Quality & Quantity

, Volume 42, Issue 6, pp 757–777 | Cite as

The historical construction of correlation as a conceptual and operative instrument for empirical research

  • Juan Ignacio Piovani
Original Paper


This article is meant to reconstruct–from the standpoint of sociology and history of science–the development of the concept and the operative instruments of statistical correlation. The starting point is the discussion of some key mathematical aspects of the Error Theory, including a detailed analysis of the various positions regarding its contributions, if any, to the theory of correlation. Then proceeds to examine how the concept (and its relative instruments) emerged in its modern sense, by the late Nineteenth century, thanks to the work of Francis Galton. Finally, it considers the numerous contributions that rendered possible the formalisation and generalisation of both Galton’s concept and methodological tools, in particular those of Karl Pearson, but also those of Walter Weldon, Francis Ysidro Edgeworth, George Udny Yule and Charles Spearman.

“Co-relation or correlation of structure”is a phrase much used in biology, and not least in that branch of it which refers to heredity, and the idea is even more frequently present than the phrase; but I am not aware of any previous attempt to define it clearly, to trace its mode of action in detail, or to show how to measure its degree.

Francis Galton (1888, 135)


Probable Error Error Theory Spurious Correlation Historical Construction Mathematical Contribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Aldrich J. (1995) Correlations genuine and spurious in Pearson and Yule. Stat. Sci. 10(4): 364–76Google Scholar
  2. Blalock H.M.: Social Statistics. Mc Graw-Hill, New York [quotations from the spanish translation, 2nd edition.: Estadística Social. Mexico: FCE, 1986] (1960)Google Scholar
  3. Bowley A.L. (1903) The Measurement of Groups and Series. Layton, LondonGoogle Scholar
  4. Bravais A. (1846) Analyse mathématique sur les probabilités des erreurs de situation d’un point. Mémoires présentés par divers savants à l’Académie Royale des Sciences de l’Istitut de France 9, 255–32Google Scholar
  5. Carpenter W. (1851) The correlation of the physical and vital forces. Br. Foreign Med.-Chir. Rev. 8, 206–38Google Scholar
  6. Darwin C. (1859) On the Origin of Species. John Murray, LondonGoogle Scholar
  7. Darwin C. (1868) The Variation of Animals and Plants under Domestication. John Murray, LondonGoogle Scholar
  8. Denis D.J.: The origins of correlation and regression. In: Proceedings of the 61st Annual Convention of the Canadian Psychological Association, Ottawa (2000)Google Scholar
  9. Edgeworth F.Y. (1892) On correlated averages. Philos. Mag. Ser. 5(34): 190–04Google Scholar
  10. Edgeworth F.Y. (1893) Statistical correlation between social phenomena. J. R. Stat. Soc. 56(4): 670–75Google Scholar
  11. Edgeworth F.Y.: The Law of Error. Encyclopædia Britannica, 10th ed., vol. 28 (supplement to 9th ed., vol. 4), pp. 280–91 (1902)Google Scholar
  12. Edgeworth F.Y. (1908) On the probable errors of freqeuncy-constants. J. R. Stat. Soc. 71(3): 499–12CrossRefGoogle Scholar
  13. Galton F. (1869) Hereditary Genius. An Inquiry into its Laws and Consequences. MacMillan, LondonGoogle Scholar
  14. Galton F. (1875) Statistics by Intercomparison. Philos. Mag. Ser. 4(49): 33–6Google Scholar
  15. Galton F. (1877) Typical laws of heredity. Proc. R. Instit. 8, 282–01Google Scholar
  16. Galton F. (1885) Address to the anthropological section of the British association. Nature 32, 507–10Google Scholar
  17. Galton F. (1886) Family likeness in stature. Proc. R. Soc. Lon. 40, 42–3CrossRefGoogle Scholar
  18. Galton F. (1888) Co-relations and their measurement, chiefly from anthropometric data. Proc. R. Soc. Lon. 45, 135–45CrossRefGoogle Scholar
