Problems with Fryer’s environmentalist proof

Note: When I started to write this, I briefly thought that Fryer and Levitt where onto something. After a few minutes of investigation I discovered otherwise. I’m posting this solely as a record of my investigation.

I see that Fryer and Levitt keep advancing their environmentalist argument. The basic argument is:

The Black-White gaps by age are: Adulthood 1 SD; Childhood .85 SD; Infancy .077 SD. The Phenotypic correlations are as follows: Mother-Infant .3, Mother Child .39, Infant-Child .30. Given the inter-correlations the magnitude of the infant Black-White gap is too small to be consistent with a genetic hypothesis of any significant magnitude.

(Gaps with age from Fryer 2010:

In Testing for Racial Differences in the Mental Ability of Young Children, Fryer and Levitt note that:

“An alternative model is one in which an individual’s intelligence has not yet fully developed at age 1, but otherwise the restrictions in the simple model are maintained. In the most extreme conceptualization of this view, one would assume that I = 00 for all individuals. Such a model can generate a small racial test score gap early in life and a one-standard deviation gap later in life if W > B. Most importantly, the model cannot explain how one observes a similar degree of correlation between parental test scores and their children’s test scores both early and later in life. Given the high degree of heritability in intelligence, one would expect that if early test scores do not reflect intelligence, then they should correlate much less strongly with parental test scores than later tests. (Fryer and Levitt, 2006. Testing for Racial Differences in the Mental Ability of Young Children.)

It’s not clear what Fryer and Levitt mean when they speak of intelligence being “not yet fully developed” or speak of tests which do not fully “reflect intelligence.” The relevant questions are (a) “Do the test score differences at age 1 capture the magnitude of the general intelligence difference at age 1?” (b) “What are the within group heritabilities at the ages in question?” (c) “What are the between group heritabilities at the ages in question?” (d) “What are the genetic correlations between IQ at the various ages?” and so on.

As for (b) and (d), I emailed Fryer (a couple of years ago) and pointed to the literature on the relevant parent-offspring correlations. For example, Plomin et al. (1997):

Correlations between biological parents (weighted averages for mothers and fathers) and their adopted-away offspring also start off at modest levels at 3 and 4 years (.12). However, unlike adoptive-parent/ adopted-child correlations, correlations between biological parents and their adopted-away offspring increase during middle childhood (.18), early adolescence (.20), and late adolescence (.38). The increasing resemblance between adopted children and their biological parents, with correlations rising from about .1 in early childhood to about .2 in middle childhood to about .3 in adolescence, suggests increasing genetic influence. Results for control parents are similar to those for biological parents: Correlations of .19 in early childhood, .24 in middle childhood, .28 in early adolescence, and .31 in late adolescence indicate again that parent-offspring resemblance for general cognitive ability is largely due to genetic influences (Plomin et al 1997 Nature, Nurture, and Cognitive Development from 1 to 16 Years: A Parent-Offspring Adoption Study)

You can find this stuff in a standard behavioral genetics books (e.g., Plomin, 1984; Plomin et al., 2006):

“Thus, the frequently cited correlation of .00 between biological mothers’ IQ and the adoptees’ scores for their first testing on the Kuhlman Revision of the Binet could be misleading as an index. (Plomin, 1984. pg. 372)”

“For example, the IQ correlation between biological mothers and their adopted-away children in infancy is about .10″ (Plomin et al., 2006. pg. 144).”

