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The many causes hypothesis

Given the absence of X-factors, the high within group heritability of intelligence poses a problem for environmentalists. Briefly, the variance between two groups can either result from factors which only act between but not within groups (X-factors) or it can result from factors which also cause variance within both groups (variable factors). Since X-factors have been empirically ruled out (1) in the said case, the difference between the groups must be due to variable factors. High heritability, though, constrains the possible influence of individual variable factors.

Given this situation, environmentalists must either maintain that gene-environment interactions confound heritability estimates (let’s call this the gene-environment hypothesis) or argue that numerous variable factors, in aggregate, cause the gap (let’s call this the many causes hypothesis). I will address the many causes hypothesis.

The many causes hypothesis was recently argued by Nisbett (2010). Nisbett holds that the gap could be due to the additive effect of wealth disadvantage, teenage motherhood, discrimination, caste-like status inhibiting “effort optimism,” unstable marriages, stereotype threat, etc. Hunt and Carlson in Hunt and Carlson (2007) agree with this idea, stating: “It is quite possible that the present discrepancy in achievement is due to multiple small and subtle social effects, many of which may be due to cultural practices in the affected groups, such as attitudes toward education, indirect effects of health practices, and relative degrees of family solidarity.”

How many possible causes have been proposed? Quite a few. How does the intricate web of Hereditarian logic stand in wake of these 5 score and some possible causes? Let’s review that web of logic:

A. As the various measures have high validity, the gap is not due to test bias of any sort. It’s real.
B. There’s no minority specific cause to the gap.
C. The gap, both in IQ and IQ correlates, persists across SES (See note 2).
D. The gap is general intelligence loaded and general intelligence has substantial structural and function neurophysiology correlates. (See note 7.) As such, the gap has a substantial biological component. According to Flynn (2010), the GQ gap is slightly larger than the IQ gap and the adult IQ gap is over 1SD.
E. If gap is 100% environmental, African-Americans adults would have to live in an “cognitive environment” equivalent to that of the bottom white 2.2 percent.

Let’s revisit that last point. Given the function BGH = WGH(rg(1-rp)/rp(1-rg), between group heritability (BGH), within group heritability (WGH), and the genetic/ environmental variance within and between groups (rg) are mathematically related. As such, the amount of within group difference needed to cause a between group difference (assuming no X-factors) can be determined given a specific BGH and WGH value. [You can use the simple formula: xSD between divided by the square root of the environmental variance = y SD within].

If we assume that the BGH is zero and that the WGH is zero:

1 SD of between group difference would require 1 SD of within group difference (1/1) or that the mean black cognitive environment was equivalent to the cognitive environment of the white lower 16 percent. You can use this calculator to transform SD to percentile.

If we assume that the adult BGH is zero and that the WGH is .75 (see note 3):

1 SD of between group difference would require 2 SD of within group difference (1/.5)or that the mean black cognitive environment was equivalent to the cognitive environment of the white lower 2.2 percent.

And this, as we said, precludes single variable factors. Imagine if the difference in IQ between college age blacks and whites was said to be due to hours of college homework done (h). If so, since h is a factor that varies within groups, we would have: 1 SD of between group difference = 2 SD of within group difference = 2 SD of difference in (h) or that the mean number of hours of homework done by African-American students is equivalent to the number of hours done by the white lower 2.2 percent. That this is not the case can easily be verified (4).

However, the above does not preclude the possibility that many factors add up to create the difference. 1 SD of between group difference = 2 SD of within group difference = 2 SD of difference in (h + A + B + C + D + etc.). There are two reasons why this is improbable. The first is conveyed by the often referred to graph of SAT differences across SES and the second follows from the second half of Jensen’s with-between group heritability argument.

1) A and D effectively rules out all testing bias explanations (Test Performance and Test-Taking Motivation, Performance of African Americans Suffers in Stereotype-Priming Situations, etc.); B, as we said, effectively rules out minority specific explanation (Castelike/Involuntary Minority Groups, Racism in Young Children, etc). This is important because such factors would more or less be equally distributed across SES. Other possible causes like poverty (e.g. Prenatal Exposure to Pollutants, Effects of Early Povert, etc) vary across SES. Since the factors which would have been equally distributed across SES have been effectively ruled out, the gap for high SES blacks would have to be caused by a different combination of factors that cause the the gap for low SES blacks. Yet (C) the difference (at least in SAT scores) is relatively constant across SES (see note 2). It’s improbable that roughly the same magnitude of difference would be caused by rather different sets of factors (Number of Toys + Postnatal Exposure to Pollutants + Inequality in Health Care) for low SES blacks and (Cultural Expectations + Oppression Resistance + Subconscious Racial Stereotypes) for high SES blacks.

