Karl Pearson Research Paper

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Karl Pearson was one of the principal architects of the modern  theory of mathematical statistics. His interests ranged from mathematical physics, astronomy, philosophy,  history,  literature,  socialism,  and  the  law  to Darwinism, evolutionary biology, heredity, Mendelism, eugenics, medicine, anthropology, and crainometry. His major contribution, however, by his lights and by posterity’s, was to establish and advance the discipline of mathematical statistics.

The  second  son  of  William  Pearson  and  Fanny Smith, Carl Pearson was born in London on March 27, 1857. In 1879 the University of Heidelberg changed the spelling of  his  name  when  it  enrolled  him  as “Karl Pearson”; five years later he adopted this variant of his name and eventually became known as “KP.” His mother came from a family of seamen and  mariners, and  his father was a barrister and Queen’s Counsel. The Pearsons were a family of dissenters and of Quaker stock. By the time Carl was twenty-two he had rejected Christianity and adopted “Freethought” as a nonreligious faith that was grounded in science.

Pearson graduated with honors in mathematics from King’s College, Cambridge University in January 1879. He stayed in Cambridge to work in Professor James Stuart’s engineering workshop and to study philosophy in preparation for his trip to Germany in April. His time in Germany was a period of self-discovery, philosophically  and professionally. Around this time, he began to write The New Werther, an epistolary novel on idealism and materialism, published in 1880 under the pseudonym of Loki (a mischievous Scandinavian god). In Heidelberg Pearson abandoned Karl philosophy because “it made him miserable and would have led him to short-cut his career” (Karl Pearson, Letter to Robert Parker, 17 August 1879. Archive reference number:  NW/Cor.23.   Helga  Hacker  Pearson papers within  Karl Pearson’s  archival material  held  at University College London). Though he considered becoming a mathematical physicist, he discarded this idea because he “was not a born genius” (Karl Pearson, Letter to Robert Parker, 19 October 1879. Archive reference number/922. Karl Pearson’s archival material held at University College London). He stayed in Berlin and attended lectures on Roman international law and philosophy.

He returned to London and studied law at Lincoln’s Inn at the Royal Courts of Justice. He was called to the bar at the end of 1881 but practiced for only a very short time. Instead, he began to lecture on socialism, Karl Marx, Ferdinand  Lassalle, and  Martin  Luther  from  1880  to 1881,  while also writing on medieval German folklore and  literature and  contributing  hymns to  the  Socialist Song Book. In the course of his lifetime, he produced more than 650 publications, of which 400 were statistical; over a period of twenty-eight years he founded and edited six academic journals, of which Biometrika is the best known.

Having  received the  Chair  of  Mechanism  and Applied Mathematics at University College London (UCL)  in  June  1884,  Pearson  taught  mathematical physics, hydrodynamics, magnetism, electricity, and elasticity to engineering students. Soon after, he was asked to edit and complete William Kingdom Clifford’s The Common  Sense of  Exact  Science (1885)   and   Isaac Todhunter’s History of the Theory of Elasticity (1886).

The Gresham Lectures on Statistics

Pearson was a founding member of the Men’s and Women’s Club, established in 1885 for the free and unreserved discussion of all matters concerning relationships of men and women. Among the various members was Marie Sharpe, whom he married in June 1890. They had three children, Sigrid, Helga and Egon. Six months after his marriage, he took up another teaching post in the Gresham  Chair  of  Geometry  at  Gresham  College in the  City  of London  (the  financial district), which he held for three years concurrently with his post at UCL. From February 1891 to November 1893, Pearson delivered thirty-eight lectures.

These lectures were aimed at a nonacademic audience. Pearson wanted to  introduce  them  to  a way of thinking that would influence how they made sense of the physical world. While his first eight lectures formed the basis of his book The Grammar of Science, the remaining thirty dealt with statistics because he thought this audience would understand insurance, commerce, and trade statistics and could relate to games of chance involving Monte Carlo roulette, lotteries, dice, and coins. In 1891 he introduced the histogram (a type of bar chart), and he devised the standard deviation and the variance (to measure statistical variation) in 1893. Pearson’s early Gresham lectures on  statistics were influenced by  the  work  of Francis Ysidro Edgeworth, William Stanley Jevons, and John Venn.

