Colorism — So much for Franz Boas

The greatest hope for the immediate future lies in a lessening of the contrast between Negroes and whites. … Intermixture will decrease the contrast between extreme racial forms. … In a race of octoroons, living among whites, the color question would probably disappear. –Franz Boas [1]

Over at Evo and Proud, Peter Frost has a good post on the colorism paradigm. He was commenting on Hersh (2008)’s questionable reasoning (in “The new immigrant worker: the effects of skin color and height, Journal of Labor Economics.”) Briefly, Hersh (2008) found direct evidence of an immigrant skin color-wage association [2]. Hersh concluded that these findings are consistent with the colorism hypothesis — a hypothesis posited to explain the intra-African American (and South and Central American) color gaps:

Thus, discrimination against immigrants with darker skin relative to those with lighter skin remains a possible explanation for the findings of this article. The results indicate that any such discrimination is not merely ethnic or racially based nor due to country of birth. Wage equations controlling for ethnicity, race, and country of birth, as well as for family background and extensive labor market characteristics, including characteristics that may themselves be affected by skin color discrimination, show that gradations of skin color affect wages. Skin color is not merely capturing the effects of ethnicity, race, or country of birth but also has an independent effect on wages.

The immigrant findings should not be unexpected. Skin color correlates with national IQ [3,4]. National IQ predicts total national productivity, national economic performance, national savings rate, etc — from which we can infer “unmeasured workers skill” [5,6]. National IQ also predicts immigrant wages just as well as US psychometric tests predict native wages [7]. Hersh (2008) just confirmed what is implied when the findings of Templer (2010) and Jones (2008) are read simultaneously: an immigrant color-skill association.

None of the above implies an ultimate cause to the association. The color-skill association could be a function of the immigrants’ home culture and environment. Moreover, it could simply be a reflection of the skill level of the particular types of immigrants immigrating, though the findings of Rindermann (2007) and Jones (2008a) seem to suggest otherwise. When Hersh (2008) controlled for numerous market factors such as home occupation, home education, father’s years of education, grasp of English, the correlation became non-significant (reducing from 0.021 (p-value<.01 ) to 0.008 (p-value =.11). What about other factors? Hersh (2008) considers two but dismisses the most important one:

Because inclusion of additional observables reduces the magnitude of the estimated skin color effect, it is worthwhile to consider what might be missing from the wage equations. Two possible omitted variables are attractiveness and some measure of ability as embodied in test scores.

The oddity is that she dismisses the possibility of an immigrant IQ mediated association — not much of one is needed — on the basis of a lack of association (according to her) amongst African Americans. This is peculiar because she clearly is trying to use the immigrant data to bolster and extend the color hypothesis beyond Mulattos and Mestiza. She writes:

The possible connection between skin color and ability has been examined using the 1982 GSS, which includes a 10-item vocabulary test as well as a measure of skin color for a sample of about 500 African Americans. Using these data, Lynn (2002) reports a positive correlation between lighter skin color and higher test scores.

However, using the same data, Hill (2002) demonstrates that controlling for education and family background eliminates the relation between skin color and test scores. [Chuck: Actually, doing so reduces the relation (warning: sociologist fallacy) to statistical non-significance; controlling for market factors, likewise, reduces the immigrant color-wage relation to statistical non-significant.] Available evidence in the scientific literature does not support a link between skin color and intelligence. In addition, the correlation between skin color and ancestry varies considerably, with low correlations in many populations of mixed ancestry (Parra, Kittles, and Shriver 2004). In the absence of genetic evidence or a high correlation between skin color and ancestry, it seems unlikely that inclusion of test scores as a measure of ability would greatly alter the skin color effects found in this article

Let’s ignore the Non sequitur and take a closer look at her reasoning with regards to African-Americans.
She contends a) that the available evidence doesn’t support a color-IQ correlation and b) the color ancestry correlation is too low, anyways, to allow IQ to mediate the African American color-wage correlation.

As we know, the low (.17) intra-African American skin color-IQ correlation is consistent with the genetic hypothesis; and the skin color-ancestry correlation is what allows for this consistency [8]. (Hersh likely mistakenly reasoned that since color only weekly correlates with IQ and since color only moderately correlates with ancestry amongst African Americans, the correlation between IQ and ancestry, if any, would be very weak at most.)

Moreover, we know that controlling for IQ reduces the Black-White wage gap (and somewhat reverses the SES gap); the findings of Murray and Herrnstein (1994) have been replicated a number of times [9,10, 11, 12]. So the question is, does controlling for IQ reduce the intra-Black (color)-wage gap? Doing so reduces the gap found in the 1982 GSS data . Otherwise, this question has yet to be tested. Until it is (I wouldn‘t hold my breath), one can not know if the “inclusion of test scores as a measure of ability would greatly alter the skin color effects found.” (The effects don’t need much reducing [see: 22]). Of course, including test scores, wouldn’t alter the relation. It would just tell us if it, like the race one, is mediated by general intelligence. As it is, there are indirect reasons for concluding that it is:

Presumably, IQ is intercorrelated with the color- wage gap. As Harris (2008), Hill (2000), and Hochschild and Weaver (2008) point out, the gap is not just a wage gap but an SES, education, and prestige gap [13, 14, 15].

Dark-skinned blacks in the United States have lower socioeconomic status, more punitive relationships with the criminal justice system, diminished prestige, and less likelihood of holding elective office compared with their lighter counterparts.– Hochschild and Weaver (2008)

Were Hersh (2008) right and were it true that there was no “link between skin color and intelligence,” then, for African Americans, IQ would have to be unassociated with SES and education. We know, however, that it is associated [17]. Since IQ correlates with African American SES and education, it correlates with African American color. And since we know that IQ is predictive and unbiased [16, 18, 21] within the African American population, we can also conclude that IQ mediates the color-wage relation. We are then left in search of the ultimate cause of the intraAfrican American disparity, IQ being a proximate one.

We are also left with the real color paradox: some factor is behind the low African American psychometric intelligence, which is a proximate cause of wage, SES, education, etc. disparities; and this factor impacts African Americans in proportion to their African appearance, which, on the population level, correlates with African genotype. Since intelligence is the proximate cause, the factor can’t be contemporaneous education and work etc. “discrimination”; the massive discrimination for African-Americans [see for example 19, 20], in the name of proportionate equality, undermines this hypothesis further. And since the factor impacts African Americans in proportion to their African-ness, it can’t simply be the legacy of racial discrimination acting by way of intelligence affecting environmental effects. As Hill (2000) has shown, “culture” fails as an explanation for the intraAfrican American gap, a gap which was present at least since the early 1900s. Likewise, family circumstance fails (i.e. Sowell’s intergenerational explanation), since the gap has been found even after controlling for family origin (14,15).

The proponents of the “colorism” paradigm have done a good job at establishing the inadequacy of “cultural” explanations. In doing so, they have unwittingly painted racial egalitarians into a corner.

