I will use the same technique as was done in the NLSY97, namely, Jensen’s method of correlated vectors. I found a total of 55 mulattoes, and 156 multiracials. The ‘mulatto’ variable specified blacks with white (i.e., european) ancestry, while the ‘multiracial’ variable specified blacks with non-black ancestry, that is to say, blacks with some mexican ancestry, or asian ancestry, or indian (american) ancestry, or white ancestry, and so forth.

The magnitude of the BB(blacks)/BW(mulattoes) gap in the g and non-g sources in ASVAB subtests can be estimated first by factor analyzing (using PAF) the 10 ASVAB subtests and producing two unrotated factors, the first explaining 58% of the total variance, the second 11%. Using then the scores in g factor and non-g factor, derived from a comparison of means program (in SPSS), I produced the following table :

The pooled sd formula estimated a non trivial gap of around 0.43 SD or 6 points difference between blacks and mulattoes. The difference, as expected, was smaller between blacks and multiracials (0.36 SD). In any case, the non-g source of variance is trivial and the sign is even negative, which means that blacks outsmart multiracials in non-g sources. Another technique is the use of partial correlation between the multiracial dichotomized variable (1=black, 2=multiracial) and each ASVAB subtests, with PAF1 as a control variable. The correlations fell near zero, but this was not the case when PAF2 is used as control variable (syntax here). This means that g is the source of those differences. The point-biserial correlations (before partialling out g) were not very high as shown below :

Excel file here. One reason for these low correlations could be that the frequency distribution of the dichotomized variable is far from being optimal. As I pointed out before, the departure from an optimal 50/50 split of any dichotomized variable will reduce the obtained correlations. For instance, the frequency distribution for my mulatto variable is 0=3024, 1=55, and for my multiracial variable 0=2925, 1=156. The relevant formulas for correcting unequal sample sizes in point-biserial correlations are provided by Hunter & Schmidt (2004, p. 280). This explains why the r_pbs for multiracial are larger than r_pbs for mulatto even if the d gap is smaller using the multiracial variable. After correction for unequal sample size, using Hunter & Schmidt formulas (with Excel functions), I produced the following table :

As can be seen, the corrected rpbs for Mulatto variable seems a little bit higher than rpbs for Multiracial variable. For AFQT (2006 revised) the corrected rpb is around 0.22 (by way of comparison, the ASVAB 1999 BB-BW gap shows a corrected rpb of 0.28, and uncorrected rpb of 0.19). In any case, using either corrected or uncorrected rpbs, we can estimate the correlation between the magnitude of BB-BW difference and the magnitude of black-white d gap, B-W g loadings, B-W non-g loadings, as shown below.

For obtaining these correlations, I use the estimates of B-W g-loadings and non-g-loadings, as well as B-W d gap reported in my earlier post on IQ regression to the mean (Hu, April.18.2013). Given this, the Jensen effect is apparent, and to this can be added another Jensen effect test by Chuck (May.9.2013) in another article on the Scarr et al. (1977) admixture data among US blacks.

Bermuda is a tiny British Overseas Territory in the North Atlantic Ocean, some 600 miles from the East Coast of the United States (population: 64,700). Even though Bermuda is 1000 miles from the Caribbean Sea, there are a number of sociological similarities between Bermuda and the Caribbean island nations; it is an associate member of the Caribbean Community. Its economy, much like the Cayman Islands and The Bahamas, is largely based on finance and tourism, and it likewise enjoys one of the highest standards of living in the world.

According to the 2000 census, Bermuda is 54.8% black and 34.1% white. IQ and the Wealth of Nations (2002) did not include intelligence data for Bermuda, but IQ and Global Inequality (2006) reported an IQ of 90, as the average of two studies. In this post I discuss some overlooked data which suggest that Bermudian blacks have an IQ that is very close to 100, and that there is no IQ gap between black and white Bermudians. There is also some overlooked test data which suggest otherwise, and we are left with some uncertainty over the meaning of the conflicting research.

Sandra Scarr is one of the very few social scientists to offer serious, original research into the causes of race differences in intelligence. Her Minnesota Transracial Adoption Study might be the single best empirical work on the topic. She also, improbably, managed to remain mostly respectable among other social scientists by walking a careful line with her hereditarianism. In her tribute to Arthur Jensen, she admitted that this acrobatic feat involved summarizing her own research in ways that weren’t entirely scrupulous:

My colleagues and I reported the [MTRAS] data accurately and as fully as possible, and then tried to make the results palatable to environmentally committed colleagues. In retrospect, this was a mistake … We should have been agnostic on the conclusions. (Scarr, 1998)

Indeed, Scarr’s research on race is cited by her “environmentally committed colleagues” just as readily as it’s cited by Jensenists. Part of this is because the new behavioral genetic methods for examining race differences were so crude, that her results were ambiguous and open to conflicting interpretations.

But one of Scarr’s findings has fallen into obscurity, and hasn’t been cited by environmentalists or hereditarians. The only rhetorical use of this finding was by Scarr (1987), in which she boasted about her contributions to the non-genetic theory of black-white IQ differences:

…In 1967, I began a program of research that continues today, employing five previously unused strategies to study the sources of racial differences in intellectual performance: (1) studies of individual differences within the U.S. black population by the twin method; (2) the study of genetic markers of degrees of African ancestry and their relation to intellectual differences within the U.S. black population; (3) the study of transracial adoption, with Richard Weinberg, by which socially classified black children are reared in the cultural environment sampled by the tests and the school; (4) cross-cultural studies in which black children are or are not socially disadvantaged; and (5) educational intervention programs with young children to test idea about reaction range and malleability. Evidence against a racial genetic hypothesis … has come from all five sources. (p. 222)

Evidence for the racial genetic hypothesis also comes from all five sources. Scarr proceeds to describe her cross-cultural evidence against the genetic hypothesis:

In Bermuda, we found that black children have IQ scores at the norm for white children in the United States at age 2; at age 4 their average IQ score is 99, and by sixth grade they score 2 years above U.S. white children in vocabulary, reading, and math on the California Achievement Test, a culturally loaded instrument to be sure! These findings amazed Bermudian officials as much as us.

Results from cognitive tests before the age of 3 are more often described as Developmental Quotients (DQs) rather the Intelligence Quotients (IQs), because these scores are influenced by non-cognitive dimensions like motor development. While white children typically score higher than black children on some test measures, like vocabulary, before the age of 2, black children often match or exceed white children on developmental cognitive tests (Bayley, 1965). But African-American deficits on IQ tests are large by the age of 3 (Peoples et al, 1995), so if Bermudian children are, in fact, exceeding white American children on cognitive tests at age 4, that is certainly an underappreciated challenge for hereditarians. Unfortunately, Scarr provided no citations in her article, and when I first read this article (2004-ish), Google Scholar and Google Books weren’t around to help me search for this Bermudian mystery study. However, several years later, in 2007, I found a different study, which strongly supported Scarr’s assertion.

Bermuda and The Adult Literacy and Life Skills Survey

“Literacy” is typically measured as a binary trait: either you can read or you can’t read. Lynn and Vanhanen (2006) correlate this kind of literacy with national IQ in IQ and Global Inequality:

The adult literacy rate is the percentage of people ages 15 and above who can, with understanding, read and write a short, simple statement related to their everyday life (Human Development Report, 2002, p. 272). Statistical data on adult literacy are in most cases estimations, which may be based on censuses or school enrollment statistics. (p. 82)

The correlation between national IQ and literacy is 0.66 (p. 103). But their data show that some undeveloped nations with the lowest IQs have high literacy levels. The ability to read and write is something that humans appear to be capable of across the entire nonpathological spectrum of IQ differences, but this does not preclude qualitative differences in literacy:

According to our hypothesis, differences in national IQs may explain a significant part of the contemporary global inequalities in literacy, although it is quite possible that, ultimately, the adult literacy rate will rise to near 100 percent in all societies. It should be taken into account, however, that there may be significant differences in the quality of literacy between countries, although the percentages are the same. (p. 111)

“Quality of literacy”, like the phrase “quality of schooling” used in some economics papers, is really a euphemism for ability differences. The Educational Testing Service (ETS) has already created these kinds of “functional literacy” tests for national and international comparisons. Linda Gottfredson (2002) makes the argument that these tests are “a surrogate measure of g” (pp. 359-367). The tests are not measuring the ability to read (performance does not improve when the questions are delivered orally) but core mental faculties such as comprehension and reasoning:

… the [Adult Literacy and Life Skills Survey] defines skills along a continuum of proficiency. There is no arbitrary standard distinguishing adults who have or do not have skills. For example, many previous studies have distinguished between adults who are either “literate” or “illiterate”. Instead, the ALL study conceptualizes proficiency along a continuum and this is used to denote how well adults use information to function in society and the economy. (Desjardins et al., 2005, p. 15)

Americans were surveyed with the National Adult Literacy Survey (NALS) in the early 1990s, and large samples were subsequently tested in nearly 30 countries with its modification, the International Adult Literacy Survey (IALS). The Adult Literacy and Life Skills Survey (ALL), another international successor to the NALS, is a comparison of representative adult population samples in 6 world regions: Bermuda, Canada, Italy, the United States, Norway, Switzerland, and Nuevo Leon, Mexico.

The four ALL sub-tests are prose literacy, document literacy, numeracy, and problem solving.

Bermuda gave a strong performance on the ALL, placing third, behind Norway and Switzerland. Bermuda’s scores were slightly ahead of Canada and the United States, and far ahead of Italy and Nuevo Leon.

Three of these nations—the US, Italy, and Norway—also participated in the TIMSS 2003 international achievement test, which included our “Greenwich IQ”, the United Kingdom. Using these three nations as a bridge between the two tests, gives us an Achievement Quotient (AQ) of 99 for Bermuda. (Table I below.)

Table I: Achievement test scores in Bermuda

Should the functional literacy test count as an achievement test or an intelligence test? At the very least the ALL and PISA include problem solving sub-tests that are not obviously related to learned material. These sub-tests seemingly have a greater conceptual claim on intelligence than, say, the Peabody Picture Vocabulary Test, the 10 item WORDSUM test from the GSS, or even a number of the sub-tests from the Wechsler tests. From a psychometric standpoint, these tests are also better constructed for international comparisons (e.g. more thoroughly checked and corrected for test bias). I will nevertheless classify them as achievement tests for now since they are not validated or popularly recognized as intelligence tests among specialists. But the ALL certainly still qualifies as evidence that Bermuda has an intelligence level comparable to Western Europe and its global diaspora.

Furthermore, the ALL classified Bermudians and Americans according to race, which allows us to see the functional literacy scores of blacks and whites in both nations on the same test. (Riley, 2006, p. 11 ; Rivera-Batiz, 2008, p. 16 ). Black-white gap? Nope. Table II shows the Achievement Quotients for all four groups, normalized against the UK TIMSS results. The U.S. gap is .74 SD, while the Bermuda gap is an invisible .03 SD.

It is perhaps noteworthy, though, that the subtest scores still show a pattern familiar in cross-cultural testing: Bermudian blacks scored highest on verbal, lower on numeracy, and lowest on abstract thinking. The only statistically significant difference between blacks and whites in the Bermuda sample was that whites scored higher on problem solving (likely the most g loaded subtest).

John Loehlin once noted that even though fullscale IQ scores did not vary with ancestry in Sandra Scarr’s crude admixture study (Scarr et al, 1977), the subtest patterns did, in fact, show a genetic correlation. Black ancestry correlated with memory performance, while white ancestry correlated with abstract problem solving (Loehlin 2000, pp.187-188). Compare this with the international sub-test patterns:

African blacks show the same test profile as US and Jamaican blacks, for example with strengths on perceptual and short term memory tasks and weakness on tests of abstract reasoning (this is for matched total IQ, remember).

The ALL survey also shows that functional literacy is strongly related to income and education in all the nations. Additionally, the data reveal no sex difference in Bermuda.

Finally, the ALL survey shows performance differences among adults aged 16-65. The average ALL score increases between the two cohorts roughly born between 1947 and 1982 by 7.46 AQ points (this is further evidence that the ALL is an intelligence test, since math and reading tests have not been shown to exhibit performance gains). This is also close to the 0.3 IQ points per year inflation rate shown on standard intelligence tests. Bermuda and the United States show the smallest score gains of the seven nations (6.51 and 3.48 points, respectively). Bermudian scores have even dipped somewhat among the youngest cohort (Riley, 2006, p. vi ).

(I can find nothing to suggest that Scarr’s California Achievement Test data for Bermuda has ever been published. But, at least through the 1980s and into part of the 1990s, the CAT was routinely administered to all the government school children in Bermuda. There is no good reason to reject Scarr’s assertion that Bermudian middle schoolers exceeded American children on this test of reading and mathematics.)

Intelligence Test Results From Bermuda

Lynn first summarized Bermudian data in IQ and Global Inequality (2006, p. 311):

Bermuda. A study by Sandoval, Zimmerman, and Woo–Sam (1983) reported an IQ of 88 for a sample of 161 7–11-year-old children in Bermuda tested with the WISC–R. Scarr and McCartney (1988) have reported a study of 125 4 year-olds given the Stanford Binet. The sample was approximately representative of the racial mix, consisting of 61 percent Africans and 37 percent Europeans (Phillips’, 1996). The IQ of the sample was 92. The average of the two studies gives an IQ of 90 for Bermuda.

Sandoval et al. (1983 ) take their data from an unpublished doctoral dissertation (Astwood, 1974). I have requested this document from its University library, and I will update this post in the future if it contains any data unreported by Sandoval. Lynn incorrectly reports the sample size from this paper, which is 92, not 161. He also incorrectly reports the IQ, which is 89, not 88. Sandoval et al, analyze the verbal subtest responses for item difficulty bias, and conclude that the test is fair for use in Bermuda.

Sandra Scarr and Kathleen McCartney collaborated on several different studies in Bermuda, which used different samples of children. The first published IQ data comes from McCartney et al (1982 ). The purpose of this research was to study the effects of day care quality on child outcomes. Bermuda was chosen as an ideal environment for examining this issue, because most Bermudian children are raised in common day care facilities for the majority of the day while their parents work (50% were found to be enrolled in day care in the first year of life, 84% by age 2, and 90% by age 3). Additionally, the parents choose day care facilities based on proximity to their workplace, and not on reputation or quality. Both of these help filter out unknown selection effects that might contaminate typical day care studies. 159 Children who had attended 9 different day care centers since infancy were tested at age 4 with the Peabody Picture Vocabulary Test-Revised. Their guardians (almost all mothers) were also given the same test. 130 of the children were black, 21 were white, and 7 were Portuguese.

