Statistical Science

Fisher in 1921

Stephen Stigler

Full-text: Open access


Ronald A. Fisher’s 1921 article on mathematical statistics (submitted and read in 1921; published in 1922) was arguably the most influential article on that subject in the twentieth century, yet up to that time Fisher was primarily occupied with other pursuits. A number of previously published documents are examined in a new light to argue that the origin of that work owes a considerable (and unacknowledged) debt to a challenge issued in 1916 by Karl Pearson.

Article information

Statist. Sci. Volume 20, Number 1 (2005), 32-49.

First available in Project Euclid: 6 June 2005

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

R. A. Fisher Karl Pearson Kirstine Smith maximum likelihood minimum chi square sufficiency history of statistics


Stigler, Stephen. Fisher in 1921. Statist. Sci. 20 (2005), no. 1, 32--49. doi:10.1214/088342305000000025.

Export citation


  • Aldrich, J. (1997). R. A. Fisher and the making of maximum likelihood 1912--1922. Statist. Sci. 12 162--176.
  • Bennett, J. H., ed. (1983). Natural Selection, Heredity, and Eugenics. Including Selected Correspondence of R. A. Fisher with Leonard Darwin and Others. Oxford Univ. Press, New York.
  • Bennett, J. H., ed. (1990). Statistical Inference and Analysis: Selected Correspondence of R. A. Fisher. Oxford Univ. Press, New York.
  • Bennett, T. L. (1908). Errors of Observation (Technical Lecture No. 4, 1907--1908; delivered February 22, 1908; Ministry of Finance, Survey Department, Egypt). National Printing Department, Cairo.
  • Bennett, T. L. (1920). The theory of measurement of changes in cost of living. J. Roy. Statist. Soc. 83 455--462.
  • Berkson, J. (1980). Minimum chi-square, not maximum likelihood! Ann. Statist. 8 457--487.
  • Box, J. F. (1978). R. A. Fisher: The Life of a Scientist. Wiley, New York.
  • Chauvenet, W. (1891). A Manual of Spherical and Practical Astronomy, 5th ed. (two volumes). Lippincott, Philadelphia. The appendix on least squares was also published separately by the same publisher in 1884 with the title A Treatise on the Method of Least Squares, or the Theory of Probabilities in the Combination of Observations.
  • Crathorne, A. R. (1926). The course in statistics in the mathematics department. Amer. Math. Monthly 33 185--194.
  • Eddington, A. S. (1914). Stellar Movements and the Structure of the Universe. Macmillan, London.
  • Edwards, A. W. F. (1974). The history of likelihood. Internat. Statist. Rev. 42 9--15.
  • Edwards, A. W. F. (1994). R. A. Fisher on Karl Pearson. Notes and Records Roy. Soc. London 48 97--106.
  • Edwards, A. W. F. (1997a). Three early papers on efficient parametric estimation. Statist. Sci. 12 35--47.
  • Edwards, A. W. F. (1997b). What did Fisher mean by ``inverse probability'' in 1912--1922? Statist. Sci. 12 177--184.
  • Fienberg, S. E. and Hinkley, D. V., eds. (1980). R. A. Fisher: An Appreciation. Lecture Notes in Statist. 1. Springer, New York.
  • Fisher, R. A. (1912). On an absolute criterion for fitting fre- quency curves. Messenger of Mathematics 41 155--160. Reprinted as paper 1 in R. A. Fisher (1974). Also reprinted in A. W. F. Edwards (1997a). Statist. Sci. 12 35--47.
  • Fisher, R. A. (1913). Applications of vector analysis to geometry. Messenger of Mathematics 42 161--178. Reprinted as paper 2 in R. A. Fisher (1974).
  • Fisher, R. A. (1915). Frequency distribution of the values of the correlation coefficient in samples from an indefinitely large population. Biometrika 10 507--521. Reprinted as paper 4 in R. A. Fisher (1974).
  • Fisher, R. A. (1918). The correlation between relatives on the supposition of Mendelian inheritance. Trans. Roy. Soc. Edinburgh 52 399--433. Reprinted as paper 9 in R. A. Fisher (1974). Also reprinted with commentary in P. A. P. Moran and C. A. B. Smith (1966). Eugenics Laboratory Memoirs XLI.
  • Fisher, R. A. (1920). A mathematical examination of the methods of determining the accuracy of an observation by the mean error, and by the mean square error. Monthly Notices Roy. Astronomical Soc. 80 758--770. Reprinted as paper 12 in R. A. Fisher (1974).
  • Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Philos. Trans. Roy. Soc. London Ser. A 222 309--368. Reprinted as paper 18 in R. A. Fisher (1974).
  • Fisher, R. A. (1925). Theory of statistical estimation. Proc. Cambridge Philos. Soc. 22 700--725. Reprinted as paper 42 in R. A. Fisher (1974).
  • Fisher, R. A. (1935). Review of Biomathematics, by W. M. Feldman. Annals of Eugenics 6 252.
  • Fisher, R. A. (1937). Professor Karl Pearson and the method of moments. Annals of Eugenics 7 303--318. Reprinted as paper 149 in R. A. Fisher (1974).
  • Fisher, R. A. (1974). Collected Papers of R. A. Fisher (5 volumes.) (J. H. Bennett, ed.). Univ. Adelaide.