  19. Galton F. (1889) Natural Inheritance. Macmillan, LondonGoogle Scholar
  20. Galton F. (1890) Kinship and correlation. North Am. Rev. 150, 419–31Google Scholar
  21. Galton F. (1897) Notes to the Memoir by Professor Karl Pearson F.R.S., on Spurios Correlation. Proc. R. Soc. Lon. 60, 498–02CrossRefGoogle Scholar
  22. Galton F. (1908) Memories of My Life. Methuen, LondonGoogle Scholar
  23. Gauss C.F. (1823) Theoria combinationis observationum minimis obnoxiae. Dieterich, GöttingenGoogle Scholar
  24. Grove W.R. (1846) The Correlation of Physical Forces. The Substance of a Course of Lectures, LondonGoogle Scholar
  25. Hendry D.F. (1980) Econometrics. alchemy or science. Economica 47, 387–08CrossRefGoogle Scholar
  26. Hooker R.H. (1908) An elementary explanatin of correlation, illustrated by rainfall and a depth of water in a well. J. R. Meteorol. Soc. 34, 277CrossRefGoogle Scholar
  27. Jevons W.S. (1874) The Principles of Science. A Treatise on Logic and Scientific Method. Macmillan, LondonGoogle Scholar
  28. Kendall M.G., Buckland W.R.: A Dictionary of Statistical Terms. Longman, London [quotations from the spanish translation: Diccionario de Estadística, Madrid: Pirámide, 1980] (1976)Google Scholar
  29. Kuhn Th. (1962) The Structure of Scientific Revolutions. University Press, ChicagoGoogle Scholar
  30. Lancaster H.O. (1972) Development of the notion of statistical dependence. Math. Chron. 2, 1–6Google Scholar
  31. Legendre A.M. (1805) Nouvelles Methodes pour la Détermination des Orbites des Comètes. Courcier, ParisGoogle Scholar
  32. MacKenzie D.A. (1981) Statistics in Britain, 1865–930. The Social Construction of Scientific Knowledge. University Press, EdinburghGoogle Scholar
  33. Melberg H.O.: (2000) From Spurious Correlation to Misleading Association: The Nature and Extent of Spurious Correlation and its Implications for the Philosophy of Science with Special Emphasis on Positivism. University of Oslo < >Google Scholar
  34. Micheli G.A., Manfredi P. (1995) Correlazione e Regressione. Angeli, MilanGoogle Scholar
  35. Nicholls N. (1998) William stanley jevons and the climate of Australia. Aust. Meteorol. Mag. 47, 285–93Google Scholar
  36. Pearson K.: The Grammar of Science. Scott, London [quotations from the 3rd revision, 1911. New York: Meridian, 1957] (1892)Google Scholar
  37. Pearson K. (1896) Mathematical contributions to the theory of evolution: regression, heredity, and Panmixia. Philos. Trans. R. Soc. Lon. 187, 253–18CrossRefGoogle Scholar
  38. Pearson K. (1897) Mathematical contributions to the theory of evolution: on a form of spurious correlation which May Arise when Indices Are Used in the measurement of organs. Proc. R. Soc. 60, 489–98CrossRefGoogle Scholar
  39. Pearson K. (1902) On the systematic fitting of curves to observations and measurements. Biometrika 1(3): 265–03CrossRefGoogle Scholar
  40. Pearson K. (1905) On the General Theory of Skew Correlation and Non-Linear Regression Draper’s Company Research Memoirs, biometric series II. Dulau, LondonGoogle Scholar
  41. Pearson K. Life and letters of Francis Galton. University Press, Cambridge (1914–930)Google Scholar
  42. Pearson K. (1920) Notes on the history of correlation. Biometrika 13(1): 25–5CrossRefGoogle Scholar
  43. Pearson K., Filon L.N.G. (1898) Mathematical contributions to the theory of evolution, IV: on the probable errors of frequency constants and on the influence of random selection on variation and correlation. Philos. Trans. R. Soc. A 191, 229–11CrossRefGoogle Scholar
  44. Pearson K., Lee A. (1897) On the distribution of frequency (Variation and Correlation) of Barometric height at divers stations. Philos. Trans. R. Soc. A 190, 423–69CrossRefGoogle Scholar