The IQ of the children was 82.8, and the IQ of the mothers was 85. Data are not reported by race, but the authors state that “White mothers scored higher on the PPVT” (p. 138), and mother’s IQ was highly correlated with mother’s ethnicity (.33). For comparison, the correlation between race and Wordsum IQ is .22 in the General Social Survey. The authors find that the mother’s race is highly correlated with child IQ, while day care variables are not:

Age of entry into group care and number of hours spent in group care in the first three to four years of life had no significant effect of [sic] PPVT scores, nor did differences in the qualities of the day care environments (p. 140)

Scarr & McCartney (1988 ) report Bermudian data for the Mother-Child Home Program. This is an experiment where trained teachers visit mothers at their home dozens of times over a period of two years and tell them ways to play and interact with their children that are hypothetically beneficial for IQ development.

Lynn reports a sample size of 125 for this study. But some of the children dropped out or died, so the child sample is actually 117. Further, the mothers were also tested with the vocabulary subtest of the Wechsler Adult Intelligence Scale, so there is additional data here for 117 more people. Lynn reports an IQ of 92, but the IQ scores reported in this paper are nowhere close to this number. The SBIS IQs are actually reported as 106.6 for the treatment group and 103.1 for the control group (p. 539). If we apply a Flynn adjustment of 2 points, this gives us an IQ of 101 for the control group. The maternal scores on the WAIS subtest were significantly lower (see Table III). The MCHP treatment program showed no significant effects on child intelligence.

Scarr’s third and largest IQ study on the island, in cooperation with the Bermuda government, involved testing nearly every 2 and 4 year old with the Stanford-Binet Intelligence Scale. This was the Islandwide Screening, Assessment, and Treatment Program. 1020 children were tested, representing some 86% of children in the targeted age range on the entire island. This is almost certainly the study Scarr was referring to in her 1987 editorial, but the full data from this study was never published.

Data from smaller subsamples of this screening program are reported by Scarr et al (1994 ). 75.5% of Bermudian children passed the screening assessment for cognitive and language disabilities (p. 206). The SBIS IQs of a small random sample who passed screening was 102.5. 10.1% of children failed the screen for cognitive disability. The average IQ of two small intervention groups who failed the cognitive screening was 82. 14.4% of the children failed the screen for language disability. The average IQ of two small intervention groups who failed the language screening was 92. A weighted average of these subsamples gives us an IQ of 100 for Bermuda—very close to the value reported by Scarr (1987). However, the Stanford-Binet norms used by these researchers were outdated by 12 years, and there is no indication the reported data were corrected for this. A Flynn adjustment of -3.6 points gives us a somewhat lower IQ of 96.

These 4 studies give us 8 IQ samples for Bermuda (Table III). A weighted average of the 6 normal samples gives us an IQ of 89 for Bermuda.

Table III: IQ test scores in Bermuda

Concluding Remarks

My own IQ average for Bermuda is actually a little lower than Richard Lynn’s. The weighted average would obviously be higher if Sandra Scarr would’ve published her data from the islandwide screening of Bermudian children. I have requested unpublished numbers from Scarr (who has so far ignored my emails), but I’m not going to freely extrapolate study details from the vague claims in her 1987 article (which doesn’t even clearly indicate she is referring to the data from the screening project). But even assuming that Scarr’s 99 IQ claim was for the islandwide screening sample (N=1020), the deviation IQs from this project reported by Scarr, et al (1994 ) do not suggest a Flynn correction was made for the outdated Stanford-Binet norms. This correction would actually give us an IQ of 95 for the screening project, and the weighted average IQ for Bermuda would still only be 92. Given the approximate demographics of the island, this would be consistent with a white IQ of 100 and a black IQ of 88.

The ALL adult literacy scores are a significant obstacle to this interpretation. This test is seemingly more like an IQ test than an achievement test, and the study is so much larger and better conducted than all the other intelligence studies that it feels like it should be weighted accordingly. On the other hand, we might somewhat reconcile the conflicting data points if we assume the ALL is an achievement test. Large IQ-achievement test discrepancies were also found for Cuba and the Dominican Republic (Which is not to imply that these discrepancies aren’t a huge problem as well). This would also be consistent with Sandra Scarr’s (unverifiable) claim that Bermudian sixth graders were outscoring US norms on the California Achievement Test during the 1980s.

The lack of race differences in the ALL are yet another problem. The ALL showed no Bermudian race differences in functional literacy, even among 60 year olds. However, there are large sociological gaps between blacks and whites in Bermuda, much as there is in the United States (I don’t intend to summarize non-cognitive gaps in my HVGIQ series, but a detailed review of black-white differences in Bermuda can be found in (Mincy et al, 2009 ). A more recent and concise summary can be read here: an article from a major Bermuda newspaper). There are large B-W differences in earnings, crime, employment, and educational attainment in Bermuda. It seems implausible that all the same racial gaps would show up in Bermuda and the US, and yet have almost completely opposite causes. (Of course, someone might similarly argue that this makes discrimination-type explanations more plausible for both places!)

Further, even though the precise gaps were not reported, race was the strongest predictor of IQ scores in McCartney et al, 1982 (p. 138 ). Which brings us back to the question of why five out of six samples showed the IQ scores that one would more reasonably expect for an island that is two-thirds black and one-third white. Given this and the large B-W social disparities in Bermuda, I’m inclined to accept these results over the ALL, but I confess to a significant amount of uncertainty over all these conflicting test scores.

REFERENCES
Astwood, N.C. (1974). A comparison of American and Bermudian children on the Wechsler intelligence scale for children-revised. Unpublished doctoral dissertation, Adelphi University, USA.

Because the hereditarian hypothesis states that the IQ advantage of white ancestry has a genetic component, it would certainly predict (contrary to the cultural hypothesis) that the magnitude of white ancestry advantage is a function of the g-loadedness of cognitive tests. If the advantage of white ancestry is larger in the genetic component of cognitive tests, this surely is not a pattern that cultural hypotheses could have predicted. One way to see obtain those estimates is to simply perform a point-biserial correlation, that is, correlating a dichotomized variable (e.g., ancestry) with an interval variable (e.g., ASVAB subtests). The larger is the (positive) correlation and the larger is the advantage.

This is what I am testing here, using again Jensen’s MCV, with the data on g-loadings, BW gaps and sibling correlations among subtests, I gathered previously. The Excel file contains those data (as for my SPSS file, just contact me). The SPSS syntax for computing the white ancestry variable, as well as its correlation with ASVAB subtests, is given here.

The values of my white ancestry dichotomized variable can be summarized as follows : 1= blacks with no parents having caucasian origins, 2= blacks with at least one parent having caucasian origins. Also, the black sample averaged 730 (males, N ~ 350; females, N ~ 370). Here is what the picture looks like.

To simplify, the difference between the ‘more’ caucasoid blacks and the ‘less’ caucasoid blacks is larger where (1) the black-white difference is larger among the subtests, where (2) the BW g-loadings are larger among subtests, where (3) the white sibling correlations among subtests are larger, where (4) the black sibling correlations among subtests are larger. Of course, the non-g sources are also correlated with the lighter-skin advantage but to a much lesser extent.

All of the above findings is fairly consistent with the hereditarian hypothesis. When black males and black females are analyzed separately, the pattern didn’t change for the correlation between BW d gap and white ancestry advantage. However, g-loadings are correlated with the white ancestry advantage among men but not among females. As for the non-g loadings, the pattern is the same as it was in the (full) black sample. Furthermore, white and black sibling correlations are no longer correlated, or so weakly, with white ancestry advantage among black females. It is among black males that the correlations were very high. Needless to say, the advantage of white admixture among black men is weakly correlated with the advantage of white admixture among black women. Obviously, we can also try to partial out the reliabilities (available here, table 7.3), as I did then, but it has little effects on the correlations.

Furthermore, the congruence coefficient, which is an index of factor similarity, is pretty high, whether we use principal component analysis (0.997) or PAF factor analysis (0.996) for the extraction of the general factor. A high CC (> 0.90 or 0.95) implies that the g factor between those two groups is virtually identical. This has been done by factor analyzing (1) the correlation matrix of the 12 ASVAB subtests from the sample of blacks without caucasian ancestry (N=639) and (2) the correlation matrix of the 12 ASVAB subtests from the sample of blacks with some caucasian ancestry (N=88). Here’s the syntax. And here’s the Excel-file. To note, it also contains the CCs across gender, with and without (self-reported) white ancestry. Even with the very small sample size of the subgroups, the CC is still higher than 0.95. In fact, they are not lower than 0.99. To compute the CC, use this online program, or the Excel formula I have created.

Still another way to test a Jensen effect is to simply compare the g-factor scores and non-g factor scores (extracted from the full sample) of blacks with and without parents having caucasian origins. The picture looks like this.

Clearly, the g-factor contributes to the differences, but not the non-g dimension. The conclusion is that white ancestry advantage among blacks is a Jensen effect, as well as skin color among blacks (Dalliard, Jan.29.2013).

Another interesting finding, now, is that the magnitude of the advantage of (lighter) skin color among subtests also correlates with black-white d gap, g-loadings, and black/white sibling correlations, as shown below :

The values at the top of the Y axis display lower negative correlations while the values at the bottom show higher negative correlations. So, a negative slope simply means that when the score advantage of lighter skinned blacks is higher, the g-loadedness of tests increases.

Surely, this is not in line with the colorism hypothesis. Furthermore, unlike the self-reported ancestry variable, the pattern of correlations for skin color doesn’t change across sex group. These correlations were equally strong, after separating the black sample into males and females. What is causing the difference then ? Maybe skin color and ancestry are not correlated among black women. It does not appear to be the case. White ancestry and skin color correlate at -0.216 (r) and -0.207 (rho) among black men and at -0.168 (r) and -0.151 (rho) among black women. Plus, the white ancestry advantage and light skin color advantage among subtests are strongly correlated for black men (around +0.80) while they were weakly correlated for black women (around +0.05 and +0.30). So, I don’t have a clear idea. Nevertheless, keep in mind that the congruence coefficients show a very high similarity in factor structure between blacks with and without white ancestry, regarding the g factor.

It can be argued that the correlation between the dichotomized (self-reported) white ancestry variable and skin color is relatively low, compared to what Parra (2004, table 1) has found (0.44%). I haven’t noticed that before, but (apart from its apparently low reliability) the departure from an optimal 50/50 split of any dichotomized variable (that is, with only two categories) would lower the obtained correlations, as Jensen (1998, p. 478) pointed out. Here’s what the histogram shows.

So the fact that ancestry was correlating more strongly with ASVAB (subtests) than does skin color, among blacks, is quite impressive when such effect has been biased downward.

As a short conclusion. Earlier, Nisbett (1995, pp. 5-6) says that one way to narrow the race-IQ debate is to establish the relationship between racial admixture and IQ. The three types of estimates are : skin color, blood groups, self-reported ancestry. The first one is defective, Nisbett argued, because it is a poor reliable estimate, although the empirically found correlation of 0.15-0.20 is not lower than what a hereditarian hypothesis would have predicted (Jensen, 1973, pp. 222-223). As for the second one, he considers the studies by Scarr (1977) and Loehlin (1973) as having successfully rejected the hereditarian hypothesis. As Jensen (1998, pp. 478-481, 525-526) noted however, this is not the case, insofar as the methodology is unsound and the indicators clearly unreliable due to the phenomenon of allele disassociation over the generations among the racially hybridized population. For the latter one, Nisbett cites the Witty & Jenkins 1934 study. But as Chuck (abc102, July.13.2008, Occidentalist, July.13.2011) and Mackenzie (1984, p. 1226) noted, this study is not without methodological problems. In any case, we have already seen that the Add Health and the NLSY97 do not replicate the Witty/Jenkins study and even found, as for the latter, a Jensen effect.

Discussion. If, for reasons mentioned above, the BW sibling regression gap cannot be fully interpreted in terms of environments, we may think of a combination of genetic and shared environmental differences…One cannot even begin to explain why blacks should be more environmentally depressed relative to whites at higher levels of IQ.

I wish here to comment on this point and to offer my own deliberations with regards to the interpretation of the results found.

As Hu (2013, April, 18) has noted, the meaning of the differential regression results has been subject to continual debate. Mackenzie (1980), commenting on Jensen (1973), argued that the results were a statistical artifact. Brody (2002), commenting on Jensen (1998), granted their statistical reality but argued that they were consistent with “virtually any” environmental hypothesis. Kaplan (2001), citing Fynn (1980), seemed to concur with Brody (2002). Murray (1999) argued that they were either consistent with a genetic hypothesis or a non shared environmental hypotheses – and he considered the latter to be implausible. Jensen and Rushton (2010), criticizing Nisbett (2009), argued that that these results were consistent with a genetic hypothesis and not readily consistent with a culture only hypothesis. Pinker (2012, August 6) indicated that they provided support for a genetic hypothesis of group differences.

There seems to be much confusion here. Let us try to shed some light on the issue.

Regression to the Mean and Inheritance of Deviance

In context to behavior genetics, people not infrequently discuss regression to the mean. Regression to the mean simply results, when it does, from deviance not being completely inherited. The inherited portion of a trait deviation from the mean is the portion conditioned by additive genetics and shared environment. It is the portion of a trait deviance that biological families (e.g., full siblings or biological parents and biological children) share. Regression to the mean is simply the non-transmission of trait deviance. It occurs, for example, when very smart parents have only somewhat smart children — because intelligence is only partially environmentally and genetically inherited. Generally speaking, we can define:

Regression to the Mean (R) = 1 – Inheritance of Deviance (I),

where, (I) =~ shared environmental and additive genetic effect.

Mostly people discuss R/I within populations but one can just as well discuss this dual phenomena as it occurs between populations. If two populations differ in terms of the inheritance of a trait, either due to differences in shared environment or to differences in additive genetics, they will show “differential regression”.

