Home > Uncategorized > Magnitude of the B-W IQ gap projected to 2008

Magnitude of the B-W IQ gap projected to 2008

(Edit: I incorrectly recorded the WAIS IV (2008) difference as .97 SD; the correct difference is 1.06SD. I adjusted the numbers in my chart, but I did not update the graphs or other calculations)

Recently, a number of folk have been declaring that the B-W IQ gap is rapidly narrowing (Flynn and Dickens 2006a; Flynn and Dickens 2006b; Nisbett, 2010; Sackett and Shen, 2008). Since closing the B-W gap is “the greatest civil rights issue of our times” (Paige, 2009) and since White (conservative) Europeans will be held responsible until the gap is closed (Rusthton and Jensen 2005), this is welcome news. The curmudgeon L. Auster summarizes the situation well:

Liberalism says that all racial and ethnic groups are equally endowed with intelligence, and prohibits any disagreement with that idea, on pain of the destruction of one’s career and place in society. But in reality blacks are significantly less capable than whites and significantly more badly behaved than whites according almost every socioeconomic indicator that matters. Since liberalism holds that all groups have the same abilities, and requires that everyone believe that all groups have the same abilities, the inferior performance of blacks cannot be due to their lesser abilities and aspirations; it must be due to some force outside themselves. And since the Civil Rights movement established it in people’s minds that whites are guilty for all black problems, the idea of white guilt continues to be applied today. Blacks’ lesser performance and outcomes are caused by something whites are doing to, or failing to do for, blacks. Whatever the specific bad thing whites are doing, or whatever specific good thing they are failing to do, it always comes down in the end to white racism. White racism is the cause of black failure.

That blacks, on average, have a lower level of general intelligence (g) than Whites or Yellows is no longer a matter of dispute. Nor is that this lower level contributes significantly to the oft fretted about disparities. So, given the setup, it’s good to hear that the g gap is finally narrowing. Claims of a narrowing, elicit two questions: what is it’s present magnitude of the gap and when did the narrowing occur. If the narrowing was recent we can infer a trend. Let’s address that first question.

A brief history of the Gap

The first quantitative estimate of the racial gap was made by Francis Galton. In Hereditary Genius (1869), he writes:

I have often discussed this subject with competent persons, and can only recall a few cases of the inferiority of the white man,—certainly not more than might be ascribed to an average actual difference of three grades, of which one may be due to the relative demerits of native education, and the remaining two to a difference in natural gifts

Two Galtonian grades between Africans and Europeans is equivalent to 21 IQ points. Since Africans are 25% Caucasian and IQ is a highly polymorphic trait, this would give us an estimate of 84.24 for the “genotypic” African-American IQ. One century after Galton’s publication of Hereditary Genius, Authur Jensen published his 1969 Harvard Educational Review article, which set in motion the IQ wars. Jensen estimated that the average African-American/ European-American IQ gap was 15 points, and he speculated that 50% to 75% of this 1 SD difference had a genetic basis:

It is a subject with a now vast literature which has been quite recently reviewed by Dreger and Miller (1960, 1968) and by Shuey (1966), whose 578 page review is the most comprehensive, covering 382 studies. The basic data are well known: on the average, Negroes test about 1 standard deviation (15 IQ points) below the average of the white population in IQ, and this finding is fairly uniform across the 81 different tests of intellectual ability used in the studies reviewed by Shuey.

More recently, Jensen and Rushton (2005) put the phenotypic gap at 1.1 SD with a genotypic gap 20% to 50% less than that. Estimates of “the IQ gap,” though, are complicated by age differences, as the B-W IQ gap now appears to increase with age (Jensen 1998; Murray 2005; Flynn 2006). The gap didn’t always change, as can be seen in Figure 2, which is why hereditarians as recent as 2005 argued that the gap was constant across the development period (e.g. Gottfredson, 2005; Rushton and Jensen, 2005). Gottfredson (2005), for example, notes that:

The black-white gap is no different at age of school entry than at age of school exit twelve years later. It has been found at age 3, which is about as young as intelligence can be measured using standard IQ testing procedures. There are fewer studies for other racial-ethnic groups in the U.S., but their averages also seem to have remained stable relative to the European-white average.

The contemporaneous increase in the gap with age — or, to put it another way, the recent reduction in the gap via intervention at younger ages — is an interesting phenomena and one that is both problematic for and potentially explainable by both environmentalists (e.g. Vincent, 1991) and hereditarians (e.g Murray 2005). Presently, though, we are interested in the average magnitude of the gap.

Recent IQ closure

Flynn and Dickens (2006) claim that the B-W IQ gap has narrowed .33 SD, across ages, relative to Jensen and Rushton’s (2005) estimate of 1.1 SD. They base this claim on norming data from the AFQT, Stanford-Binet, WISC, and WAIS (median age 15). Rushton and Jensen (2006/2010) issued a rebuttal, arguing Flynn and Dickens excluded pertinent data; Murray (2006) offers additional evidence form NLSY in support of Rushton and Jensen.

