One of the more frequently cited studies by environmentalists in their case against the genetic hypothesis is the study of the association between IQ and African ancestry by Scarr et al. (1977). Unfortunately for environmentalists, the study was inconclusive.

Scarr et al. (1977) tested the genetic hypothesis in two ways. First, they looked to see if g was associated with an index of African ancestry and found a statistically non-significant -.05 correlation (which was reduced to -.02 after controlling for SES and Skin color), and, second, they divided their subjects into thirds based on their index of ancestry and compared the g scores of the top third to the bottom third; the latter analysis showed a non-significant difference of .11 SD between the groups.

Scarr et al. concluded: “An extrapolation from the contrast between extremes within the hybrid group to the average differences between the races **predicts that not more than one third of the observed difference between the races could be due to genetic differences**. In view of the negligible correlations between estimated ancestry and intellectual skills even this seems unlikely” (emphasis added).

As Scarr et al. pointed out, the findings from their second test are consistent with a weak version of the genetic hypothesis, a version which proposes a between group heritability (BGH) of less than .5. It’s not particularly clear how they derived their “not more than one third,” though. In a footnote, they give the following rationale:

“The rough calculation for the estimate of the difference between upper and lower thirds of the black group proceeds as follows. If the resultant difference in standard deviations is 0.9 between the races when the mean difference in degree of Caucasian ancestry is about 0.77 (0.99 – 0.22 = 0.77) then the difference between upper and lower thirds of the black group alone should be about 0.23SD when the difference in Caucasian ancestry is about (0.35 – 0.15) = 0.20. Furthermore, if three-fourths of that mean difference is due to racial genetic differences alone the smallest expected difference is (0.75 x 0.23) = 0.18. So, about one-fifth to one-fourth of a SD would be the expected mean difference between upper and lower thirds of the black group.”

Based on this reasoning (expected BGH x 0.23 = difference between upper and lower thirds), and their findings of a .11 SD difference, the BGH could be as high as ½. not 1/3. Of course, this assumes a difference of 20% in admixture between the upper and lower thirds of the sample and an average admixture of about 20%. Based on more recent data (e.g., Parra et al., 1998), which indicates that the admixture in Philadelphia, from where the subjects came, is lower than average, this may represent an overestimate of admixture and therefore an underestimate of the possible BGH. Even if we grant the .33, though, as the average age of the study’s subjects ranged from 10-16, and as the heritability of IQ increases with age, the findings, taken as such, could still be consistent with a strong version of the genetic hypothesis, at least one that takes into account the heritability x age effect. (For reference, Scarr et al found a within group heritability of .48 for the blacks sample; the typical adult heritability estimate is .75 to .8).

All of this, of course, assumes that the index of ancestry used by Scarr et al. had a high reliability. As Reed (1997) pointed out, it likely didn’t. To some extent, we can see this simply by comparing the correlation Scarr et al. found between their index of ancestry and skin color (.27) with the correlation found between more sophisticated indexes of African Ancestry and skin color (.44) (Parra, Kittles, Shriver, 2004). The correlation Scarr et al. found was significantly lower than that found using modern techniques.

Whatever the case, Scarr et al. went onto insist that the found -.05 correlation between the test scores and their index of ancestry argued against even a weak genetic hypothesis. Putting aside the issue of the problematic nature of their index as pointed out by Reed (1997), the trouble with the authors’ contention is that it depends on an assumed predicted magnitude of the IQ-individual ancestry (IA) correlation, given some proposed BGH of IQ. The IQ-index correlation should be the product of the index-IA and IQ-IA correlations. If the environmental hypothesis is correct, the IQ-IA correlation would be zero, and so the index-IA correlation should also be zero or not significantly different from that. It’s not clear, though, what the IQ-index correlation would be, were genetic hypothesis correct, since it’s not clear what the predicted IQ-IA correlation would be. In making their case, Scarr et al. cited a speculation made by Arthur Jensen about the predicted magnitude of the IQ-IA correlation. In “Educability and Group differences,” Jensen speculated that the correlation between IQ and IA in the African American population would be higher than that between IA and skin color (~.40), “since more genes are involved in intelligence.” This was just a speculation though. Later, in reply to Scarr et al., Jensen argued and provided a deduction demonstrating that the predicted correlation would be less than .10 and, as such, that the predicted IQ-index correlation would be less than .05. Scarr (1981) objected to these low estimate but was unable to provide a defense of the estimate her group used.

The uncertainty about the predicted IQ-IA correlation – in addition to the study’s methodological problems as noted by Reed (1997) — has left the findings open to interpretation.