References

[1] As quoted in Roger Sanjek, “Intermarriage and the Future of Races in the United States,” in Race, ed. Steven Gregory and Roger Sanjek.
[2] Hersch, 2008. Profiling the new immigrant worker: the effects of skin color and height, Journal of Labor Economics.
[3] Templer, 2010. IQ and Skin Color: The Old World Reexamined and the New World
[4] Templer and Arikawa, 2006. Temperature, skin color, per capita income, and IQ: An international perspective
[5] Rindermann, 2007. The big g‐factor of national cognitive ability
[6] Jones, 2008a. Cognitive Ability and Technology Diffusion: An Empirical Test
[7] Jones, 2008b. IQ in the Production Function: Evidence from Immigrant Earnings

[8] Shuey (1966) reviewed 18 studies relating IQ and skin color. In 12/18, lighter colored African Americans scored higher on all tests; in 4 studies, lighter colored African Americans scored higher on the majority of the tests (3/5, etc.). In 2, there was no evidence of a relation. The correlations found by Herskovits (1926) = .17, Klineberg (1928) = .12, Peterson and Lanier (1929) =.18/.30, and Scarr, Pakstis, Katz and Barker (1977)* = .155 for g, Lynn (2002) = .17. Average = .17, N = 1130.* Nisbett concurs with this in "Race, genetics, and IQ," stating that "the typical correlations with skin color are around .15.” If the African American Skin color -Ancestry correlation is .44 (Parra, Kittles, and Shriver 2004), a .17 IQ -skin color correlation would predict a .39 African American IQ-Ancestry correlation. Since no one has modeled it, no one knows what magnitude of a genotypic IQ gap this .39 correlation would predict. *Scarr et al.’s Ns varied. I could not locate the N for the color-IQ measure.

[As for the IQ-Ancestry correlation, I’m just reversing an equation that I already discussed:

“The expected mean correlation between IQ and skin color (SC) would be the square root of the product of the reliabilities (i.e square) of the correlation between IQ and individual ancestry (IA) and SC and individual ancestry (IA), assuming some between group heritability (BGH) of IQ. The average SC-IA correlation for African Americans is around .44 (ranging from .34 to .54); the reliability of skin color as a predictor of African American Ancestry is, therefore, .19. The average IQ-IA correlation obviously has yet to be determined. Assuming a BGH of 1, the IQ-IA correlation could range anywhere from .25 to .50, giving predictive validities of .05 to .25. (The IQ-IA correlation would most certainly be less than 1; consider that siblings who share the same ancestry (and half their genes) only have an IA- IQ correlations of ~.50!) Using .44 as the SC-IA correlation, the maximum and minimum expected IQ-SC correlations, assuming a BGH of 1, would be around 11% and 22%, respectively.”

[9] Herrnstein and Murray, 1994. The bell curve
[10] Darity and Myers, 1998. Persistent disparity: Race and economic inequality in the United States since 1945
[11] Johnson and Neal, 1998. Basic skills and the black-white earnings gap
[12] Kanazawa, 2005. The Myth of Racial Discrimination in Pay in the United State
[13] Harris, 2008. From color line to color chart?: Racism and colorism in the new century
[14] Hill, 2000. Color Differences in the Socioeconomic Status of African American Men: Results of a
Longitudinal Study
[15] Hochschild and Weaver, 2008. The Skin Color Paradox and the American Racial Order
[16] Sacket, et al, 2001. High-stakes testing in employment, credentialing, and higher education:
Prospects in a post-affirmative-action world

[17] Schmidt and Hunterm 2004. General Mental Ability in the World of Work: Occupational Attainment
and Job Performance

[18] Viswesvaran and Chockalingam, 2002. Agreements and Disagreements on the Role of General Mental Ability (GMA) in Industrial, Work, and Organizational Psychology.
[19] Gottfredson, Racially gerrymandering the content of police tests to satisfy the U.S. Justice Department: A case study.
[20] McDaniel, 2009. Gerrymandering in personnel selection: A review of practice
[21] Sackett, et al., 2008. High-Stakes Testing in Higher Education and Employment Appraising the Evidence for Validity and Fairness. page 222-224

[22] While the .17 IQ-color correlation is low, the intra-African American gaps in need of explanation are small. For example in “When Do People ¬Not Protest Unfairness? The Case of Skin Color Discrimination,” Hochschild (2006) notes:

Consider some illustrative evidence. The Multicity Study of Urban Inequality (MCSUI) was conducted in 1992-94 in four cities — Boston, Detroit, Atlanta, and Los Angeles (Bobo et al. 2000). There were almost 9000 respondents, including over 3000 blacks. In the MCSUI data, just over a quarter of African Americans had earned college degrees. But light-skinned blacks were more likely to have a college degree than were medium- or dark-skinned blacks; conversely, dark- and medium-skinned members were less likely to have completed high school. Put another way, dark-skinned blacks received on average 12.2 years of schooling; medium-skinned blacks received 12.5 years, and light-skinned blacks enjoyed 12.9 years of schooling. The results are highly statistically significant. Although these are not huge substantive differences, the gap between finishing high school and achieving a year of college education is very meaningful for one’s life chances. (For similar results using different data sets, see Keith and Herring 1991; Hunter 2002; Allen, Telles and Hunter 2000; Seltzer and Smith 1991; and Krieger, Sidney and Coakley 1998).

The same pattern holds for income. Mean family incomes range from about $23,200 for the dark-skinned, to $24,800 for the medium-skinned, to $25,900 for the light-skinned. Put another way, families of dark-skinned African Americans enjoy about nine-tenths as much income as families of light-skinned African Americans. This too is not a trivial difference; in 1994, the mean family income for blacks was almost two-thirds that of whites. (For similar findings, see the articles cited above, as well as Edwards 1972; Keith and Herring 1991; Murguia and Telles 1996; Cotton 1997; Hill 2000; Gomez 2000; Bowman, Muhammad and Ifatunji 2004).

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30 Responses to Colorism — So much for Franz Boas

  1. KC says:

    Sorry, this is OT, but I’m just reading this thread. This commentator is arguing that continental racial groups/populations are misleading because “They give the unwarranted impression that unrelated people are more closely related than they actually are.” He goes on:

    “Human populations” has the meaning “genetically related populations.” “Racial groups” means “groups of people, often unrelated, associated by geography or vague phenotype or any other sysem of classification that looks good to a particular observer at a particular time,” (i.e., some social construct)…

    I’m surprised to even see Risch employ the word “Caucasian.” I’d be curious to know who he includes in that group and whether he really believes that a Swede is closer, genetically, to a Sri Lankan than to an Ethiopian or whether the Ethiopian is more distant from a Yemeni than a Swede or a Sri Lankan. Does he include Tahitians with the Mongoloids or with an Oceanic people?

    And note, again, that Rosenberg failed to find actual relatedness among the groups, only statistical pairing by junk DNA as a legacy of migrations. Within the various groups, enough change has occurred that the geographical groups tend to be composed of actually dissimilar smaller groups.”

    http://boards.straightdope.com/sdmb/showthread.php?t=601006&page=5

    As far as I’m aware it isn’t correct that statistical pairing simply relates to ‘junk dna’. Sure you can make more accurate classifications of smaller groups, but the larger groups also reflect relatedness?