Pearson’s  last twelve Gresham  lectures signified a turning point in his career owing to the Darwinian zoologist W. F. R. Weldon (1860–1906), who was interested in using a statistical approach for problems of Darwinian evolution. Their emphasis on Darwinian population of species, underpinned  by biological variation, not  only implied the necessity of systematically measuring variation but also prompted the reconceptualization of a new statistical methodology, which led eventually to the creation  of  the  Biometric  School  at  University College London in 1894. Earlier vital and social statisticians were mainly interested in  calculating averages and  were not concerned with measuring statistical variation.

Pearson adapted the mathematics of mechanics, using the method of moments to construct a new statistical system  to  interpret  Weldon’s  asymmetrical distributions, since no  such  system existed at  the  time.  Using  the method of moments, Pearson established four parameters for curve fitting to show how data clustered (the mean), and spread (the standard deviation), if there were a loss of symmetry (skewness),  and  if the  shape of the  distribution was peaked or flat (kurtosis). These four parameters describe the essential characteristics of any empirical distribution  and  made  it  possible to  analyze data  that resulted in various-shaped distributions.

By the time Pearson finished his statistical lectures in May 1894, he had provided the infrastructure of his statistical  methodology.  He  began  to  teach  statistics at University College in October. By 1895 he had worked out the mathematical properties of the product-moment correlation  coefficient  (which  measures the  relationship between two continuous variables) and simple regression (used for the linear prediction between two continuous variables). In 1896 he introduced a higher level of mathematics into statistical theory, the coefficient of variation, the standard error of estimate,  multiple  regression, and multiple correlation, and in 1899 he established scales of measurement for continuous  and  discrete variables. Pearson devised more than eighteen methods of correlation from 1896 to 1911, including the tetrachoric, polychoric, biserial, and triserial correlations and the phi coefficient. Inspired and supported by Weldon, Pearson’s major contributions to statistics were: (1) introducing standardized statistical data-management procedures to handle very large sets of data; (2) challenging the tyrannical acceptance of the normal curve as the only distribution on which to base the interpretation  of statistical data; (3) providing a set of mathematical statistical tools for the analysis of statistical variation, and (4) professionalizing the discipline of mathematical statistics. Pearson was elected a Fellow of the Royal Society in 1896 and awarded its Darwin Medal in 1898.

Pearson’s ongoing work throughout  the 1890s with curve fitting signified that he needed a criterion to determine how good the fit was. He continued to work on improving his methods until  he devised his chi-square goodness of fit test in 1900 and introduced the concept of degrees   of  freedom. Although  many  other  nineteenthcentury scientists attempted to find a goodness of fit test, they did not give any underlying theoretical basis for their formulas, which Pearson managed to do. The overriding significance of this test meant that statisticians could use statistical methods that did not depend on the normal distribution to interpret their findings. Indeed, the chisquare goodness of fit test represented Pearson’s single most important  contribution  to  the modern  theory of statistics, for it raised substantially the practice of mathematical statistics. In  1904  Pearson established the  chisquare   statistic for  discrete  variables to  be  used  in contingency tables. Pearson published his statistical innovations from his Gresham and UCL lectures in a set of twenty-three papers, “Mathematical Contributions to the Theory of Evolution,” principally in Royal Society publications from 1893 to 1916. He established the first degree course in statistics in Britain in 1915.

Pearson’s Four Laboratories

In the twentieth century Pearson founded and managed four  laboratories. He  set  up  the  Drapers’  Biometric Laboratory in 1903  with a grant from the Worshipful Drapers’  Company  (who  funded  the  laboratory until 1933). The methodology incorporated in this laboratory involved the use of his statistical methods and numerous instruments. The problems investigated by the biometricians included natural selection, Mendelian genetics and Galton’s law of ancestral inheritance, crainometry, physical anthropology, and theoretical aspects of mathematical statistics. A year after Pearson established the Biometric Laboratory, the Worshipful Drapers’ Company gave him a grant to launch an Astronomical Laboratory equipped with a transit circle and a four-inch equatorial refractor.