More still, the number of possible explanations for the high SES black-white gap are severely constrained. Given Dthe gap must be partially developmental in nature; it is a biological gap the emerges across the development periods of Black and white children and young adults. Poverty explanations (Prenatal Exposure to Pollutants, etc) could account for this amongst low SES blacks but obviously not high SES blacks. For high SES blacks, the explanations (for differences in g) are limited to “cultural” factors which could influence the developmental process and create substantially biological differences (e.g a history of not exercising one’s brain). These “cultural” explanations, in turn, are constrained by heritability.

If we control for SES, the adult B-W g-gap is .8 SD. To explain that difference, 1.6 SD of general intelligence (i.e. biological) affecting “cultural” is needed; this “culture” of course must be unrelated to SES. This means that black SES independent “culture” must be equivalent to the “culture” of the lower white 6 percent; it isn’t.

2) Since, assuming BGH = 0, 1 SD of between group difference = 2 SD of within group difference, and since 1 SD of IQ = 15 points, an adult between group difference of 15 points would be equivalent to a within group difference of (15 x 2) = 30 points. As BGH is said to be zero, groups are considered to be genetically equal. So the 20 point difference would be equivalent to a 30 point difference between pairs of Monozygotic twins as opposed to the expected ~6.5 points. The largest ever reported difference between MZ twins, however, was 24 points (or 1.5 SD). Moreover, the average absolute difference (due to both genetics and environment) between all random pairs of individual in a population would be 17 points (or 1.1284 SD). Given this, it’s highly improbable that BGH = 0.

[We can continue with the line of thinking and derive what we found above in another manner. To say that the B and W subpopulations are genetically identical, is to say that these subpopulations are equivalent to being sets of identical twins. As we said, the total average difference between twins raised in modern Western environments is ~6.5 points (as compared to ~17 for any random pair of individuals). Given a total average difference of 6.5 points, the standard deviation between twins is about 5 points (see note 6). Since the B-W difference is 15 points, there must be 3 SD (15/5) of environmental effect between them, which is to say that Bs must live in a cognitive environment equivalent to the Ws 0.14 percent. Which they don’t.]

This is why Jensen (1981) concluded that “[t]he constraining implication of h^2/W for h^2/B can be escaped only by making a different assumption (note that it is presently an assumption) — namely, that the phenotypic difference between the groups is attributable to a source of monogenetic variation (other than measurement error and sampling error) that does not contribute to phenotypic variation (i.e individual differences within either group.”

Taken together these two reasons make the many factors (h^2=0) hypothesis highly improbable — Which is why Flynn decided to explore the gene-environment hypothesis. Unlike Nisbett (2010) and Hunt and Carlson (2007), Flynn grasped the strength of Jensen’s argument.

[Now, it could be argued that the IQ difference is no longer 1 SD and when it was 1 SD, that the heritability of IQ for African American adults was significantly lower than 75%. One could, for example, cite Flynn and Dickens (2006); when projecting their data out to year 2002, Flynn and Dickens found an average IQ of 88 for African Americans below the age of 24. This would give a within difference of only 1.29SD (.8/.62) or 15.5 points; this is higher than the expected 6 points but not unexplainable by environmental causes. Yet Flynn and Dickens, nonetheless, found an average IQ of 83.5 for African Americans above the age of 24 (see note 5); and now there is no reason to think that the heritability of IQ for African Americans is lower than 0.75. Moreover, when one focuses only on the average between family environmental difference (< .12), which is the only relevant portion of the difference when it comes to B-W gap, one gets (1/.34) or ~ 3 SD of needed environmental affect! [Note: I recalculated the average IQ gap and derived and average of .9 to .95.


(1) Both Flynn and Nisbett have conceded this. This is substantial given that an X-factor explanation was long held to be the cause of the gap. For example, refer to Sandra Scar’s A reply to some of professor Jensen’s Commentary. In: Race, social class, and individual differences in I.Q.

