International Statistical Review

The Language of the English Biometric School

John Aldrich

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

This paper considers the language devised by Karl Pearson and his associates for discussing distributions, populations and samples, the basic language for frequentist inference. The original language-some of which is still in use-is described and also the changes it underwent under the influence of R.A. Fisher and of Russian and American mathematicians. The period covered is roughly 1890-1950.

Article information

Source
Internat. Statist. Rev., Volume 71, Number 1 (2003), 109-129.

Dates
First available in Project Euclid: 17 March 2004

Permanent link to this document
https://projecteuclid.org/euclid.isr/1079557578

Zentralblatt MATH identifier
1114.62301

Keywords
Statistical notation Karl Pearson R.A. Fisher

Citation

Aldrich, John. The Language of the English Biometric School. Internat. Statist. Rev. 71 (2003), no. 1, 109--129. https://projecteuclid.org/euclid.isr/1079557578


Export citation

References

  • [1] Airy, G.B. (1861/79). \textit{On the Algebraical and Numerical Theory of Errors of Observations and the Combination of Observations}, third edition in 1879. London: Macmillan.
  • [2] Aldrich, J. (1997). R.A. Fisher and the Making of Maximum Likelihood 1912-22. \textit{Statistical Science}, \textbf{12}, 162-176.
  • [3] Aldrich, J. (1998). Doing Least Squares: Perspectives from Gauss and Yule. \textit{International Statistical Review}, \textbf{66}, 61-81.
  • [4] Aldrich, J. (2001). \textit{Karl Pearson: A Reader's Guide}, on the website:\newline $\mathtt{http://www.economics.soton.ac.uk/staff/aldrich/kpreader.htm}$
  • [5] Anderson, O. (1914). Nochmals Über ``The Elimination of Spurious Correlation Due to Position in Time or Space''. \textit{Biometrika}, \textbf{% 10}, 269-279.
  • [6] Anderson, T.W. (1959/84). \textit{An Introduction to Multivariate Statistical Analysis}, second edition in 1984. New York: Wiley.
  • [7] Bartlett, M.S. (1933). On the Theory of Statistical Regression. \textit{Proceedings of the Royal Society of Edinburgh},\textbf{ 53}, 260-283.
  • [8] Bennet, J.H. (1990). \textit{Statistical Inference and Analysis: Selected Correspondence of R.A. Fisher}. Oxford: Oxford University Press.
  • [9] Bertrand, J. (1908). \textit{Calcul des Probabilités}, second edition reprinted in 1965 by Chelsea New York.
  • [10] Brunt, D. (1917). \textit{The Combination of Observations}. Cambridge: Cambridge University Press.
  • [11] Chauvenet, W. (1863). \textit{A Manual of Spherical and Practical Astronomy}. Philadelphia: Lippincott.
  • [12] Chuprov (Tchouproff), A.A. (1918/19). On the Mathematical Expectation of the Moments of Frequency Distributions (in two parts). \textit{Biometrika}, \textbf{12}, 140-169 & 185-210.
  • [13] Church, A.E.R. (1925). On the Moments of the Distribution of Squared Standard Deviations for Samples of $N$ Drawn from an Indefinitely Large Population. \textit{Biometrika}, \textbf{17}, 79-83.
  • [14] Cornish, E.A. & Fisher, R.A. (1937). Moments and Cumulants in the Specification of Distributions. \textit{Revue de l'Institut International de Statistique}, \textbf{5}, 307-320.
  • [15] Cramér, H. (1937). \textit{Random Variables and Probability Distributions}. Cambridge: Cambridge University Press.
  • [16] Cramér, H. (1946). \textit{% Mathematical Methods of Statistics}. London: Princeton University Press.
  • [17] Cramér, H. (1976). Half a Century with Probability Theory: Some Personal Recollections. \textit{Annals of Probability}, \textbf{4}, 509-546.
  • [18] David, H.A. (2001). First (?) Occurrence of Common Terms in Statistics and Probability, Appendix B and pp. 219-228 in David & Edwards (2001).