In 1907 Francis Galton  (who was then eighty-five years old) wanted to step down as director of the Eugenics Record Office, which he had set up three years earlier; he asked Pearson to take over the office, which Pearson subsequently renamed the Galton Eugenics Laboratory. Pearson had, by then, spent the previous fourteen years developing the foundations of his statistical methodology. His work schedule was so demanding that he took on this role only as a personal favor to Galton. Because Pearson regarded his statistical methods as unsuitable for problems of eugenics, he further developed Galton’s actuarial death rates and family pedigrees for the methodology of the Eugenics Laboratory. The  latter  procedure  led  to  his twenty-one-volume Treasury of Family Inheritance (1909–1930). In 1924 Pearson set up the Anthropometric Laboratory, made possible by a gift from his student, Ethel Elderton. When Galton died in January 1911, his estate was bequeathed to UCL and he named Pearson as the first professor of eugenics. The Drapers’ Biometric and the  Galton  Eugenics laboratories, which continued  to function separately, became incorporated into the Department of Applied Statistics.

Although  Pearson  was a  eugenicist, he  eschewed eugenic policies. For him and his British contemporaries (e.g., Herbert  Spencer, George Bernard  Shaw, H.  G. Wells, Marie Stopes, and Virginia Woolf ), eugenics was principally a discourse about class, whereas in Germany and America the focus was on racial purity. The British were anxious that the country would be overrun by the poor unless their reproduction lessened; the middle classes were thus encouraged to have more children. In any case eugenics did not lead Pearson to develop any new statistical methods, nor did it play any role in the creation of his statistical methodology.

His wife, Marie Sharpe, died in 1928, and in 1929 he married  Margaret Victoria Child,  a  co-worker in  the Biometric Laboratory. Pearson was made Emeritus Professor in  1933  and  given a  room  in  the  Zoology Department  at  UCL,  which he used as the  office for Biometrika. From his retirement until his death in 1936, he published thirty-four articles and notes and continued to edit Biometrika.

Scholarship on Pearson

Pearson’s statistical work and innovations, his philosophy and  his ideas about  Darwinism,  evolutionary biology, Mendelism, eugenics, medicine, and elasticity have been of  considerable interest  to  innumerable  scientists and scholars for more than a century. Throughout the twentieth century, many commentators viewed Pearson as a disciple of Francis Galton  who merely expanded Galton’s ideas on correlation and regression. Consequently, a number of scholars have falsely assumed that Pearson’s motivation for creating a new statistical methodology arose from problems of eugenics. Among writers who have taken this view are Daniel  Kevles, Bernard Norton,  Donald Mackenzie, Theodore  Porter,  Richard  Soloway, and Tukufu Zuberi. However, using substantial corroborative historical evidence in Pearson’s archives, Eileen Magnello (1999) provided compelling documentation that Pearson not only managed the Drapers’ Biometric and the Galton Eugenics laboratories separately but also that they occupied separate physical spaces, that he maintained separate financial accounts, that he established very different journals, and that he created two completely different methodologies. Moreover, he took on  his work in the Eugenics Laboratory very reluctantly and wanted to relinquish  the  post  after one  year. Pearson emphasized to Galton that the sort of sociological problems that he was interested in  pursuing  for  his  eugenics program  were markedly different from the research that was conducted in the Drapers’ Biometric Laboratory.

Juxtaposing Pearson alongside Galton and eugenics has distorted the complexity and totality of Pearson’s intellectual enterprises, since there was virtually no relationship  between his  research in  “pure” statistics and  his agenda for the eugenics movement. This long-established but  misguided impression can be attributed  to  (1) an excessive  reliance on secondary sources containing false assumptions, (2)  the  neglect of  Pearson’s  voluminous archival material, (3) the use of a minute portion of his 600-plus published papers, (4) a conflation of some of Pearson’s biometric and crainometric work with that of eugenics, and (5) a blatant misinterpretation and misrepresentation of Pearsonian statistics.