    • Chuck says:

      KC,

      I’m not sure what you are talking about — let alone who you are (KC/OT?). This post isn’t about population genetics. As for genetic relatedness, you might want to read this paper: There is a zero probability that an ethnic Swede is more genetically related to a Sri Lankan than to another ethnic Swede. If you wish to discuss this we can, perhaps here. As for ‘race,’ you might want to read my discussion of the concept here: http://abc102.wordpress.com/ Race means regional ancestry. The concept is necessarily tied to that of genetic relatedness.

  2. KC says:

    Yeah, sorry for posting off topic. Thanks for the link. I thought it was an interesting example of arguments used (by a forum moderator in this case) against the existence of races.

    I am going to email Hersch and ask for her comments on some of the points you have raised.

  3. Chuck says:

    KC,

    I don’t mind the off topic-ness. I’m just not sure what you are talking about. It’s not clear if you are defending the concept of race or criticizing it. I’ve tried to work out a multiple part defenses of the race concept, for example here: http://abc102.wordpress.com/2008/03/20/a-semantic-defense-of-the-ordinary-race-concept/ If you’re interested, I’d be happy to work out a comprehensive defense of the concept and map out a series of counters for common criticisms.

    Anyways, if you email Hersh and get a reply, I would appreciate if you would let me know what she says.

  4. KC says:

    ***I’m just not sure what you are talking about. It’s not clear if you are defending the concept of race or criticizing it***

    Defending it. I was just quoting comments from tomndebb as an example of the kind of arguments against it (he accepts there are populations, but not races).

    Thanks, I’ll have a read of your link a bit later. I read your blog pretty regularly so would be interested in further posts on the topic.

    And yes, I’ll let you know what Hersch says.

  5. @Chuck
    In the 8th footnote you state:
    “If the African American Skin color -Ancestry correlation is .44 (Parra, Kittles, and Shriver 2004), a .17 IQ -skin color correlation would predict a .39 African American IQ-Ancestry correlation.”

    I have a mathematical background and I’m not sure I understand your reasoning here. I suspect many of your readers are likewise confused. It seems that you have assumed that the 0.17 IQ-skin colour correlation is entirely due to the indirect effect of the skin colour-ancestry correlation of 0.44. Hence yielding a 0.17/0.44 = 0.386363… = approx. 0.39 ancestry-IQ correlation. Is that right?

    There is another interesting effect to consider. It is possible and I think likely that part of the IQ-skin colour correlation is independent of (degree of nonwhite) ancestry. If both lighter skin and higher IQ (or factors which correlate with IQ) are deemed desirable in a population then one would expect higher IQ individuals to be more likely to reproduce with light-skinned individuals (since both groups are desirable and desirable individuals would be more likely to reproduce with each other). This would generate an IQ-skin colour correlation independently of racial ancestry. This correlation would be even stronger if those with light skin formed an assortatively mating subpopulation as there would be gradual infusions of higher IQ genes over time that would then become locked into the population. I think we see this effect in Latin America and probably also to some degree with the South Asian caste system. In other words, overtime light skin and (nonwhite) ancestry would become decoupled due to stochastic sorting (assuming that they are correlated to start with) while light skin and IQ would become/remain coupled.

    @KC:
    The guy you quoted is an easy target. The position he is pushing makes no sense. He, like many anti-racists, seems to be missapplying the sorites paradox. The sorites paradox isn’t some problem that only applies to race. Rather, it is a philosophical issue that applies to a huge number of different categories. The basic idea of sorites is that humans have a tendency to try to force continuously distributed variables into vague discrete categories. Doing so helps us to communicate and to think in terms of patterns and relations. This is true of most categories we use. Race is no different. For example, at what height does a person cease to be tall (or short)? It is not an easy question to answer precisely but that does not mean that the words tall and short are useless nor that they do not refer to actually existing traits.

    Also, the sorites paradox only applies to race in its discrete sense. Race also has a widely accepted meaning as a continuously distributed set of traits. Otherwise, it would make no sense for people to use (or have used) terms such as mixed-race, mulatto, meztizo, octaroon, quadroon, etc. Race is something that can be mixed. That doesn’t mean that it isn’t real or meaningful. Shit and icecream can be mixed, yet I don’t think anyone but the insane would claim that shit and icecream aren’t real or that they aren’t meaningful categories. And even if one were to suppose that shit and icecream weren’t real and weren’t meaningful categories, would they then conclude that shit and icecream are basically the same?

    The term “junk DNA” has largely fallen out of favour as it appears that much DNA that was thought to be “junk DNA” (ie noncoding DNA) actually has important functional effects (having to do with regulation and gene expression etc.). The vast majority of the DNA differences between humans have little or no functional effects. Such differences are called neutral differences. Many of these neutral differences are even located in coding regions of DNA since more than one version of a gene can code for exactly the same thing. The statistical techniques used to find clusters and genetic distances etc. usually do not distinguish between functional and neutral DNA but since the vast majority of genetic variability of DNA is neutral this fact doesn’t mean as much as one might think. Determining which genetic differences are neutral and which are functional is very tricky and hence we don’t have much data on how functional differences are distributed between and among populations. Of course these neutral genetic differences reflect relatedness – how one could think otherwise is truly baffling.

    Finally, a picture is worth a thousand words:
    Check out figure 2 from the link below which clearly demonstrates that Europeans cluster with each other to an extreme degree. Also, from the Fst table (table 1 from the link) we see that, using the Fst as a measure of genetic distance, France, Germany, and the UK are each 1/300 as distant from each other as any of them are from Nigeria. And Spain and Russia are 1/30 as distant from each other as they are from Nigeria.

    http://www.nature.com/ejhg/journal/v16/n12/fig_tab/ejhg2008210ft.html

  6. Chuck says:

    Fascist,

    “I have a mathematical background and I’m not sure I understand your reasoning here. I suspect many of your readers are likewise confused. It seems that you have assumed that the 0.17 IQ-skin colour correlation is entirely due to the indirect effect of the skin colour-ancestry correlation of 0.44. Hence yielding a 0.17/0.44 = 0.386363… = approx. 0.39 ancestry-IQ correlation. Is that right?”

    No. I’m just reversing an equation that I already discussed:

    “The expected mean correlation between IQ and skin color (SC) would be the square root of the product of the reliabilities (i.e square) of the correlation between IQ and individual ancestry (IA) and SC and individual ancestry (IA), assuming some between group heritability (BGH) of IQ. The average SC-IA correlation for African Americans is around .44 (ranging from .34 to .54); the reliability of skin color as a predictor of African American Ancestry is, therefore, .19. The average IQ-IA correlation obviously has yet to be determined. Assuming a BGH of 1, the IQ-IA correlation could range anywhere from .25 to .50, giving predictive validities of .05 to .25. (The IQ-IA correlation would most certainly be less than 1; consider that siblings who share the same ancestry (and half their genes) only have an IA- IQ correlations of ~.50!) Using .44 as the SC-IA correlation, the maximum and minimum expected IQ-SC correlations, assuming a BGH of 1, would be around 10% and 22%, respectively.”