  • [19] David, H.A. & Edwards, A.W.F. (Eds.) (2001). \textit{Annotated Readings in the History of Statistics}. New York: Springer.
  • [20] Edgeworth, F.Y. (1883). On the Method of Least Squares. \textit{% Philosophical Magazine, 5th Series}, \textbf{16}, 360-375.
  • [21] Eisenhart, C. (1979). On the Transition from Student's $z$ to Student's $t$. \textit{American Statistician}, \textbf{33}, 6-10.
  • [22] Elderton, W.P. (1906). \textit{Frequency-Curves and Correlation}. London: Layton.
  • [23] Elderton, W.P. & Johnson, N.L. (1969). \textit{Systems of Frequency Curves}. Cambridge: Cambridge University Press.
  • [24] Feller, W. (1950). \textit{An Introduction to Probability Theory and its Applications volume 1}. New York: Wiley.
  • [25] Fisher, R.A. (1912). On an Absolute Criterion for Fitting Frequency Curves. \textit{Messenger of Mathematics}, \textbf{41}, 155-160.
  • [26] Fisher, R.A. (1915). Frequency Distribution of the Values of the Correlation Coefficient in Samples from an Indefinitely Large Population. \textit{Biometrika}, \textbf{10}, 507-521.
  • [27] Fisher, R.A. (1918). The Correlation between Relatives on the Supposition of Mendelian Inheritance. \textit{% Transactions of the Royal Society of Edinburgh}, \textbf{52}, 399-433.
  • [28] Fisher, R.A. (1919). The Genesis of Twins. \textit{Genetics},\textbf{ 4}, 489-499.
  • [29] 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 of the Royal Astronomical Society, 80, 758-770.
  • [30] Fisher, R.A. (1921). On the `Probable Error' of a Coefficient of Correlation Deduced from a Small Sample. \textit{% Metron}, \textbf{1}, 3-32.
  • [31] Fisher, R.A. (1922). On the Mathematical Foundations of Theoretical Statistics. \textit{Philosophical Transactions of the Royal Society A}, \textbf{222}, 309-368.
  • [32] Fisher, R.A. (1922a). On the Interpretation of $χ^{2}$ from Contingency Tables, and the Calculation of $P$. \textit{Journal of the Royal Statistical Society}, \textbf{85}, 87-94
  • [33] Fisher, R.A. (1922b). The Goodness of Fit of Regression Formulae, and the Distribution of Regression Coefficients. \textit{Journal of the Royal Statistical Society,} \textbf{85}, 597-612.
  • [34] Fisher, R.A. (1924/8). On a Distribution Yielding the Error Functions of Several Well Known Statistics. \textit{% Proceedings of the International Congress of Mathematics, Toronto,} \textbf{2% }, 805-813.
  • [35] Fisher, R.A. (1925). \textit{Statistical Methods for Research Workers} (second edition in 1928, fourth in 1932). Edinburgh: Oliver & Boyd.
  • [36] Fisher, R.A. (1925a). Applications of `Student's' Distribution. \textit{Metron}, \textbf{5}, 90-104. CP43.
  • [37] Fisher, R.A. (1925b). Theory of Statistical Estimation. \textit{Proceedings of the Cambridge Philosophical Society}, \textbf{22}, 700-725.
  • [38] Fisher, R.A. (1925c). Sur la Solution de l'\'{E}quation Intégrale de M.V. Romanovsky. \textit{Comptes Rendus}, \textbf{180}, 1897-1899.
  • [39] Fisher, R.A. (1928). The General Sampling Distribution of the Multiple Correlation Coefficient. \textit{% Proceedings of the Royal Society, A}, \textbf{121}, 654-673.
  • [40] Fisher, R.A. (1929). Moments and Product Moments of Sampling Distributions. \textit{Proceedings of the London Mathematical Society, Series 2}, \textbf{30}, 199-238.
  • [41] Fisher, R.A. (1935). \textit{The Design of Experiments}. Edinburgh: Oliver & Boyd.
  • [42] Fisher, R.A. (1939). ``Student''. \textit{Annals of Eugenics}, \textbf{9}, 1-9.
  • [43] Fisher, R.A. (1948). Conclusions Fiduciaires. \textit{Annales de l'Institute Henri Poincaré}, \textbf{10}% , 191-213.
  • [44] Fisher, R.A. (1955). Statistical Methods and Scientific Induction. \textit{Journal of the Royal Statistical Society, B% }, \textbf{17}, 69-78.
  • [45] Fisher, R.A. (1956). \textit{Statistical Methods and Scientific Inference}. Edinburgh: Oliver & Boyd.
