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The Logic of the Normal Law of Error in Mental Measurement

Edwin G. Boring
The American Journal of Psychology
Vol. 31, No. 1 (Jan., 1920), pp. 1-33
DOI: 10.2307/1413989
Stable URL: http://www.jstor.org/stable/1413989
Page Count: 33
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Notes and References

This item contains 72 references.

[Footnotes]
  • 1
    This reference contains 3 citations:
    • I. Todhunter, History of the mathematical theory of probability, 1865
    • Pascal and Fer- mat in 1654
    • Laplace: 624 pp.
  • 2
    G. U. Yule, Introduction to the theory of statistics, 4th ed., 1917, 256.
  • 3
    This reference contains 4 citations:
    • Joh. von Kries, Die Principien der Wahrscheinlichkeitsrechnung, 1886, 6. The book is "eine logische Untersuchung."
    • A. Kaufmann, Theorie und Methoden der Statistik, 1913, 43ff.
    • C. Stumpf, in Sitzunlgsber, d. k. bayr. Akad. zu München (philos.-philol. Cl.), 1892, 37-120
    • 41, 61-79
  • 4
    G. Boole, An investigation of the laws of thought, 1854, 370.
  • 5
    Op. cit., 10f.
  • 6
    H. Westergaard, Grundzüge der Theorie der Statistik, 1890, 4.
  • 7
    Loc. cit.
  • 8
    J. Venn, Logic of chance, 3rd ed., 1888, discusses probability as "amount of belief," where " ignorance of the individual is pre- supposed" and "causation . . . denied, within considerable limits: " p. 122.
  • 9
    This reference contains 2 citations:
    • A. Fisher, Mathematical theory of probabilities, 1917, vol. I, 9.
    • Kaufmann's, loc. cit.
  • 12
    This reference contains 6 citations:
    • F. Y. Edge- worth, Mind O. S. 9, 1884, 230
    • K. Pearson approves this view: Grammar of science, 3rd ed., 1911, pt. i, 146.
    • Edgeworth in article on Probability, Ency. Brittanica, 1911, xxii, 377, 391
    • Edgeworth, Cam. Philos. Trans. 20, 1905, 128ff.
    • Pearson, Chances of death, 1897, i, 13ff., 48
    • Westergaard, op. cit., 21-56
  • 13
    This reference contains 4 citations:
    • Venn's chapter on Measurement of belief, op. cit., 119ff.. q. v.
    • F. M. Urban, Ueber den Begriff der matematischen Wahrscheinlichkeit, Vierteljahrschrift f. wiss. Philos. u. Soziol. 35, 1911, 1-49, 145-185.
    • Venn, 152-162
    • Venn, 118
  • 14
    This reference contains 7 citations:
    • De Moivre, 1718
    • Todhunter, op. cit. 71f., 136, 191ff., 552f.
    • Laplace's Theorie analytique des probabiliteés brought together and supplemented in 1812 his work of thirty-five years, and gives the development of the law of error on pages 275ff.
    • Todhunter, 485
    • Gauss gives the formula in Article 178 of the Theoria inotus corporumn coelestium, 1809
    • Abhand'lungen zur Methode der kleinstem Quadrate, 1887, 102f.
    • ibid., 207.
  • 15
    Todhunter, op. cit.
  • 16
    W. S. Jevons, Principles of science, 1883, 375-385.
  • 17
    This reference contains 3 citations:
    • Jevons, op. cit., 380f.
    • L. D. Weld, Theory of errors and least squares, 1916, 41-56
    • E. G. Boring, Am. J. Psychol. 28, 1917, 465ff.
  • 18
    This reference contains 2 citations:
    • Gauss, op. cit., 4
    • 92ff., 129, 139ff., etc.
  • 19
    Urban, Psychol. Rev. 17, 1910, 242.
  • 20
    Op. cit., 240-244.
  • 21
    This reference contains 17 citations:
    • Graunt, 1662
    • Craig, 1699
    • N. Ber- noulli, 1709
    • Arbuthot, 1699
    • De Moivre, 1718
    • Simpson, 1757
    • D. Bernoulli, 1760
    • Lambert, 1773
    • Lagrange, 1798
    • Laplace, 1812
    • Todhunter, op. cit., 37, 41, 54f., 193, 196, 211, 228f., 265, 320, .335, 349, 423, 426, 446, 500f., 546, 589-613, 615ff.