It would probably be a mistake to leave this at that, without clearly demonstrating that the results are consistent with a genetic hypothesis. We can do this several ways:

(1).

a. According to Scarr et al. the difference between the upper and lower thirds of the distribution was 0.11 SD. Assuming a normal curve approximation, the upper and lower thirds of a distribution are 2.2 SD apart. If the upper and lower thirds are 2.2 SD apart and the correlation between IQ and ancestry is, according to Scarr et al. 0.05, we would expect that the difference between the thirds would be 0.11 SD (2.2 x o.05). So the *low* correlation is consistent with the mean difference.

b. Now it’s clear that Scarr et al.’s index of ancestry was unreliable so we have to correct for that. Based on partial correlations, Jensen calculated the validity of the index to be 0.49. We can calculate it alternatively by simply dividing the mean found skin color-ancestry correlation in the US Black population (0.44) to the skin color-index correlation that Scarr et al. found (.27). We get a validity of .61, which might be an overestimate, as some of the correlation between skin color and Scarr et al.s index of ancestry could be due to the correlation between blood groups and skin color genes as Scarr et al. noted (quoted below.)

c. Using the higher estimated reliability (.61), the corrected mean difference is 0.18 (0.11/.61).

d. Plugging this into Scarr et al.’s formula above (expected BGH x 0.23 = 0.18), we get a between group heritability of 0.78 on a measure that showed a between race difference of 0.9 SD.

(We should also correct for the test reliability which is typically 0.9 –correcting for this, the expected heritability would be 0.866)

(2).

a. According to recent analyses, the mean African admixture is 20% and the standard deviation of admixture is 15%. According to Zakharia, et al. (2009):

“Numerous studies have estimated the rate of European admixture in African Americans; these studies have documented average admixture rates in the range of 10% to 20%, with some regional variation, but also with substantial variation among individuals [1]. For example, the largest study of African Americans to date, based on autosomal short tandem repeat (STR) markers, found an average of 14% European ancestry with a standard deviation of approximately 10%, and a range of near 0 to 65% [1], whereas another study based on ancestry informative markers (AIMs) found an average of 17.7% European ancestry with a standard deviation of 15.0% [2].…

…These results were confirmed in the estimation of IA by using the program frappe (also in Figure 1). The amount of European ancestry shows considerable variation, with an average (± SD) of 21.9% ± 12.2%, and a range of 0 to 72% (Table 1).”

Based on this we can calculate an expected IQ-ancestry correlation.

b. One interpretation of a correlation coefficient is: amount of change in x, change y or, in this case, the amount of change in admixture per change in genetically conditioned test score. In this case the genetically conditioned difference between Blacks and White would be 0.75 SD, since we are proposing that 75% of the gap is genetic; the ancestry difference would be 5.3 SD, which is the number of SDs separating Blacks who are 20% White and Whites, given that 1 SD of admixture equals 15% Whiteness ((100-20)/15=5.3). The correlation between test scores and genotypic ancestry, would then be 0.75/5.3 or 0.14.

c. This would be the correlation for an index that had perfect reliability. Correcting for the unreliability (see 1b), the the correlation between IQ and the index would be 0.085

d. This would be the correlation between IQ and Scarr’s index, assuming that the within population heritability was 1, as a lower within population heritability will attenuate the correlation. According to Scarr et al., the within population heritability was 0.48. Correcting for the lowered correlation between IQ and genes, we get 0.06 (0.085*SQRT(.48)), which is approximately the correlation found. (We should also correct for the test reliability which is typically 0.9 –correcting for this, the expected correlation would be 0.05.)

e. The difference between the upper and lower thirds would then be .13, which was approximately what was found.

The above demonstrates that Scarr et al. (1977) does not contradict a genetic hypothesis. It doesn’t support it, because the findings were non-significant, but the findings are nonetheless in agreement with a genetic hypothesis of substantial magnitude.

Reed (1997):