  45. Piovani J.I. (2004) L’epistemologia di Karl Pearson. Sociol. ricerca sociale 75, 5–8Google Scholar
  46. Porter Th. (1986) The Rise of Statistical Thinking, 1820–900. University Press, PrincetonGoogle Scholar
  47. Ricolfi L. (1993) Tre variabili. Un’introduzione all’analisi multivariata. Angeli, MilanGoogle Scholar
  48. Schols C.M. (1886) Théorie des erreurs dans le plan et dans l’espace. Ann. l’Ecole polytechnique de Delft 2, 123–78Google Scholar
  49. Seal H.L.: Studies in the history of probability and statistics. XV: the historical development of the gauss linear model. Biometrika 54(1/2), 1–4 (1967)Google Scholar
  50. Spearman C.E. (1904a) The proof and measurement of association between two things. Am. J. Psychol. 15, 72–01CrossRefGoogle Scholar
  51. Spearman C.E. (1904b) General intelligence, objectively determined and measured. Am. J. Psychol. 15, 201–93CrossRefGoogle Scholar
  52. Spearman C.E. (1910) Correlation Calculated from Faulty Data. British J. Psychol. 3, 271–95Google Scholar
  53. Stigler S.M. (1978) Francis Ysidro Edgeworth, statistician. J. R. Stat. Soc. A 141, 287–22CrossRefGoogle Scholar
  54. Stigler S.M. (1981) Gauss and the invention of least squares. Ann. Stat. 9, 465–74CrossRefGoogle Scholar
  55. Stigler S.M. (1986) The History of Statistics: The Measurement of Uncertainty Before 1900. Harvard University Press, Cambridge, MAGoogle Scholar
  56. Stigler S.M. (1999) Statistics on the Table: The History of Statistical Concepts and Methods. Harvard University Press, CambridgeGoogle Scholar
  57. Tankard J.W. (1984) The Statistical Pioneers. Schenkman, CambridgeGoogle Scholar
  58. Walker H.M. (1929) Studies in the History of Statistical Method. Williams and Wilkins, BaltimoreGoogle Scholar
  59. Wallace H.A., Snedecor G.W. (1925) Correlation and Machine Calculations. Iowa State College Press, AniesGoogle Scholar
  60. Weldon W.F.R. (1890) The variations occurring in certain decapod Crustacea. Proc. R. Soc. 47, 445–53CrossRefGoogle Scholar
  61. Weldon W.F.R. (1892) Certain correlated variations in crangon Vulgaris. Proc. R. Soc. 51, 2–1CrossRefGoogle Scholar
  62. Weldon W.F.R. (1893) On certain correlated variations in carcinus Moenas. Proc. R. Soc. 54, 318–29CrossRefGoogle Scholar
  63. Westergaard H. (1932) Contributions to the history of statistics. P. S. King, LondonGoogle Scholar
  64. Winter A. (1997) The construction of orthodoxies and heterodoxies in the early victorian life sciences. In: Lightman B. (eds) Victorian Science in Context. University Press, ChicagoGoogle Scholar
  65. Yule G.U. (1897a) On the significance of Bravais–formulae for regression, in the case of Skew correlation. Proc. R. Soc. Lon. 60, 477–89CrossRefGoogle Scholar
  66. Yule G.U. (1897b) On the theory of correlation. J. R. Stat. Soc. 60(4): 812–54Google Scholar
  67. Yule G.U. (1900) On the association of attributes in statistics. Philos. Trans. R. Soc. Lon. A 194, 257–19CrossRefGoogle Scholar
  68. Yule G.U. (1909) The application of the method of correlation to social and economic statistics. J. R. Stat. Soc. 72(4): 721–30CrossRefGoogle Scholar
  69. Yule G.U. (1911) An Introduction to the Theory of Statistics. Griffin, LondonGoogle Scholar
  70. Yule G.U. (1926) Why do we sometimes get nonsense correlations between time-series? A study in sampling and the nature of time-series. J. R. Stat. Soc. 89(1): 1–3CrossRefGoogle Scholar
  71. Yule G.U. (1986) On the correlation of total pauperism with proportion of out-relief. Econ. J. 6(24): 613–23CrossRefGoogle Scholar
  72. Yule G.U. (1938) Notes of Karl Pearson’s lectures on the theory of statistics 1894–6. Biometrika 30(1/2): 198–03CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.National University of La PlataLa PlataArgentina

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