Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-22T05:57:41.021Z Has data issue: false hasContentIssue false
  • English
  • Français

Karl Pearson's Gresham lectures: W. F. R. Weldon, speciation and the origins of Pearsonian statistics

Published online by Cambridge University Press:  05 January 2009

M. Eileen Magnello
M. Eileen Magnello
Affiliation:
Wellcome Institute for the History of Medicine, 183 Euston Road, London NW1 2BE.
Get access Rights & Permissions [Opens in a new window]

Extract

The scientific legacy of Karl Pearson and his role as one of the principal architects of the modern theory of mathematical statistics, has generated enough interest to have created an intellectual enterprise on various aspects of his life and work. Despite this interest, Pearson's earliest and most formative statistical work which he delivered in thirty of his thirty-eight Gresham lectures from 17 November 1891 to 11 May 1894 has, to date, been given very little consideration. Pearson is perhaps, best known to historians of science for his first eight Gresham lectures, delivered in London in February and May, 1891, on ‘The Scope and Method of Modern Science’, as these lectures were published with modification in the Grammar of Science in 1892. The only discussions which have emerged from some of the other thirty lectures have come from Egon Pearson and Steve Stigler. As the great bulk of these lectures have not been fully utilized, previous attempts to identify the impetus to his statistical work have been derived either from his teaching of correlation at University College London in 1895–96 or from his third statistical paper which, in part, addresses Francis Galton's work on simple correlation and simple regression. In spite of the emphasis on Galton's work on simple correlation and regression, little attention has been given to Pearson's more innovative work in that paper, which includes his development of the following statistical methods: multiple correlation, multiple regression, the standard error of estimate, the coefficient of variation and the use of determinantal matrix algebra for biometrical methods. This use of a higher form of algebra not only provided a most striking departure from earlier forms and uses of statistics, but it led to an increasing specialization in the emerging discipline of ‘mathematical statistics’.

Type
Research Article
Information
The British Journal for the History of Science , Volume 29 , Issue 1 , March 1996 , pp. 43 - 63
Copyright
Copyright © British Society for the History of Science 1996

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1 More than forty articles and books have been written on Pearson. The standard work on Pearson's statistical work includes the following: Pearson, Egon, ‘Karl Pearson: an appreciation of some aspects of his life and work’ Part 1. 1857–1905, Biometrika (1936), 28, 193–257Google Scholar; Part 2. 1906–1936, ibid. (1938), 29, 61–248 (reprinted, Cambridge, 1936); Farrall, Lyndsay, ‘The Origins and Growth of the English Eugenics Movement. 1865–1925’, Ph.D. thesis, University of Indiana, 1970Google Scholar; Hilts, Victor, Statist and Statistician, New York, 1981Google Scholar; Mackenzie, Donald, ‘Statistical theory and social interests: a case study’, Social Studies of Science (1978), 8, 35–83CrossRefGoogle ScholarPubMed and Statistics in Britain 1865–1930: The Social Construction of Scientific Knowledge, Edinburgh, 1981Google Scholar; Norton, Bernard, ‘Karl Pearson and statistics: the social origin of scientific innovations’, Social Studies of Science, (1978), 8, 3–34CrossRefGoogle Scholar and ‘Karl Pearson and the Galtonian Tradition: Studies in the Rise of Quantitative Social Biology’, Ph.D. thesis, University of London, 1978; Porter, Theodore, The Rise of Statistical Thinking: 1820–1900, Princeton, 1986Google Scholar; and Stigler, Steven M., The History of Statistics: The Measurement of Uncertainty before 1900, Cambridge, MA, 1986.Google Scholar

2 The first twelve lectures dealt with graphical statistics, the next eight with probability and the final ten with goodness of fit testing. For all syllabuses, see KP:UCL #48 and for extant lectures, see KP:UCL #49–51.

3 Pearson, Karl, Grammar of Science, London, 1892; 2nd edn, 1900; 3rd edn, 1911.CrossRefGoogle Scholar

4 Pearson, Egon, ‘Some incidents in the early history of biometry and statistics’, Biometrika (1968), 55, 5Google Scholar, and Stigler, , op. cit. (1), 326–7.Google Scholar Egon Pearson also included most of the syllabuses of the lectures in his book, see Pearson, E., op. cit. (1), 132–54.Google Scholar

5 Pearson, Karl, ‘Mathematical contributions to the theory of evolution (MCTE). III. Heredity, regression and panmixia’, Philosophical Transactions A (1896), 187, 253–318CrossRefGoogle Scholar; Abstract in Proceedings of the Royal Society (1895), 59, 69–71.Google Scholar