Scarr et al. (1977) used Black twins from the Philadelphia area, and the number (181) was large enough, using both Fy ~ and Fy b of the Duffy group, to give a useful estimate ofP w. Gm serum groups were determined (testing for four factors) and could also have given a useful estimate of P,. Ten other groups were also tested. Scarr et al. attempted to obtain for each individual a measure of individual ancestry to associate with an estimate of cognitive ability, but this measure is deeply flawed. They used an “odds coefficient,” log[AtAzA3…/BtBzB3…], in which A was one ancestral population (e.g., African) and B was the other ancestral population, and the subscripts were the loci of the different blood and serum groups. A t was the frequency of an individual’s phenotype (group) at Locus 1 in Population A, Bt was the frequency of his or her phenotype in Population B at that locus, and so on. This coefficient was intended to give a rank ordering of individuals according to their degree of ancestry from one population, say A. Now consider the effect of one uninformative Locus X, for example the MN blood groups, on this coefficient. Because A/B x varies essentially at random, and Ax/B x multiplies all the other ratios, the odds coefficient acquires considerable randomness. Add the random effects of other only slightly informative loci, such as the ABO, and the coefficient will necessarily lose much of its potential for ancestry identification. Scarr et al.’s (1977) procedure for dealing with zero phenotype frequencies—replacement by .0001- further distorts the coefficient, particularly for the informative Duffy and Gm groups. This is because, with the usual sample sizes, absence of a phenotype at Locus Y does not mean that its true frequency is not of the order of.01 -.001. This procedure would often bias log(A/By) by about ± 1 to ± 2. With the above problems, it is not surprising that the correlations between the odds coefficient and the measures of cognitive skills were nonsignificant; it would be surprising if they were otherwise. (Incidentally, although Scarf et al. thanked me and others for “consultation on the design and analysis of the study” [p. 86], I did not have any part in the design or analysis.)

Jensen (1981b).

Paraphrased:

1. The Predictive validity of the blood groups is 0.49

2. Given a normal distribution, the upper and lower thirds of the sample are 2.2. SD apart. If the upper and lower thirds of the sample, respectively, have 35% and 15% European admixture, with a difference of 20%, then 1 SD of difference is equivalent to .09 % ancestry.(.2/2.2 = .09).

3. Scarr’s group gives 0.9 SD as the average difference in test scores between Whites and Blacks in the sample. If we suppose a between group heritability of IQ of .625, on the same scale the genetic difference would be .565 SD (.625 x .9). Since Blacks in sample only have 80% African genes, the genetic difference between a European population and a 100% African population would be, on the same scale, .7SD (.56SD/.8).

4. One interpretation of a correlation coefficient is: amount of change in x, change y.

Accordingly, one shift in ancestry equals a 0.063 shift in test scores (.09 x .7 =.063) and .063 would be the correlation between test scores and genotypic ancestry.

5. Given our test score-genotypic ancestry correlation, the expected correlation between test scores and ancestry as indexed by blood groups, which have a predictive validity of 0.49, would be 0.031 (0.063x.49=.031), which is lower than the correlation found.

6. Given our predicted correlation of 0.031 the difference between the top and bottom thirds of our distribution would be 0.07SD (.031 x2.2 =.07SD), which is lower than the difference found.

Scarr et al. notes: “There is another hypothesis, however, to explain the correlation between skin color and blood group markers: that one skin color locus is closely linked to Gm and/or Fy (Gershowitz and Reed, 1972; Cavalli-Sforza, personal communication 1974). Indeed, skin color was found to be more highly correlated with Gm than any other single locus (r= 0.20), followed by Duffy, Transferrin (r= 0.13 for each) and AB0 (r = 0.11). These loci are good markers for ancestry, however, and could be correlated with skin color for that reason. Skin color variation probably depends upon a few good markers of ancestry. If skin color phenotypes correlate with ancestral odds, because ancestral genes have not been dispersed throughout the black population, then any three good blood group markers ought to correlate positively with other markers from the same ancestral population. If, instead, the relationship between skin color and ancestry depends upon the close linkage between a skin color locus and Fy/Gm, then three blood group markers should not correlate positively with the rest, and skin color should not correlate with any set of blood groups lacking the linked marker….

…All of the correlations among skin color and the odds coefficients were in a positive direction. Three of the eight were statistically significant, including the correlations between skin color and the sample odds, with and without Gm and Duffy (r = 0.22 and 0.18 respectively). The correlations between the sets of three and nine blood group markers were not statistically significant. While no firm conclusions can be drawn, the relationship between skin color and the blood.”

Parra, E. J., Marcini, A., Akey, J., Martinson, J., Batzer, M. A., Cooper, R., … & Shriver, M. D. (1998). Estimating African American admixture proportions by use of population-specific alleles. American journal of human genetics, 63(6), 1839.

Parra, E. J., Kittles, R. A., & Shriver, M. D. (2004). Implications of correlations between skin color and genetic ancestry for biomedical research. Nature genetics, 36, S54-S60.

Jensen, 1981b. Obstacles, problems, and pitfalls in differential psychology. In S. Scarr (Ed.), Race, social class, and individual differences in IQ. In: Scarr, S. (1981). Race, social class, and individual differences in IQ. Psychology Press.

Reed, T. E. (1997). The genetic hypothesis”: it was not tested but it could have been. American Psychologist, 52, 77-78.

Scarr, S., Pakstis, A. J., Katz, S. H., & Barker, W. B. (1977). Absence of a relationship between degree of White ancestry and intellectual skills within a Black population. Human genetics, 39(1), 69-86.