To assess the change in the gap with the “totality of the evidence” included, I plotted the change over time using scores from the AFQT, Stanford-Binet, WISC, WAIS, WAIS, Raven, Woodcock, DAS, Wonderlic, and NLSY Peabody (i.e. every test mentioned by Flynn (2006) and J & R (2006/2010), except Kaufman ABC for the reason Jensen (1998), Murray (2005), and Flynn (2006) gave. [1])

With all of the scores added, there is still a narrowing. It seems that the IQ gap is .9SD — which is what one gets if one just averages the score differences of the top 5 well standardized IQ/g loaded tests (WISC, WAIS, Binet, AFQT, Woodcock) or if one averages the most recent differences of all of the IQ/g-loaded tests mentioned, minus Kaufman. One could quibble over whether there was a .2SD reduction relative to an estimated 1.1 SD gap or just a .1SD reduction relative to a 1SD gap – but there was a reduction and “the gap” stands at about ~.9 SD. (If one wanted to niggle over a few points, one could argue that the total gap projected to 2008 is ~.95 SD. See: note 3)

Sailer and a few gene expression bloggers suggested that the narrowing could have been among the youth, but it seems that Flynn and Dickens were correct about the across the age spectrum narrowing. Using the age breakdowns found in Gottfredson (2005) and Dickens and Flynn (2006), I was able to generate the graph below. (The graph is a rough approximation. Not having the full age breakdowns, I had to make a few judgement calls when it came to assigning scores to age groups).

My guess is that we are seeing two things. There was a gap narrowing which acted across the age spectrum and which resulted from social changes in the 60’s and 70’s (e.g. Chay, et al. 2009, Murray, 2007); and there was, is, and will be an ongoing closing which is concentrated in the youths. The occurrence of these two narrowings together is leading to the divergence of interpretation (e.g Murray, 2007; Dickens and Flynn, 2006; R & J, 2010). Flynn, for example, sees an across the age narrowing of .33SD, yet if we go with Flynn and Dickens’ .33SD estimate (see figure above), the 1972 age 24 gap would have been 1.5 SD — as derived from data which shows a maximum gap of 1.23 SD! Rushton and Jensen on the other hand argue that the narrowing was only .2SD at max, yet the present age 2-12 gap says otherwise.

Other more contemporaneous evidence

We can fill out our estimate of “the gap” by including more contemporaneous evidence. There has been apparently little change in the high stakes test gap (age 18-26)

High stakes

SAT (V+M) 08’ .99 (87’ .99)
ACT (composite) 07’ 1.02 (97‘ .98)
GRE 88’-97 1.34
(change + 0)

There has been quite a bit of narrowing on academic achievement tests (age 6-18), though the scores are consistent with a 1.1SD difference. (The maximum the IQ gap could be, based on .81M+V gap and assuming .7 assessment-IQ correlation, is 1.16.)

70’s NAEP M+V= 1.04
90’s NAEP M+V = .81 Change = -.23

70’s NAEP,EEO,PSID, ECLS-K = .95
97-04’ NAEP,EEO,PSID, ECLS-K = .81
Change = -.14

The persistence of the achievement gap on high stakes tests suggests that the Black IQ is not exactly skyrocketing. Nonetheless, the score increases on the gold-standard IQ tests have to be given some weight when assessing the magnitude of the IQ gap. That said, a contemporaneous gap of .9 SD is still a good deal above Jensen’s suggested genotypic gap of .5 to .75 [2] — even after 4 decades of extensive intervention directed at closing it.


[1] Murray, 2005. Inequality Taboo.

The Kaufman Assessment Battery for Children (K-ABC) is a test that has consistently shown smaller black-white differences than other IQ tests. There are a number of reasons for this, one being that subtests showing large black-white differences were excluded (the K-ABC includes forward-digit span but not backward-digit span, for example). See Jensen (1984) for a full discussion. But though the black-white difference is smaller, it has not changed. In the manual for the original standardization published in 1983, the means on the “Mental Processing Composite” ( K-ABC’s version of an IQ score) for the white and black samples were 102.0 and 95.0 respectively (A. S. Kaufman and Kaufman 1983: 152). Twenty-one years later, those means were both within a point of their 1983 values—102.7 and 94.8 respectively (A.S. Kaufman and N.L. Kaufman 2004: 96). Which is more meaningful? The smaller black-white difference shown by the K-ABC? Or the absence of any convergence over time?”

[2] The genotypic gap can operantly be defined as the gap that remains after environmental factors are controlled for. Gap (genptypic) = gap (phenotypic) – gap (environmental)

[3] The across age gap would be:


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

Dickens and Flynn, 2006. Common ground and differences

Chay, et al., 2009. Birth cohort and the black-white achievement gap: The roles of access and health soon after birth

Galton, 1869. Hereditary Genius

Gottfredson, 2005. Implications of cognitive differences for schooling within diverse societies

Gottfredson, 2006. Social consequences of group differences in cognitive ability

Jensen, 1969. How Much Can We Boost IQ and Scholastic Achievement?

Paige, 2009. The Black-White Achievement Gap: Why Closing It Is the Greatest Civil Rights Issue of Our Time

Sackett and Shen, 2008. Subgroup differences on Cognitive tests in contests other than personal selection

Murray, 2007. The magnitude and components of change in the black-white IQ difference from 1920 to 1991: A birth cohort analysis of the Woodcock-Johnson standardizations

Murray, 2006. Changes over time in the black-white difference on mental tests: Evidence from the children of the 1979 cohort of the National Longitudinal Survey of Youth

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

Rushton and Jensen, 2005. “Thirty years of research on race differences in cognitive ability

Vincent, 1991. Black/white IQ differences: Does age make the difference

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