    • Laplace in the Essai philosophique sur les probabiliteés
    • Théorie (op. cit.)
    • A. Quetelet was a Belgian statistician, who published an Essai de physique sociale in 1835
    • Lettres sur la thiéorie des probabiliteés in 1846
    • W. Lexis, Zur Theorie der Massener- scheinungen in der menschlichen Gesellschaft, 1877, II
    • Kaufmann, op. cit., 12, 163.
  • 22
    This reference contains 3 citations:
    • Letters on the theory of probabilities, trans. 1849, 91-96.
    • pp. 95f.
    • "Thomme moyennne" in Kauf- mann, op. cit., 110ff.
  • 23
    Letters, pp. 97f.
  • 24
    This reference contains 3 citations:
    • F. Galton, Hereditary Genius, 1869, 26-36
    • Gauss: Elemente der Psychophysik, i, 1859, 104
    • Revision der Hauptpuncte der Psychophysik, 1882, 40f., 45
  • 25
    This reference contains 2 citations:
    • M. R. Trabue, Completion-test language scales, 1916, 29-60
    • note, p. 31
  • 26
    This reference contains 2 citations:
  • 27
    M. Merriman, Textbook of the method of least squares, 1884, 14.
  • 28
    This reference contains 2 citations:
    • Quetelet: Letters, 96f.
    • Philos. Trans. 1862, i, 1895, 344f
  • 29
    This reference contains 2 citations:
    • Quetelet, Letters, 286-295
    • Venn, Nature, 36, 1887, 411ff.
  • 30
    P. 290.
  • 31
    P. 286.
  • 32
    This reference contains 2 citations:
    • Proc. Roy. Soc. 29, 1879, 365-367.
    • D. McAlister, ibid., 367-376
  • 33
    Philos. Trans., loc. cit.
  • 34
    Philos. Mag., 5th ser., 50, 1900, 173.
  • 36
    This reference contains 3 citations:
    • " Skew variation in homogeneous material " are Philos, Trans. 186A, i, 1895, 343-414
    • 197A, 1901, 443-459
    • "On the general theory of skew correlation and non-linear re- gression, " Drapers' Co. Research Memoir, 1905
  • 37
    J. Bertrand, Calcul des probabilitiés, 1889, 180f.
  • 40
    Lexis, op. cit.; see especially 34ff.
  • 41
    Fisher's translation of unternormal and übernormal as " sub- normal " and " hypernormal " is due presumably to his otherwise ex- cellent " dano-English," for which he so modestly apologizes : op. cit., 125 and xv.
  • 43
    V. Fisher, op. cit., 124ff.
  • 44
    E. Czuber, Wahrscheinlichkeitsrechnung, 2 Aufl., 1910, 34-78.
  • 45
    Op. cit., 226ff.
  • 46
    Op. cit., 241.
  • 47
    Op. cit. 10-83.
  • 48
    R. Pearl, Variation and differentiation in Ceratophyllum, 1907; especially 90f.
  • 49
    This reference contains 17 citations:
    • Bravais, 1845
    • Quetelet (admitted Bravais' argument), 1846
    • Lexis, 1877
    • Galton, 1879
    • McAlister, 1879
    • Bertrand, 1889
    • Pearson, 1895 and emphatically in 1900
    • Pearl, 1904
    • Urban, 1910
    • R. L. Ellis, Philos Mag., 3 ser., 1850, 321-328
    • Jevons, op. cit., 1883, 374ff.
    • Venn, Nature, 36, 1887, 411ff.
    • Logic of chance, 1888, 23-52, 501ff.
    • Fisher, op. cit., 1917, 149
    • Urban, op. cit., 241
    • Fisher, loc. cit.
    • C. S. Pierce, Report of U. S. Coast Survey, 1870, 212ff.
  • 50
    This reference contains 2 citations:
  • 51
    foot-note above, p. 12.
  • 52
    This reference contains 3 citations:
    • Pp. 30ff.