6 Stigler, , op. cit. (1), 322–5Google Scholar, has shown that Edgeworth developed a similar form of matrix algebra in 1892 which Pearson discussed in 1896. See Pearson, K., op. cit. (5), 302.Google Scholar Arthur Cayley (1821–95), who was the Sadlerian Professor of Pure Mathematics and one of Pearson's tutors at Cambridge, created determinantal matrix algebra by his discovery of the theory of invariants during the middle of the nineteenth century. Cambridge University Reporter (1878–1879), 38.Google Scholar

7 A comprehensive analysis of the two different methodological practices in Pearson's Drapers' Biometric and Galton Eugenics Laboratories, in addition to an assessment of the infrastructure of Pearson's four laboratories (including the Astronomical and the Anthropometric Laboratories), will be discussed in a separate paper.

8 In Pearson's letter to Mrs Weldon on 29 April 1906, he wrote that Weldon was ‘the closest friend he ever had’, KP:UCL #266/8.

9 Pearson, Karl, ‘Contributions to the mathematical theory of evolution’ (CMTE), Philosophical Transactions A (1894), 185, 71–100CrossRefGoogle Scholar; Abstract in Proceedings of the Royal Society (1893), 54, 329–33Google Scholar; and ‘CMTE. II. Skew variation in homogeneous material’, Philosophical Transactions A (1895), 186, 343–414Google Scholar; Abstract in Proceedings of the Royal Society (1894), 57, 257–60.Google Scholar

10 Farrall, , op. cit. (1), 189Google Scholar; Mackenzie, , Statistics in Britain, op. cit. (1), 88–9Google Scholar; and Norton, , ‘Pearson and statistics’, op. cit. (1), 5–6.Google Scholar

11 Egon Pearson, letters to Norton, Bernard, 15 07 1977Google Scholar and 22 February 1978 (Egon Pearson Papers).

12 Eisenhart, C., ‘Karl Pearson’, DSB, x, 449Google Scholar; Haldane, J. B. S., ‘Karl Pearson’ in Speeches Delivered at a Dinner held in University College London on the Occasion of the Karl Pearson Centenary Celebration, London, 1958, 8Google Scholar; and Hilts, , op. cit. (1), 571.Google Scholar

13 Stigler, , op. cit. (1), 305Google Scholar; Edwards, A. W. F., ‘Galton, Karl Pearson and modern statistical theory’ in Sir Francis Galton, FRS. The Legacy of his Ideas (ed. Keynes, Milo), London, 1993, 8Google Scholar; Bowler, Peter, Evolution: The History of an Idea, Berkeley, 1984, 240–2Google Scholar; and Olby, Robert, ‘The dimensions of scientific controversy: the biometrician-Mendelian debate’, BJHS (1988), 22, 299–320.CrossRefGoogle Scholar

14 With the exception of letters to his first wife, Marie, Pearson's correspondence with Weldon and his wife, Florence Joy Weldon, is the most extensive set in the Pearson collection held in UCL and consists of nearly 1000 letters, postcards and telegrams.

15 Karl Pearson, letter to Francis Galton, 14 August 1906, FG:UCL #293/G.

16 Karl Pearson, letter to Galton, Francis, 16 11 1898Google Scholar, FG:UCL #293/A. See also Weldon, W. F. R., Nomination ‘Prof. Karl Pearson’ (Darwin Medal)Google Scholar, Medal claims, Royal Society of London Library, (1873–1909), 12.

17 Karl Pearson, letter to Weldon, W. F. R., 28 02 1899Google Scholar, KP:UCL #266/9.

18 For Pearson's reaction to the loss of Weldon, see Pearson, letters to Francis Galton, 29 April, 2 July and 23 August 1906, KP:UCL #293/G.

19 Karl Pearson, letter to Galton, Francis, 10 12 1908Google Scholar, FG:UCL #293/J.

20 Francis Galton, Referee Report to the Royal Society, 22 October 1893, Royal Society of London Archives, RR. 12.22.

21 Pearson and David Heron remarked that ‘Galton never used Pearson's product-moment correlation coefficient to find his index of correlation’. See Pearson, Karl and Heron, David, ‘Theories of association’, Biometrika (1913), 9, 164.CrossRefGoogle Scholar

22 William Conway referred to this alliance in his letter to Pearson on 22 November 1934. University Library, Cambridge, K/36a.

23 Stigler, , op. cit. (1), 345–53 and 359.Google ScholarMackenzie, , Statistics in Britain, op. cit. (1), 180Google Scholar, argued that Yule had a greater influence on the development of statistics than did Pearson.

