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Spearman, C. E.

Spearman, C. E.



Charles Edward Spearman (1863-1945) is known for two major contributions to behavioral science: a methodological one—what we now call factor analysis; and a substantive one—the development of a rational basis for determining the concept of general intelligence and for validating intelligence testing. In addition, his name is associated eponymously with the Spearman rank-order correlation coefficient. But few psychologists today would agree with his judgment that his most important work was the enunciation of noegenetic cognitive laws.

Spearman’s work on factor analysis and on intelligence are historically intertwined, and it would be difficult to say whether his philosophical interest in the notion of a single general ability forced him to study statistical correlational methods more creatively or whether his intrinsic love of clear and ingenious methods generated his two-factor theory of intelligence. The former is more likely. In any case, his 1904 article, “’General Intelligence’ Objectively Determined and Measured,” is a landmark in psychological thought and involves both of his major interests.

Factor analysis. Methodologically, Spearman began by recognizing that E. L. Thorndike, Clark Wissler, and James McKeen Cattell had failed to discover the structure of abilities through correlational methods; more particularly, they had been unable to find a general factor, because they had not allowed for the systematic influence of random error of measurement. Spearman demonstrated the attenuating effect of error on the correlation coefficient. Furthermore, he realized that the attenuation correction formula made it possible to discover what any two inter-correlated variables, X and Y, have in common with any other two intercorrelated variables, W and Z. This insight, backed by an evaluation of the standard error of the tetrad difference, led to the invention of factor analysis capable of demonstrating a single common factor plus specific factors. This made it possible to explain the individual differences in test scores as due primarily to differences in a single general ability as well as to something quite specific to each test. As Cyril Burt has pointed out, the beginning of the concept of factor analysis may be found in Karl Pearson’s work, but Spearman’s development of the concept cannot be explicitly traced to Pearson.

In the first quarter of this century the study, by tests, of individual differences grew apace, and Spearman’s discovery of factor analysis, as well as his statistical contributions in such formulae as the rank correlation coefficient and the Spearman-Brown prophecy formula, prevented the work in this field from becoming completely chaotic. (Since the more active and less scholarly failed to understand what Spearman was saying, the field became a sorry mess notwithstanding, especially in intelligence testing.) Spearman’s two-factor theory of intelligence—or of “g” as he preferred to symbolize the discovered general factor—states that any cognitive performance is a function of two “factors”—the general ability common to most cognitive performances and an ability specific to a given test. Since it is possible to determine this general factor objectively, disputes about the validity of intelligence tests can be settled by assessing the loadings of the tests on the general factor. High loadings have been found particularly for analogies, classifications, and series—either in words or in perception material—and for problem solving.

Two major developments followed in psychology. In the first place, Spearman’s important example taught psychologists to look beyond particular concrete criteria and test scores to underlying factors. Not all learned the lesson; some self-styled practical psychologists called factor analysis “mysticism”—a curious name for a basically scientific procedure. Second, it gave to intelligence testing a more positive theoretical basis than had the basically atheoretical empirical approaches of men like Binet and Wechsler, whom Spearman severely criticized, and whose work ultimately led, as Spearman and others clearly foresaw, to the scientifically cynical view that “intelligence is what intelligence tests measure.” If the methodological elegance of Spearman’s contributions had been more generally appreciated, many pointless experiments based on arbitrary “intelligence tests” would never have been conducted and the generations of psychologists who were working between 1900 and 1925 would have been spared many wrong leads and outright misconceptions.

Even among those who took up factor analysis, Spearman’s theories soon ran into difficulties (see, e.g., Thurstone 1947). Godfrey Thompson pointed out that an alternative model could fit the same statistics (1939). Experiments also appeared showing that the correlational hierarchy requiring the postulation of a single general ability was found only with certain choice of variables. Spearman has been reproached by some for arbitrarily removing variables that produced “group factors,” and his first major book, The Nature of “Intelligence” and the Principle of Cognition (1923), certainly shows how impatient he was to establish a general factor. At that time he was concerned only with purifying the concept of intelligence. By the time his second book, The Abilities of Man, appeared in 1927, he had accepted the reality of several group factors—perseveration, oscillation, persistence, and fluency—and had, with his students and associates, done more than anyone else to define them.

It was at this point that Hotelling, Truman Kelley, and Thurstone generalized Spearman’s factor analysis into what we now know as multiple factor analysis, and in so doing they incorporated purely mathematical notions that lay ready for such integration with Spearman’s methodological ones. As a result, all broad factors found then assumed equal status. Psychologists, unfortunately, have been slower than physicists to perceive the importance of mathematical models to the scientific growth of their ideas, and around 1930, when Thurstone began to publish, only a minority—though an impressive minority—reacted favorably or even intelligently to these radical ideas. Among clinicians, for example, a common reaction was that factors were “unreal abstractions” unrelated to their problems. Or, again, psychologists teaching the history or methodology of their discipline often mistook multiple factor analysis for a revival of faculty psychology, oblivious to the vast difference between creating a faculty by giving it a name and discovering a functional unity by correlation. The manipulative experimenters, in the classical tradition of Wundt, were puzzled by the absence of manipulation in factor analytic investigations, for Spearman, although he was trained by Wundt (he obtained his PH.D. at Leipzig in 1908), rejected the fine atomism of experiments on perception and sensation and sought instead to “connect the psychics of the laboratory with those of real life” (quoted in Burt & Myers 1946, p. 68). Incidentally, gestalt psychology, which was moving in the same direction at the same time, never recognized that what we now call the multivariate experimental method, built on procedures implicit in and developed on the basis of Spearman’s work, contains an effective holistic and “real life” treatment of social and general behavior.