    So we have .17 (SC-IQ) = sqrt [(.44^2 SC-IA)(X^2 IQ-IA)]
    Solve for X. .17
    This predicts a .39 IQ-IA correlation, assuming no colorism.

    “There is another interesting effect to consider. It is possible and I think likely that part of the IQ-skin colour correlation is independent of (degree of nonwhite) ancestry. If both lighter skin and higher IQ (or factors which correlate with IQ) are deemed desirable in a population then one would expect higher IQ individuals to be more likely to reproduce with light-skinned individuals”

    That’s a good point. Another possibility is pleiotropy.

  7. Chuck says:

    Fascist,

    “I have a mathematical background”

    The point about junk DNA is noted. That said, I like inverting antiracist arguments. As such, I constructed the argument below as a counter to the Lewontin argument (i.e only 15% difference!). To convert total genetic variance (paragraph 3) to predicted genotypic IQ mean difference (in SDs), I just decomposed the variance. Is that correct?

    “This is an important point, so let’s clarify it. Cavalli-Sforza and Lewontin claim, respectively, that the total genetic variance between continental races (CR) and continental races + populations (CR+P) is insufficient to allow for socially significant differences in general intelligence. Obviously, to say that there can’t be such differences with any certainty presupposes that we’re using a coherent concept of CR and CR+P. (You can’t argue Montagu and this point at the same time.) Neither Lewontin or .Cavalli-Sforza explain their reasoning. Here’s mine:

    To determine how much between variance in genotypic IQ the total between genetic variance can allow for, we have to make an assumption about the distribution of IQ genes within the total variance. For now, let’s assume that IQ genes are randomly distributed throughout the total genetic variances. Under this assumption, how much between genotypic IQ variance would we predict? Using Cavalli-Sforza’s estimates (in Barbujani et al., 1997), the total between genetic CR and CR+P variance is 10.8% and 15.5% respectively.

    Now there’s a caveat. When we’re talk about genotypic IQ variance between CR and CR + P, we’re talking about variance between populations of individuals. Likewise, when we’re inquiring about the amount of genotypic IQ variance that the total between genetic variance would predict (given our assumption), the relevant total between genetic variance is the total between individual, between CR and CR + P genetic variance. Since we are diploid organisms, Cavalli-Sforza’s estimates refer to a) the between CR and CR + P genetic variance, b) the between individual within CR and CR + P genetic variance, and c) the within individual genetic variance. As the later component is not relevant to us, we have to extract it. Roughly, the within population variance should spit equally between inter-individual variance (CR= 44.6%; CR + P = 42.25%) and intra-individual variance (CR= 44.6%; CR + P = 42.25%). Adjusting accordingly, the between individual, between CR and CR + P total variance is 24% and 36%.

    How much between CR and CR + P genotypic IQ variance (in Sds) would this predict? Assuming within population SDs of 15 (variance = 225), the predicted between population SDs would be roughly CR= 1.1 SD and CR+P =1.5 SD [.24/.36 = between variance for IQ/(225 + between variance for IQ); solve for between group variance = 68/127. Assuming equally numerous populations, (Sqrt (between group variance)) = [(Mean population A – joint mean)^2 + (Mean population B – joint mean)]^2/N =2. Solve for Mean A, B difference =16.5/22.5 IQ points; transform to SD: 16.5/15 = 1.1 SD, 22./15 = 1.5 SD.]”

  8. KC says:

    Chuck,

    If you have a spare moment here’s someone you may be able to assist. The commentator Alex V is asking for research on:

    “So do they have a lower IQ because of economics or because they are black? I would assume because of economics. …So, if someone can give me true data that accounts for socioeconomic factors that is not another blog or random site, or news institution (since most of the time the news does not provide correct interpretation of the research) provide me with a real scholarly journal.”

    http://www.halfsigma.com/2011/03/more-about-the-hispanic-crime-rate.html#tp

  9. KC says:

    ***The guy you quoted is an easy target. ***

    Thanks for the detailed comments Fascist. I’ve seen the likes of Tim Wise use the junk dna argument before too. The commentator is now trying to argue that for populations to be related, they would need to show similar susceptibility to diseases. So I posted some examples showing that is in fact, statistically, the case.

  10. Chuck says:

    “So do they have a lower IQ because of economics or because they are black”

    KC,

    You can confidently reply that the proximate cause of much of the economic disparity is lower general intelligence. To establish the gap, you can cite:

    Roth et al., 2001. Ethnic group differences in cognitive ability and educational setting: A meta-analysis

    To establish the predictivity of the gap, you can cite:

    Schmidt and Hunterm 2004. General Mental Ability in the World of Work: Occupational Attainment
    and Job Performance

    For a specific example, you can cite

    Kanazawa, 2005. The Myth of Racial Discrimination in Pay in the United State

    The commentator, however, is asking about the ultimate cause of the IQ (g) gap. Obviously, this is in dispute — if it wasn’t, we wouldn’t be blogging. You can point out, though, that the between race (in the US) IQ-gap represent a biological gap and that that within races IQ gaps are highly heritable (by adulthood, little of the variance is explained by factors that vary between families — factors like SES) . This limits the possible causal pathways for the between race gaps (in the US)

    (I tried to illustrate that here: http://abc102.files.wordpress.com/2011/02/indirect6.png)

    • JL says:

      KC, I think this graph is the most striking piece of evidence for the fact that the b-w IQ gap is not due to black poverty or lack of education: http://upload.wikimedia.org/wikipedia/commons/a/a6/TBC-BW-IQ-SES-withDiff.png

      Of course, it’s from “The Bell Curve” by Murray and Herrnstein, so many people will simply refuse to believe it.

      In a book called “The Black-White Test Score Gap”, a bunch of anti-hereditarian scholars attempted to statistically eliminate the gap by controlling for dozens of environmental factors (many of them actually proxies for genetic differences), but even that only partially eliminates the gap. There are few findings in social sciences as robust.

  11. KC says:

    Thanks JL, yes anti-hereditarians did a pretty good PR job dismissing TBC. I think Chris Brand has a similar graph in his book ‘the g factor’.