24 Stigler, , op. cit. (1), 266.Google Scholar

25 Karl Pearson, Application ‘To the Members of the Gresham Committee. (City Side)’ (18 November 1890), KP:UCL #11/9, 5–6.

26 KP:UCL #11/9, 6.

27 KP:UCL #11/9, 6.

28 This lecture was subsequently published in Nature (1891), 63, 223.Google Scholar

29 A syllabus of each set of lectures, with the dates, was posted before the term began.

30 Karl Pearson, letter to Venn, John, 24 03 1891Google Scholar, Venn Papers C58/3.

31 KP:UCL #11/9, 6.

32 Pearson, Karl, ‘Chance in Roulette’ (1 02 1893)Google Scholar, KP:UCL #51, 22.

33 Anon, ‘K. P.’, News Chronicle, 1 05 1936.Google Scholar

34 Pearson, Karl, ‘The Frequency of the Improbable’ (31 01 1893)Google Scholar, KP:UCL #49, 1.

35 Pearson, Karl, Application ‘To the Electors of Natural Philosophy in the University of Edinburgh’, 1901Google Scholar, KP:UCL #11/9.

36 Pearson, Karl, ‘The Geometry of Statistics’ (18 11 1891), KP:UCL #49, 25.Google Scholar

37 Pearson, Karl, ‘The Geometry of Statistics. Curves and Diagrams’ (19 11 1891), KP:UCL #49, 22.Google Scholar

38 Pearson, Karl, ‘Chance in Roulette’, KP:UCL #51, 16.Google Scholar Pearson referred to this initially as the ‘standard divergence’ in his lecture on ‘The Frequency of the Improbable’, 31 01 1893, KP:UCL #49, 39–41.Google Scholar John Venn had used the term ‘divergence’ for deviation two years earlier in his ‘Theory of Statistics, Lecture XIV. The Probable Error’ (1891, Venn Papers).

39 See Galton, Francis, ‘On a proposed statistical scale’, Nature (1874), 9, 342–3.CrossRefGoogle Scholar

40 Pearson, Karl, ‘Maps and Chartograms’ (20 11 1891), KP:UCL #49, 21.Google Scholar

41 KP:UCL #49, 22.

42 Pearson, Karl, Syllabus for ‘The Geometry of Statistics’, Michaelmas Term 1891, KP:UCL #48, 2.Google Scholar John Venn had established a series of ratios to determine ‘mathematical life-chances’ in 1891, and he used the geometrical mean ‘in accordance with Fechner's law’ for his asymmetrical curves of death rates in his ‘Theory of Statistics: Lecture XII. The General Nature of Averages’ (1891, Venn Papers).

43 Ernst Mayr thus considered Darwin to have introduced population thinking into biology. Mayr, Ernst, The Growth of Biological Thought: Diversity, Evolution and Inheritance, Cambridge, MA, 1982, 45–7.Google Scholar

44 Bowler, , op. cit. (13), 12.Google Scholar

45 Sewall Wright remarked in 1931 that ‘a statistical process was indeed necessary to bring the new species into predominance’, Wright, Sewall, ‘Evolution in Mendelian populations’, Genetics (1931), 16, 98.Google ScholarPubMed

46 Darwin, Charles, ‘On the male and complemental male of certain cirripedes’, Nature (1873), 8, 132.CrossRefGoogle Scholar

47 See Galton, Francis, ‘Typical laws of heredity. III’, Nature (1877), 15, 532–3.Google Scholar

48 W. F. R. Weldon, letter to Galton, Francis, 14 05 1889Google Scholar, FG:UCL #340sol;A. See also Weldon, W. F. R., ‘Certain correlated variations in Crangon vulgaris’, Proceedings of the Royal Society (1892), 52, 2–21.Google Scholar

49 W. F. R. Weldon, letter to Galton, Francis, 27 11 1892Google Scholar, FG:UCL #293sol;A.

50 FG.UCL #291/A.

51 FG:UCL #293/A.

52 Suggested by Peter Bowler, personal correspondence, 9 September 1994. Polyploidy is one genetic mechanism which can produce instantaneous speciation; polyploids have been found in many groups of plants and earthworms. See Cain, A. J., Animal Species and their Evolution, London, 1954, 179–80.Google Scholar

53 W. F. R. Weldon, letter to Pearson, Karl, 27 11 1892Google Scholar, KP:UCL #891/A.

54 Pearson, Karl, ‘The Geometry of Chance’ (3 02 1893), KP:UCL #49, 5–6.Google Scholar

55 [Karl Pearson], ‘A Course of Lectures on Special Applications of the Laws of Chance’ The Gresham Committee kindly permitted the delivery of these lectures by deputy. Easter Term 1893. KP:UCL #48.