  • [46] Galton, F. (1889). \textit{Natural Inheritance}. London: Macmillan.
  • [47] Greenwood, M. (1924). Review of \textit{The Calculus of Observations% } by E.T. Whittaker & G. Robinson. \textit{Journal of the Royal Statistical Society, }\textbf{87}, 291-293.
  • [48] Greenwood, M. (1926). Professor Tschouprow on the Theory of Correlation. \textit{Journal of the Royal Statistical Society, }\textbf{89}, 320-325.
  • [49] Hald, A. (1998). \textit{A History of Mathematical Statistics from 1750 to 1930}. New York: Wiley.
  • [50] Halperin, M., Hartley, H.O. & Hoel, P.G. (1965). Recommended Standards for Statistical Symbols and Notation. \textit{American Statistician% }, \textbf{19}, 12-14.
  • [51] Hardy, G.H. & Littlewood. J.E. (1914). Some Problems of Diophantine Approximation. \textit{Acta Mathematica}, \textbf{37}, 155-191.
  • [52] Helmert, F.R. (1876). Die Genauigkeit der Formel von Peters zur Berechnung des wahrscheinlichen Fehlers directer Beobachtungen gleicher Genauigkeit. \textit{Astronomische Nachrichten}, \textbf{88}, 113-132. (extract translated in David and Edwards (2001)).
  • [53] Hotelling, H. (1928). Review of R.A. Fisher's \textit{Statistical Methods for Research Workers. Journal of the American Statistical Association% }, \textbf{23}, 346.
  • [54] Hotelling, H. (1930). The Consistency and Ultimate Distribution of Optimum Statistics. \textit{Transactions of the American Mathematical Society}, \textbf{32}, 847-859.
  • [55] Jeans, J.H. (1904). \textit{The Dynamical Theory of Gases}. Cambridge: Cambridge University Press.
  • [56] Jeffreys, H. (1939). \textit{Theory of Probability}. Oxford: Oxford University Press.
  • [57] Kendall, M.G. (1943). \textit{The Advanced Theory of Statistics, vol 1}. London: Griffin.
  • [58] Kotz, S. & Johnson, N.L. (1992). \textit{Breakthroughs in Statistics Volume 2}. New York: Springer.
  • [59] Kruskal W.H. & Stigler, S.M. (1997). Normative Terminology, revised version in Stigler (1999).
  • [60] Lehmann, E.L. (1959). \textit{Testing Statistical Hypotheses}. New York: Wiley.
  • [61] Lehmann, E.L. (1999). ``Student'' and Small-Sample Theory. \textit{Statistical Science}, \textbf{14}, 418-426.
  • [62] Markov, A.A. (1912). \textit{Wahrscheinlichkeitsrechnung}. Leipzig: Teubner.
  • [63] Maxwell, J.C. (1860). Illustrations of the Dynamical Theory of Gases. \textit{Philosophical Magazine}, \textbf{19}, 19-32.
  • [64] Maxwell, J.C. (1867). On the Dynamical Theory of Gases. \textit{Philosophical Transactions of the Royal Society}, \textbf{157}, 49-88.
  • [65] Miller, J. (Ed.) (continuing) \textit{Earliest Known Uses of Some of the Words of Mathematics} on the website:\newline $\mathtt{http://members.aol.com/jeff570/mathword.html}$
  • [66] Miller, J. (Ed.) (continuing) \textit{% Earliest Uses of Various Mathematical Symbols} on the website: \newline $\mathtt{\noindent http://members.aol.com/jeff570/mathsym.html}$
  • [67] Neyman (Splawa-Neyman), J. (1925). Contributions to the Theory of Small Samples Drawn from a Finite Population (in Miscellanea). \textit{% Biometrika}, \textbf{17}, 472-479.
  • [68] Neyman, J. (1934). On the Two Different Aspects of the Representative Method (with discussion). \textit{Journal of the Royal Statistical Society, }\textbf{97,} 558-625.
  • [69] Neyman, J. (1967). R.A. Fisher (1890-1962): An Appreciation. \textit{Science}, \textbf{156}, 1456-1460.
  • [70] Neyman, J. & Pearson, E.S. (1928). On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference. \textit{% Biometrika}, \textbf{20}, 175-240 and 263-294.
  • [71] Pearson, E.S. (1936/8). Karl Pearson: An Appreciation of Some Aspects of his Life and Work, In Two Parts. \textit{Biometrika}, \textbf{28}% , 193-257, \textbf{29}, 161-247.
  • [72] Pearson, K. (1874-7). Lecture Notes on the Theory of Probability, held in Manuscript Room University College London Library list number 46.