X-Factors were empirically ruled out by the following studies:

Lubke, et al. 2003. On the relationship between sources of within- and between-group differences and measurement invariance in the common factor model

Rowe, 1994. No more than skin deep. American Psychologist; Rowe and Cleveland, 1996. Academic achievement in Blacks and Whites: Are the developmental processes similar?

Rowe, et. al., Vazsonyi 1994. No more than skin deep: Ethnic and racial similarity in developmental process.

Rowe, et. al., 1995. Ethnic and racial similarity in developmental process: A study of academic achievement.

(2) Controlling for SES, there is a 12 point (0.8 SD) IQ difference. If we assume that none of the SES difference is due to genetics, and assume a .75 within race heritability at age 24 (since at the same SES, there is no reason to assign a lower black h^2 than white h^2), we get 1.6 SD of difference, meaning that controlling for SES, for a 0 genetic hypothesis to be true, blacks must live in a cognitive environment equivalent to the white lower 5.5 percent. (.8/sqrt .2) = 1.6 SD.

(3) The h^2 of IQ (and GQ) increases with age. By adulthood the heritability of general intelligence approaches .80 in industrialized countries (Deary, Penke and Johnson, 2010). Similar heritabilities have been found elsewhere; Pal, Shyam and Singh (1997) found a heritability of .81 for rural adult (mean age 21) Indians; Nathawat and Puri (1995), as reported by Pal, Shyam and Singh (1997), found a heritability of .9 for urban adult Indians.

(4) From U.S. Department of Education survey of the conduct and attitudes of the parents of American students from kindergarten through grade 12 (2005):
93% of Black parents but only 82% of White parents regularly check to see that their children complete their homework assignments.
46% of Black parents but only 32% of White parents help their children with their homework three or more days a week.
49% of Black parents but only 41% of White parents visited a library with their children.

(5) I’ll address this in another post. Basically the “default hypothesis” (i.e. Hereditarian hypothesis) proposes that the between group differences are caused by the same factors which cause within group differences (genes and environment). Given that the heritability of IQ increases with age within groups, it should increase with age between groups. (Though, to note, Rushton has often argued (in error in my opinion) that the differences are more or less constant from age 6 up.) Another way to say this is that genetic differences impose themselves more as one ages. Differences in children at younger ages that are out of proportion to the expected genetic affect, accordingly, are due to environmental influences (the IQ of parents) — differences which can be reduced (e.g. by outsourcing parenting by means of preschools, etc).

(6) Jensen (1973) gives the twin standard deviation formula:

The MZ Twin SD (4.74) is equal to sqrt of the environmental variance [sqrt (22.5)]. The environmental variance (22.5) is equal to the total variance (15^2) minus the genetic variance (.85 x 15^2) and the error variance (-1.95(15^2). The genetic variance is the twin correlation X the population SD (15). The twin correlation (.85) is r = 1-(|dk|/|dp|)^2, where
|dk| is the mean absolute difference between kin
|dp| is the mean absolute difference between all random people
|dp|=2pi/sqrt(pi) = 1.13SD

(7) In representative studies Karama et al (2009) and Karama et al (2011) found that general intelligence correlated with cortical thickness and that general intelligence completely mediated the correlation between cortical thickness and cognitive performance.

The same relation between psychometric g and neurological g exists for both Blacks and Whites.


Deary, Penke and Johnson, 2010. The neuroscience of human intelligence differences

Flynn and Dickens, 2006. Black Americans reduce the racial IQ gap.

Hunt and Carlson, 2007. Research on group differences in intelligence is scientifically valid and socially important

Jensen, 1981. Obstacles, problems, and pitfalls in differential psychology

Jensen, 1998. Population Differences In Intelligence: Causal Hypotheses. In: The g Factor: The Science of Mental Ability

Karama, et al., 2009. Positive association between cognitive ability and cortical thickness in a
representative US sample of healthy 6 to 18 year-olds

Karama et al., 2011. Cortical thickness correlates of specific cognitive performance accounted for by the
general factor of intelligence in healthy children aged 6 to 18

Pal, Shyam and Singh (1997), Genetic analysis of general intelligence ‘g’: A twin study

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