STIGLER, Stephen M.
The history of statistics
2000
ISBN 067440341X
 

Contents
Introduction  1
PART ONE
The Development of Mathematical Statistics in Astronomy and Geodesy before 1827  9
1. Least Squares and the Combination of Observations 11 Legendre in 1805
12
Cotes's Rule 16
Tobias Mayer and the Libration of the Moon 16
Saturn, Jupiter, and Euler 25
Laplace's Rescue of the Solar System 31
Roger Boscovich and the Figure of the Earth 39
Laplace and the Method of Situation 50
Legendre and the Invention of Least Squares 55
2. Probabilists and the Measurement of Uncertainty 62
Jacob Bernoulli 63
De Moivre and the Expanded Binomial 70
Bernoulli's Failure 77 De Moivre's Approximation 78
De Moivre's Deficiency 85
Simpson and Bayes 88
Simpson's Crucial Step toward Error 88
A Bayesian Critique 94
3. Inverse Probability 99
Laplace and Inverse Probability 100
The Choice of Means 105
The Deduction of a Curve of Errors in 1772-1774 109
The Genesis of Inverse Probability 113
Laplace's Memoirs of 1777-1781 117
The Error Curve of 1777 120
Bayes and the Binomial 122
Laplace the Analyst 131
Nonuniform Prior Distributions 135
The Central Limit Theorem 136
4. The Gauss -Laplace Synthesis 139
Gauss in 1809 140
Reenter Laplace 143
A Relative Maturity: Laplace and the Tides of the Atmosphere 148
The Situation in 1827 157
PART TWO
The Struggle to Extend a Calculus of Probabilities to the Social Sciences 159
5. Quetelet's Two Attempts 161
The de Keverberg Dilemma 163
The Average Man 169
The Analysis of Conviction Rates 174
Poisson and the Law of Large Numbers 182
Poisson and juries 186
Comte and Poinsot 194
Cournot's Critique 195
The Hypothesis of Elementary Errors 201
The Fitting of Distributions: Quetelismus 203
6. Attempts to Revive the Binomial 221
Lexis and Binomial Dispersion 222
Arbuthnot and the Sex Ratio at Birth 225
Buckle and Campbell 226
The Dispersion of Series 229
Lexis's Analysis and Interpretation 233
Why Lexis Failed 234
Lexian Dispersion after Lexis 237
7. Psychophysics as a Counterpoint 239
The Personal Equation 240
Fechner and the Method of Right and Wrong Cases 242
Ebbinghaus and Memory 254
PART THREE
A Breakthrough in Studies of Heredity 263
8. The English Breakthrough: Galton 265
Galton, Edgeworth, Pearson 266
Galton's Hereditary Genius and the Statistical Scale 267
Conditions for Normality 272
The Quincunx and a Breakthrough 275
Reversion 281
Symmetric Studies of Stature 283
Data on Brothers 290
Estimating Variance Components 293
Galton's Use of Regression 294
Correlation 297
9. The Next Generation: Edgeworth 300
The Critics' Reactions to Galton's Work 301
Pearson's Initial Response 302
Francis Ysidro Edgeworth 305
Edgeworth's Early Work in Statistics 307
The Link with Galton 311
Edgeworth, Regression, and Correlation 315
Estimating Correlation Coefficients 319
Edgeworth's Theorem 322
10. Pearson and Yule 326
Pearson the Statistician 327
Skew Curves 329
The Pearson Family of Curves 333
Pearson versus Edgeworth 338
Pearson and Correlation 342
Yule, the Poor Law, and Least Squares: The Second Synthesis 345
The Situation in 1900 358
Appendix A. Syllabus for Edgeworth's 1885 Lectures 363
Appendix B. Syllabus for Edgeworth's 1892  Newmarch Lectures 367
Suggested Readings 370
Bibliography 374
Bibliography
The works listed below have all been consulted in the edition or editions for which full bibliographical details are given. When a reprint has been accessible, that edition has been cited also, although the listing of reprints is far from complete. When a published translation is available, I have cited it in the bibliography and consulted it in preparing my own version. In general, translations presented in the text are my own; exceptions are indicated in the bibliography by notes stating that page references are to a translation.
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1898. Das Gesetz der Kleinen Zahlen. Leipzig: Teubner.
1909. Statistique. In Encyclopédie des sciences mathématiques pures et appliquées 1 (4): 453-480.
1918. Homogeneität and Stabilität in der Statistik. Särtryck ur Skandinavisk Aktuarietidskrift 1- 2: 1- 81.
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1883a. The law of error. Philosophical Magazine, 5th series, 16: 300-309. 1883b. The method of least squares. PhilosophicalMagazine, 5th series, 16: 360-375.
1883c. On the method of ascertaining a change in the value of gold.
Journal of the Royal Statistical Society 46: 714-718.
1884. Review of Investigations in Currency and Finance by W. S. Jevons. Academy July 19, 1884: 38-39.
1885a. Observations and statistics: an essay on the theory of errors of observation and the first principles of statistics. Transactions of the Cambridge Philosophical Society 14: 138-169. Abstracted in Proceedings of the Cambridge Philosophical Society 5: 310-312; corrigendum in Proceedings of the Cambridge Philosophical Society 6: 101-102.