  • Geisser, S. (1992). Introduction to ``On the mathematical foundations of theoretical statistics,'' by R. A. Fisher. In Breakthroughs in Statistics 1 (S. Kotz and N. L. Johnson, eds.) 1--10. Springer, New York.
  • Hald, A. (1998). A History of Mathematical Statistics From 1750 to 1930. Wiley, New York.
  • Hinkley, D. V. (1980). Theory of statistical estimation: The 1925 paper. R. A. Fisher: An Appreciation. Lecture Notes in Statist. 1 85--94. Springer, New York.
  • Kiefer, J. C. (1959). Optimum experimental designs. J. Roy. Statist. Soc. Ser. B 21 272--319.
  • Kruskal, W. (1980). The significance of Fisher: A review of R. A. Fisher: The Life of a Scientist (by Joan Fisher Box). J. Amer. Statist. Assoc. 75 1019--1030.
  • Merton, R. K. (1967). On Theoretical Sociology. Free Press, New York.
  • Moran, P. A. P. and Smith, C. A. B. (1966). Commentary on R. A. Fisher's paper on ``The correlation between relatives on the supposition of Mendelian inheritance.'' Eugenics Laboratory Memoirs XLI. Published for the Galton Laboratory, University College London, by Cambridge Univ. Press.
  • Neyman, J. (1951). Review of R. A. Fisher's Contributions to Mathematical Statistics. The Scientific Monthly 72 406--408.
  • Neyman, J. and Pearson, E. S. (1928). On the use and interpretation of certain test criteria for purposes of statistical inference: Part I. Biometrika 20A 175--240.
  • Norton, B. and Pearson, E. S. (1976). A note on the background to, and refereeing of, R. A. Fisher's 1918 paper ``On the correlation between relatives on the supposition of Mendelian inheritance.'' Notes and Records Roy. Soc. London 31 151--162.
  • Pearson, E. S. (1938). Karl Pearson: An Appreciation of Some Aspects of His Life and Work. Cambridge Univ. Press, Cambridge. Originally published in 1936, 1938 in parts: Biometrika 28 193--257, 29 161--248.
  • Pearson, E. S. (1968). Some early correspondence between W. S. Gosset, R. A. Fisher and Karl Pearson, with notes and comments. Biometrika 55 445--457.
  • Pearson, K. (1936). Method of moments and method of maximum likelihood. Biometrika 28 34--59.
  • Pearson, K. and 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. Roy. Soc. London Ser. A 191 229--311.
  • Porter, T. M. (2004). Karl Pearson: The Scientific Life in a Statistical Age. Princeton Univ. Press.
  • Pratt, J. W. (1976). F. Y. Edgeworth and R. A. Fisher on the efficiency of maximum likelihood estimation. Ann. Statist. 4 501--514.
  • Rao, C. R. (1961). Asymptotic efficiency and limiting information. Proc. Fourth Berkeley Symp. Math. Statist. Probab. 1 531--546. Univ. California Press, Berkeley.
  • Rao, C. R. (1962). Efficient estimates and optimum inference procedures in large samples (with discussion). J. Roy. Statist. Soc. Ser. B 24 46--72.
  • Savage, L. J. (1976). On rereading R. A. Fisher (with discussion). Ann. Statist. 4 441--500.
  • Sills, D. L. and Merton, R. K. (1991). Social Science Quotations. Macmillan, New York. First appeared in 1991 as Vol. 19 of the International Encyclopedia of the Social Sciences.
  • Smith, K. (1916). On the ``best'' values of the constants in frequency distributions. Biometrika 11 262--276.
  • Smith, K. (1918). On the standard deviations of adjusted and interpolated values of an observed polynomial function and its constants and the guidance they give towards a proper choice of the distribution of observations. Biometrika 12 1--85.
  • Smith, K. (1922). The standard deviations of fraternal and parental correlation coefficients. Biometrika 14 1--22.
  • Stigler, S. M. (1973). Laplace, Fisher, and the discovery of the concept of sufficiency. Biometrika 60 439--445. Reprinted in M. G. Kendall and R. L. Plackett, eds. (1977). Studies in the History of Statistics and Probability 2 271--277. Griffin, London.
  • Stigler, S. M. (1976). Contribution to discussion of ``On rereading R. A. Fisher,'' by L. J. Savage. Ann. Statist. 4 498--500.
  • Stigler, S. M. (1978). Mathematical statistics in the early states. Ann. Statist. 6 239--265.
  • Stigler, S. M. (1986). The History of Statistics: The Measurement of Uncertainty Before 1900. Harvard Univ. Press.
  • Stigler, S. M. (1999a). Statistics on the Table: The History of Statistical Concepts and Methods. Harvard Univ. Press.
  • Stigler, S. M. (1999b). The foundations of statistics at Stanford. Amer. Statist. 53 263--266.
  • Stigler, S. M. (2001). Ancillary history. In State of the Art in Probability and Statistics. Festschrift for Willem R. van Zwet (M. de Gunst, C. Klaassen and A. van der Vaart, eds.) 555--567. IMS, Beachwood, OH.
  • Zabell, S. (1989). R. A. Fisher on the history of inverse probability (with discussion). Statist. Sci. 4 247--263.
  • Zabell, S. L. (1992). R. A. Fisher and the fiducial argument. Statist. Sci. 7 369--387.