An Illustrated Guide to Racial Anthropometry: Or, the Narcissism of Small Differences

Despite the long-standing scholarly consensus that race is a social construct — more precisely, that it is a real abstraction; a fiction with all-too-real social consequences — essentialism refuses to relinquish its hold on the popular imaginary. Everyday folk suspect that the scholarly consensus is an artifact of rampant political correctness in academia. The vast majority of Westerners, while somewhat unsympathetic to notions of an unchanging racial hierarchy rooted in biology, imagine that there are indeed biological differences between Whites, Blacks, and Asians; differences that are relevant to understanding the social order.

Samuel G. Morton (1799-1851) pioneered the techniques of craniology in 1839, thereby founding the American school of ethnology. Morton and his followers were the advance vanguard of scientific racialism. He was the first to make inferences about racial hierarchy on the basis of measured cranial capacity. Big brained Caucasians, he argued, were demonstrably superior to small-brained Negros. Whatever the validity of the brain size=intelligence equation, is there any empirical support for the differences in skull-size championed by Morton and his intellectual descendents all the way down to Rushton today?

Physical differences between say national populations are in fact not a function of biology. Rather, they reflect nutritional status and disease burdens. Indeed, anthropometric measures like (the population means of) stature and BMI capture everyday living standards much more reliably than per capita income. We’ve previously interrogated the time-variation and international cross-sectional variation in these indicators to get an handle on global polarization that is largely independent of, and complementary to, national economic statistics. Following in the footsteps of Fogel, Waaler, and Kim, our investigation yielded a measure of living standards that we called effective stature that combined height and BMI. But if we are wrong and physical differences are in fact a function of biology, then that confounds our interpretation of at least the cross-sectional variation in effective stature. So independent of testing the claims of high racialists, it is very important for us to get to the bottom of this. (We’ll revisit that issue in a future post.)

The top panel in Table 1 displays the racial averages of a number of anthropometric measures for men in the US military. BMI is the ratio of weight in kilograms to squared height in meters; cranial capacity (CC) is the volume of the interior of the braincase measured in cubic centimeters estimated via the Lee-Pearson-Rushton formula for men from head length (L) and head breadth (B) [CC=6.752(L-11)+11.421(B-11)-1434.06]; brain mass is then computed via the Ruff et al. (1997) formula [brain mass=1.147CC^0.976]; encephalization quotient (EQ) is calculated from Martin’s relationship in mammals [EQ=brain mass/(11.22 body weight^0.76)]; and the cephalic index equals 100 times the ratio of head breadth to head length. The last has a particularly sordid history in the annals of racial craniology. And as opposed to brain size, which is only problematic, the cephalic index as a measure of intelligence potential has been totally debunked. We only include it here for the sake of completeness.

Table 1. Anthropometric measures of American men by “race.”
“Race” Sample size Stature (cm) Weight (kg) BMI Cranial capacity (cc) Head Circumference (cm) Brain Mass (g) EQ CI
White 2,817 176.4 85.8 27.6 1,474.3 57.4 1,419.3 7.6 77.1
Black 642 176.2 87.5 28.2 1,489.3 57.8 1,433.4 7.5 76.9
Hispanic 440 171.8 83.7 28.3 1,465.3 57.2 1,410.9 7.7 78.7
Asian 117 169.9 74.8 25.9 1,470.6 56.5 1,415.9 8.4 82.4
Other 66 172.9 84.0 28.0 1,481.4 57.1 1,426.0 7.7 79.3
All 4,082 175.6 85.5 27.7 1,475.7 57.4 1,420.7 7.6 77.4
Z scores
“Race” Stature Weight BMI Cranial capacity Head Circumference Brain Mass EQ CI
White 0.11 0.02 -0.03 -0.02 0.00 -0.02 -0.04 -0.09
Black 0.08 0.14 0.12 0.16 0.23 0.16 -0.07 -0.14
Hispanic -0.56 -0.13 0.15 -0.12 -0.17 -0.12 0.07 0.36
Asian -0.83 -0.75 -0.45 -0.06 -0.59 -0.06 0.91 1.39
Other -0.40 -0.11 0.08 0.07 -0.19 0.07 0.18 0.53
Source: ANSUR II (2012), author’s computations.

The second panel in Table 1 displays the z scores that tell us how much the racial means differ from the overall population means. Z scores within (-1.96,+1.96) indicate insignificance at the standard 5 percent confidence level. All the entries in the second panel lie within this interval, so right off the bat we can tell that anatomical differences between the “races” are statistically insignificant. As for brain size, whatever trivial differences that exist are in favor of African-Americans.

We have seen the means, but what do the distributions look like? In order to visualize these distributions, we assume that all measures are normally distributed. We collect and display the graphs for the distribution of all these variables in the following slideshow.

This slideshow requires JavaScript.

From Table 1 and the distributional graphs we can see that Asians are a bit shorter and skinnier than Whites and Blacks. But despite their smaller bodies, their brain size is comparable to Whites and Blacks (since their encephalization quotient is a bit higher). And their heads are a bit more globular (their cephalic index is also a bit higher). But again these are minor differences. Interracial variation is swamped by intraracial variation.

The most extreme differences we can detect are in the encephalization quotient and the cephalic index between Asians and non-Asians. The next figure displays the two indices for Asians and Blacks. (There are too many observations for Whites, which clutters the scatter plot.) We see that even here, the overlap is substantial. Moreover, there is no evidence whatsoever that either measure has anything to do with intelligence or anything else of relevance to the social order.


The same is true of head circumference and cranial capacity. See next figure. Yes, Asian heads a bit more globular. But the overlap is still substantial. Note also the minor differences in the intercepts (12cc) and slopes (0.6cc per cm).


From the distributions it is clear that the most extreme phenotypic differences (although still statistically insignificant) are between Asians and non-Asians. This doesn’t mean that Asians can be identified as a biological race (in the sense of subspecies). There is substantial variation in human populations. But race is a poor way to understand it. Human populations vary continuously. What we have is geographic clines (which look like differences between discrete races in settler countries where geographically distant populations live cheek by jowl). However, this is not so much due to climatic adaptations (as skin reflectance would suggest) as due to population bottlenecks and founder effects (along with genetic drift) in human dispersal from Africa. Basically our race left our African homeland in small bands that had by definition much less genomic variation than the population left behind. This is why Africa has more genomic variation than the rest of the world combined. And why the best handle we have on phenotypic variation is distance from Africa. But more on that another time.

The bottomline is that race gives us no handle whatsoever on variation in human bodies, and above all, claims of racial differences in brain size have no basis in empirical reality. 

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