Measure and Meaning of Differential Regression

Differential regression is frequently measured by matching individuals on a trait between populations and then comparing the traits of their full siblings. Typically, graphs of the sibling regression lines are presented. A between population deviation in sibling regression lines results from some set of factors causing a population deviance. This deviation, of course, in itself, does not tell one anything more than what one already knows: that there is a population mean difference in the trait being investigated. This is the point that environmentalists such as Fynn (1980) have tried to make. However, the point that hereditarians, such as Jensen (1973), seemed to have tried to make is that the slopes of the regression lines do tell one something. Unfortunately for this debate, hereditarians have not spelled out, precisely, what they mean. We will do that below:

Differential regression tells one something about the within population distribution of a between population trait difference. To illustrate, using Meng Hu’s NLSY 1979 White sibling scores and the scores of created pseudo White siblings, I modeled four different environmental effects:

(1) The first graph shows the sibling regression lines produced by a uniformly distributed non-shared environmental difference which induces 1.2 SD of between population difference. Here, the regression line for White siblings is shown in blue. In purple is shown the regression line for pseudo White siblings. Since the between population effect is non shared, 2.4 standardized units was randomly subtracted from one of the pseudo White siblings per pseudo White pair (2.4/2 =1.2). The scores of the first White and first pseudo White siblings were then matched and averaged per tenth of a standard deviation and the scores of the second siblings were compared. As can be seen, the result is a non linear regression for the pseudo White group.

(2) The second graph shows the sibling regression lines produced by a partially uniformly distributed shared environmental difference which induces 1.2 SD of between population difference, where 10% of the depressed population is unaffected. Here we see that the regression line for the pseudo Whites is linear and that it converges with that of the Whites as IQ increases. This is because the 10% percent of unaffected sib pairs have higher IQs, on average, being unaffected, and because unaffected individuals will show no differential regression.

(3) The third graph shows the sibling regression lines produced by a normally distributed shared environmental difference which induces 1.2 SD of between population difference, where the standard deviation of depressive effect is 0.6. In this case, ~2.2% of the pseudo White groups is completely unaffected. Here, again, we see that the regression line for the pseudo Whites is linear and that it converges with that of the Whites as IQ increases. This is, again, because the less affected sib pairs have higher IQs and so higher IQ individuals tend to be less affected and so show less differential regression.

(4) The fourth graph shows the sibling regression lines produced by a normally distributed shared environmental difference which induces 1.2 SD of between population difference, where the standard deviation of depressive effect is 0.3. In this case, ~0.15% of the pseudo White groups is completely unaffected. Here, again, we see that the regression line for the pseudo Whites is linear but we also see that it shows little convergence. This is because the variability in depressive effect is minimal.

Discussion

We can now compare the above theoretical results to the actual results presented by Meng Hu, which look like:

Clearly (1) and non shared environmental effect models, in general, are untenable. The Black regression line is linear — and, moreover, the magnitude of the found difference in regression lines, at its maximum is not in line with these types of model. Another way to look at this is in terms of the sibling1-sibling2 correlations — in the NLSY79, the White and the Black sibling g-factor correlations were, respectively 0.59 and 0.47 (based on the data Meng Hu gave me); in model 1, the White and the pseudo-White g-factor correlations were, respectively 0.59 and -0.51). The negative correlation resulted from the large 2.4 SD difference being randomly subtracted from one of the pseudo White sibs per pair. Models (2) and (3), which represent shared environmental effects, are also untenable, since the results of Hu (2013, April, 18) and Murray (1999) show that the differential regression lines do not converge or even narrow with increasing IQ. On the other hand, the found results are somewhat consistent with model (4), that is, with a shared environmental model which proposes that the standard deviation of the depressive effect is less than 0.6. Other considerations, particularly concerning measurement invariance, imply that the SD of the depressive effect can not be zero or near zero — as this is equivalent to having an x-factor. If so, this would violate MI, but MI has repeatedly been found to hold in the case of the Black-White differential. As such, any tenable environmental hypothesis must be a mostly shared environmental hypothesis which proposes that the effect depressing the Black mean is narrowly distributed in the Black population i.e., 0 > SD < 0.6.

Now, to note, for comparison, the standard deviation of depressive effect due to shared environment within populations is about 0.45 SD (note 1). So this hypothesized narrow variability in the between group difference within the Black population (i.e., the variance in how much Blacks are adversely impacted, on the account of hypothesized shared environmental differences, relative to Whites) is not overly inconsistent with the variability in the with group differences within the Black population (i.e., the variance in how much Blacks are adversely impacted, on the account of shared environment, relative to Blacks). Readers familiar with this debate will spot the problem, though: the amount of total shared environmental difference between populations that would be needed to account for the (1.2 SD) difference would be 2.7 SD (note 2, 3). This simply does not exist. There have been attempts to deconstruct the estimates of shared environmentality, but these are of no help, in this case, because if the variance due to shared environmentality is increased within population it will likely be so between populations leading to differential regression results that match with models (2-3). To put this point another way, you can shared environmentally explain the differential regression results by positing that there is not much variance in depressive effect and you can explain the dearth of this variance by pointing out that there is not much within population variance on the account shared environment, but then this leads, inevitably, to the question of why there are such large differences between populations in the first place given the impotency of shared environments. If you try to explain this by shattering heritability (or shared environmentality) estimates, you are led back to the problem of non-convergence of differential regression lines. The only apparent escape from this catch 22 is simply to not deal with the totality of the evidence — and this generally seems to be the strategy employed.

Conclusion

Meng Hu claimed:

One cannot even begin to explain why blacks should be more environmentally depressed relative to whites at higher levels of IQ

I agree with Meng Hu that this situation is curious. Nonetheless, it seems to me that the general regression to the mean results, while consistent with a additive genetic model of group differences, are also, at least when taken in isolation, consistent with some shared environmental models. Another possibility is that the found differential regression slopes could be due to some combination of shared environmental and unshared environmental effect. It might be worthwhile to explore these models. With regards to shared environmental models, no models by which an appreciable portion (e.g., more than 2.5%) of the Black population is unaffected are tenable. Likewise, by all tenable models, more than 85% of the Black population must be depressed by at least 0.6 SD (using a conservative estimate).

Are the remaining environmental models plausible? In my estimation, no — when taking into account the totality of the evidence. But to answer this query properly, we would have to look at specific models and explanations or classes of them and evaluate them in particular. In general, it is curious, though, that between the time of Jensen's early work and the NLSY 97, the regression lines have not begun to converge — as would have happened if a non-trivial portion of the Black population (e.g., 10%) managed to escape the cumulative effect depressing the Black mean. Eventually, if the gap is to close, subsections of the African-American population will need to escape the mysterious cognitive depressing effect, an event which will result in a convergence of the sibling regression lines at the right end of the spectrum (model 2, 3). Insofar as there is no convergence, again, the results are consistent with an additive genetic model.

Notes

(1) It would be: SQRT((SD^2)*C^2)), where SD is the variance in the trait and C^2 is the portion of variance due to shared environment. The C^2 found for IQ is typically around 0.2, age depending.

(2) The difference in g-scores is ~1.2 SD. The shared envrionmentality is about 0.2– and so the correlation between cumulative shared environmental effect and g-scores is about 0.4 (e.g., SQRT(0.2). The amount of cumulative shared environmental effect, then, needed to explain a ~1.2 SD difference would then be ~1.2/0.4 or 2.7 SD.

(3) Some have argued that there are 2.7 or so standard deviations of shared environmental effects between contemporaneous Black and White Americans on the account that there are 2.7 or so standard deviations in cumulative “environmental” differences (e.g., Fryer and Levitt). But those who have have failed to grasp the distinction, among other things, between environmental factors and external factors. The shared envrionmentality of external factors (e.g., parental income, number of book read to by parents, peer groups, home “environment”) is only about 0.5 (Vinkhuyzen et al., 2009; Plomin and Bergeman, 1991). As such, the total amount of difference in cognitive affecting external factors needed to account for the difference would have to be 2.7 SD/ SQRT(0.5). or 3.6 SD. There would have to be almost no overlap. Also, the relevant amount of cumulative external factor difference would not be the sum of the effects but the sum of the independent effects of external factors determined with multiple regressions. Interested readers can explore the possibility that there is such a difference using the publicly available NLSY79 Children and Young Adults survey.

References

Brody, N. (2002). Jensen’s Genetic Interpretation of Racial Differences in Intelligence: Critical Evaluation. In: Nyborg, Helmuth, ed. The Scientific Study of General Intelligence: Tribute to Arthur Jensen. Pergamon.

Flynn, J. (1980). Race, IQ and Jensen, London and Boston: Routledge & Kegan Paul.

Hu, M. (2013, April, 18). IQ Regression to the Mean : the Genetic Prediction Vindicated. Accessed at: http://humanvarieties.org/2013/04/18/iq-regression-to-the-mean-the-genetic-prediction-vindicated/

Jensen, A. (1973). Educability and Group Differences. Harper & Row.

Kaplan, J. (2001). Misuses of statistics in the study of intelligence: The case of Arthur Jensen. Chance, 14(4), 14-26.

Mackenzie, B. (1980). Fallacious use of regression effects in the iq controversy. Australian Psychologist, 15(3), 369-384.

Murray, C. (1999). The Secular Increase in IQ and Longitudinal Changes in the Magnitude of the Black-White Difference: Evidence from the NLSY. In Behavior Genetics Association Meeting.

Nisbett, R. E. (2009). Intelligence and how to get it: Why schools and cultures count. New York, NY: Norton

Pinker, S. (2012, August 6). Steve Pinker Responds to Ron Unz. Accessed at: http://www.amren.com/news/2012/08/steve-pinker-responds-to-ron-unz/

Rushton, J. P., & Jensen, A. R. (2010). Race and IQ: A theory-based review of the research in Richard Nisbett’s Intelligence and How to Get It. The Open Psychology Journal, 3(1), 9-35.

First, let’s look at the cognitive gap between light-skinned blacks and dark-skinned blacks. With the appropriate SPSS syntax (here), I recoded the skin color variable into a two-categories variable, to make comparison easier.

The gap, using the following formula would be :

5.67-4.69/SQRT((69 x 1.9² + 99 x 1.7²)/(69 + 99))
1/SQRT((249 + 286)/(168))
1/SQRT(535/168)
1/SQRT(3.18)
1/1.78
0.56

This gives us 0.56*15 = 8.4 verbal IQ points. By way of comparison, the mean Wordsum score for whites in 2012 is 6.22, and for the cumulative years (1972-2012) it was 6.26 when I re-ran the comparison of means analysis without filter. The black-white wordsum gap for the last year of survey, that is, 2012, is :

6.22-5.13/SQRT((947 x 1.9² + 191 x 1.8²)/(947 + 191))
1.1/SQRT((3418 + 619)/(1138))
1.1/SQRT(4037/1138)
1.1/SQRT(3.55)
1.1/1.88
0.58

Or, 0.58*15 = 8.7. And the wordsum gap between whites and light skinned blacks is :

6.22-5.67/SQRT((947 x 1.93² + 69 x 1.87²)/(947 + 69))
0.55/SQRT((3527 + 241)/(1016))
0.55/SQRT(3768/1016)
0.55/SQRT(3.71)
0.55/1.92
0.28

Or, 0.28*15 = 4.2 verbal IQ points. In other words, light skinned blacks fall intermediate between whites and blacks. Using this calculator, which divides the black-white mean difference by the averaged SD of the two groups, produces similar results. And, to see whether or not there is a colorism effect, due to a so-called color-based discrimination, I perform a multiple regression, as follows :

RATETONE variable is a 10-point scale variable, going from 1 (lightest) to 10 (darkest). A negative sign means that when skin color becomes darker, the respondent’s income decrease. But the negative coefficient is only about -0.029 in Model 2, when Wordsum has been held constant.

The reason for including respondent’s wordsum score, is that a colorism effect, as the discrimination hypothesis predicts, is universal and affect all people, regardless of their race and/or gender. If, after controlling for education, IQ, parents background, and all other socio-economic background characteristics possible, the coefficients of skin color among blacks fall to near zero, the discrimination hypothesis is nullified. Because, according to colorism, the effect of such discrimination is independent of characteristics such as skills, experience, competence, intelligence, and so forth. It argues that colorism effect has to do with physical appearance, and absolutely nothing more than that. In other words, probably the best way to test colorism is to look at the effect of skin color, net of SES and/or IQ. Here, verbal IQ (i.e., Wordsum) alone explains the lion’s share of skin color-income association.

I haven’t added GSS “degree” variable. The reason is that controlling for SES and/or IQ is like matching people on genetic characteristics, and therefore, removing the causal role of factors linked to genes. SES, of course, has a genetic component (Jensen, 1973, pp. 116-117, 155-156). That the effect of skin color among blacks diminished after holding SES constant is exactly what the genetic hypothesis is predicting. Anyway, even when I replaced wordsum by degree in Model 2, the effect of skin color hasn’t diminished (-0.146 to -0.125).

Now, if we conduct a regression of degree on skin color, holding wordsum constant, something unexpected happens :

Skin color among blacks is positively associated (0.123) with education level. A positive sign, here, means that the darker the skin and the higher the educational attainment. Just the opposite of what colorism would have predicted. Overall, the color-outcome association in the GSS data is consistent with what I have previously found in the Add Health and NLSY97 data, and as others did too. Of course, all the above analyses are weighted (by WTSSNR, see GSS codebook, Sampling Design & Weighting, Appendix A, p. 2110).

Finally, a technical note about the multiple regressions I conducted, is that the residuals were initially not normally distributed. Generally, the cause behind this is that the dependent variable is not normally distributed. This was the case for income, and to a lesser extent degree. Those two variables showed some skewness towards the left (we can check this out using histogram). So I simply used the square root transformation, in order to get a more normally distributed pattern of residuals.

Introduction. Although regression to the mean is sometimes interpreted as a strong support for the hereditarian hypothesis with regard to the nature of the black-white IQ difference (Jensen, 1973, pp. 110-119; 1998, pp. 468-472; Rushton & Jensen, 2005, p. 263), others suggest that this phenomenon fails to narrow the race-IQ debate.

The hereditarians argued that regression occurs because parents and children share 50% of their genes, this phenomenon is simply reflecting the non-transmission of heritable traits (that is, they are not shared). The degree of regression increases when the degree of kinship decreases. Environmentalists, however, believe that regression to the mean can also be understood in terms of differences in culture or environment. Racial differences regarding sibling regression to the mean could be interpreted as a between-family difference, insofar as black and white siblings with equal IQs do not necessarily have the same home environment quality. After all, environmentalists may argue that black parents will provide a poor cognitive environment to their children, even if black and white parents were perfectly matched for IQ. But if the environmental theory of race differences is really tenable, we should expect a convergence in differential sibling regression to the mean. Any other result purely contradicts this theory.