Continuing  to  link Galton  with Pearson, Michael Bulmer (2003) suggested that the impetus to Pearson’s statistics came from his reading of Galton’s Natural Inheritance. However, Magnello (2004) argued that this view failed to take into account that Pearson’s initial reaction to Galton’s book in March 1889 was actually quite cautious. It was not until 1934, almost half a century later, when Pearson was 78 years old, that he reinterpreted the impact Galton’s book had on his statistical work in a more favorable light—long after Pearson had established the foundations to modern statistics.

The central role that Weldon played in the development of Pearson’s statistical program has been almost completely overlooked by most scholars, except for Robert Olby (1988) and Peter Bowler (2003), who gave Weldon greater priority than Galton in Pearson’s development of mathematical statistics as it related to problems of evolutionary biology. Weldon’s role in Pearson’s early published statistical papers was acknowledged by Churchill Eisenhart (1974),  Stephen Stigler (1986),  and  A. W.  F. Edwards (1993). In all her papers, Magnello addressed Weldon’s pivotal role in enabling Pearson to construct a new mathematically based statistical methodology.

Norton (1978a, 1978b) and Porter (2004) argue that Pearson’s iconoclastic and positivistic Grammar of Science played a role in the development of Pearson’s statistical work. However, Magnello (1999, 2005a) disputed this and argued that while The Grammar of Science represents his philosophy of science as a young adult, it does not reveal everything about his thinking and ideas, especially those in connection with his development of mathematical statistics. Thus, she maintains, it is not helpful to see this  book  as an  account  of  what  Pearson was to  do throughout the remaining forty-two years of his working life.

Although long-standing claims have been made by various commentators throughout the twentieth and early twenty-first centuries that  Pearson rejected Mendelism, Magnello (1998)  showed that  Pearson did  not  reject Mendelism completely but that he accepted the fundamental idea for discontinuous variation. Moreover, Philip Sloan (2000) argued that the biometricians’ debates clarified issues in Mendelism that otherwise might not have been developed with the rigor that they were to achieve.

Additionally, virtually all historians of science have failed to acknowledge that Pearson’s  and Galton’s  ideas, methods, and outlook on statistics were profoundly different. However, Bowler (2003) detected differences in their statistical thinking because of their different interpretations of evolution, and Stigler acknowledged their diverse approaches to  statistics in  his The  History of Statistics (1986). Magnello (1996, 1998, 1999, 2002) explained that whereas Pearson’s main focus was goodness of fit testing, Galton’s emphasis was correlation; Pearson’s higher level of mathematics for doing statistics was more mathematically complex than Galton’s; Pearson was interested in very large data sets (more than 1,000), whereas Galton was more concerned with smaller data sets of around 100 (owing to  the  explanatory power of percentages); and Pearson undertook long-term projects over several years, while Galton  wanted  faster results. Moreover, Galton thought all data had to conform to the normal distribution, whereas Pearson emphasised that empirical distributions could take on any number of shapes.

Given  the  pluralistic nature  of  Pearson’s  scientific work and the complexity of his many statistical innovations twinned  with his multifaceted persona, Pearson will no doubt continue to be of interest for many future scholars. Pearson’s legacy of establishing the foundations of contemporary mathematical statistics helped to create the modern world view, for his statistical methodology not only transformed our vision of nature but also gave scientists a set of quantitative tools to conduct research, accompanied with a universal scientific language that  standardized scientific writing in the twentieth century. His work went on to provide the foundations for such statisticians as R. A. Fisher, who went on to make further advancements in the modern theory of mathematical statistics.


