the IQ-GDP relationship again loses strength, because all these countries not only create new innovations, but additionally are capable of immediately adopting any innovation by the other developed countries.

But why is this a better interpretation than the exponential fit?

We have seen that the exponential fit improves the overall correlation significantly. The three section theory says, that this is an artefact of the positioning of the three sections and not an attribute inherent to any of the sections.

The preindustrial section has a significant IQ-GDP correlation of 0.469, the exponential fit reduces it to 0.418. The developed section has a significant correlation of 0.599, which is reduced to 0.566 by the exponential fit.
Only the middle income section sees a slight increase of the correlation from 0.780 to 0.805. And even that slight curving might be explained away by these sections not being completely pure.

What the three section theory tells us, is that for preindustrial countries an IQ point is worth just 125 dollars. For the middle income countries its 1488 and for the developed countries 1886. The difference between the developed countries and the middle income countries is in that respect smaller than it seems, because the line of best fit in the developed world is not particularly robust. Instead the major difference seems to be an extra 10,000 dollars afforded to the developed countries, which may be due to being ahead of the curve in technology.

IQ-GDP VI: The Contribution Distribution

One of the interesting aspects of the smart fraction theory is that it explicitly provides a “contribution distribution”. This is a function, that details how much each section of the bell curve contributes to the economy. In the smart fraction theory, this function is a step function, which is zero below the threshold (IQ=106) and some constant value above zero beyond the threshold. This can obviously only be a crude approximation of the true contribution distribution.

So, what is the true contribution distribution?

We can try to approximate the true contribution distribution by splitting the IQ spectrum into several sections and finding out for each country, how big the percentage of the population in each section is. Together with the GDP values, this gives us a system of linear equations, where the sum of (percentage of the population * contribution of IQ section) = GDP, for all countries.

Unfortunately, solving this equation doesn’t give us a sensible contribution distribution. The smart fraction theory already showed us, that assigning a GDP value to a single IQ section is enough for an excellent fit. Giving this equation more degrees of freedom just ends up with contribution values all over the place.

However, we can also infer the contribution distribution directly from the exponential function fitted to the data. By either using fancy math or basic logic, we conclude that the contribution distribution connected to the exponential fit, has the same form a*10^bx, with the same b but a different a, as the exponential function fitted to the data. (The fancy maths involves fourier transforms, the basic logic says that the contribution distribution has to rise as fast as the exponential fit.)

Fitting this function to the GDP data gives us the following contribution distribution:

Of course there are issues with the concept of the contribution distribution.

The contribution possible for each IQ segment will depend strongly on the overall economy. This global contribution distribution is bound to overestimate what smart people can do in poor societies and it might underestimate what not-so-smart people can contribute in rich societies.

The exponential takeoff looks somewhat insane. I stopped plotting at IQ=130, because otherwise it becomes ridiculous. A contribution distribution derived on the basis of the smart-fraction fit might be more realistic. However, at this point we do not really know the diminishing return on IQ.

It is also worth keeping in mind that the contribution of each segment is a mean average. It could very well be the case that the median contributions of each segment lie much closer to each other, and only the increasing number of massive outliers in terms of contribution results in the exponential rise.

Still, the contribution distribution is worth exploring, because it allows us to go beyond mean IQ.

IQ-GDP V: Reverse Causality

The relationship between ethnic composition and GDP/IQ that we investigated in the previous blogpost, allows us to compute an upper limit of the reverse causality, that is of the causal effect of GDP on IQ. To do that we predict IQ from ethnic composition, and use that function to correct our IQ values for ethnicity. That way we remove the influence of ethnicity from the IQ data. Only the remaining IQ differences can be caused by GDP or other environmental factors.

We start again with the mainland countries of South and Middle America. The correlation between IQ and percentage of the population that identifies as white is quite strong with 0.838 (p<5.1e-5). The red line is the best fit according to least squared error. Now, by looking at the deviation of the actual IQ values from the values predicted by the white percentage, we can try to find effects on IQ apart from ethnicity.

In this case, however, we come up empty. The residual IQ values do not correlate significantly with GDP (0.25, p<0.35). This does not mean that there is no reverse causality from GDP to IQ, only that if there is any, it is hidden in a feedback loop. I.e. smart people have a strong economy, which makes them even smarter. The takeaway is still that for these countries ethnic composition explains both IQ, and via IQ, also GDP, with each IQ point being worth 1419 dollar in GDP.

The situation is quite different for the South and Middle American islands. Here, black percentage explains a large part of the IQ differences (correlation of -0.58, p<0.03). However, black percentage does not correlate with GDP. This is due to a large fraction of countries that got relatively wealthy by non-industrial means, ie. as tax havens or tourist destinations. Nonetheless, there is a correlation of 0.658 (p<0.011) between IQ and GDP!

So, ethnicity correlates with IQ. IQ correlates with GDP. But ethnicity does not correlate with GDP! This implies that the GDP-IQ correlation in this case is not caused by ethnicity. And indeed, if we control for black percentage, the IQ residual still correlates 0.644 (p<0.013) with GDP.

Here we finally have some nice evidence for reverse causality. We can see a leveling off after 20,000 dollar. The Bahamas and Trinidad &Tobago are still on the level of Barbados, and Puerto Rico and Saint Kitts & Nevis are still on the level of Dominica etc., despite being much richer. Between 10,000 and 20,000 dollar GDP per capita there seems to be a strong effect on IQ, with every 500 dollar or so buying an IQ point.

Note that the overall relationship of a single IQ point with GDP, as observed in the mainland countries, is almost three times as large. This should give rise to a feedback effect, where every IQ point gained, nets enough GDP to further increase IQ by two points. Consequently, countries in this zone should converge towards their ceiling. A runaway IQ effect. Which, of course, still takes generations.