56 Karl Pearson, letter to Galton, Francis, 28 02 1893, FG:UCL #293/A.Google Scholar

57 John Venn, W. F. R. Weldon, Rev. W. A. Whitworth and Sir Robert S. Ball, ‘Special Applications of the Laws of Chance’ (18 to 21 April 1893), KP:UCL #49.

58 Pearson, Karl, ‘General Notions’ (21 11 1893), KP:UCL #49, 1.Google Scholar

59 Weldon, W. F. R., ‘On certain correlated variation in Carcinus mœnas’, Proceedings of the Royal Society (1893), 54, 324.CrossRefGoogle Scholar

60 Weldon, , op. cit. (59).Google Scholar

61 Weldon, , op. cit. (59), 328.Google Scholar

62 Pearson, K., ‘CMTE’, op. cit. (9).Google Scholar

63 Francis Galton, letter to Pearson, Karl, 25 11 1893, FG:UCL #905.Google Scholar

64 Pearson, Karl, ‘General Notions’ (21 11 1893)Google Scholar, KP:UCL #48. Pearson received a substantial amount of material relating to games of chance from a number of his students including Herbert Beale, Arthur Cleghorn, Alfred Fincham, T. W. F. Parker and Martha Whitely, KP:UCL #53.

65 Pearson, Karl, ‘Normal Curves’ (22 11 1893), KP:UCL #49, 3.Google Scholar

66 KP:UCL #48, 15.

67 Pearson, E., op. cit. (4), 9.Google Scholar

68 KP:UCL #48, 7.

69 KP:UCL #48, 2.

70 In Pearson's second lecture on 3 March 1891, he introduced ‘Clapeyron's Theorem of the Three Moments’, which provided the foundation for his method of moments. See Pearson, Karl, ‘Note on Clapeyron's theorem of the three moments’, Messenger of Mathematics (1890), 19, 129–35Google Scholar and ‘Syllabus of a Course of Lectures in Higher Graphics. Part II. The Graphical Theory of Elasticity’, February 1891, KP:UCL #49, 3.

71 Pearson, Karl, ‘Skew Curves’ (23 11 1893), KP:UCL #48, 18–20.Google Scholar

72 KP:UCL #48, 18.

73 Adolphe Quetelet made one of the earliest attempts to fit a set of observational data to a normal curve in 1840 which Galton was using in 1863. See Stigler, op. cit. (1), 205Google Scholar and Galton, Francis, Memories of my Life, London, 1908, 394.Google Scholar Similar tests had also been used by Louis-Adolphe Bertillion in 1863 and by Luigi Perrozo and Erastus Lymon de Forest in 1873. See Pretorious, S. J., ‘Skew bi-variate frequency surfaces, examined in light of numerical illustrations’, Biometrika (1930), 22, 121Google Scholar and de Forest, Erastus ‘On the grouping of signs of residuals’, Analyst (1878), 9, 65–72Google Scholar, in Stigler, Steven M., ‘Mathematical statistics in the early states’, Annals of Statistics (1980), 6, 254–5.Google Scholar

74 Pearson, K., ‘CMTE’, op. cit. (9), 332.Google Scholar

75 Fisher, R. A. coined the word variance in ‘The causes of human variability’, Eugenics Review (1918), 10, 213.Google Scholar

76 Pearson, K., ‘CMTE’, op. cit. (9), 332.Google Scholar

77 Pearson, Karl, ‘Skew Curves’, KP:UCL #49, 19.Google Scholar

78 Pearson, Karl, ‘Compound Curves’ (24 11 1893), KP:UCL #49, 1.Google Scholar

79 In his first supplement to his family of curves in 1901, he defined Types VI and V, and then Types VIII and IX in his second supplement of 1916. See Pearson, Karl, ‘Mathematical contributions to the theory of evolution. X. Supplement to a memoir on skew variation’, Philosophical Transactions A (1901), 197, 443–59CrossRefGoogle Scholar, and ‘Mathematical contributions to the theory of evolution. XIX. Second supplement to a memoir on skew variation’, Philosophical Transactions A (1916), 216, 429–57.Google Scholar

80 Pearson, Karl, Syllabus for Michaelmas Term, ‘The Geometry of Chance’, 1893, KP:UCL #49, 4.Google Scholar

81 KP:UCL #48, 3.

82 KP:UCL #48, 3.

83 Sulloway, Frank, ‘Geographical isolation in Darwin's thinking: the vicissitudes of a crucial idea’, Studies in the History of Biology (1975), 3, 23–65.Google Scholar