  12. @Chuck
    Me:
    “It seems that you have assumed that the 0.17 IQ-skin colour correlation is entirely due to the indirect effect of the skin colour-ancestry correlation of 0.44. Hence yielding a 0.17/0.44 = 0.386363… = approx. 0.39 ancestry-IQ correlation. Is that right?”
    You:
    “So we have .17 (SC-IQ) = sqrt [(.44^2 SC-IA)(X^2 IQ-IA)]
    Solve for X. .17
    This predicts a .39 IQ-IA correlation, assuming no colorism. ”

    Your equation is the same as the one I proposed. The square root of a product of squares is identically equal to the product so we have:
    .17 (SC-IQ) = sqrt [(.44^2 SC-IA)(X^2 IQ-IA)]
    -> .17 (SC-IQ) = (.44 SC-IA)(X IQ-IA)
    -> X IQ-IA = (.17 SC-IQ)/(.44 SC-IA)
    -> X IQ-IA = 0.17/0.44

    “The point about junk DNA is noted. That said, I like inverting antiracist arguments. As such, I constructed the argument below as a counter to the Lewontin argument (i.e only 15% difference!). To convert total genetic variance (paragraph 3) to predicted genotypic IQ mean difference (in SDs), I just decomposed the variance. Is that correct? ”
    I am pretty sure it isn’t. The 15% figure comes from the value of the Fst statistic between Europeans and most SS-Africans. The Fst is based on a different notion of variance than the one used in statistics. The Fst uses heterozygosity as a measure of genetic variance.
    Fst = (Ht – Hs)/Ht
    with
    Ht = total (theoretically expected) heterozygosity
    Hs = average subpopulation heterozygosity

    An individuals’ Heterozygosity is the fraction of SNPs (Single Nucleotide Polymorphisms, ie locations in the human genome that tend to very from one human to the next) for which there are 2 different alleles (allele = variant, with there being one allele present for each of the 2 homologous (paired) chromosomes at any given SNP). At every SNP a person is either heterozygous (2 different alleles present) or homozygous (the same 2 alleles present). The notion of heterozygosity can be extended even further to groups of individuals. One way to do this is to calculate the heterozygosity of each of the individuals and then take the average. This method is only used for determining the degree of inbredness of individuals relative to the theoretical heterozygosity of the population to which they belong. For the Fst the heterozygosity of a group of individuals is instead calculated by taking all the alleles present in the group of individuals at the given SNPs, and then, for each SNP, calculating the theoretically expected heterozygosity of a hypothetical individual formed by randomly assigning the alleles (corresponding to each SNP) into pairs and then taking the average of those heterozygosities. Ht is calculated by taking members from the 2 populations being compared and placing them in the same group and then calculating the heterozygosity of that group. Hs is calculated by placing individuals into 2 different groups with each group corresponding to population membership, then calculating each groups’ heterozygosity, and then taking the average of the 2 heterozygosities. There is an adjusted form of Fst which allows for the 2 groups to have different sizes and corrects for the biases which result. Hs is always smaller than Ht. The greater the difference between Hs and Ht relative to the size of Ht, the larger the Fst. Fst admits values between 0 and 1 (except for the adjusted form which I think might be able to be negative – compare with the notion of “adjusted R squared” from statistics which can be negative).

    As you can hopefully see now, the genetic variances (heterozygosities) cannot be divided the way you have done here.

    @anyone
    I have a correction to make wrt the definition of neutrality. Neutrality is a subtly different concept from functionality. A neutral difference is a difference which has no (or negligible) effect on the reproductive success of its carrier. A difference can be neutral while still having functional significance.

    Also, I think I misinterpreted the guy KC quoted. The stuff I wrote still stands but I now think he was/is using a different but equally wrong argument. I will address that later.

    Feel free to ask me about anything.

    • Chuck says:

      Fascist,
      “Your equation is the same as the one I proposed. The square root of a product of squares is identically equal to the product so we have:”

      You mean: “The square root of a product of squares is identically equal to the product of the absolute values of the correlations, so we have…” But I get your point… I realized that that’s what you were saying after I posted the comment.

      Anyways, your point was that I was assuming no colorism and no assortative mating. I wasn’t. My comment in the text was that this correlation “is consistent with the genetic hypothesis.” The footnote went on to explain why. Obviously, if I thought that the skin color-IQ correlation established an IQ-Ancestry correlation, I wouldn’t be blogging about this. The gist of my point was that 1) the skin color IQ correlation is consistent with a genetic hypothesis, 2) a genetic hypothesis (of IQ differences) can account for the colorism findings, 3) the colorism findings rule out complete “cultural” explanations, 4) independent evidence undermines the colorism thesis, 5) ergo…

      (If the above wasn’t clear in my post let me know, so I can reword it.)

      ” am pretty sure it isn’t….As you can hopefully see now, the genetic variances (heterozygosities) cannot be divided the way you have done here.”

      The 15% comes for Lewontin’s estimate. Lewontin and others interpret this as meaning that only 15% of the total human genetic variability is between populations. They further interpret this as meaning that very little of the phenotypic variance between populations could be mediated by genetics. Based on that, I simply estimated what that genotypic variability would translate to, given some standard assumptions. A similar exercise was performed by Levin (2002). Also see Meisenberg (2003).

      I think your point is that doing the above is silly. Yet, Lewontin’s argument is silly. I was simply showing that, based on the assumptions required for the argument, a large genetically phenotypic variability is predicted.

  13. “The 15% comes for Lewontin’s estimate. Lewontin and others interpret this as meaning that only 15% of the total human genetic variability is between populations. They further interpret this as meaning that very little of the phenotypic variance between populations could be mediated by genetics. Based on that, I simply estimated what that genotypic variability would translate to, given some standard assumptions. A similar exercise was performed by Levin (2002). Also see Meisenberg (2003).

    I think your point is that doing the above is silly. Yet, Lewontin’s argument is silly. I was simply showing that, based on the assumptions required for the argument, a large genetically phenotypic variability is predicted.”

    I’m pretty sure that Lewontin’s estimate was based on Fst but regardless a similar problem to the following would still apply. A way of thinking about the problem with what you are doing would be to note that heterozygosity is only one among many different ways of quantifying genetic variance. Variance is an abstract concept that refers to the spread or variability of the data. If you think of Fst as a statistic that compares variances in general rather than only heterozygosities in particular then you will find that depending on which measure of variance is used you can get any Fst value from the same genetic data. Suppose you instead used heterozygosity raised to the tenth power as your measure of variance then the inter-racial Fst, instead of being 0.15, would be:
    Fst = (Ht^10 – Hs^10)/Ht^10 = 1 – (Hs/Ht)^10 = 1 – (0.85)^10 = 1 – 0.197 = 0.803
    That’s a huge difference and hence would yield a hugely different estimate for the genotypic IQ gap.
    Similarly, if you were to use heterozygosity raised to the power 1/10 as the measure of genetic variance then you would get:
    Fst = 1 – (0.85)^(1/10) = 1 – 0.98 = 0.02

    The above analysis is meant only as an illustration of the problem of trying to compare completely different notions of variance. It is an apples to oranges comparison. The variance of the normal distribution (IQ) is neither obviously nor simply related to heterozygosity. The Fst (using heterozygosities) is often thought of in terms of comparing variances in an absolute or universal sense but that isn’t accurate. There is no one “true variance” as such. But if one understands how Fst is derived and what its limitations are then it is a very useful statistic. It has become a standard statistic for use in population genetics analyses and as such it is assumed that those in the field know what it means. I should emphasize that the problem isn’t simply one of determining the right variance but rather that such a task is nonsensical in the first place. There is also a problem with how you relate the genetic variance with IQ variance. What is the causal link between the distributions? Which distributions are used?