  • [73] Pearson, K. (1893). Contributions to the Mathematical Theory of Evolution (Abstract). \textit{Proceedings of the Royal Society, }\textbf{54}, 329-333.
  • [74] Pearson, K. (1894). Contributions to the Mathematical Theory of Evolution. \textit{Philosophical Transactions of the Royal Society A}, \textbf{185}, 71-110.
  • [75] Pearson, K. (1894-6). Notes on Karl Pearson's lectures on the theory of statistics taken by G.U. Yule. University College London Library list number 84/2.
  • [76] Pearson, K. (1895). Contributions to the Mathematical Theory of Evolution. II. Skew Variation in Homogeneous Material. \textit{Philosophical Transactions of the Royal Society A}, \textbf{186}, 343-414.
  • [77] Pearson, K. (1896). Mathematical Contributions to the Theory of Evolution. III. Regression, Heredity and Panmixia. \textit{Philosophical Transactions of the Royal Society A}, \textbf{187}, 253-318.
  • [78] Pearson, K. (1900). On the Criterion that a Given System of Deviations from the Probable in the Case of Correlated System of Variables is such that it can be reasonably Supposed to have Arisen from Random Sampling. \textit{Philosophical Magazine}, \textbf{50% }, 157-175.
  • [79] Pearson, K. (1901). Mathematical Contributions to the Theory of Evolution. X. Supplement to a Memoir on Skew Variation. \textit{Philosophical Transactions of the Royal Society A}, \textbf{197}, 443-459.
  • [80] Pearson, K. (1903). (Editorial) On the Probable Errors of Frequency Constants. \textit{Biometrika}, \textbf{2}, 273-281.
  • [81] Pearson, K. (1905). On the General Theory of Skew Correlation and Non-linear Regression. \textit{Drapers' Company Research Memoirs, Biometric Series II}. Cambridge: Cambridge University Press.
  • [82] Pearson, K. (1914). \textit{Tables for Statisticians and Biometricians}. Cambridge: Cambridge University Press.
  • [83] Pearson, K. (1915). (Editorial) On the Distribution of the Standard Deviations of Small Samples: Appendix I to Papers by ``Student'' and R.A. Fisher. \textit{Biometrika}, \textbf{10}, 522-529.
  • [84] Pearson, K. (1916). Mathematical Contributions to the Theory of Evolution. XIX. Second Supplement to a Memoir on Skew Variation. \textit{Philosophical Transactions of the Royal Society A}% , \textbf{216}, 529-557.
  • [85] Pearson, K. (1916a). On the General Theory of Multiple Contingency with Special Reference to Partial Contingency. \textit{Biometrika}, \textbf{11}, 145-158.
  • [86] Pearson, K. (1920). Notes on the History of Correlation. \textit{Biometrika}, \textbf{13}, 25-45.
  • [87] Pearson, K. (1922) (Ed.) \textit{Tables of the Incomplete }$Γ$\textit{-Function}. Cambridge: Cambridge University Press.
  • [88] Pearson, K. (1925). Further Contributions to the Theory of Small Samples. \textit{Biometrika,} \textbf{17% }, 176-199.
  • [89] Pearson, K. (1931). (Editorial) Historical Note on the Distribution of the Standard Deviations of Samples of any Size Drawn from an Infinitely Large Normal Parent Population. \textit{% Biometrika}, \textbf{23}, 416-418.
  • [90] Pearson, K. (1936). Method of Moments and Method of Maximum Likelihood. \textit{Biometrika}, \textbf{28}, 34-59.
  • [91] 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. \textit{Philosophical Transactions of the Royal Society A,} \textbf{191}, 229-311.
  • [92] Porter, T.M. (1986). \textit{The Rise of Statistical Thinking 1820-1900}. Princeton: Princeton University Press.
  • [93] Rietz, H.L (1927). \textit{Mathematical Statistics}. Chicago: Open Court.
  • [94] Romanovsky, V. (1925). Sur Certaines \'{E}spérances Mathématiques et sur l'Erreur Moyenenne du Coefficient de Corrélation. \textit{Comptes Rendus}, \textbf{180}, 1897-1899.