Another kind of criticism (Kaplan, 2001, p. 16-18; Neuroskeptic, 2010) focuses on the interpretation of the regression to the mean per se. It was suggested that this phenomenon is just a statistical artifact. An example may help to understand the argument. Suppose in the next month, the number of car accidents in the country will suddenly double. The government responds by placing additional cameras, strengthening surveillance systems. This strategy will fail because in the next month, the number of accidents will go back to its initial level. Regression to the mean. In other words, the regression is thought to be a cyclical phenomenon of whatever luck and chance.

But that’s not clear at all. What kind of luck explains the fact that the children of high-IQ parents have lower IQs while they are reared in cognitive stimulating environments, when the children of low-IQ parents who were raised in chaotic environments still have higher IQs than their parents ? The IQs regress halfway (50%) to the population mean at both sides of the IQ distribution. If we stick to the Dickens-Flynn model (2001) of feedback loops, one would expect that children of high-IQ parents have higher IQ and children of low-IQ parents an IQ even lower. But the opposite happens. This criticism, in the end, does not provide any explanation for the fact that the regression is homogeneous across the different levels of IQ. As Jensen made it clear, the IQ subgroups do not depart from linearity for an IQ range going from 50 to 150.

While some say that regression to the mean occurs because of some kind of (random) measurement errors, it should be noted that IQ regression to the mean analyses are usually performed by using the method of estimated true scores, that is, IQ scores corrected for measurement error, or unreliability, with the formula :

Tˆ = r_XX′ (X − M_X) + M_X

where Tˆ is the estimated true score, X the observed score, r_XX′ the reliability coefficient of the test, and M_X being the mean of the group. Why this method reduces the “luck” factor has been explained in Bias in Mental Testing (1980, pp. 276-277) by Jensen himself :

The net effect of using such estimated true scores, besides increasing the accuracy of measurement, is to reduce the higher scores of persons belonging to low-scoring subgroups and boost the lower scores of persons belonging to high-scoring subgroups. Such an outcome may seem unfair from the standpoint of members of the lower-scoring subgroups, but it is merely the statistically inevitable effect of increasing the accuracy of measurement. When higher scores are preferred in the selection procedure, the “luck” factor resulting from unreliability statistically favors persons belonging to lower-scoring groups. The “luck” factor is minimized by using estimated true scores instead of obtained scores.

[...] If test reliability is quite high (i.e., above .90), however, the slight gains in accuracy and predictive validity from using estimated true scores may hardly repay the extra computational effort.

But given that the reliability of AFQT is about 0.95 (Winship & Korenman, 1999), this method will leave the results unaffected in any case.

Still another critique, from Mackenzie (1984, p. 1220) this time, made the case that blacks and whites will regress to the same mean if the parent-child correlations or sibling correlations were calculated from pooled samples of blacks and whites. Of course, this tells us nothing about the causes of the racial differences in sibling regressions. Because, on the contrary, when the levels of IQ increase, the racial differences in sibling regressions will tend to converge, according to the environmental hypothesis. If this is not the case, the environmental interpretation is untenable. This was exactly what Jensen (1973) wanted to know : if one of the IQ subgroups at both ends shows some deviations from linearity. Or stated differently, to see if the regression lines converge at higher levels of IQ.

But the fact that the black-white IQ difference increases with SES levels (Jensen, 1973, pp. 241-242; Herrnstein & Murray, 1994, pp. 287-288; Jensen, 1998, p. 358; Gottfredson, 2003, Table 2; Hu, Jan.1.2013, Jan.18.2013) is hardly explainable from the environmental standpoint. Thus, Jensen (1973, p. 119) believed that it could be easily explained by the BW difference with regard to sibling regression toward the mean.

Method and Data. NLSY79 and NLSY97 were used for the present analysis, because sibling data and IQ subtests were available. Factor analysis can be performed for extracting g (analysis #1) and Jensen’s method of correlated vectors can be used for testing the association between sibling correlations on ASVAB subtests and black-white gaps as well as g-loadings in those subtests (analysis #2).

If one wants to replicate the present finding using my syntax and variables for NLSY79 (here) and NLSY97 (here), recall that SPSS is needed. Creating a free NLS Investigator account is needed if we wish to collect the relevant variables. Then, do a quick search by terms, keywords, as shown below :

Then, download your collection of selected variables, and copy/paste the files into a new file. Before running the syntax page, recall that the handle file should look like this.

Regarding the differential sibling regression to the mean, the purpose was to replicate and extend further Murray’s analysis on the NLSY79. I recoded the key variable as follows : BHW=1 for blacks, BHW=2 for hispanics, BHW=3 for whites, SIBLING=1 for full siblings, SIBLING=2 for unrelated and half siblings. Thanks to the CASESTOVARS command, it was possible to identify the NLSY full siblings. This command breaks a variable into a certain number of categories (depending on the number of values of this variable). So, when a variable ended with an .1 or an .2, this was the numero of the identified sibling : .1 for sibling #1 and .2 for sibling #2. The numbers after the sign “=” designate the categories of my dummy variables.

But because I was unable to find a magical SPSS syntax, I have to delete the missing values manually. The easiest way to do this hopefully is to simply use the “Sort Ascending” option in the SPSS data editor page for the relevant column. This will list the empty cells first. So I use this option for deleting missing values among siblings #1 and then among siblings #2. (“Copy Dataset” is a very useful function that duplicates the data window if some cases have been deleted by error)

Of course, some anomalies have been detected. For example, when one sibling self-identified as black or hispanic and the other sibling self-identified as white, and both responded that they are full siblings. These cases are deleted. Similarly, even when both agreed about their racial identification, sometimes the first sibling said the other one is a full sibling while this second sibling said the other one is not a full sibling. These cases, too, are deleted. Here’s an example of anomaly :

Also, there should be no missing values in either SIBLING.1 or SIBLING.2. Missing values in BHW (my race variable) is of no concern when both siblings said they are not full siblings. But if they were full siblings, empty values of BHW pose a problem because of the way I coded BHW, empty values are the respondents who are not either blacks, hispanics or whites. Those cases are deleted. For doing this, use Sort Ascending option on SIBLING.1 and SIBLING.2 columns. Values of 1 are listed first. Then re-use this option on the BHW column. This will put at the top of the list the full siblings who have empty values in BHW (in other words, full siblings who are not either blacks, whites or hispanics).

Because the data points are scattered everywhere when performing an overlay scatter plot (with option ‘Exclude cases variable by variable’) in order to display the regression lines for each racial group, I also display a graph with IQ subgroups, as Murray (1999) did :

To do this with the appropriate SPSS syntax (here), I categorized the IQs of siblings #1 for each race by averaging the IQs of all same-race subjects that have an IQ between -3 SD and -2 SD below the mean of the full sample analyzed, and IQ between -2 SD and -1 SD below the mean, and so forth. Filters and comparisons of means were used for this purpose.

Because WordPress doesn’t allow SPSS file, you have to send me a mail, if you want it. Hopefully, WordPress allows Excel file to be uploaded. If you don’t have Excel however, Kingsoft Spreadsheets is a good alternative.

NLSY79 g factor MCV regression to the mean and sibling correlations
NLSY97 g factor MCV regression to the mean and sibling correlations

I also assembled the data from half and unrelated siblings but I haven’t reported the result here because I found it uninformative (range of restriction of cognitive abilities, small sample size, …).

Results. The first analysis compares the BW sibling regression lines in the g dimension and non-g dimension of cognitive tests. The second analysis aims to replicate Jensen’s findings using his method of correlated vectors.

Analysis 1. The (PAF) factor analysis of the NLSY (97 and 79) ASVAB subtests allows the extraction of a g-factor score and a non-g factor score, represented by the loadings in the first factor and the second factor in the factor matrix. The interest is to see whether or not the degree of regression toward the mean is changing accordingly from the g dimension to the non-g dimension of cognitive tests.

Here, I display a graph showing the sibling regression without grouping IQs and another graph with IQ subgroups. The advantage of the latter, as stated above, is to have a better look at any deviation from linearity, as Murray did. Here’s what the NLSY97 sibling regressions look like :

The x axis (horizontal, from left to right) shows the IQs of sibling #1. The y (vertical) axis shows the IQs of sibling #2. As we can see, there is no convergence in the regression lines at higher levels of IQ. The BW sibling gap may appear even larger. The BW sibling difference is about 0.50 SD.

Above are the graphs showing the sibling regression lines for the NLSY79. Here again, we see no convergence in the g-factor dimension. The hispanic line falls once again between the black and white lines.

Consistent with Murray (1999) and Jensen (1973), none of the above data points representing the IQ subgroups show any deviation from linearity. Now, let’s look at the non-g factor dimension, first for the NLSY97 and then for the NLSY79 :

Regarding the R² values for IQ subgroups, we shouldn’t put much faith on them. It’s obvious that they are totally uninformative here. What is of significance here is that the racial sibling gap is trivial. The IQs of siblings #2 move just slightly (-0.5 SD to +0.5 SD) as the IQs of sibling #1 are changing (-2 SD to +2 SD).

If the degree of regression is a function of the g-loadedness of IQ tests, with more regression among the less heritable component of IQ tests, it is hard to believe that this phenomenon is a mere statistical artifact. Next analysis provides another test of this assumption.

Analysis 2. Now we test Jensen’s predictions. In The g Factor (pp. 471-472), he wrote :

A number of different mental tests besides IQ were also given to the pupils in the school district described above. They included sixteen age-normed measures of scholastic achievement in language and arithmetic skills, short-term memory, and a speeded paper-and-pencil psychomotor test that mainly reflects effort or motivation in the testing situation. [50] Sibling intraclass correlations were obtained on each of the sixteen tests. IQ, being the most g loaded of all the tests, had the largest sibling correlation. All sixteen of the sibling correlations, however, fell below +.50 to varying degrees; the correlations ranged from .10 to .45., averaging .30 for whites and .28 for blacks. (For comparison, the average age-adjusted sibling correlations for height and weight in this sample were .44 and .38, respectively.) Deviations of these sibling correlations from the genetic correlation of .50 are an indication that the test score variances do reflect nongenetic factors to varying degrees. Conversely, the closer the obtained sibling correlation approaches the expected genetic correlation of .50, the larger its genetic component. These data, therefore, allow two predictions, which, if borne out, would be consistent with the default hypothesis:

1. The varying magnitudes of the sibling correlations on the sixteen diverse tests in blacks and whites should be positively correlated. In fact, the correlation between the vector of sixteen black sibling correlations and the corresponding vector of sixteen white sibling correlations was r = +.71, p = .002.

2. For both blacks and whites, there should be a positive correlation between (a) the magnitudes of the sibling correlations on the sixteen tests and (b) the magnitudes of the standardized mean W-B differences (average difference = 1.03σ) on the sixteen tests. The results show that the correlation between the standardized mean W-B differences on the sixteen tests and the siblings correlations is r = +.61, p < .013 for blacks, and r = +.80, p < .001 for whites.

Note that with regard to the second prediction, a purely environmental hypothesis of the mean W-B differences would predict a negative correlation between the magnitudes of the sibling correlations and the magnitudes of the mean W-B differences. The results in fact showing a strong positive correlation contradict this purely nongenetic hypothesis.

To recall, the default hypothesis (Jensen, 1998, p. 448) posits that the genetic and the environmental factors that cause the between-groups difference exist within each group (but not necessarily in equal degrees).

First of all, let’s see what the relationship between the vector of sibling correlations and the vector of g-loadings looks like. In the NLSY97, the BW g-loadings correlate strongly with white sibling correlations (+0.80) and black sibling correlations (+0.90). The HW g-loadings also displayed a strong relationship with both white and hispanic sibling correlations (+0.80). And again, the BH g-loadings also show a strong positive correlation with hispanic and black sibling correlations (respectively, +0.90 and +0.80). In the NLSY79, BW g-loadings correlate with sibling correlations for whites at about +0.80 and for blacks around +0.35 and +0.15. The HW g-loadings correlate strongly with white sibling correlations (around +0.75) and with hispanic sibling correlations (around +0.75). What is unexpected is that BH g-loadings correlate negatively with sibling correlations for blacks (around -0.20) and for hispanics (about -0.30 and -0.50).

Another method (apparently suggested by Bartholomew, 2004) that might improve the reliability of estimates consists in grouping two by two the subtest g-loadings and/or sibling correlations, by order/rank of estimates. For example, if GS and AR subtests have the two highest loadings, we first average the g-loadings of GS and AR, and then average the sibling correlations of GS and AR, and we repeat the process for the two next highest loadings, and so forth. But we can also group by d gaps, by averaging the two highest d gaps, and repeating the process for the second two highest d gaps, and so on, and finally by averaging the corresponding g-loadings in the column vector. And as the above picture shows, the correlation between the magnitude of BW g-loadings and the black sibling correlations is a little bit higher (+0.43 and +0.28, if we use g grouping; or +0.55 and +0.24 if we use sib r’s grouping).

Generally speaking, this finding supports the view that the magnitude of sibling regressions toward the mean diminishes as the g-loadedness of the test increases, which is also consistent with Analysis #1.

But what about the (non-g) loadings of the second factor with sibling correlations ? In the NLSY97, these associations are usually negative and none of them showed a positive slope for all races. In the NLSY79, however, the white full sibling correlations were strongly and positively associated (r and rho) with non-g loadings for BW non g-loadings, but this relationship is much smaller for HW non g-loadings. Among blacks, this relationship is positive but much smaller and looks like a random dispersion of dots for BW non g-loadings, or is near zero for BH non g-loadings. Among hispanics, they were small negative or small positive.

Now, regarding Jensen’s first prediction, the NLSY97 shows a very strong positive correlation between the vector of white sibling correlations and the vector of black sibling correlations (around +0.80 and +0.90). Between hispanics and whites, the correlations were also very high (around +0.90). Between hispanics and blacks, the correlations were about +0.80 and +0.90. In the NLSY79 I found a moderate positive correlation between the vector of white sibling correlations and the vector of black sibling correlations (around +0.40). Between whites and hispanics, the correlations turned to be about +0.40 or +0.50. Between blacks and hispanics, the correlations were around +0.30.

