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Home/Historical IQ Tests/Spearman 1904
1904 · American Journal of PsychologyInteractive

Spearman's g: why every mental test correlates with every other.

Charles Spearman, a former army officer then studying psychology at Leipzig, compared village schoolchildren's school rankings with simple sensory tests. The correlations fell into a regular pattern, which he read as one general factor running through them all plus something specific to each. That 1904 paper is where “g” comes from.

Explore the correlation table →Correct a correlation
AMERICAN JOURNAL OF PSYCHOLOGY · VOL. XV · APRIL 1904
“General Intelligence,” Objectively Determined and Measured
C. SPEARMAN
pp. 201–292
THE PUZZLE HE STARTED WITH

Mental tests had just “failed.” Spearman blamed the arithmetic.

In 1901 Clark Wissler had found that Cattell's sensory and reaction tests at Columbia barely correlated with each other or with college grades. Spearman argued that such studies were spoiled by unreliable measurement and unsuitable samples. Correlations computed from noisy measures are pulled toward zero, and he proposed a way to correct for it.

He gathered his own data from schoolchildren in a village school and a boys' preparatory school. He ranked them by teachers' and peers' judgements and by school subjects, and tested them on discrimination of pitch, light and weight.

HIS BOLDEST CLAIMAfter correction, general discrimination and general intelligence correlated at about 1. He concluded they were, in effect, the same underlying function.
Why it mattered: it moved the question from “does this test measure intelligence?” to “how much of what this test measures is shared with every other test?” That shift is the root of factor analysis.
What didn't survive: the near-perfect link between sensory discrimination and intelligence. Later work found sensory tests load only modestly on g.
THE HIERARCHY OF CORRELATIONS

Ordered by strength, every row falls in step

Click any cell. Spearman's argument was that if one factor explains the table, any two columns are proportional: r(a,c)/r(b,c) is about the same for every c. Each measure's loading on g can then be estimated from any triad as √(r_ab · r_ac / r_bc).

ClassFrencEngliMathsPitchMusic
Classics
French
English
Maths
Pitch
Music
Classics and French correlate 0.83. Ratios of their correlations with the other four measures: 1.16, 1.04, 1.02, 1.11. The closer these are to each other, the better one general factor fits.
ESTIMATED g LOADINGS
Classics
0.96
French
0.89
English
0.81
Maths
0.75
Pitch
0.66
Music
0.64
Values are the 1904 correlations (corrected for attenuation) as reproduced in later histories; loadings are our averaged triad estimates, not Spearman's printed figures.
CORRECTION FOR ATTENUATION · 1904

How noisy tests hide a real correlation

Spearman's companion paper divided an observed correlation by the square root of the two tests' reliabilities, which he estimated by testing twice. Move the sliders: with unreliable measures, a modest observed r can imply a much stronger true relation.

r_true = r_xy / √(r_xx · r_yy)
OBSERVED0.40
CORRECTED0.73
With these reliabilities, the true relation is about 1.8× the observed one.
1904Two papers, one yearBesides the g paper, Spearman published “The proof and measurement of association between two things,” which introduced both the correction for attenuation and the rank-correlation coefficient still named after him.
DataVillage school, simple testsHe ranked children in school subjects and gave them sensory discrimination tasks such as pitch, light and weight. The overlap between discrimination and school rank was his evidence that one common factor ran through both.
1927The Abilities of ManSpearman's later book defended the two-factor theory: g plus a factor specific to each test.
1938Thurstone's replyThurstone's multiple-factor analysis found several primary abilities. The two views were reconciled as a hierarchy, with g above broad abilities, now the Cattell–Horn–Carroll model.
NINETY YEARS OF ARGUMENT

Is g a thing, or a pattern?

Godfrey Thomson showed that a hierarchy of correlations can arise without any general factor, if tests simply sample overlapping sets of many small “bonds.”Sources [5]
CHARLES EDWARD SPEARMAN · 1863–1945

An army officer who came late to psychology

1863Born 10 September in London.
c. 1883–97Officer in the British Army, serving in India, until resigning as a captain to study psychology.
1897–1906Studies at Leipzig under Wundt, with periods at Würzburg and Göttingen; doctorate from Leipzig.
1904Publishes the g paper and the correlation paper in the American Journal of Psychology.
1907Joins University College London, succeeding to the Grote chair of Mind and Logic in 1911.
1923–27The Nature of “Intelligence” and the Principles of Cognition, then The Abilities of Man.
1924–31Fellow of the Royal Society 1924; professor of psychology at UCL from 1928 until retiring in 1931.
1945Dies 17 September in London.
REFERENCES
  1. [1]Spearman, C. (1904). “General intelligence,” objectively determined and measured. American Journal of Psychology, 15(2), 201–292.Classics in the History of Psychology
  2. [2]Spearman, C. (1904). The proof and measurement of association between two things. American Journal of Psychology, 15(1), 72–101.doi
  3. [3]Wikipedia. g factor (psychometrics).en.wikipedia.org
  4. [4]Wikipedia. Charles Spearman.en.wikipedia.org
  5. [5]Thomson, G. H. (1916). A hierarchy without a general factor. British Journal of Psychology, 8(3), 271–281.doi
  6. [6]Spearman, C. (1927). The Abilities of Man: Their Nature and Measurement. Macmillan (Internet Archive).archive.org
  7. [7]Carroll, J. B. (1993). Human Cognitive Abilities: A Survey of Factor-Analytic Studies. Cambridge University Press.doi
  8. [8]Wissler, C. (1901). The correlation of mental and physical tests. Psychological Review Monograph Supplements, 3(6).doi
  9. [9]Wikipedia. Spearman's rank correlation coefficient.en.wikipedia.org

Editorial record: new page in this project. The 1904 paper is public domain and transcribed online, but was not re-read for this revision; figures follow standard reproductions and are flagged as such. The study description, debate timeline and life dates were written from general histories and have not been checked against the sources.

KEEP EXPLORING
1938 · The counter-argumentThurstone's Primary Mental AbilitiesThurstone rotated factors to find seven primaries, then accepted a second-order g.1884 · Where correlation came fromGalton's Anthropometric LaboratorySpearman built on Galton's idea of correlation and on sensory tests like Galton's.1936 · Built for gRaven's Progressive MatricesRaven, Spearman's student, designed matrices to measure the eductive part of g.1890 · The tests that didn't correlateCattell's Mental TestsWissler's 1901 analysis found Cattell's tests barely correlated with grades, the puzzle Spearman reframed.
Part of the Historical IQ Tests Archive. Editorial content under CC BY-SA 4.0.

One g, four domains.

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