  1. Bowler, Peter 2003. Evolution: The History of an Idea. 3rd ed. Berkeley: University of California Press.
  2. Bulmer, M 2003. Francis Galton: Pioneer of Heredity and Biometry. Baltimore, MD: Johns Hopkins University Press.
  3. Edwards, W. F. 1993. Galton, Pearson and Modern Statistical Theory. In Sir Francis Galton, FRS, The Legacy of His Ideas,
  4. Milo Keynes. London: Palgrave Macmillan.
  5. Eisenhart, Chur 1974. Karl Pearson. In Dictionary of Scientific Biography 10, 447–473. New York: Scribner’s.
  6. Hilts, Victor. Statist and Statistician. New York: Arno Press, 1981.
  7. Kevles, D 1985. In the Name of Eugenics: Genetics and the Uses of Human Heredity. New York: Knopf.
  8. Mackenzie, D 1981. Statistics in Britain 1865–1930: The Social Construction of Scientific Knowledge. Edinburgh: Edinburgh University Press.
  9. Magnello, Eileen. 1996. Karl Pearson’s Gresham Lectures: W. F. R. Weldon, Speciation and the Origins of Pearsonian Statistics. British Journal for the History of Science 29: 43–64.
  10. Magnello, Eileen. 1998. Karl Pearson’s Mathematisation of Inheritance: From Galton’s Ancestral Heredity to Mendelian Genetics (1895–1909). Annals of Science 55: 35–94.
  11. Magnello, Eileen. 1999. The Non-correlation of Biometrics and Eugenics: Rival Forms of Laboratory Work in Karl Pearson’s Career at University College London. Part 1. History of Science 37: 79–106; Part 2, 38: 123–150.
  12. Magnello, Eileen. 2002. The Introduction of Mathematical Statistics into Medical Research: The Roles of Karl Pearson,  Major Greenwood and Austin Bradford Hill. In The Road to Medical Statistics, eds. Eileen Magnello and Anne Hardy,  95–124. New York and Amsterdam: Rodopi.
  1. Magnello, Eileen. 2004. Statistically Unlikely. Review of Francis Galton: Pioneer of Heredity and Biometry, by Michael Bulmer. Nature 428: 699.
  2. Magnello, Eileen. 2005a. Karl Pearson and the Origins of Modern Statistics: An Elastician Becomes a Statistician. The Rutherford Journal: The New Zealand Journal for the History and Philosophy of Science and Technology. http://rutherfordjournal.org/. (Vol. 1, December).
  3. Magnello, Eileen. 2005b. Karl Pearson, Paper on the ChiSquare Goodness of Fit Test. In Landmark Writings in Western Mathematics: Case Studies, 1640–1940, ed. Ivor Grattan-Guinness, 724–731. Amsterdam: Elsevier.
  4. Norton, Bernar 1978a. Karl Pearson and the Galtonian Tradition: Studies in the Rise of Quantitative Social Biology. PhD diss., University College London.
  5. Norton, Bernar 1978b. Karl Pearson and Statistics: The Social Origin of Scientific Innovation. Social Studies of Science 8: 3–34.
  6. Olby, Rober 1988. The Dimensions of Scientific Controversy: The Biometrician-Mendelian Debate. British Journal for the History of Science 22: 299–320.
  7. Pearson, E 1936–1938. Karl Pearson: An Appreciation of Some Aspects of His Life and Work. Part 1, 1857–1905. Biometrika (1936): 193–257; Part 2, 1906–1936 (1938): 161–248. (Reprinted Cambridge, U.K.: Cambridge University Press, 1938).
  8. Pearson, 1914–1930. The Life, Letters and Labours of Francis Galton. 3 vols. Cambridge, U.K.: Cambridge University Press.
  9. Porter, Theodore 1986. The Rise of Statistical Thinking: 1820–1900. Princeton, NJ: Princeton University Press.
  10. Porter, Theodore 2004. Karl Pearson: The Scientific Life in a Statistical Age. Princeton, NJ: Princeton University Press.
  11. Sloan, Philip 2000. Mach’s Phenomenalism and the British Reception of Mendelism. Comptes Rendus de l’Académie des sciences 323: 1069–1079.
  12. Soloway, Richard 1990. Demography and Degeneration: Eugenics and the Declining Birthrate in Twentieth-Century Britain. Chapel Hill: University of North Carolina Press.
  13. Stigler, Stephen 1986. The History of Statistics: The Measure of Uncertainty before 1900. Cambridge, MA: Belknap Press.
  14. Stigler, Stephen 1999. Statistics on the Table: The History of Statistical Concepts and Methods. Cambridge, MA: Harvard University Press.
  15. Zuberi, T 2001. Thicker Than Blood: How Racial Statistics Lie. Minneapolis: University of Minnesota Press.

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