Finally, with regard to Jensen’s second prediction, the NLSY97 shows that the magnitude of the BW d gap is not related with the magnitude of black sibling correlations (near zero) or the white sibling correlations (around +0.20 or +0.15). The correlation between the HW d gap and sibling correlations is not trivial for whites (around +0.25 and +0.40) and for hispanics (around +0.40 and +0.50). Curiously, the correlation between BH d gap and sibling correlations is small for hispanics (around +0.10 and +0.15) but negative for blacks (-0.10 or -0.20). In the NLSY79, the magnitude of BW d gap correlates with black sibling correlations at about +0.10 and with white sibling correlations at about +0.05. The magnitude of HW d gap is positively correlated with sibling correlations for whites (around +0.40) and for hispanics (around +0.80 and +0.90). The magnitude of BH d gap shows a non-trivial negative relationship with sibling correlations for blacks (around -0.15 and -0.30) and for hispanics (around -0.25 and -0.50).

Using again Bartholomew’s method, the correlation between the magnitude of BW d gap with white sibling correlations becomes a little bit higher (at about +0.49 for r’s, and +0.23 for rho) while for black sibling correlations, it remains very low (+0.10 and -0.03, respectively) in the NLSY97. Regarding this, it should be noted that MCV totally failed to show a correlation between BW d gap and BW g-loadings in the NLSY97 even if there was in fact such a Spearman effect.

This method of course will not generate correlations as high as what Jensen found (about +0.60 and +0.80). But because none of these relationships were negative with regard to the black-white IQ gap, we can say that the environmental hypothesis is clearly rejected. Overall, my 2nd analysis attempting to replicate Jensen’s finding is mixed. It is not a great success, but it is not a failure either. The finding is still consistent with the hereditarian hypothesis but perhaps less than what he might have suggested.

Limitations. As explained above, regressed true scores were not used in analysis #1, but given the high reliability coefficient of AFQT (0.95), it will probably not affect the above result. Also, regarding the graphs of grouped IQs for g factor scores, the dots at both ends of the IQ distribution comprise in fact a very small sample size, with sometimes 10 or 20 sibling pairs.

Jensen’s method of correlated vectors used in analysis #2 is not without critics (Dolan, 2000, p. 46; Dolan & Hamaker, 2001, pp. 16-19; Ashton & Lee, 2005, p. 438). Dolan is confident that MGCFA, rather than MCV, allows one to demonstrate that the g model fits better than the competing models, and at the same time, he says that Jensen’s procedure provides no goodness of fit testing, with no test of B-W difference in covariance. Among other things, a hierarchical factor analysis was not used as a secondary check of the existence of a general factor, and this poses a problem since Jensen (1998, pp. 96-97) has made it clear that hierarchical factor analysis could easily overcome the problem of what he calls a psychometric sampling error (that is, a situation where the extracted g is in fact a distorted g resulting from a biased representativeness of the tests in the test battery), although Ashton and Lee argued that its use does not overcome the many problems associated with a biased selection of subtests. On the other hand, Rushton (2007, p. 11) also defended the MCV. He made the case that the failure of Jensen’s MCV can be due in fact to a biased criterion (i.e., dependent variable). In Bias in Mental Testing (1980, pp. 310, 383), Jensen indeed wrote the following :

A biased criterion is one that consistently overrates (or underrates) the criterial performance of the members of a particular subpopulation. A good example is sex bias in school grades: teachers generally give slightly higher grades to girls than to boys, even when the sexes are perfectly matched on objective measures of scholastic achievement.

When the criterion itself is questionable, we must look at the various construct validity criteria of test bias. If these show no significant amount of test bias, it is likely (although not formally proved) that the criterion, not the test, is biased. In a validity study, poor criterion measurement can make a good test look bad.

However, I don’t see why this point should apply to the present analysis. But perhaps Jensen’s MCV used in conjunction with meta-analyses along with further corrections for artifacts (sampling error, range restriction of g-loading vectors, perfect construct validity, …) could yield a very promising results (te Nijenhuis, 2007, 2012; Joep Dragt, 2010).

Another significant difference between Jensen’s application of MCV and mine, is that when he uses MCV to test the Spearman Hypothesis, his histogram (in, The g Factor, p. 382) shows a normal frequency distribution of g-loadings (g) and standardized mean B-W differences (d) for 149 subtests from 12 different test batteries (N = 286,901). But, in both the NLSY97 and NLSY79, it is clear that those distributions do not display normality in the frequency. As Jensen pointed out, a test of a Spearman effect using MCV should require, ideally, “large g loadings on the subtests and maximum variation among the subtests’ g loadings; also, large mean group differences on the subtests and maximum variation among the group differences”. So, this could be one of the reasons why the results from the MCV in Analysis #2 may appear sometimes contradictory.

If to be correctly applied, Jensen’s MCV required a multitude of conditions, it appears that I haven’t met those conditions in any case. If true, my findings related to the 2nd analysis must be considered with a pinch of salt.

Discussion. If, for reasons mentioned above, the BW sibling regression gap cannot be fully interpreted in terms of environments, we may think of a combination of genetic and shared environmental differences. But what kind of environment, exactly ? Chuck (Dec.8.2012), on “More thoughts on differential regression to the mean studies”, argues for a shared environmental effect, and Murray (1999) for a non-shared. Jensen (1973) seems to argue against shared environmental effects. In Educability & Group Differences, pp. 118-119, Jensen expresses his thoughts :

It can be claimed that though the white and Negro children are matched for IQ 120, they actually have different environments, with the Negro child, on the average, having the less intellectually stimulating environment. Therefore, it could be argued he actually has a higher genetic potential for intelligence than the environmentally favored white child with the same IQ. But if this were the case, why should not the Negro child’s siblings also have somewhat superior genetic potential? They have the same parents, and their degree of genetic resemblance, indicated by the theoretical genetic correlation among siblings, is presumably the same for Negroes and whites.

What Jensen has in mind would possibly be the idea that the absence of a convergence in the regression lines is difficult to explain in terms of differences in shared environment. But this would be true, also, with regard to non-shared environment. One cannot even begin to explain why blacks should be more environmentally depressed relative to whites at higher levels of IQ.

I had noted previously that there is diminishing interest in classic HBD topics, such as race and IQ. And, I pointed out elsewhere that virtually no one in the US with an IQ above the 85th percentile currently takes the hereditarian position on race and IQ seriously, at least as judged by the General Social Survey 2012 responses. So, perhaps, the views of HBD proponents are finally coming in line with those of the vast majority of the US population. Indeed, one of the leading minds in this field has recently stated:

Like many of us who are fascinated with human diversity, she has little or no interest in what are called race differences…. No one it seems cares much about that any longer. (Harpending, H. (April 14, 2013). West Hunter).

This increasing disinterest might explain why my colleague’s recent eloquent defense of general intelligence netted 53 comments while my post on my exhaustive analysis of color and IQ amongst siblings of different races, a topic hitherto never explored, netted precisely 0. There are other possible reasons for this, of course. Whatever the case, the nexus between race and IQ doesn’t seem to be as popular of a topic as it once was so it seems that I will do less unwell if I shift my focus elsewhere.

One race unrelated issue worth further exploring is that of Jews, meritocracy, and elite admissions. Ron Unz has fairly recently made a splash with his Meritocracy article, an article in which he argued that Jews were disproportionately overrepresented in elite schools relative to their aptitude. I have commented before on some of Ron’s questionable estimations, but I haven’t had a chance to wrestle with this one, my current constitution being what it is. For readers who are unaware of the issue, Ron marshaled a large amount of evidence demonstrating that Jews were overrepresented in elite universities and that Jewish academic ability has plummeted over the last several decades. Based on these two points, he inferred — and not unreasonably so — that Jews were over represented in elite scores relative to their aptitude. From this, Ron deduced that there was a sort of pro-Jewish discrimination. But as one of Ron’s more perceptive critics has pointed out, to truly test the Jewish bias hypothesis one needs to compare the scores of Jews at elite universities to those of non-Jews. (The same holds for testing anti-Asian bias hypotheses). Ron’s model logically predicts that Jews at these universities will be sub par, in aptitude, compared to comparable gentiles. Simply: if group A is disproportionately selected, conditioned on aptitude, relative to group B, selected members of groups A will have a lower aptitude than selected members of group B. This basic phenomenon can be seen at work in regards to racial and ethnic groups in the US. For example, Blacks attending (and graduating) from medical school are greatly inferior to Whites in mental ability. This is an inevitable product of the federally mandated discrimination for Blacks, given the mean differences in the population at large and the basic principle concerning selectivity and selectees noted above.

Now, if Ron’s thesis is correct, we should find a similar pattern for Jews, as with other discriminated for groups, in elite schools. I have been unable to find an ideal sample in which to test this thesis, but I was able to locate an acceptable one, the National Longitudinal Survey of Freshmen. This survey is described thusly:

The National Longitudinal Survey of Freshmen (NLSF) follows a cohort of first-time freshman at selective colleges and universities through their college careers. Equal numbers of whites, blacks, Hispanics, and Asians were sampled at each of the 28 participating schools. Among other uses, the data has been collected with the testing of several competing theories of minority underperformance in college in mind.

It is a survey of attendees at selective universities. It will be noted from the start that the scores soon to be discussed are based on self reported SAT and ACT scores. As I said, this sample is not ideal — just acceptable. That said, a large body of research shows that self-reported scores correlate reasonably well — at about 0.8 –with verified scores. See, for example, Kuncel et al. (2005):

(From: Kuncel, et al. (2005). The validity of self-reported grade point averages, class ranks, and test scores: A meta-analysis and review of the literature.)

Now, a note on method: I simply compared the self-reported aptitude scores of self reported Jews and Gentiles and also of self reported White Jews and White Gentiles. I also decomposed Jews in to two groups — those who reported only Jewish family background and those who reported Jewish plus some other family background (e.g., Catholic). For scores, I scaled SAT scores on ACT scores using an ACT conversion chart and then created a composite SAT+ACT score. I also presented ACT and SAT scores. Official ACT scores range from 1 to 36. As such, reported 0s were recoded as 1. SAT M+V scores range from 400-800. As such reported scores below 400 were recoded as 400.

The results are below:

Generally, as expected, Jews were over represented in this sample. Jews made up 6.3% of the total sample and White Jews made up 18.1% of the White sample. In comparison, in the US at large Jews constitute about 2.2% of the population and self identifying White Jews constitute no more than 4% of the non Hispanic White population. Since this sample was not representative with regards to race — rather roughly equal, not representative, sample sizes of different racial ethnic groups were selected — the overall percentages are not very meaningful. What is meaningful, though, is the percentage of White Jews relative to White Gentiles, assuming, of course, that there was no positive survey selection bias for White Jews relative to White gentiles. And I have not been able to find any indication that there was.

Despite their vast over-representation, Jews did not have lower aptitude scores compared to comparable populations as Ron’s model would have predicted. The self-reported aptitude of Jews was 0.49 SD higher than that of Gentiles in general and the self-reported aptitude of White Jews was 0.39 SD higher than that of White Gentiles. It is possible that these results are biased, given the self reported nature of the aptitude measure. Perhaps not only is there entrance selection bias for Jews, controlling for aptitude, but perhaps there is also Jewish self estimation bias. University admitted Jews might be less apt as predicted by Ron’s model but might report being more apt. Since all the measures in the NLSF are self reported, this issue can not be resolved based on the results in this survey. That said, academic achievement measures (not reported) show a similar pattern. So, if Jews are biased in their self reporting, they are consistently so. This, of course, is possible. On this point, readers are referred to Kevin MacDonald’s extensive research on Jewish group-over estimation and self deception. I would suggest, though, that in light of these results the issue needs to be further explored. To do this further, measures of the aptitude of Jews at select universities are needed. Generally, though, the NLSF results do not support Ron’s pro-Jewish discrimination hypothesis — Perhaps it will turn out that other surveys don’t likewise.

In case that some readers are curious, one can compare the Jews-Gentile score differences to the White-Black score differences found in the same study:

Readers can refer to the excel file attached below for a more complete decomposition of scores. What they will find is that Black and Hispanic individuals tend to have significantly lower reported scores than White and Asian individuals — as we would expect given the extensive selection discrimination for the former two groups and the basic basic principle concerning selectivity and selectees noted above.

Now, while doing this analyses I also happened to look at the correlation between self reported aptitude and skin color by race and by nativity for US born individuals. The results are summarized below:

In this sample, color and aptitude were unassociated for Whites and Asians. Predictably — by my assortative exogamy + ancestral genetic model — they were associated for Blacks and Hispanics, though not consistently so across immigrant generations. Specifically, US born Blacks who had two reported foreign born biological parents showed no correlation between aptitude and color. And US born Hispanic who had one reported foreign born biological parent and one reported US biological born parent likewise showed no correlation. The lack of correlation for the US born offspring of foreign born Blacks is consistent with my model insofar as many of these individuals do not descend from exogamous parings or have substantial ancestral genetic admixture. They most likely are less admixed as attested by the higher color ratings — though, I have, as yet, been unable to verify this as the NLSF staff has not been very forthcoming with the needed variables. (Of course, I have run into this general problem before; it seems to occur when I clearly articulate the scientific paradigm which I am working under.) Similarly, the GSS shows that there is no correlation between wordsum and color for first generation Blacks — though this sample is very small. These results are shown below:

The positive correlation coefficient indicates that darker tone is (non significantly) positively correlating with Wordsum scores. In contrast, results for native born Black persons can be seen here.

My proposed explanation could be best tested by looked at the correlation between color and backwards digit span (BDS) — a relatively culturally fair tests which simply involves counting backwards and is non-trivially correlated with g — in the National Immigrant Survey. I would predict that there would be little correlation between color and cognitive ability amongst first generation Black immigrants (assuming a non trivial number came from regions in which there was little admixture). As it is, I have shown that BDS correlates with color in the native born African American population, so there is no a priori reason why it couldn’t so correlate in the foreign born Black population. And I would also predict that there would be a negative correlation between lightness of color and IQ amongst first generation Hispanic immigrants, since virtually all Hispanics descent from generations of exogamous parings. That said, with regards to the Hispanics in the NLSF sample, I am unable to account for the anomalous zero correlation between color and aptitude for US born individuals with just one foreign born parent. It might be worth checking to see if the same pattern can be found in the GSS, Add Health, and NLSY samples.