  • [95] Seneta, E. (1994). Probability in Russia before Kolmogorov. In \textit{Companion Encyclopedia to the History and Philosophy of the Mathematical Sciences}. Ed. I. Grattan-Guiness, chapter 10.6 and pages 1325-1334. London: Routledge.
  • [96] Snedecor, G.W. (1934). \textit{Calculation and Interpretation of Analysis of Variance and Covariance}. Ames, Iowa: Collegiate Press.
  • [97] Soper, H.E. (1913). On the Probable Error of the Correlation Coefficient to a Second Approximation. \textit{Biometrika}, \textbf{9}, 91-115.
  • [98] Soper, H.E., Young, A.W., Cave, B.M., Lee, A. & Pearson, K. (1917). On the Distribution of the Correlation Coefficient in Small Samples. Appendix II to the Papers of `Student' and R. A. Fisher. A Cooperative Study. \textit{Biometrika}, \textbf{11}, 328-413.
  • [99] Stigler, S.M. (1976). Discussion of ``On Rereading R.A. Fisher''. \textit{Annals of Statistics}, \textbf{4}, 441-500.
  • [100] Stigler, S.M. (1986). \textit{A History of Statistics}. \textit{The Measurement of Uncertainty before 1900}. Cambridge, MA: Belknap Press.
  • [101] Stigler, S.M. (1999). \textit{Statistics on the Table}. Cambridge, MA: Belknap Press.
  • [102] Student (1908). The Probable Error of a Mean. \textit{Biometrika}, \textbf{6}, 1-25.
  • [103] Student (1908a). Probable Error of a Correlation Coefficient. \textit{Biometrika}, \textbf{6}, 302-310.
  • [104] Student (1909). The Distribution of the Means of Samples which are not Drawn at Random. \textit{Biometrika}, \textbf{7}, 210-214.
  • [105] Student (1921). An Experimental Determination of the Probable Error of Dr Spearman's Correlation Coefficients. \textit{Biometrika}, \textbf{13}, 263-282.
  • [106] Student (1925). New Tables for Testing the Significance of Observations. \textit{Metron}, \textbf{5}, 105-108.
  • [107] Thomson, W. & Tait, P.G. (1867). \textit{Treatise on Natural Philosophy volume 1}. Oxford: Clarendon Press.
  • [108] von Plato, J. (1994). \textit{Creating Modern Probability}. Cambridge: Cambridge University Press.
  • [109] Wald, A. (1939). Contributions to the Theory of Statistical Estimation and Testing Hypotheses. \textit{Annals of Mathematical Statistics}% , \textbf{10}, 299-326.
  • [110] Walker, H.M. (1929). \textit{Studies in the History of Statistical Method}. Baltimore: Williams & Wilkins.
  • [111] Weatherburn, C.E. (1946). \textit{A First Course in Mathematical Statistics}. Cambridge: Cambridge University Press.
  • [112] Weldon, W.F.R. (1890). The Variations Occurring in Certain Decapod Crustacea-I. \textit{Crangon vulgaris}. \textit{Proceedings of the Royal Society}, \textbf{47}, 445-453.
  • [113] Weldon, W.F.R. (1893). On Certain Correlated Variations. In \textit{Carcinus Møe nas}, \textit{Proceedings of the Royal Society, }\textbf{54}, 318-329.
  • [114] Whitworth, W.A. (1901). \textit{Choice and Chance}, fifth edition. Cambridge: Deighton Bell.
  • [115] Wilks, S.S. (1944). \textit{Mathematical Statistics}. Princeton: Princeton University Press.
  • [116] Yule, G.U. (1896). Notes on the History of Pauperism in England and Wales from 1850, Treated by the Method of Frequency-curves; with an Introduction on the Method. \textit{Journal of the Royal Statistical Society}% , \textbf{59}, 318-357.
  • [117] Yule, G.U. (1897). On the Significance of Bravais' Formulae for Regression, &c., in the Case of Skew Correlation. \textit{Proceedings of the Royal Society of London}, \textbf{60}, 477-489.
  • [118] Yule, G.U. (1907). On the Theory of Correlation for any Number of Variables, Treated by a New System of Notation. \textit{Proceedings of the Royal Society A}, \textbf{79}, 182-193.
  • [119] Yule, G.U. (1911). \textit{An Introduction to the Theory of Statistics}. London: Griffin.
  • [120] Yule, G.U. & Kendall, M.G. (1950). \textit{An Introduction to the Theory of Statistics}, 14th edition. London: Griffin.