1885b. Methods of statistics. Jubilee Volume of the Statistical Society, pp. 181-217.
1885c. On methods of ascertaining variations in the rate of births, deaths and marriages. Journal of the Royal Statistical Society 48: 628-649. Abstracted in the Report of the British Association for the Advancement of Science for 1885, pp. 1165-1166.
1885d. Calculus of probabilities applied to psychical research, I. Proceedings of the Society for Psychical Research 3: 190-208.
1886a. Progressive means. Journal of the Royal Statistical Society 49: 469475.
1886b. The law of error and the elimination of chance. Philosophical Magazine, 5th series, 21: 308-324.
1886c. Problems in probabilities. Philosophical Magazine, 5th series, 22: 371-384.
1887a. The empirical proof of the law of error. PhilosophicalMagazine, 5th series, 24: 330-342.
1887b. On observations relating to several quantities. Hermathena 6:279285.
1887c. Metretike: or, The Method of Measuring Probability and Utility. London: Temple.
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1888a. The mathematical theory of banking. Journal of the Royal Statistical Society 51: 113 - 127. Abstracted in the Report of the British Association for the Advancement of Science for 1886, pp. 776-778.
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1889. Review of Natural Inheritance by F. Galton. Nature 39: 603604.
1890. The element of chance in competitive examinations. Journal of the Royal Statistical Society 53: 460-475, 644-663. Abstracted in the Report of the British Association for the Advancement of Science for 1890, p. 920.
1892a. Correlated averages. Philosophical Magazine, 5th series, 34: 190204.
1892b. The law of error and correlated averages. Philosophical Magazine, 5th series, 34: 429-438, 518-526.
1893a. A new method of treating correlated averages. PhilosophicalMagazine, 5th series, 35: 63-64.
1893b. Exercises in the calculation of errors. Philosophical Magazine, 5th series, 36: 98-111.
1893c. Note on the calculation of correlation between organs. Philosophical Magazine, 5th series, 36: 350-351.
1893d. Statistical correlation between social phenomena. Journal of the Royal Statistical Society 56: 670-675. Abstracted in the Report of the British Association for the Advancement of Science for 1893, pp. 852-853.
1894a. Asymmetrical correlation between social phenomena. Journal of the Royal Statistical Society 57: 563-568.
1894b. The asymmetrical probability curve. Proceedings of the Royal Society of London 56: 271-272.
1895. On some recent contributions to the theory of statistics. Journal of the Royal Statistical Society 58: 506-515.
1896a. Bemerkungen über die Kritik meiner "Methoden der Statistik" von Dr. v. Bortkewitsch. Jahrbücher für Nationalökonomie and Statistik, 3rd series, 11: 274-277.
1896b. Eine Erwiderung. Jahrbücher für Nationalökonomie und Statistik, 3rd series, 12: 838-845.
1896c. Supplementary notes on statistics. Journal of the Royal Statistical Society 59: 529-539.
1898. Miscellaneous applications of the calculus of probabilities, contd. Journal of the Royal Statistical Society 61: 119-131.
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1905. The law of error. Transactions of the Cambridge Philosophical Society 20: 36-65, 113- 141.
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1911. Probability. In Encyclopaedia Britannica, 11th ed. New York: Encyclopaedia Britannica.
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1768. Lettres à une princesse d'Allemagne sur divers sujets de physique & de philosophie, 3 vols. St. Petersburg: Académie imperiale des sciences.
1778. Observationes in praecedentem dissertationem. Acta Academiae Scientiarum Imperialis Petropolitanae for 1777, pars prior, 24- 33. Reprinted in translation, with Kendall, 1961.
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[Farr, William]. 1848. Eighth Annual Report of the Registrar-General of Births, Deaths, and Marriages, in England. London: W. Clowes and Sons.
Fechner, Gustav Theodor. 1831. Massbestimmungen über die Galvanische Kette. Leipzig: Brockhaus.
1860. Elemente der Psychophysik, 2 vols. Vol. 1 translated, 1966; as Elements of Psychophysics, trans. Helmut E. Adler, ed. Davis H. Howes and Edwin G. Boring. New York: Holt, Rinehart & Winston. Page references are to this translation.
1882. Revision der Hauptpuncte der Psychophysik. Leipzig: Breitkopf and Hartel.
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1928. On a distribution yielding the error functions of several well known statistics. Proceedings of the International Mathematical Congress Held in Toronto, 1924, 2: 805-813.
1935. The Design of Experiments. Edinburgh: Oliver and Boyd.
1959. Statistical Methods and Scientific Inference, 2nd ed. Edinburgh: Oliver and Boyd.
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Galloway, Thomas. 1839. A Treatise on Probability. Edinburgh: Adam and Charles Black.
Galton, Francis. 1853. The Narrative of an Explorer in Tropical South Africa. London: John Murray.
1863. Meteorographica, or Methods of Mapping the Weather. London: Macmillan.
1869. Hereditary Genius: An Inquiry into its Laws and Consequences. London: Macmillan (2nd ed., 1892).
1874a. On a proposed statistical scale. Nature 9: 342-343.
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