    • pp. 54ff.
    • J. B. Miner, Deficiency and delinquency, 1918, 252ff.
  • 53
    foot-note on p. 31
  • 54
    This reference contains 7 citations:
    • Pear- son, for example, in his study of " The relationship of intelligence to size and shape of head, and to other physical and mental characters, " Biometrika 5, 1906, 105-146.
    • pp. 106f., 118
    • Miner's discussion, op. cit., 254-276
    • 255f.
    • 267ff., 272-276
    • 272ff.
    • pp. 255 and 273f.
  • 55
    Pearson, Phil. Mag., op. cit.
  • 58
    This reference contains 6 citations:
    • Westergaard, op. cit., 21-38
    • Pear- son, Chances of Death, 1897, i, 11-25, 44-62
    • pp. 57f.
    • Westergaard's experiment is in op. cit., 36f.
    • Pearson's computations are in Phil. Mag., 5 ser., 50, 1900, 167ff.
    • Fisher, op. cit., 127-145.
  • 59
    This reference contains 2 citations:
    • note below
    • W. Shanks, Proc. Roy. Soc. 21, 1873, 319.
  • 61
    Venn, op. cit., 111-118, 247f.
  • 62
    Edgeworth, Cam. Philos. Trans. 20, 1905, 128-130.
  • 63
    S. Newcomb, " Note on the frequency of use of the different digits in natural numbers," Amer. J. Math. 4, 1881, 39f.
  • 64
    This reference contains 2 citations:
    • Biometrika 3, 1904, 142f.
    • Pearson and A. Lee, ibid. 2, 1903, 357-462
  • 66
    This reference contains 2 citations:
    • Biometrika 3, 1904, 147.
    • ibid. 5, 1906, 105ff.
  • 67
    This reference contains 3 citations:
    • Pearson and G. A. Jaederholm, Mendelism and the probliem of mental defect, II: On the continuity of mental defect, 1914
    • Pearson, Mendelism and the problem of mental defect, III: On the graduated character of mental defect, etc., 1914
    • II, 28-36, 46f.
  • 68
    Opp. citt., Mendelism, etc., 11, 46.
  • 69
    This reference contains 2 citations:
    • Miner, op. cit., 267-279
    • p. 275.
  • 70
    Miner's distinction between "physical units" and "more equivalent biological units," op. cit., 255
  • 71
    This reference contains 2 citations:
    • Pearson, Mendelism, etc., II, 36ff.
    • Miner, op. cit., 260ff.
  • 72
    Pearson has appointed himself " watch-dog " of "logic in scientific procedure ", Mendelism, etc., III, 3f.
  • 73
    This reference contains 4 citations:
    • Urban, op. cit., 257ff.
    • Arch. f. d. ges. Psychol. 16, 1909, 168-227, espec. 224f.
    • H. Keller's experiments, Psychol. Stud. 3, 1907, 49-89
    • Urban's discussion of them, Arch. f. d. ges. Psychol. 18, 1910, 400-410
  • 74
    Boring, Amer. J. Psychol. 28, 1917, 465ff.
  • 75
    Psychol. Rev. 17, 247.
  • 76
    S. S. George's experiment, Amer. J. Psychol. 28, 1917, 1-37.
  • 77
    This reference contains 6 citations:
    • Ueber einige Begriffe und Aufgaben der Psychophysik, Arch. f. d. ges. Psychol. 30, 1913, 113-152
    • Amer. J. Psychol. 24, 1913, 274
    • The Application of Statistical Methods to the Problems of Psychophysics, 1908, 5, 14
    • Arch. f. d. ges. Psychol. 15, 1909, 264f.
    • Psychol. Rev. 17, 229
    • Arch. 30 (op. cit.)
  • 78
    Psychol. Rev. 17, 243
  • 80
    E. B. Titchener, Experimental psychology, Quantitative student's manual, 1905, xix-xxxvii.
  • 81
    E. B. Holt, The Freudian wish, 1916, espec. 153ff.
  • 82
    O. Klemm, A history of psychology, trans. 1914, 150-155, 232-267
  • 83
    C. J. West, Introduction to mathematical statistics, 1918, 94