The Abilities of Man: Their Nature and Measurement

Spearman's central thesis is that all cognitive performances can be expressed as a linear function of two factors: a general factor 'g' common to all abilities, and a specific factor 's' unique to each task . He rejects both the 'unitary intelligence' view that a single test can capture intelligence directly and the 'faculty' doctrine that broad powers like judgment or memory function as independent units . The tetrad difference equation — that for any four abilities, the products of alternating correlations should be equal — serves as his mathematical proof that only one common factor exists . This was a more rigorous formulation than his earlier work on the same theme.

The Nature review (August 1927) launched a detailed statistical assault on Spearman's evidence, arguing that he had made his mean tetrad difference artificially zero by rendering the distribution symmetrical, and that he provided no real test of whether tetrads differed from zero within random sampling limits . The reviewer noted a scale error in one diagram where tetrad differences were given one-tenth their true values, and calculated that for Simpson's 3003 tetrads, the observed mean squared tetrad differed from the theoretical value by some 8.8 times the probable error — a 'signal failure' rather than striking agreement . Spearman published a rebuttal in Nature (November 1927), acknowledging the controversy but defending his approach .

The tetrad difference equation, derived from the assumption that 'g' correlates with all abilities while specific factors are mutually uncorrelated, provided the first testable criterion for a single common factor in a correlation matrix . If tetrad differences vanish within sampling error, Spearman argued, the two-factor theory is confirmed; if not, the theory fails. This criterion became a foundational problem in factor analysis, though the tetrad method was later superseded by multiple-factor techniques . Spearman's approach is historically significant as the first attempt to determine the dimensionality of mental ability through mathematical rather than introspective means, a question that continues to drive psychometric research.

Thurstone's The Vectors of Mind (1935) argued that Spearman's two-factor method was 'inadequate to analyze the multi-dimensionality of mental traits' because it assumed a single general factor and could not deal with group factors that appear when tests share more than just 'g' . Using improved matrix algebra and a battery of 57 tests on large samples, Thurstone concluded that seven primary abilities fitted the data better than one 'g' . Eysenck later argued the apparent conflict was partly methodological: Spearman worked with random samples and selected heterogeneous tests, while Thurstone used students and more homogeneous tests, which artificially created group factors . Thurstone later incorporated hierarchical structure with 'g' at the top .

The book synthesized over twenty years of work by more than thirty of Spearman's students and colleagues at University College London, including Holzinger, whose data on 378 tetrads Spearman cited as evidence . The collaborative nature was central to Spearman's method: he directed a research program in which pupils tested the two-factor theory across diverse populations and test batteries. A Mental Welfare review noted that Spearman admitted the existence of certain limited and supplementary capacities but maintained they were 'extremely specific' and often acquired rather than inborn . The book stands as a cumulative record of this collective empirical enterprise.

Both. The specific claim that the tetrad equation proves the existence of 'g' has not survived statistical scrutiny — the Nature reviewer's objections about non-normal tetrad distributions and correlated tetrads were never fully answered . However, the book's core insight that correlations among diverse cognitive tests reflect some common source remains central to psychometrics. Modern factor-analytic research consistently finds a higher-order general factor, though whether it is 'the same' as Spearman's 'g' or an artifact of test selection remains debated. The Abilities of Man is indispensable for understanding how the quantitative study of intelligence began and why its central concept remains contested.