    Also, the bit about decomposing the within population variance into within-individual and between-individual components makes no sense if we are using heterozygosity as our measure of variance. Within a population, the within-individual heterozygosity is generally very close to the between-individual heterozygosty. The two are only substantially different if consanguineous reproduction is widespread. In other words, without inbreeding, the two concepts would refer to the same thing.

    Some more interesting facts to keep in mind:
    The Fst between two populations can be arbitrarily small even if the two populations share zero alleles in common. For example, 2 populations, sharing no alleles in common, each with a heterozygosity of 0.99, would have an Fst of no more than 0.02. At the opposite extreme, 2 populations that were identical at all but 1 of a million SNPs, each with zero heterozygosity, would have an Fst of 1.

  14. Chuck says:

    Facist,

    “I’m pretty sure that Lewontin’s estimate was based on Fst but regardless a similar problem to the following would still apply.”

    Here’s Meisenberg (2003).’s analysis:

    “According to the population geneticist Luigi Luca CavalliSforza and his associates, 84.4% of our DNA diversity is accounted for by differences between individuals. 10.8% are “racial” differences between continental populations, and the remaining 4.7% are “ethnic” differences between populations on the same continent. Through gene flow by interbreeding and short-range migration, neighboring populations are always more similar to one another than geographically distant ones (Barbujani et al., 1997). Most of the DNA variation used in these studies is in non-coding junk DNA and is presumably not subject to natural selection. Findings like this, showing the small contribution of between-population differences to overall genetic diversity, spawned the widespread belief that between-population differences in mental abilities and other psychological traits must be minimal as well.

    That this conclusion is premature has been demonstrated by Jensen. When Jensen analyzed IQ variation in a group of 622 black and 622 white children in California, he found that 44% of the variation was within families, 29% between families within socioeconomic and racial groups, 8% between socioeconomic groups, and only 14% between races. The rest was measurement error. In this study the two races differed by 12 IQ points (Jensen, 1980, p. 43). Jensen’s value of 14% for the influence of race is close to the value for racial + ethnic variation in Cavalli-Sforza’s calculation. If IQ genes float as randomly in the gene pool as Cavalli-Sforza’s DNA variations, then the difference in “genotypic” intelligence between the most divergent human populations should be about as great as the measured difference between black and white children in California: about 12 IQ points. We can further predict that there is no conspicuous geographic patterning, only that neighboring populations usually are more similar than distant ones.”

    …………………….

    What exactly are you saying is wrong with it? You keep point out FST numbers — but this is not how Lewontin’s percent’s are interpreted. They are interpreted by everyone as meaning % of between population variability which, granting a few assumptions, can be translated into predicted variance.

    Look, You are either saying that the above interpretation (15% between population variability) is flawed or you are saying that my manipulation of it is. I’ve already stated: “Yet, Lewontin’s argument is silly. I was simply showing that, based on the assumptions required for the argument, a large genetically phenotypic variability is predicted.” So you must mean that my manipulation is. If so explain why. Pointing to the meaning of Fst values does not help given the the working assumptions.

    …………..

  15. “What exactly are you saying is wrong with it? You keep point out FST numbers — but this is not how Lewontin’s percent’s are interpreted. They are interpreted by everyone as meaning % of between population variability which, granting a few assumptions, can be translated into predicted variance.

    Look, You are either saying that the above interpretation (15% between population variability) is flawed or you are saying that my manipulation of it is. I’ve already stated: “Yet, Lewontin’s argument is silly. I was simply showing that, based on the assumptions required for the argument, a large genetically phenotypic variability is predicted.” So you must mean that my manipulation is. If so explain why. Pointing to the meaning of Fst values does not help given the the working assumptions.”

    Both.

    To my mind there many things wrong with the analysis. There is the way you inflated the between population variance based on spurious notions about within-individual variance versus between-individual variance within a population. That is something that you are proposing here that does not make any sense to me and that I have not seen elsewhere. To explain what is wrong with it I have to refer to the details of Fst and heterozygosity because that is where these numbers are coming from. This is an important point as you have more than doubled the estimates of the variances based on this idea.

    There is the fact that variance is a vague abstract concept not a uniquely determined trait of all distributions. You can’t just compare totally different types of variances as if they were the same except by throwing rigour out the window so to speak.

    You also seem to be confused about “between” and “total”. When it is said that Fst measures the proportion of variance that is between-population what is meant is that the ratio of the within-variance to the total variance is treated as the proportion of variance that is within-population and what is left over is treated as the proportion that is between-population. Mathematically Fst = (Ht – Hs)/Ht –> Fst = 1 – Hs/Ht –> 1 = Fst + Hs/Ht. Therefore Fst = between-variance proportion and Hs/Ht = within-variance proportion. But the actual variances are Hs and Ht, the heterozygosities. You wrote “the total between genetic CR and CR+P variance is 10.8% and 15.5% respectively.” I can’t ascertain for sure what you mean here as you are confusingly mixing the ideas of total and between. For the equation you came up with to relate IQ to Fst, on the side of the equation dealing with IQ, you should have something equal to the IQ analogue of Fst, but you don’t. Once again, Fst = (Ht – Hs)/Ht with t=total and s=within subpopulation but you instead have written the IQ equivalent of something like Fst = Hb/(Hb + Hs) with s=within and b=between. The closest thing to an Hb is the Fst itself so you have something like Fst = Fst/(Fst + Hs) which is obviously false. The correct relation would be Fst = (Ht – Hs)/Ht –> Ht(Fst) = Ht – Hs –>
    Hs = Ht – Ht(Fst) –> Hs = Ht(1 – Fst) –> Ht = Hs/(1 – Fst)
    translated:
    Fst = between genetic variance proportion = 0.15 = between IQ variance proportion = (total IQ variance – within IQ variance)/(total IQ variance)
    –> total IQ variance = within IQ variance/(1 – 0.15) = 225/0.85 = 264.7

    You have:
    “[.24/.36 = between variance for IQ/(225 + between variance for IQ); solve for between group variance = 68/127. ”
    “Adjusting accordingly, the between individual, between CR and CR + P total variance is 24% and 36%.”
    “Using Cavalli-Sforza’s estimates (in Barbujani et al., 1997), the total between genetic CR and CR+P variance is 10.8% and 15.5% respectively.”

    Back to the previous analysis. Now that you have the total IQ variance = 264.7 there then remains the question of how to interpret this. The most analogous way to interpret it would be to treat it as the variance of the IQ distribution formed by mixing, with equal weights, the normal IQ distributions of the two populations (races) being compared. The distribution that is formed is not normal. It is possible to derive what the difference between the means of the 2 race-specific IQ distributions would have to be to yield a total variance of 264.7 but I have no idea how to actually go about solving such a(n) (I think) challenging problem.

    You can’t analyse the 15% figure properly without grounding the analysis with a firm understanding of Fst. Fst is where the number comes from.

    There is more to say but I have other things to do and I have given you plenty to chew on for now.