The mid-parent-offspring correlation can be seen as a rough index of the portion of the correlation that is genetically mediated. Alternatively, you can merely multiply the 0.5 genetic correlation between parent and child by the estimated heritability of IQ at the given ages. It’s difficult for me to understand how Fryer and Levitt missed this. Whatever the case, a slightly more informed version of the argument pops back up in Fryer (2010):

A model in which parents’ scores influence their offspring’s environment is, however, equally consistent with mean racial gaps in G of one standard deviation. For this to occur, G must exert little influence on the baby’s test score, but be an important determinant of the test scores of children. Take the most extreme case in which G has no influence on the baby’s score (i.e., _b = 0). If genetic factors are not directly determining the baby’s test outcomes, then environmental factors must be important. Assuming…. (Fryer, 2010. Racial inequality in the 21st century: The declining significance of discrimination)

In the discussion, Fryer makes a number of blunders such as telling us that “where the 0.5 in the first two equations reflect the assumed genetic correlation between mother and child, and the values 0.36, 0.39, and 0.30 are our best estimates of the empirical values of these correlations based on past research cited above….” Fryer cites Yeates, et al (1983), who give simple parent-offspring correlations which aren’t genetically informative. Moreover, the “assumed genetic IQ correlation between mother and child,” as noted above, would not be 0.5.

And an important consideration that Fryer neglects is the genetic correlation between IQ at age 1 and other ages. IQ at two ages can be perfectly heritable but genetically uncorrelated, such that the genes that explain variance at one age do not explain variance at another. As for the genetic correlation between ages 1 and on, it’s not clear. Typically, it’s found to be significantly less than 1 (Brody, 1992 pg. 160; see also Plomin et al. 2008 pg. 169.). To the extent different genes are involved at different ages, genetic variance between populations at one age does not necessitate genetic variance at another.

Whatever the case, we then have the following:

Phenotypic correlations (Fryer, 2010)
Mother-Infant .3
Mother Child .39
Infant-Child .30

Correlations mediated by genes (Plomin et al., 1997; Brody, 1992)
Midparent-infant <.1
Midparent-Child .2
Infant-Child undetermined but <.3

Gaps (Fryer, 2010)
Adult 1
Childhood .83
Infancy .077

Now what is readily noticeable is that the Black-White Infant phenotypic gap is noticeably smaller than one would predict given the Adult phenotypic gap and the portion of the correlation attributable to the environment. It should be 1SD x (Mother-Infant Phenotypic correlation – Mother-Infant genotypic correlation). Following Fryer and Levitt's own logic, we can conclude that there are factors boosting the performance of Black infants relative to White infants. This positive influence, of course, would work against any negative influence due to general intelligence genes.

Anyways, after inputting the correct values we see that there is no inconsistency except that the childhood gap is larger then it should be were g genes alone involved. (But we already know this.)

Now there are other points that can be made but will not be because the above is more than sufficient to dismiss this silly argument — one of least informed that I’ve seen — which will no doubt be cited by others.


Brody, 1992. Intelligence

Plomin, 1986. Development, genetics, and psychology

Plomin et al., 1997. Nature, Nurture and Cognitive development from 1 to 16 years: A parent offspring adoption study.

Plomin et al., 2006. Nature and nurture during infancy and early childhood

Plomin et al., 2008. Behavioral genetics

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11 Responses to Problems with Fryer’s environmentalist proof

  1. j says:

    did fryer e-mail you back? isn’t he like a big harvard superstar black researcher or something?

    • Chuck says:

      No, he didn’t…but I think my email led him to modify his conclusion from “Most importantly, the model cannot explain…” to “A model in which parents’ scores influence their offspring’s environment is, however, equally consistent with mean racial gaps in G of one standard deviation.” He still goofed the latter argument.

  2. j says:

    Economist lists Fryer as one of the top 8 young economists in the world.[9] In 2011, Fryer was a recipient of a MacArthur Fellowship, commonly referred to as a “Genius Grant”.[10]

    So is this guy really as brilliant as he’s made out to be?

  3. Kiwiguy says:

    There’s now a debate on Straightdope about whether differences are largely genetic. Not sure if I can be bothered. May see how bad the comments are.

  4. j says:

    Where’d your latest post go?

  5. x says:

    or just give me yours so i can contact you privately

  6. x says:

    thanks, having trouble with the PW you sent tho.. it wont let me log in

  7. x says:

    done & done – emails gone, posts gone (but they are still available for you) i did not do anything else. change the password now i would recommend.

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