Also consistent with my general model was the finding that native Blacks at selective colleges are lighter than typical (1). This is what one would expect if schools discriminated for more intelligent individuals and if intelligence correlated with lightness in the applicant population, barring some type of counter discrimination aimed at reducing “adverse impact” resulting from cognitive discrimination. Again, this follows from the basic principle concerning selectivity and selectees discussed above.

Overall these results are consistent with my overall theoretical position and the results from NLSY ’97, Add Health ’94-’08, and GSS ’12.

Now I, a simple HBD scribber, take the more general lesson from this analysis on Jews and Gentiles and Color Groups to be that outcome difference simply can not and should not be taken at face value as evidence of bias or discrimination. But I have come to believe that that when it comes these topics, nothing is learnable. Especially by the intellectual class.

Excel file here.

(1)I discussed this elsewhere. I noted:

I compared The NLSF (native) Black sample and the ADDHealth Black national sample in terms of scores and two indices of admixture. To save myself some effort, I used Massey et al. (2007) as a reference for the NLSF data.

1. Nationally, Blacks (born of native parents) score about 850 on V+M SATs (SD= about 200). In the NLSF study, they scored, on average, 1193 circa 1998. So they were, in this sample, maybe 1.75 SD above the population mean. Being 1.75 SD above the national mean, we would expect the NLSF cohort to be at least 1.75 SD x 0.15 above the color mean if the IQ color correlation is around 0.15.

In the ADD health data, the mean color score was 2.34 (SD = 1.06) on a 1-5 scale running from black to white. In the NLSF, the mean score was 4.79 on a 0-10 scale running from white to black (In a figure, Massey et al. describes the scale as 1-10, but the “NATIONAL LONGITUDINAL SURVEY OF FRESHMEN PUBLIC RELEASE CODING MANUAL” indicates that it was a 0-10 scale.) Using the metrics of the Add Health data, Blacks in the NLSF have an equivalent color score of 2.85 or are 0.45 SD more light colored, which coheres with our expectation:

a. Convert the score from the 11 point scale to a score on a 10 point scale going from white to black ( 4.79 x (10/11) = 4.35)
b. Reverse scale to a black to white scale (10-=4.35 = 5.65) and reduce by ½ to a 5 point scale (5.65/2=2.825)
c. Convert to STDV (2.825-2.34)/1.06 =.45 SD)
d. Compare with expectation

3. Likewise with color, we would expect the NLSF cohort to be somewhat more admixed. Being 1.75 SD above the national mean, we would expect the NLSF cohort to be at least 1.75 SD x (some predicted IQ-ancestry correlation — I’ve estimated this to be 0.25) above the national admixture mean, if the IQ white ancestry correlation was (some predicted IQ-ancestry correlation).

In the NLSF study, going by the data in Massey et alia, 16% of the native black group reported being mixed race (i.e. having one black and typically one white parent). In the ADD health data, according to Rowe (2002), out of a Black sample of 4271:

“127 adolescents were self-identified as inter-racial children because they had selected both the White and Black self-descriptors. Of these individuals, 102 were classified as Black by the interviewer. Parental reports were also used to identify possible inter-racial children. The head of household (usually the mother) reported her own race and that of her current spouse or partner. When one parent was reported as Black and the other as White and both lived in the household, the child was classified as interracial. Of 442 interracial children, 56 were classified by the interviewer as Black.”

This gives us a mixed race percent ranging from 3-10 percent. Using the midpoint as our estimate, the ratio of mixed to not is 0.07; and the ratio in the NLSF is .18. Which means that the NLSF cohort is .55 SD more admixed, which coheres with our expectation. (The NLSF cohort was born around 1981 and the inter-racial marriage rate was about 5% then, so this would likely be an underestimation of the NLSF mixed race overrepresentation – if that makes sense).

1. What did Cosma Shalizi claim about the positive manifold?

I wrote that according to Shalizi, the positive manifold is an artifact of test construction and that full scale scores from different IQ batteries correlate only because they are designed to do that. This has been criticized as misrepresenting Shalizi’s argument. I based my interpretation of his position on the following passages, also quoted in my original post:

The correlations among the components in an intelligence test, and between tests themselves, are all positive, because that’s how we design tests. […] So making up tests so that they’re positively correlated and discovering they have a dominant factor is just like putting together a list of big square numbers and discovering that none of them is prime — it’s necessary side-effect of the construction, nothing more.

[…]

What psychologists sometimes call the “positive manifold” condition is enough, in and of itself, to guarantee that there will appear to be a general factor. Since intelligence tests are made to correlate with each other, it follows trivially that there must appear to be a general factor of intelligence. This is true whether or not there really is a single variable which explains test scores or not.

[…]

By this point, I’d guess it’s impossible for something to become accepted as an “intelligence test” if it doesn’t correlate well with the Weschler [sic] and its kin, no matter how much intelligence, in the ordinary sense, it requires, but, as we saw with the first simulated factor analysis example, that makes it inevitable that the leading factor fits well.

It is true that Shalizi does not explicitly claim that it would be possible to construct intelligence tests that do not show the usual pattern of positive correlations. However, he does assert, repeatedly, that the reason that the correlations are positive is because that’s the way intelligence tests are designed. I don’t think it’s an uncharitable interpretation to infer that Shalizi thinks that a different approach towards designing intelligence tests would produce tests that are not always positively correlated. Why else would he compare test construction to “putting together a list of big square numbers and discovering that none of them is prime”?

Another issue is that it can never be inductively proven that all cognitive tests are correlated. However, intelligence testing has been around for more than 100 years, and if there were tests of important cognitive abilities that are independent of others, they would surely have been discovered by now. Correlations with Wechsler’s tests or the like is not how test makers decide which tests reflect intelligence. There’s a long history of attempts to go beyond the general intelligence paradigm.

2. Can random numbers generate the appearance of g?

Steve Hsu noted that people who approvingly cite Shalizi’s article tend to not actually understand it. A big source of confusion is Shalizi’s simulation experiment where he shows that if hypothetical tests draw, in a particular manner, on abilities that are based on randomly generated numbers, the tests will be positively correlated. This has led some to think that factor analysis, the method used by intelligence researchers, will generate the appearance of a general factor from any random data. This is not the case, and Shalizi makes no such claim. The correlations in his simulation result from the fact that different tests tap into some of the same abilities, thus sharing sources of variance. If the randomly generated abilities were not shared between tests, there’d be no positive manifold.

3. What I mean by “sampling”

Several commenters have thought that when I wrote about the sampling model, I was referring specifically to Thomson’s original model which is the basis for Shalizi’s simulation experiment. This is not what I meant. It’s clear that Thomson’s model as such is not a plausible description of how intelligence works, and Shalizi does not present it as one. I should have been more explicit that I regard sampling as a broad class of different models that are similar only in positing that many different, possibly uncorrelated neural elements acting together can cause tests to be correlated. Shalizi argues that evolutionary considerations and neuroscience findings favor sampling as an explanation of g. My argument is that none of this falsifies general intelligence as a trait.

4. Race and g

Previously, I did not discuss racial differences in g, because that issue is largely orthogonal to the question of whether g is a coherent trait. Arthur Jensen argued that the black-white test score gap in America is due to g differences, but the existence of the gap is not contingent on what causes it. James Flynn pointed this out when criticizing Stephen Jay Gould’s book The Mismeasure of Man:

Gould’s book evades all of Jensen’s best arguments for a genetic component in the black-white IQ gap, by positing that they are dependent on the concept of g as a general intelligence factor. Therefore, Gould believes that if he can discredit g, no more need be said. This is manifestly false. Jensen’s arguments would bite no matter whether blacks suffered from a score deficit on one or 10 or 100 factors.

Regarding whether group differences in IQ reflect real ability differences, Shalizi has the following to say:

The question is whether the index measures the trait the same way in the two groups. What people have gone to great lengths to establish is that IQ predicts other variables the same way for the two groups, i.e., that when you plug it into regressions you get the same coefficients. This is not the same thing, but it does have a bearing on the question of measurement bias: it provides strong reason to think it exists. As Roger Millsap and co-authors have shown in a series of papers going back to the early 1990s […] if there really is a difference on the unobserved trait between groups, and the test has no measurement bias, then the predictive regression coefficients should, generally, be different. [15] Despite the argument being demonstrably wrong, however, people keep pointing to the lack of predictive bias as a sign that the tests have no measurement bias. (This is just one of the demonstrable errors in the 1996 APA report on intelligence occasioned by The Bell Curve.)

Firstly, the APA report does not claim that a lack of predictive bias suggests that there’s no measurement bias. The report simply states that as predictors of performance, IQ tests are not biased, at least not against underrepresented minorities. This is important because a primary purpose of standardized tests is to predict performance.

Secondly, research does actually show that the performance of lower-IQ groups is often overpredicted by IQ tests and other g-loaded tests, something which is alluded to in the APA report as well. This means that the best-fitting prediction equation is not the same for all groups. For example, the following chart (from this paper) shows how SAT scores and high school GPA over- or underpredict first-year college GPA for different groups:

There’s consistent overprediction for blacks, Hispanics, and native Americans compared to whites and Asians. Female performance is underpredicted compared to males, which I’d suggest is largely due to sex differences in personality traits.

As another example, here are some results from a new study that investigated predictive bias in the Medical College Admission Test (MCAT):

Again, the performance of blacks and Hispanics is systematically overpredicted by the MCAT. Blacks and Hispanics are less likely to graduate in time and to pass a medical licensure exam than whites with similar MCAT scores.

But as noted by Shalizi, the question of predictive bias is separate from the question of whether a test measures the same thing across groups. These days, psychometricians maintain that to establish that the same traits are being measured in different groups there must be an analysis of what is called measurement invariance. Several studies have investigated this question with respect to the black-white IQ gap, and they affirm that the gap can generally be regarded as reflecting genuine differences in the latent traits measured (Dolan 2000; Dolan & Hamaker 2001; Lubke et al. 2003; Edwards & Oakland 2006).

In contrast, analyses of test score gaps between generations (or the Flynn effect) indicate that score gains by younger cohorts cannot be used to support the view that intelligence is genuinely increasing (Wicherts et al. 2004; Must et al. 2009; Wai & Putallaz 2011). Measurement invariance generally holds for black-white differences but not for cohort differences. Wicherts et al. 2004 put it this way:

It appears therefore that the nature of the Flynn effect is qualitatively different from the nature of B–W [black-white] differences in the United States. Each comparison of groups should be investigated separately. IQ gaps between cohorts do not teach us anything about IQ gaps between contemporary groups, except that each IQ gap should not be confused with real (i.e., latent) differences in intelligence. Only after a proper analysis of measurement invariance of these IQ gaps is conducted can anything be concluded concerning true differences between groups.

The Dominican Republic shares the island of Hispaniola with Haiti, but has a much higher standard of living. Jared Diamond offered some characteristically plausible-sounding reasons for this disparity in his 2005 book Collapse, and these ideas received a fair bit of media coverage following the Haiti earthquake in 2010. While race and human capital both played a part in those explanations, Diamond did not mention intelligence differences (having already rejected this line of thinking as “loathsome” in Guns, Germs, and Steel (1997)). However, the theoretical relevance of this variable is obvious: intelligence and achievement tests are a more direct measure of individual human capital than input variables like education. Jones and Schneider (2006) found IQ to be “the most robust human capital measure” in an expansive dataset of international comparison measures—a better predictor of economic development than variables like educational spending and enrollment.

IQ and the Wealth of Nations (2002) did not include data for either Haiti or the Dominican Republic, but Lynn’s dataset has included one study for the Dominican Republic since the publication of IQ and Global Inequality (2006).

Here I scrutinize Lynn’s use of this reference and introduce a few more small studies. The data available for the Dominican Republic is quite meager.

As I walk through the IQ data used by Richard Lynn, I am increasingly upset by the number of errors (and I haven’t even gone through very many nations yet). IQ and Global Inequality (2006) offered a major new source of data for Latin America:

UNESCO (1998) gives data for approximately 4,000 10-year olds in each of 11 Latin American countries (Argentina, Bolivia, Brazil, Chile, Columbia, the Dominican Republic, Honduras, Mexico, Paraguay, Peru, and Venezuela) given in the table. The tests were verbal and mathematical abilities and are averaged to give IQs calibrated against an IQ of 88 for Mexico. (p 313)

Six of these eleven nations, including the Dominican Republic, were new to Lynn’s dataset. The reference was listed as “Unesco. (1998). Statistical Yearbook 1998. Paris: Unesco Publishing & Bernan Press.” No US libraries carried this dense reference book, so I was forced to buy it used from Amazon for $30. I was therefore displeased when I leafed through it twice and discovered it contained no such data. Another error.

I reasoned that Lynn was probably describing the data from the First International Comparative Study (a regional study of academic skills in Latin America, which I discussed in the Cuba post), but this explanation didn’t entirely add up. Lynn listed data for Peru, which was not included in the First Comparative Study reports, and he did not include data for Cuba, which not only participated in the study, but also became something of its focal point after scoring some 1-2 standard deviations higher than all the other participating nations. Further, the inclusion of this study would be inconsistent with the way that Lynn has classified data from all the other international achievement tests. For example, Lynn did not report data from PISA and TIMSS as IQ measurements, even though including them as such would have expanded his dataset much more than the Latin American study.

The newest book (Lynn & Vanhanen, 2012) does confirm that this is the data Lynn was describing. The faulty statistical yearbook reference has been corrected to “UNESCO. (1998). Primero estudio internacional comparativo. Santiago, Chile: UNESCO”. This reference reaffirms the problems I just noted: it explicitly states that data is not included for Peru (p. 12), so it’s not obvious how Lynn created the IQ score from this reference, outside of mistakenly using the data from the sample size tables as math and reading scores (this would at least explain why he reports “4000” as the sample size for every country instead of the actual sample sizes given in the reference, which range from 2,864 to 5,053 (p. 19). And it’s difficult to avoid the idea that Lynn simply omitted the achievement data for Cuba, without comment, because it would have given him an IQ score close to 115 and injured the predictive power of his dataset.

In addition to fixing these errors, Lynn should either stop using the achievement data from this reference as IQ scores, or start using data from all the other international achievement tests as IQ scores. Neither decision is unjustifiable, but the dataset should have more consistent inclusion/exclusion criteria.

I will report the IQ score equivalents from international achievement tests, but when I eventually upload the tabulated data files I will also leave a distinction so that the two kinds of test data can be analyzed jointly or separately. I’ve discovered that many standardized tests of math and reading skills, such as the Wide Range Achievement Test, the Stanford Achievement Test, and the Wechsler Individual Achievement Test, are also used across many cultures, and can also be incorporated into the achievement test dataset.

