Comments on Fagan and Holland (2007)’s racial equality paper

Someone sent me some questions on this study:

African-Americans and Whites were asked to solve problems typical of those administered on standard tests of intelligence. Half of the problems were solvable on the basis of information generally available to either race and/or on the basis of information newly learned. Such knowledge did not vary with race. Other problems were only solvable on the basis of specific previous knowledge, knowledge such as that tested on conventional IQ tests. Such specific knowledge did vary with race and was shown to be subject to test bias. Differences in knowledge within a race and differences in knowledge between races were found to have different determinants. Race was unrelated to the g factor. Cultural differences in the provision of information account for racial differences in IQ.

I don’t recall reading it before, but I can see why environmentalists would love it. It has 44 citations according to GScholar.

Fagan (1992, 2000) assumes that the IQ score is a measure of knowledge. Knowledge depends on information processing ability and on the information given by the culture for processing. The term intelligence, in Fagan’s theory , means information processing ability. Fagan assumes that not all have had equal opportunity for exposure to the information underlying the knowledge being quizzed on standard tests of IQ. Given such assumptions, if group differences in IQ are not accompanied by group differences in information processing ability, then group differences in IQ are due to differences in access to information.

Timeline of US Black-White gap based on ~100 datapoints of heterogeneous data. Orange line = linear fit (slope is ~0). Mean gap is different from the intercept because some datapoints had no test year, so weren’t used for the fit for the plot but were used for calculating the mean in the top left corner.

So, it’s an “equality of opportunity” argument. The basic idea doesn’t even pass the smell test. US Black-White IQ gap has been about constant for ~150 years (see figure), including with the advent of the internet and public libraries. Obviously, anyone who wants and is able to to learn stuff can very easily do so on the internet for free too. Yet the racial gaps stay the same. So, we know already that access to information is not a big independent factor. Rather, exposure to information is something that comes from within — smarter and more curious people seek out exposure to information. It’s textbook active gene-environment correlation.

The paper has a few fairly obvious methodological errors, aside from the small samples in some of their substudies (n’s = 77 students, 65 students, 86 students, 223 students). One of the more obvious ones is that they disregard group factors and differences in them. If we control for item performance on tests with “specific knowledge”, the group difference on other items may be zero, or it may not. It depends on various things like the g-loading of the “specific knowledge” items, measurement error, group differences on whatever abilities underlie performance on these kinds of items. Blacks have been found to have an advantage on some memory tests, for instance, when controls for g, indicating some advantage on non-g abilities related to that. See e.g.:

where they report group differences of:

These are from a bi-factor model, so the non-g gaps are independent of g (~same as controlling for g in a hierarchical model framework). We see that Whites seem to be quite a bit better at visual processing (d = 0.8) and maybe on verbal comprehension (d = 0.23), while Blacks did somewhat better on long-term retrieval (d = -.35). The latter two are quite uncertain (confidence interval is wide and close to 0).

The general issue with papers like Fagan is that they attack a strawman, namely that Black-White gap is IQ is solely due to gap in g factor. Here’s Jensen in 1985:

For the sake of precision, Spearman’s hypothesis should be stated in two forms that can be termed strong and weak, respectively, although Spearman himself did Black-white difference not suggest this distinction. The strong form of the hy­pothesis holds that the magnitudes of the black-white differences (in standard score units) on a variety of tests are directly related to the tests’ g loadings, because black and white populations differ only on g and on no other cognitive factors. The weak form of the hypothesis holds that the black-white difference in various mental tests is predominantly a difference in g, although the populations also differ, but to a much lesser degree, in certain other ability factors besides g.

Jensen has never subscribed to the strong form as far as I know, and indeed in his 1985 (!) study, he wrote that:

A study of the national standardization sample of the WISC-R (Jensen & Reynolds 1982), based on 1,868 white and 305 black children, bears out Spearman’s hypothesis but contradicts it in its strong form, because significant, but small, black-white differences were found on other factors besides g. When the WISC-R is subjected to a Schmid-Leiman hierarchical factor analysis, it yields four factors that are virtually identical for both populations: g, verbal, spatial, and memory. When factor scores on each of these four factors are computed for every black and white subject, the populations show significant mean differences on all four factors, a finding that contradicts the strong form of Spearman’s hypothesis. But the weak form is strongly upheld, as the g factor accounts for more than seven times as much of the between-population variance as the other three factors combined. Black testees exceed white testees on the Memory factor (0.32o-), whereas white testees exceed black testees on the g (1.14cr), Verbal (0.20rr), and Performance (0.20cx) factors.

See also:

Spearman’s Hypothesis holds that the magnitude of mean White–Black differences on cognitive tests covaries with the extent to which a test is saturated with g. This paper evaluates Spearman’s Hypothesis by manipulating the g saturation of cognitive composites. Using a sample of 16,384 people from the General Aptitude Test Battery database, we show that one can decrease mean racial differences in a g test by altering the g saturation of the measure. Consistent with Spearman’s Hypothesis, the g saturation of a test is positively and strongly related to the magnitude of White–Black mean racial differences in test scores. We demonstrate that the reduction in mean racial differences accomplished by reducing the g saturation in a measure is obtained at the cost of lower validity and increased prediction errors. We recommend that g tests varying in mean racial differences be examined to determine if the Spearman’s Hypothesis is a viable explanation for the results.

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