Case Study Five: Black-White Convergence

Herrnstein and Murray review data showing a closing black-white test-score gap, and say, in summary, that what has occurred is "a narrowing of approximately .15 to .25 standard deviation units, or the equivalent of two to three IQ points overall," between blacks and whites.

Robert Hauser looks at this statement in some detail in a paper available on the Web. He found, first, that on the tests Herrnstein and Murray used, the closing of the gap was actually significantly greater. In an appendix they report that they lowered the figures by an apparently arbitrary discounting factor to account for the tests' not having been IQ tests per se. (As discussed above, they are happy enough to use imperfect stand-ins for IQ when the results serve their purposes.) Even with the discounting factor, Hauser found that on one test, the National Assessment of Educational Progress, the black gain was "between 2.5 and 3.4 points, which is not bad for aggregate change in an immutable quality over a twenty year period."

Then Hauser dug up the original data. He found that, "To begin with, several of the numbers in the table [on this subject in The Bell Curve] are simply wrong. There are no fewer than five copying or multiplication errors in age- and test-specific entries in the body of the table." Then he found that Herrnstein and Murray, by not reading the original data tables carefully, adopted a too-high measure of the standard deviation in the scores: "The effect of choosing too large a standard deviation was to understate both the initial black-white differences and the changes in test scores across time." Rerunning the data with a more accurate standard deviation, Hauser came up with a significantly higher black-white IQ convergence of between 3.5 and 4.7 points.

Murray would surely hasten to point out that since The Bell Curve was published, new data from the National Assessment of Educational Progress show that the closing of the black-white gap has stalled in recent years. Hauser is making a different point, though: Herrnstein and Murray misused the data that they had before them as they were writing, and their errors were all in the direction of minimizing the convergence in IQs between blacks and whites.

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