    • Chuckwiththehippo says:

      “To my mind there many things wrong with the analysis. There is the way you inflated the between population variance based on spurious notions about within-individual variance versus between-individual variance within a population. That is something that you are proposing here that does not make any sense to me and that I have not seen elsewhere. To explain what is wrong with it I have to refer to the details of Fst and heterozygosity because that is where these numbers are coming from. This is an important point as you have more than doubled the estimates of the variances based on this idea.”

      This idea comes from Harpending in Sarich and Miele’s “Race: The Reality of Human Difference”:

      “Yet the world had to wait until 2002 for someone to explain the basic problems with Lewontin’s famous 15 percent. It was Henry Harpending replying to a question from Frank Salter. Lewontin had noted that 85 percent of the genetic variability was among individuals within populations, and only an additional 15 percent was added when individuals in different populations were compared. However, this analysis omits a third level of variability—the within-individual one. The point is that we are diploid organisms, getting one set of chromosomes from one parent and a second from the other. To the extent that your mother and father are not especially closely related, then, those two sets of chromosomes will come close to being a random sample of the chromosomes in your population. And the sets present in some randomly chosen member of yours will also be about as different from your two sets as they are from one another. So how much of the variability will be distributed where?

      First is the 15 percent that is interpopulational. The other 85 percent will then split half and half (42.5 percent) between the intra- and interindividual within-population comparisons. The increase in variability in between-population comparisons is thus 15 percent against the 42.5 percent that is between-individual within-population. Thus, 15/42.5 = 35 percent, a much more impressive and, more important, more legitimate value than 15 percent.”
      …………..
      I’m just putting Harpending, Sarich, Miele, Levin, and Meisenberg’s point together. As it is, I tend to trust their interpretation of this more than yours. My reasoning follows from the claim that “85 percent of the genetic variability was among individuals within populations, and only an additional 15 percent was added when individuals in different populations were compared.” So, as best I can tell, the issue isn’t my argument but rather the premise that: “85 percent of the genetic variability is among individuals within populations, and only an additional 15 percent was added when individuals in different populations were compared.”

      If we agree on this point then I am up for discussing Fst values and the true meaning of the findings. If not explain what is wrong, given the above premise.

  16. “I’m just putting Harpending, Sarich, Miele, Levin, and Meisenberg’s point together. As it is, I tend to trust their interpretation of this more than yours. My reasoning follows from the claim that “85 percent of the genetic variability was among individuals within populations, and only an additional 15 percent was added when individuals in different populations were compared.” So, as best I can tell, the issue isn’t my argument but rather the premise that: “85 percent of the genetic variability is among individuals within populations, and only an additional 15 percent was added when individuals in different populations were compared.”

    If we agree on this point then I am up for discussing Fst values and the true meaning of the findings. If not explain what is wrong, given the above premise.”

    You have provided some original analysis here, no? It would be helpful if you provided quotes of the relevant material. You reference Miele discussing Harpending. Can you give a direct quote from Harpending? What was said doesn’t make sense to me. If you read what I wrote (skim it if you will) you will see that I directly addressed what people refer to with the 15% vs. 85%. I don’t deny that they refer to this often. You should also reference professionals in the field and not just race realist commentators. There is an issue with your argument. Check again.

    “You also seem to be confused about “between” and “total”. When it is said that Fst measures the proportion of variance that is between-population what is meant is that the ratio of the within-variance to the total variance is treated as the proportion of variance that is within-population and what is left over is treated as the proportion that is between-population. Mathematically Fst = (Ht – Hs)/Ht –> Fst = 1 – Hs/Ht –> 1 = Fst + Hs/Ht. Therefore Fst = between-variance proportion and Hs/Ht = within-variance proportion. But the actual variances are Hs and Ht, the heterozygosities. You wrote “the total between genetic CR and CR+P variance is 10.8% and 15.5% respectively.” I can’t ascertain for sure what you mean here as you are confusingly mixing the ideas of total and between. For the equation you came up with to relate IQ to Fst, on the side of the equation dealing with IQ, you should have something equal to the IQ analogue of Fst, but you don’t. Once again, Fst = (Ht – Hs)/Ht with t=total and s=within subpopulation but you instead have written the IQ equivalent of something like Fst = Hb/(Hb + Hs) with s=within and b=between. The closest thing to an Hb is the Fst itself so you have something like Fst = Fst/(Fst + Hs) which is obviously false. The correct relation would be Fst = (Ht – Hs)/Ht –> Ht(Fst) = Ht – Hs –>
    Hs = Ht – Ht(Fst) –> Hs = Ht(1 – Fst) –> Ht = Hs/(1 – Fst)
    translated:
    Fst = between genetic variance proportion = 0.15 = between IQ variance proportion = (total IQ variance – within IQ variance)/(total IQ variance)
    –> total IQ variance = within IQ variance/(1 – 0.15) = 225/0.85 = 264.7”

    • Chuck says:

      I’ll have to look into it latter. To clarify:

      “You wrote “the total between genetic CR and CR+P variance is 10.8% and 15.5% respectively”

      By “total between genetic variance,” I just mean “between genetic variance (with respect to the total amount of variance — as opposed to with respect to the variance for trait X genes). The question is: how much between population phenotypic variance in trait X (which has an SD of 15) would be predicted if there was a 1 to 1 correlation between phenotype and genotype for that trait and if the genes for trait X were dispersed randomly throughout the (total) genetic variance, and if there was a 15% genetic variability between populations.

      Here was Levin’s analysis:

      A related issue concerns between-group differences in gene frequency. With striking consistency, the variance in gene frequencies within single populations, including small communities, has been found to be 85% of the variance in frequencies across the human race (Barbujani, Magagni, Minch, & Cavalli-Sforza, 1995; Jorde, Watkins, Bamshad, Dixon, Ricker, Seielstad, & Batzer, 2000), a finding sometimes cited to show that the between-group variance component is too small to support the race concept. Cavalli-Sforza, Menozzi, and Piazza (1994, p. 19) write….

      ….And the variance data too must be interpreted carefully, for, given reasonable assumptions and standards of importance, a 15% between-group variance component may be highly important. To take a simplified but not wholly unrealistic example, suppose variation among certain genes corresponds in 1-1 fashion to a normally distributed phenotype, for instance IQ. In particular, imagine equally numerous populations A and B for which µ(A) = 95 and µ(B) = 105, while ƒÐ(A) = ƒÐ(B) = 14 (var = 196). Then var for A ¾ B is 225, of which the betweengroup component is somewhat less than 15%”

      ,,,,,,,,,

      “You have provided some original analysis here, no? It would be helpful if you provided quotes of the relevant material. You reference Miele discussing Harpending”

      As best I can tell, nothing I’m saying is original. As for Harpending: henry.harpending@anthro.utah.edu

  17. I now realize that I made a pretty big mistake. I still think that your inflation of the Fst is invalid (at least if you are going to use it to estimate the racial difference in mean IQ) but my criticism of your formula for calculating the between variance was wrong. I mistakenly thought that the heterozygosities were a type of variance and that the Fst was not based on properly defined statistical variances. The following website was very helpful to me for clearing up these issues:
    http://www.uwyo.edu/dbmcd/molmark/lect05/lect5.html