Achievement Test Data for the Dominican Republic

The First International Comparative Study is also called the LLECE (Laboratorio Latinoamericano de Evaluación de la Calidad de la Educación, or in English, “the Latin American Laboratory for Assessment of the Quality of Education”).

Lynn calculates IQ scores from the LLECE by normalizing the scores against his average IQ for Mexico (88). So, for example, if a nation scored 1 SD higher than Mexico in math and reading scores, its IQ would be 103. This method gives him an IQ of 82 for the Dominican Republic.

One problem with this method is that Latin American scores on international achievement tests are generally worse than Latin American scores on IQ tests. We should compare like with like. Four of the nations that participated in the LLECE assessments in 1997 also participated in the PISA assessments in 2000: Argentina, Brazil, Chile, and Mexico. Compared with the United Kingdom (which serves as our “Greenwich IQ” for international comparisons), Argentina had a PISA “Achievement Quotient” of 81, Brazil 76, Chile 81.3, and Mexico 75.5. So the average PISA AQ of these four nations was 78.5 in comparison with the UK. The average math+reading scores of these four nations was 263 in the LLECE, with a set standard deviation of 50. The Dominican Republic scored about three-fifths of a standard deviation below this average (lower than any other participating nation), giving us an AQ of 69.8 (Casassus et al, 2000).

The LLECE was followed by the Second Regional Comparative and Explanatory Study (SERCE) in 2006. Five of the participating Latin American nations were also included in the 2006 PISA assessments. Once again, using the scores of these nations as our bridge, the AQ of the Dominican Republic was 66.3. The Dominican Republic was also the lowest scoring nation in the 2006 assessment. In fact, the next lowest scoring nation—Guatemala—scored almost one half of a standard deviation higher (Valdes et al., 2008).

The average of the two tests gives us an AQ of 68 for the Dominican Republic (Table I). For comparison, Altinok & Murseli (2007) also put the data from LLECE, PISA, and other international assessments on a common scale, using their own methods. Their results give the Dominican Republic an AQ of 74.7 in comparison with the UK.

Table I: Achievement test scores in the Dominican Republic

Intelligence Test Data for the Dominican Republic

I’ve located two small studies with intelligence test data for the Dominican Republic. The first study (Castillo Ariza et al, 1988 ) compares the test scores of 7-9 year old children who were hospitalized for malnutrition in their first two years of life, with their 6-13 year old siblings who were never hospitalized for malnutrition. These two groups were tested with the Spanish version of the Wechsler Intelligence Scale for Children. Presumably the study authors are using the version normed on Puerto Rican children somewhere around 1955 (Roca, 1955). The IQ scores are reported as 68.2 for the malnourished children and 71.3 for their siblings, but these low scores actually become much lower after we account for the Puerto Rican norms and the three decades of Flynn inflation: these adjustments give us an IQ of 46.3 for the malnourished group and 49.4 for the sibling group. I’m rating the normalcy of the samples the same way I did for Jamaica: children that were hospitalized for malnutrition are a Mostly Disadvantaged subset of Dominicanos, while their non-hospitalized siblings must be, at least, a Slightly Disadvantaged subset.

The second small study looks at the IQ scores of Dominicanos with complete androgen insensitivity syndrome in comparison with their healthy relatives (Imperato-McGinley et al, 1991 ). These two groups were tested with the Spanish version of the Wechsler Adult Intelligence Scale, which was normed in Puerto Rico in 1965 (Green et al., 1967). There aren’t strong a priori reasons to suspect that androgen insensitive males should have lower IQs, but it seems prudent to classify them as Slightly Disadvantaged. The Flynn and norm adjusted IQ of the 13 androgen insensitive males was 83.4, while the IQ of the 34 healthy controls was 91.7.

The four small samples from the two studies are listed in Table II. Only one of the groups consists of normal, healthy Dominicanos. This sample gives us an IQ of 92 for the Dominican Republic. I find it probable that this number is too high. The IQ scores of the disadvantaged samples in Jamaica suggest a deficit not larger than 1 standard deviation. So it is implausible that the control siblings in Castillo Ariza et al (1988) are straying that much farther from the population norm. And certainly the achievement data suggest a much lower IQ.

Lynn’s number (82) certainly feels more correct, but it is not well grounded in actual measurements. 92 is a more cautious placeholder until we have better data for the Dominican Republic. This IQ is more than 1 and a half standard deviations higher than 68, which is my current value for Haiti.

Table II: IQ test scores in the Dominican Republic

REFERENCES

Nearly 100 years ago George Ferguson tested the racial genetic hypothesis of IQ differences and found the following remarkable results, as reported by Baker (1974):

Just a couple of days ago, the awesome Audacious Epigone pointed out that the GSS (2012) contains a color ratings scale. GSS (2012) gives us the following results:

Color-Wordsum, African Americans (inclusively defined: IDs as Native Non-Hispanic Black)

Color-Wordsum, African Americans (self identified mixed race individuals excluded: IDs as Native non-Hispanic Black and no other race)

Color-Education, African Americans (inclusively defined)

Color-Education, controlling for Wordsum, African Americans (inclusively defined)

Color-Income, African American (inclusively defined)

Color-Income controlling for Wordsum, African American (inclusively defined)

(To note: the color-income results are complex because there is a strong sex x color interaction. Darker colored Black women do better than lighter colored Black women after measures of Human capital are accounted for, but the reverse holds for darker colored Black men and lighter colored Black men. But as my colleague has noted: “If we accept the premise that color-based discrimination should affect all people of both sexes, at every level, colorism is not borne out….” “Colorism” can only be salvaged by transforming it into “income-color-sexism.” But of course, there is an HBD perspective on the “gendered-race” phenomena, too. More on that later.)

As for the Color-IQ association, such an association should not be surprising. The GSS shows that self-identified mixed race Black-White individuals have intermediate Wordsum scores:

“White”
RACECEN1(1); BORN(1) M=6.42, N=4700

“Black and White”
RACECEN1(2); RACECEN2(1); Born(1) M=5.86, N=27
RACECEN1(2); RACECEN3(1); BORN(1) M=5.32, N=6
RACECEN1(1); RACECEN2(2); BORN(1) M=6.02, N=22
RACECEN1(1); RACECEN3(2); BORN(1) M=5, N=2

“Black”
RACECEN1(1); RACECEN2(0); BORN(1) M=5.15, B=875

On the account of this “bi-racism“, which I have now documented in dozens of recent samples (e.g., NAEP and more NAEP, TIMSS, PIRLS, PISA, HSLS2009, NLSY97, etc.) using many different methods of identification (e.g., participant’s racial ID, parental ID of participant’s race, biological parents’ racial IDs, parents’/ individual’s reported national ancestry ID, etc.), there will inevitably be “colorism”. And the product of intermarriage, historic and recent, does in fact seem to be the major source of this when it comes to IQ. For summaries, readers are referred to Shuey’s review of mixed race IQ studies (1914-1964), my review of more recent studies (1961-2004), and my own investigations based on recent surveys (1994-2012) — 100 years of data points to one undeniable conclusion: The offspring of one Black and one White parent have IQ and color scores (in childhood, adolescence, and adulthood) that fall intermediate to those of the offspring, respectively, of two Black parents and of two White parents.

Complexities

Three decades ago, the late great Arthur Jensen (1980) noted:

The positive correlation between lightness of skin pigmentation and IQ in the American black population (studies reviewed by Jensen, 1973, pp. 222-224) may or may not be an intrinsic correlation; no one has yet determined the WF and BF correlations between IQ and skin color. If the WF correlation is zero, it would rule out the hypothesis which explains the observed correlation in the black population in terms of adverse effect on IQ of social prejudice against darker skin. (Jensen, 1980. Uses of Sibling Data in Educational and Psychological Research) [Emphasis added.].

In short, results from a Between/Within family study could rule out a discriminatory explanation of the IQ-Color correlation. More recently, he noted:

The pleiotropy hypothesis makes sense in terms of evolutionary genetics. But can we empirically reject this pleiotropy hypothesis? After all, the possibility of outright empirical rejection of a hypothesis is the Popperian criterion of scientific argumentation. I do think it is possible to meet this criterion. I propose that it can be done by determining whether the IQ skin color correlation is what I have elsewhere termed an intrinsic correlation, as contrasted with an extrinsic correlation (Jensen,1980;Jensen & Sinha,1993). The presence of an extrinsic correlation in the absence of an intrinsic correlation rules out pleiotropy. The methodology of making this distinction has been applied to the correlation of IQ with physical stature (extrinsic), of IQ with head size (intrinsic), and of IQ with myopia (intrinsic) (Jensen,1980; Jensen&Johnson,1994; Cohn,Cohn, & Jensen, 1988). An extrinsic correlation between variables X and Y is one in which the absolute value of r XY in the population and is not 0 within families (i.e., within full sibships). An intrinsic correlation is one for which the absolute value of r XY > 0 both in the population and within families. Although every pair of full siblings (including DZ twins) has exactly the same unique ancestral genealogy, the members of each pair differ in the particular selection of the parental genes they inherit at conception. An individual who inherits a pleiotropic gene manifests both of its phenotypic effects, such as lighter pigmentation and higher IQ, as would be hypothesized in the case of these two variables. All of the IQ skin color correlations reported in the literature are entirely population correlations, hence they are not informative regarding pleiotropy. But with a reasonably large sample of full sibling pairs it would be possible to rule out pleiotropy. It would be ruled out if no statistically significant with- in-families correlation were found between siblings’ IQs and the siblings’ values on a linear index of skin pigmentation as objectively measured by one of the standard procedures used in physical anthropology. Pleiotropy implies that within each sibling pair the individual having the higher IQ would also more frequently have the lighter skin color. If this is not found to be the case, the pleiotropic hypothesis would have to be rejected. But if, on the other hand, the IQ skin color correlation turns out to be pleiotropic, and if this result can be adequately replicated, it would constitute a key item of evidence for the co-evolution of IQ (or more specifically g) and skin color. Unless geneticists can find sufficient fault with this line of reasoning as to render the proposed study scientifically worthless or technically unfeasible, I would hope that such a study will soon be forthcoming. (Jensen, 2006. Comments on correlations of IQ with skin color and geographic–demographic variables). [Emphasis added].

In short, results from a Between/Within family study could also rule out a pleiotropic explanation of the IQ-Color correlation.

We decided to follow Jensen’s call and to decompose the IQ-color correlation with and between families. Originally, we had designed this analysis such to disentangle the effects of additive genetics, discrimination, shared environment, and pleiotropy on IQ. Discrimination hypotheses typically propose that color associated IQ differences are consequent to color associated outcome differences which themselves are consequent to color associated discrimination. We have shown that the discriminatory hypothesis is untenable for a number of reasons, the most basic being that the differences in adulthood can be traced back to adolescence. The most plausible explanations for the IQ-color correlations are: shared environment (a between family effect, which should be unrelated to sibship), pleiotropy (a within family effect, which should show up between full sibs), and additive genetics. With regards to additive genetics, Jason Malloy recently articulated our framework:

This post discusses the expected differences in IQ between differently colored black siblings in an additive genetic model of race differences, while the colorism posts are predicated on an expected lack of IQ differences between differently colored black siblings in an additive genetic model of race differences. Contradiction?

In an important post, Dalliard explained why a lack of correlation is expected under hereditarian theory:

The significance of this family study design is that hereditarian theory predicts that skin color will be substantially associated with IQ between families, but not within families. That is, if we have two African American siblings the darker one should be approximately as likely as the lighter one to be the smarter of the two. This is because skin color is controlled by a handful of genes, scattered across different chromosomes, and each (full biological) sibling is equally likely to inherit any variant. Skin color cannot be used as a proxy for ancestry when comparing siblings. (Malloy, 2013. Cryptic Admixture, Mixed-Race Siblings, & Social Outcomes.)

We took additive genetics to be a between family only effect between full siblings, and a between and within family effect between less genetically related siblings. The crucial assumption was that color differences were under the control of a few genes of large effect. This assumption has been recently challenged, as explained by genetics researcher and pundit, Razib Khan:

Overall the biggest result out of this paper is found in the abstract: “We identify four major loci…for skin color that together account for 35% of the total variance, but the genetic component with the largest effect (~44%).” The implication, which they lay out, is that in this admixed population the genetic architecture is such as that within that 44% there may be smaller effect genes which diffused through the genome, and strongly correlated with differential ancestry (i.e., European ancestral segments have more “light” alleles, African segments the “dark” ones). This is not entirely unreasonable. If pigmentation loci are targets of selection (their results suggest that this is so) then one might see change on large effect loci first, and then graduate convergence to the adaptive peak via small effect loci. But, I also believe that the fact that the European source population is on the darker side also is having an effect. The allele frequency differences between Swedes and Yoruba, would be larger than Portuguese and Yoruba (though to be sure the Portuguese and Swedes would still be far closer). (Khan, 2013. Pigmentation: the simplest of complex traits not so simple?)

The implication of these new findings is that skin color can be used as a proxy for ancestry when comparing full siblings. Nonetheless, since mixed race siblings differ little in racial ancestry, the possible effect of ancestry differences between full siblings on outcome differences would have to be quite small even were there large ancestral differences between populations in the trait in question. (I have estimated that on the account of being Whiter, lighter Black sibs could at most be 0.05 SD phenotypically smarter. My reasoning: The correlation between ancestry and color between full siblings should not be greater than it is between random individuals; given the IQ-ancestry correlation of rho = 0.4 in the African American population, the mean difference in White ancestry between lighter versus darker full siblings would be 0.4 times the mean difference in color in standardized units; in the NLSY97, the latter value between sibs who differed in color is 1.7 standard deviations (from section F.7, one sample t-statistic descriptives); assuming that this measure of color is reasonably reliable, lighter sibs would be about 0.7 SD more White than darker sibs (1.7 x 0.4); the standard deviation of White admixture in the Black population, based on other studies, is about 10-15%, so lighter sibs would be about 9% more White at most (this seems to be too high to me); if the mean geneotypic g difference between African Americans who are ~20% White and Whites who are ~95% White is 1 — which is what Hereditarians typically argue — then a 9% increase in ancestry would be equal to at most an 0.12 SD increase in geneotypic g. The correlation between geneotypic g and phenotypic g as measured by AFQT is maybe 0.8 (i.e., heritability = 0.65). So the phenotypic differences would be at most 0.1 SD. But color as indexed by color charts probably are not particularly reliable indexes of ancestry. So we have to correct down the figure, maybe to 0.05 SD or so.)