Both Spearman’s method and his specific views on ability and other structures have necessarily been further developed, as are all fertile contributions to science. Factor analysis is now multiple factor analysis; and multivariate experimental design, assessing the simultaneous effects of many variables, is recognized as a new principle of research. The general factor that Spearman sought is now regarded as being a second order rather than a primary factor, and it is thought to consist perhaps of two factors—fluid and crystallized general intelligence.

Noegenetic laws. Spearman’s cognitive laws have not had the important impact on the development of psychology that his contributions to methodology and his work on intelligence have had. His interest in establishing these laws was rooted in his profound sense of the history and philosophy of science, which made him keenly aware of the absence of any adequate general laws in psychology. He believed that English associationism (of Locke, Hume, Bain, et al.) was the only existent systematic attempt to formulate such laws (apart from a few theories limited, for example, to perception, such as the Weber-Fechner law or the merely descriptive reflexological laws of conditioning), but he regarded the laws of association as only anoe-genetic explanations of the reproduction of mental content, not as explanatory of the genesis of new mental content. The noegenetic laws, in contrast, assert that the perception of two fundaments tends to evoke a relation between them, and that the presentation of a fundament and a relation will tend to educe a new fundament. This applies in principle to even the simplest cognitive activity, as well as to the processes determined by the general intelligence factor. Whether the “tendency” to perceive a relation between, say, π and e, eventuates in a perception depends on the intelligence of the perceiver. An analogies test, for example, immediately illustrates in its two parts both of these noegenetic laws. In his penultimate (and slender) book, Creative Mind (1930), Spearman developed further the implications of his noegenetic laws, aware that this aspect of his work had received little recognition.

Spearman’s last major work, Psychology Down the Ages (1937), was an ambitious attempt to describe and interpret the development of psychology over two thousand years. The book has many powerful ideas and insights, even if Spearman’s earnest commitment to the validity of his own theories prevented it from being an ideally detached history; Cyril Burt has described it as an attempt to show “how all the acceptable formulations were really dim foreshadowings of the fundamental noegenetic laws” (see Burt & Myers 1946, p. 71). The book permitted Spearman, in his early seventies, a leisurely return to the contemplative philosophical interests of his youth.

In Spearman’s case, it seems particularly necessary to relate his scientific creativity to his life and his personality. It would be hard to imagine a life pattern less similar to the academic norm. Coming from an English family of established status and some eminence, Spearman became an officer in the regular army because, he said, this offered him more leisure and freedom to study than did other professions. He served in the Burmese war and held the rank of major. Resigning after the Boer War, at 40, he was recommended by McDougall to a newly created position at University College, London. His first book, The Nature of “Intelligence,” appeared in his sixtieth year. Although a person of very definite opinions, whose students worked on thesis topics that fitted into his own monumental work (and enjoyed it), he possessed remarkable charm and a capacity to stimulate and reassure. As Burt, who worked with and succeeded him, remarked, “Few have possessed his gift of coordinating the research interests of pupils ... on one single dominating and fertile theme” (see Burt & Myers 1946, p. 71). On retiring he went to America and with a former student, Karl Holzinger, worked on a unitary-traits project.

In addition to making a major contribution to the theory of human abilities in the first quarter of the twentieth century, Spearman gave great impetus to those multivariate experimental methods that have since revolutionized other areas, and thus he takes his place with the few great names in psychology during that period.

Raymond B. Cattell

[For discussion of the subsequent development of Spearman’s ideas, seeExperimental Design; Factor Analysis; Intelligence and Intelligence Testing; Nonparametric Statistics, article on Ranking Methods; and the biographies ofCattell; KELLEY; Thorndike; THURSTONE.]


1904 “General Intelligence” Objectively Determined and Measured. American Journal of Psychology 15:201-293.

(1923) 1927 The Nature of “Intelligence” and the Principle of Cognition. 2d ed. London: Macmillan.

1927 The Abilities of Man: Their Nature and Measurement. London: Macmillan.

(1930) 1931 Creative Mind. New York: Appleton.

1937 Psychology Down the Ages. 2 vols. London: Macmillan.

1950 Spearman, C. E.; and Jones, Llewellyn W. Human Ability. London: Macmillan. → A continuation of Spearman’s The Abilities of Man (1927).


Burt, Cyril; and Myers, C. S. 1946 Charles Edward Spearman, 1863-1945. Psychological Review 53:67-71.

Thomas, Frank C. 1935 Ability and Knowledge: The Standpoint of the London School. London: Macmillan.

Thompson, Godfrey (1939) 1951 The Factorial Analysis of Human Ability. 5th ed. Boston: Houghton Mifflin.

Thompson, Godfrey 1947 Charles Spearman: 1863-1945. Royal Society, London, Obituary Notices of Fellows 5:373-385.

Thurstone, Louis L. 1947 Multiple-factor Analysis: A Development and Expansion of The Vectors of Mind. Univ. of Chicago Press.

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