84 Sulloway, , op. cit. (83), 58–9.Google Scholar

85 Bateson, William, Materials for the Study of Variation: Treated with Especial Regard to Discontinuity in the Origin of Species, London, 1894, 54–75.Google Scholar

86 DeVries, Hugh, Species and Varieties: Their Origin by Mutations (ed. McDougal, Daniels Trembley), Chicago, 1904, p. vii.Google Scholar

87 DeVries, , op. cit. (86).Google Scholar

88 Galton, Francis, Natural Inheritance, London, 1898, 32.Google Scholar

89 W. F. R. Weldon, letter to Pearson, Karl, 6 08 1893Google Scholar, KP:UCL #891/A.

90 Pearson, K., ‘CMTE’, op. cit. (9).Google Scholar

91 Bowler, Peter, personal correspondence, 9 09 1994.Google Scholar

92 Pearson, , ‘Normal Curves’, KP:UCL #48, 17–18Google Scholar and ‘Compound Curves’, KP:UCL #48, 10.

93 Pearson, , ‘Compound Curves’, KP:UCL #48, 9–10.Google Scholar

94 KP:UCL #48, 10.

95 KP:UCL #48.

96 KP:UCL #48, 11–12.

97 W. F. R. Weldon, letter to Galton, Francis, 4 12 1893, FG:UCL #293/A.Google Scholar

98 W. F. R. Weldon, letter to Galton, Francis, 18 12 1893, FG:UCL #293/A.Google Scholar

99 Galton, Francis, Miscellaneous Manuscripts, vol. 15Google Scholar, Royal Society of London Archives, #87 (26 December 1893).

100 Pearson, Karl, ‘Problems in Evolution’ (1 02 1894), KP:UCL #48, 167.Google Scholar

101 Karl Pearson, Syllabus of ‘A Further Course of Lectures on the Geometry of Chance: Problems in Evolution’ (Hilary Term, 1 February 1894), KP:UCL #49, 3.

102 KP:UCL #49, 16.

103 KP:UCL #49.

104 KP:UCL #49.

105 W. F. R. Weldon, letter to Galton, Francis, 28 10 1894Google Scholar, FG:UCL #340/C.

106 W. F. R. Weldon, letter to Pearson, Karl, 8 01 1895Google Scholar, KP:UCL #891/A.

107 Pearson, Karl, ‘W. F. R. Weldon. 1860–1906’, Biometrika (1906), 5, 25.Google Scholar

108 Pearson, K., ‘CMTE’, op. cit. (9).Google Scholar

109 Anon, ‘The retirement of Karl Pearson’, UCL Magazine (Summer 1933), 166.Google Scholar

110 Pearson, Karl, ‘Report to the Count of the Worshipful Company of Drapers’ (1918), KP:UCL #233, 4.Google Scholar

111 Udny Yule, George, ‘Notes from Karl Pearson's Lectures: “Mathematical Contributions to The Theory of Evolution of 1894 and 1895”, Vol. II’ (04 1895)Google Scholar, KP:UCL #84/2.

112 KP:UCL #84/2, 84.

113 Pearson, K., ‘CMTE. II’, op. cit. (9).Google Scholar

114 Pearson, K., ‘CMTE. II’, op. cit. (9).Google Scholar

115 Karl Pearson, letter to Galton, Francis, 25 12 1896Google Scholar, FG:UCL #293/A.

116 Eisenhart, , op. cit. (12), 461.Google Scholar

117 Pearson, Karl, ‘On the criterion that a given system of deviations from the probable in the case of a correlated system of variables that is such that it can be reasonably supposed to have arisen from random sampling’, Philosophical Magazine, (1900), 50, 157–75.Google Scholar Though the chi-square goodness of fit test replaced Pearson's method of moments for curve fitting for biologists in the 1970s, econometricians, however, continue to use the method of moments in their work. See, e.g., Hansen, Lars P., ‘Large sample properties of generalized method of moments estimators’, Econometrics (1982), 50, 1029–54CrossRefGoogle Scholar and Hamilton, James D., ‘Generalized method of moments’, in Time Series Analysis, Princeton, 1994, 409–34.Google Scholar I am grateful to Neil Shephard for bringing this material to my attention.

118 Pearson, Karl, ‘The method of moments and the method of maximum likelihood’, Biometrika (1936), 28, 34–59.CrossRefGoogle Scholar

119 Pearson, Karl, ‘Mathematical contributions to the theory of evolution. XIII. On the theory of contingency and its relation to association and normal correlation’, Drapers' Company Researc Memoirs. Biometric Series 1 (1904), 1–47.Google Scholar