But there are more problems….if the genetics of color is more complex than hitherto thought, then it’s not just genetic ancestry that can condition a within family, between full sibling, genetic correlation. This point was made in a discussion at the 2001 Novartis Foundation symposium: The nature of intelligence [Emphases added]:

Houle: I’m interested in the point you’ve made about within- versus between- family correlations because it seems to me that you are drawing an incorrect conclusion. Assortative mating involving pairs of traits, such as height or brain size, for example, even if they are not causally related to each other at all, will cause genetic associations between these traits through linkage disequilibrium. This effect will be stronger for loci that are closely linked to each other. This will cause within-family correlation. The conclusion I would draw when you have assortative mating and and a lack of within-family correlation, is that the assortative mating is actually not on the genetic component of the traits being considered, but on the environmental deviations from the breeding value.

Jensen: That’s possible, but I have been told by geneticists that the linkage disequilibrium would not account for within-family correlations beyond the first generation. This is something that washes out very quickly. In the general population, if you have a large sample and look for these correlations, very little of it would be caused by linkage. It would be more pleiotropic, meaning that one gene has two or more apparently unrelated effects.

Houle: It depends on the assumptions you make. If you assume very simple genetics
for example, one gene in influencing each trait
they are very unlikely to be closely linked. This would, to a large extent, get rid of this effect, but not entirely. Since traits such as brain function and height are the product of many genes some loci are bound to be closely linked, so any association would decay slowly for these loci; it’s very unlikely that you would be able to wash that out completely. The thing about assortative mating is that it occurs every generation so those correlations are constantly being reinforced: they won’t be large, perhaps, but they won’t be zero either. So if you can confidently say there’s no within-family correlation, you’re actually making a strong statement about the genetic relationship of genes to those traits.

Jensen: That’s a good point.

In short, in presence of cross assortative mating for color and IQ — or assortative exogamy on IQ between populations of different colors — you will get a genetic association between color and IQ between full siblings in proportion to the genetic complexity of color. That said, in absence of pleiotropy, I would still predict a practically significantly lower color-IQ association between full siblings within families versus between families. The genetics of color is still relatively simple.

Now about our method: We have been employing a within, between family design. The basic set up is commonly utilized in behavioral genetics. For the within family component of the analysis, we are examining the correlations between the signed sibling differences in traits. For the between family component, we are examining the correlations between sibling averages in the trait. These two sets of correlations can be compared after they are corrected for reliability. For these analyses it is standard to use absolute difference scores and the absolute average scores.. The results based on absolute values are given by Pearson’s r. As a robustness check I have included ranked difference scores and ranked average scores. These results are given by Spearman’s rho.

An incomplete project

I will note from the start that this is an incomplete project. I was unable to resolve the following issues:

Weights: Two well published statisticians gave Meng Hu and I conflicting advice on whether or not to use weighted values. I have decided to included weighted and unweighted values in most instances. Parametric Assumptions: The results based on parametric and non-parametric analyses are importantly different. As such both were included. It’s not clear to me, though, which is a more accurate description of the “true” relationship. Correction for unreliability of measures. The (linear) associations were not corrected for unreliability because the reliability of the skin color index was not known. Because the results are not-corrected readers are advised to not fixate on p-values. Corrections will tend to increase the within family correlations more than the between family correlations — but such corrections only make sense in context to linear relations (i.e., r) and yet virtually no such relation exists within families. The basic formula is:

Between family
reliability (sib means) = (AFQT (reliability) + (color-IQ correlation, between))/(l + (color-IQ correlation, between))

Within Family
reliability (sib differences) = (AFQT (reliability) – (color-IQ correlation, within)/(l – color-IQ correlation, within)

Where (sib means) is the reliability of the sib average correlation and r(sib differences) is the reliability of the sibling difference correlation. And the corrected correlations are then:

corrected IQ-color, between = (color-IQ correlation, between)/ r(sib means)
and
corrected IQ-color, within = (color-IQ correlation, within)/ r(sib differences)

Take the following example. The reliability of AFQT is about 0.95, the uncorrected color-AFQT BF is 0.15, the uncorrected color WF is 0.05. The corrections then would be:

Between family
reliability(sib means) = (0.95 + 0.15)/(l + 0.15)
= 0.96

Within Family
reliability (sib differences) = (0.95 – 0.05)/(l – 0.05)
= 0.95

corrected IQ-color, between = 0.15/0.96 = 0.157
and
corrected IQ-color, within = 0.15/0.95 = 0.052

The reliability of the color index

It was noted above that the true reliability of the color index is not known. Nonetheless, one can get a sense of the reliability by examining the MZ twin correspondence, since the heritability of true skin color should be close to 1. Comparing identical twin 1 to identical twin 2 at time 3, for a trait with a heritability approaching 1, is similar to comparing individual 1 at time 1 to individual 1 at time 2. In general, the twin correspondence was not particularly high. I was able to locate 20 identical twin pairs with color scores. Of these, 10 pairs had corresponding color scores. (Note: the AFQT scores are percentiles; if readers wish to compare the MZ twin AFQT correspondence to the MZ twin color correspondence using the same scales they can do so simply by dividing the AFQT scores by 10000 and then round up; this will give one AFQT and Color scores on a 10 point scale. The results are below:

Excel here.

Results

Section A. The “raw” correlations between color and outcomes for African Americans:
A.A, Color-PIAT correlations; A.B, Color-PIAT correlations if AFQT scores are missing; A.C, Color-AFQT correlations; A.D, Color-g correlation; A.E, Color-t correlations; A.G, Color-HGE correlations; A.H, n-weighted average AFQT correlations and PIAT correlations, when AFQT is missing; A.I, n-weighted average PIAT correlations and AFQT correlations, when PIAT is missing.

Section B. Color-AFQT and Color-HGE when partailing out the effect of age and sex.

The color-AFQT and color-HGE correlations are presented with age and sex difference/averages partailed out. Age and sex had little effect on AFQT but these variables had some effect on HGE. The directions of the correlations remained the same. The raw correlations are presented below. To increase sample size, I averaged the n-weighted color-PIAT difference/average and the n-weighted color-AFQT difference/average correlations when one or the other value was missing. I placed my preferred (weighted) (linear) associations in boxes.

Section C. Scatter plots between color and AFQT.

Scatter and best fitting plots are shown for the color-AFQT relation.

Section D. Cubic versus Linear fit for rank differences within families.

This was a demonstration that a non-linear model was a better fit for the differences within families based on rank values. The relevance of this is that Spearman’s rho assumes monotonicity, which seems semi questionable.

Section E. Correlations between ranked and unranked color and AFQT within families.

I tried the identify which variable was driving the parametric/non-parametric difference in correlations within families. (For this analysis I used all possible Black sibling pairs.) I correlated: AFQT differences, ranked AFQT differences, color differences, ranked color difference. Both variables contributed to the difference. r, AFQT, rank-color = 0.03; r, rank-AFQT, color = 0.06; r, rank-AFQT, rank-color = 0.09.

Section F. 1. Descriptive statistics for AFQT, Color, and HGE showing the variance within families and between families.

Here, I further explored the associations and possible explanations for the with/between family difference and the parametric/non-parametric difference. In 1, I compared the variance within and between families in the traits in question. The variance was greater between full siblings within families (e.g., color: SD = 1.84, mean absolute difference = 1.35) than between families (e.g., color: SD= 1.62, mean absolute difference = 1.29), so restriction of range within families is not a plausible explanation for the lowered within family association.

2. More model fit exploration, AFQT-color.

I look at more models within and between families for AFQT and color. Generally, I was unable to identify a noticeably better fitting model for the within family association. A linear non-association seems to be a fair description of the within family color-AFQT relation.

3. AFQT-color correlations based on different sampling approaches: First minus second full sib; including all full sib pairs when there were multiple pairs within families; averaging full sib pairs when there were multiple pairs within families.

In 26 Black families there were multiple pairs of full siblings. In all of the previous analyses I had selected the first pair. To investigate further, I ran the correlations after including all possible full sibling pairs (so some families had multiple scores). I then averaged the multiple sibling pair differences and averages to create average family difference and average values and I then ran the correlations again. The correlations derived from these different methods are reported below. I did not apply weights here. Compare with the correlations above in section A.

4. Robust General Linear Regression.

I ran robust regression for AFQT and color using the different values discussed in (3). The program used can be located at: http://www.stat.wmich.edu/slab/RGLM/ A concise discussion of the method can be found in Erceg-Hurn and Mirosevich (2008).

The results are shown below. Assumption violations with respect to the dependent variable (AFQT) are not causing the non association within families.

5. AFQT-Color and HGE-Color controlling for sex and age results.

These results were reported above.

6. Bootstrapping correlation results.

I looked at the confidence intervals of the correlations.

7. Alternative Analyses with Dichotomous color coding.

The method here was discussed previously. Quote:

Returning to the question of whether color is association with cognitive ability within families, we conducted a number of analyses based on dichotomously coded color. The concern was that the color scale was only a semi-interval scale. It’s possible that the treatment of color differences as interval scaled differences masks a “true” color-ability association.
Within populations: We looked at lighter siblings versus darker siblings. If the first sibling was lighter we coded them as being so (first, lighter sib =1, all else =0). If the first sibling was darker we coded them as being so (first darker sib, all else =0). We then entered these two dummy variables into linear regressions. Next we created a dichotomous variable (first = darker sib =1, first = lighter sib =0) and then computed the point-biserial correlation, r(pb). The purpose here was to remove the attenuating effect of sibling pairs for which there were no color differences. Finally, we added the scores of the first siblings = lighter to those of the first siblings = darker multiplied by (-1) and conducted a simple t-test. The logic here is that if there is no significant association between color and cognitive ability then the mean AFQT difference scores, which were computed by subtracting the scores of sib1 from those of sib2, should not be significantly different from zero when dealing separately with first sibs who were lighter or first sibs who were darker, or since we are working with a dichotomous pair, the first sibs who were lighter + first sibs who were darker*-1. The results of this t-test, of course, are the same as those of the point biserial correlation since the statistic is the same. This is just another way of presenting the results. This way, the mean score differences can be seen. Between populations: We repeated the above analyses comparing the average scores of the lightest half of the sib pairs to the average scores of the darkest half of the sib pairs. To split the population we used median color scores (since the mean color scores were skewed.

Generally, the association within families was weaker than that between families. None of the within family associations were significant at traditional levels of significance. In practical terms, within families lighter full siblings were, on average, 0.1 SD more intelligent than their darker bothers and sisters. Between families, lighter pairs of full siblings were, on average, 0.3 SD more intelligent than darker pairs.

8. Test for interval scaling for color by correlating the sibling difference scores with the sibling average scores.

I conducted a within/between family test for interval scaling for color using the method discussed by Jensen (1980). The results are consistent with the claim that the color scale is an interval scale.

Discussion

The results for African Americans are very similar to those I reported for the full sample. I noted:

1. Simple binomial association (lighter sib — dichotomously coded — is smarter —- dichotomously coded). Difference: 55% to 45%. Significant. 2. Point biserial correlation (lighter sib — – dichotomously coded — is smarter). Difference: r(pb) = 0.07. Non-significant, but trending. 3. Spearman’s correlation (rank lightness associated with rank smartness). Difference: rho(unweighted) = 0.05. Not-significant, but close. 4. Pearson’s correlation (lightness — interval scale — associated with smartness — interval scale). Difference: r(unweighted) = 0.02. Not-significant, not even close.

One would have to change the numbers around a little, but the main effect is the same. No detectable association is found when parametric analyses are conducted. If however, you strip down the analysis as simple as possible and simply look at the frequency at which the lighter full sibling is the smarter full sibling you see a statistically significant effect. Intermediate methods e.g., rank correlations, t-tests using dichotomously coded Darker/Lighter show intermediate and typically non-significant effects.

Previously, I continued:

This effect could be because the underlying statistical assumptions were violated and therefore more info equals more bias; alternatively. it could be that the “true” association within families between FS is almost undetectable

I no longer think the former. The absolute association between color and IQ between full siblings is virtually undetectable. But yet there is nonetheless some association — and this can be seen when one strips the analysis down to the most basic form. Both of these conclusions are robust. As Jensen noted: “Pleiotropy implies that within each sibling pair the individual having the higher IQ would also more frequently have the lighter skin color.” This is true. But it’s also true that r Color-AFQT is not even close to being significantly different from zero within families.

I continued:

Whatever the case, since the cognitive ability scores which we are looking at, measured in adolescence as they were, are antecedent to adult outcomes, an association within families, if substantiated, would not support “colorism”, which holds that cognitive ability difference are consequent to outcome difference, themselves, which are consequent to labor market discrimination. But then what could be the cause of such differences?…. Before indulging in more speculations, though, we had better first look at “colorism” within socially defined races (e.g., Blacks).

And here we are…left with some puzzles…

Excel File here.

References:

Baker, J. R. (1974). Race. New York: Oxford Univ. Press.

Bock, Gregory; Goode, Jamie; Webb, Kate, eds. (2000). The Nature of Intelligence. Novartis Foundation Symposium 233. Chichester: Wiley. Pages 49-51.

Erceg-Hurn, D. M., & Mirosevich, V. M. (2008). Modern robust statistical methods: an easy way to maximize the accuracy and power of your research. American Psychologist, 63(7), 591.

Jensen, A. R. (2006). Comments on correlations of IQ with skin color and geographic–demographic variables. Intelligence, 34(2), 128-131.

Jensen, A. R. (1980). Uses of sibling data in educational and psychological research. American Educational Research Journal, 17(2), 153-170.

Malloy, J. (2013, March 29). Cryptic Admixture, Mixed-Race Siblings, & Social Outcomes. Retrieved from: http://humanvarieties.org/2013/03/29/cryptic-admixture-mixed-race-siblings-social-outcomes/

Razib, K. (2013, March 24). Pigmentation: the simplest of complex traits not so simple? Retrieved from: http://blogs.discovermagazine.com/gnxp/2013/03/pigmentation-the-simplest-of-complex-traits-not-so-simple/#.UWIQTFdBgdU

Shuey, A. M. (1966). The testing of Negro intelligence. New York: Social Science Press.