    Now to the inflation of the Fst. The formula you used related the inflated Fst to the IQ analogue of the Fst. But that doesn’t make sense (from what I can tell). Now, assuming Harpending actually said what Miele claims he said, and what he said was true, it still seems to me that you incorrectly inflated the Fst for your calculation. Let me explain. Harpending seems to be proposing an alternative to Fst. But in the formula you are using this alternative to Fst as though it was Fst. To use the alternative to Fst (ie the inflated Fst) you would have to equate the alternative with the IQ analogue of the alternative to Fst not the IQ analogue of the regular Fst.
    0.15 = Fst = between-variance/total-variance = (between-variance)/(between-variance + within-variance)
    While the alternative that Harpending is proposing relates between-individual-within-population to between-individual-between-population variances. But what would the IQ analogue to these variances be? What would the within-individual variance of IQ be? It makes no sense (or if it does it would be great to have an explanation). But you are clearly using straightforward IQ analogues to between-variance and within-variance not IQ analogues to between-individual-within-population and between-individual-between-population variances. Hence you should be using the regular Fst for your calculations.
    So we would have:
    Fst = 0.15 = between-variance/total-variance = (between-variance)/(between-variance + within-variance)
    –> between-IQ-variance = 225(0.15)/0.85 = 39.7
    and racial difference in mean IQ = 2(sqrt(39.7)) = 12.6 IQ pts = 0.84 stdv
    Therefore the analysis would predict a Black-White genotypical mean IQ difference of 0.84 stdv.

    • Chuck says:

      While we’re at it, maybe you had an idea about this one:

      “I’m looking over Wicherts’ African IQ data. Wicherts states: “The full database includes 109 samples totaling 37,811 test-takers. The N-weighted mean of
      these studies is 76.5 (SD=6.7),” (in “The dangers of unsystematic selection methods and the representativeness of 46 samples of African test-takers” page 32.)

      In all the samples reported, the African SDs are lower than European SDs, For example, in “A systematic literature review of the average IQ of sub-Saharan Africans,” Wicherts notes:
      “Hence, the SD of IQ in African samples appears to be around 13 and sampling bias does not appear to be an issue in the current review.”

      Now, referring back to the average of 76.5, is this condition on a pooled standard deviation of 15? Obviously, if the African SD was 13 and the European SD was 15, the pooled SD would be 14 (assuming equally numerous people). A 23.5 point gap (based on different SDs) would then translate into 1.68 SD gap or 25 point gap on White metrics. I’m guessing that the adjustments have already been made — I was curious as to your opinion”

  18. Chuck says:

    “While the alternative that Harpending is proposing relates between-individual-within-population to between-individual-between-population variances. But what would the IQ analogue to these variances be? What would the within-individual variance of IQ be? It makes no sense (or if it does it would be great to have an explanation).”

    Yes, I’m using an IQ analogue (and assuming a 1:1 relation between genotypic and phenotypic IQ).

    Genetic (total) variance: 15% between populations/ (42.5% within populations, between individuals) + ((42.5% within populations, within individuals)

    Genotypic/Phenotypic IQ variance: y% between populations/ z%within population.

    Now, as you say, when we talk about phenotypic differences and the genetic variance that mediates them, the 42.5% within population, within individual genetic variance is irrelevant. So we have to extract it, giving us 35%/65%

    Genetic (total) variance: 35% between populations/ 65% within populations (between individuals)
    Genotypic/Phenotypic IQ variance: y% between populations/ z%within population. (between individuals)

    Relative to the genotypic variance that mediates phenotypic variance, the total genotypic variance between and within population is greatly inflated, which was Harpending’s point.. Hence we have, using your much simplified formulation, (thanks):

    between-IQ-variance = 225(.35)/(.65) = 121
    [or should it be: between-IQ-variance = 225(.15)/(0.425) = 79]?
    and racial difference in mean IQ = 2(sqrt(121)) = 22 IQ pts = 1.47 SD

  19. “While we’re at it, maybe you had an idea about this one:

    “I’m looking over Wicherts’ African IQ data. Wicherts states: “The full database includes 109 samples totaling 37,811 test-takers. The N-weighted mean of
    these studies is 76.5 (SD=6.7),” (in “The dangers of unsystematic selection methods and the representativeness of 46 samples of African test-takers” page 32.)

    In all the samples reported, the African SDs are lower than European SDs, For example, in “A systematic literature review of the average IQ of sub-Saharan Africans,” Wicherts notes:
    “Hence, the SD of IQ in African samples appears to be around 13 and sampling bias does not appear to be an issue in the current review.”

    Now, referring back to the average of 76.5, is this condition on a pooled standard deviation of 15? Obviously, if the African SD was 13 and the European SD was 15, the pooled SD would be 14 (assuming equally numerous people). A 23.5 point gap (based on different SDs) would then translate into 1.68 SD gap or 25 point gap on White metrics. I’m guessing that the adjustments have already been made — I was curious as to your opinion””

    In the paper they indicate that they calculated “mean IQ in terms of British norms after correction for the Flynn effect”. I don’t know what sort of corrections they made for the Flynn effect. Based on that quote from the paper and also on how “foreign” IQs are usually calculated, I expect that they simply took the average of the African IQs based on the IQ distribution of Britain. That is, the IQs were probably calculated based on the same standard deviation and mean as for the British distribution.

    Also, the standard deviation of pooled samples is always larger than the average of the standard deviations of the constituent samples. The standard deviation of the pooled sample can even be larger (much larger) than any of the constituent samples’ standard deviations. That is because the differences in the means of the constituent samples result in a greater spread for the resultant distribution. The resultant distribution has “heavy tails”. eg take 2 samples each with an SD of 1 and a difference in means of 50, pool them and you get a crazy bimodal distribution with a much larger SD than 1.

    • Chuck says:

      When you compare 2 groups, usually you divide the difference by the SD of the pooled IQ:

      (Xa-Xb)/Square root [ (Na SDa^2 + Nb SDb^2)/Na + Nb)]

      X = mean
      N= population size
      SD = SD

      (Assuming normal distributions) the pooled SD is necessarily intermediate to the two population SDs.
      Example: Assume equal population sizes and respective SDs of 15 and 13: Square root [ (15^2 + 13^2) / (1 + 1)] = 14

      ……………..

      So my question was something like — are the African IQs in European SDs? I mean, if the African SD was only 6.5 and the mean was 76.5, that means that only 2.5% of the African IQ can get equivalent to a European 90. It’s hard for me to believe that. On the other, It’s not obvious to me how one can correct for the SD and put it in European metrics.

      ……………

      Anways —

      With regards to the other question, assuming we factor out the within population within individual variance:

      between-IQ-variance = 225(.35)/(.65) = 121??

      or should it be: between-IQ-variance = 225(.15)/(0.425) = 79]?

      or neither? What’s your opinion?

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