The Mismeasure Of Man

In Chapter 6, Gould provides a brief overview of the science of factor analysis. As a process of “attempting to discover ‘underlying’ structure in large matrices of data,” factor analysis reveals positive, negative, and zero correlations between different measurements (268). These correlations (relationships) are measured by the correlation coefficient r; however, Gould notes that correlation shows a relationship, only, and does not indicate cause (270, 273). As a mathematical tool, researchers can identify multiple factors of measurement and reduce them into fewer dimensions (the first principal component and second principal component) in order to simplify relationships and arrive at a reasonable explanation of results through inference (275, 280). Gould also notes that the first principal component is a representation of a “mathematical abstraction” and “not a ‘thing’ with physical reality” (280).

Gould then introduces Cyril Burt (1883-1971), an educational psychologist and advocate for the statistical analysis of IQ tests. Both Burt and his mentor and predecessor, Charles Spearman, recognized the importance of using factor analysis in “provid[ing] a theoretical justification” for their belief in heritable and measurable intelligence (269). However, it was Charles Spearman who first identified a correlation coefficient (g), which he claimed was the “unitary quality underlying all cognitive mental ability” (281). Gould notes that Spearman’s g attempts to serve as a measurement of intelligence; however, since g can be interpreted in “either a purely hereditarian or purely environmental way,” its measurement of intelligence is problematic (282). Moreover, since the components of g can be separated into two rotating axes, it is possible to avoid the conflating of intelligence factors altogether (285).

Gould then presents a closer examination of Charles Spearman (1863-1945), a psychologist and statistician who posited a “two-factor” theory to study intelligence testing, whereby variance for individual tests (s) and an underlying factor of intelligence (g) “would reduce to a single underlying entity” (287). In his original work, Spearman used a method for analyzing four measures, which he called the “tetrad difference” (288). According to this method, a tetrad value of zero indicates the existence of a single general factor. In finding evidence for the existence of g, Spearman determined that the best measure of g would be “the average score for a large collection of individual tests of the most diverse kind” (294). After identifying “a single abstract factor” for g, Spearman attempted to find a physical “form of energy” for g (296). By the publication of his last book, Spearman had stepped back from his efforts to locate g in a physical form.

In hereditarian theories, Spearman’s g represents the identification of intelligence as a “thing,” with the inference that it resides in a physical form. While Spearman shared basic views that the strength of a person’s g “reflects heredity alone” and that blacks performed most poorly on tests of “innate general intelligence,” he was not interested in using g to prove differences among groups of people based on gender, class, or race (300, 301).

Gould then reintroduces Cyril Burt and his belief in hereditarianism. In his studies of intelligence, Burt discounted the influence of environmental factors. Instead, he correlated intelligence with parental intelligence, and concluded that upper-class boys were “smarter,” while low-achieving students possessed “innate stupidity” (305, 310). However, when research questions focused on the less-controversial topics of juvenile delinquency and left-handedness, Burt was able to identify possible environmental factors for measured differences.

While Burt did not apply heritable intelligence to groups by race or gender, he was a firm believer that inherited intelligence was reflected in a person’s social class. In his discussion on factors of intelligence, Burt referenced three possibilities: 1) intelligence as a mathematical abstraction, 2) intelligence as physically identifiable properties within the brain, and 3) intelligence as categories of thought existing on a “psychic reality” (322).

In furthering Spearman’s work on factor analysis, Burt introduced an expansion of Spearman’s g and s to include additional “group factors” (additional specialized abilities) and “accidental factors” (attributes of a trait measured once)(316, 317). He also added a technique to calculate correlations between individual people (Q-mode factor analysis) (315). The political impact of his Q-mode factor analysis led to the testing and separation of British students into university (20%) or non-university (80%) tracks.

Gould then examines the work of L.L. Thurstone (1887-1955), a professor of psychology at the University of Chicago and the man responsible for problematizing Spearman’s g. Thurstone’s primary disagreement was in the placement of Spearman and Burt’s factor axes; he argued that “faculties of the mind” are measured by tests, but that they do not vary in position regardless of how many tests measure these factors (327). In Spearman’s model, g shifts depending on the type of tests that are included in the sample. In addition, Thurstone disagreed with Burt’s theory that his group factors could have a negative projection, as “a test could not have a negative projection upon a real vector of mind” (328).

To address these issues, Thurstone proposed calculating the Spearman-Burt principal components and “rotat[ing] them to different positions” until they match the positions of actual clusters of vectors. This reflected Thurstone’s “simple structure,” which redistributes information and implies that intelligence tests measure “a small number of independent” primary mental abilities (PMAs), which he also emphasized had, as a source, “inborn biology” (331, 336).

Thurstone had introduced a second school of factor analysis. With Spearman’s g, individuals could be tested and “ranked on a single scale of innate intelligence”; with Thurstone’s PMAs, individuals are shown to excel in “different and independent qualities of mind” (334). In response, Spearman and Burt claimed that Thurstone had merely produced “an alternative mathematics for the same data” (339). In later years, Thurstone introduced the idea of oblique axes (vs. his original criterion of perpendicular axes), which led to the introduction of a “second order g” (343).

Gould concludes the chapter with a reference to Arthur Jensen, America’s best-known modern hereditarian. In his writings, Jensen does not see Thurstone’s work as a criticism of Spearman’s g, in part due to the addition of a “second order g” (349). According to Jensen’s reading of Spearman and Thurstone, g remains a means of ranking human intelligence, and also a means of measuring the statistical difference in IQ between blacks and whites as “an innate deficiency of intelligence among blacks” (350).