The History of Statistics

by Stigler, Stephen M.

• ISBN13: 9780674403413
• ISBN10: 067440341X
• Edition: Reprint
• Format: Paperback
• Copyright: 1990-03-01
• Publisher: Belknap Pr

Summary

This magnificent book is the first comprehensive history of statistics from its beginnings around 1700 to its emergence as a distinct and mature discipline around 1900.Stephen M. Stigler shows how statistics arose from the interplay of mathematical concepts and the needs of several applied sciences including astronomy, geodesy, experimental psychology, genetics, and sociology. He addresses many intriguing questions: How did scientists learn to combine measurements made under different conditions? And how were they led to use probability theory to measure the accuracy of the result? Why were statistical methods used successfully in astronomy long before they began to play a significant role in the social sciences? How could the introduction of least squares predate the discovery of regression by more than eighty years? On what grounds can the major works of men such as Bernoulli, De Moivre, Bayes, Quetelet, and Lexis be considered partial failures, while those of Laplace, Galton, Edgeworth, Pearson, and Yule are counted as successes? How did Galton's probability machine (the quincunx) provide him with the key to the major advance of the last half of the nineteenth century?Stigler's emphasis is upon how, when, and where the methods of probability theory were developed for measuring uncertainty in experimental and observational science, for reducing uncertainty, and as a conceptual framework for quantative studies in the social sciences. He describes with care the scientific context in which the different methods evolved and identifies the problems (conceptual or mathematical) that retarded the growth of mathematical statistics and the conceptual developments that permitted major breakthroughs.Statisticians, historians of science, and social and behavioral scientists will gain from this book a deeper understanding of the use of statistical methods and a better grasp of the promise and limitations of such techniques. The product of ten years of research, The History of Statistics will appeal to all who are interested in the humanistic study of science.

Table of Contents

Introduction	1	(8)
PART ONE The Development of Mathematical Statistics in Astronomy and Geodesy before 1827	9	(150)
Least Squares and the Combination of Observations	11	(51)
Legendre in 1805	12	(4)
Cotes's Rule	16	(1)
Tobias Mayer and the Libration of the Moon	16	(9)
Saturn, Jupiter, and Euler	25	(6)
Laplace's Rescue of the Solar System	31	(8)
Roger Boscovich and the Figure of the Earth	39	(11)
Laplace and the Method of Situation	50	(5)
Legendre and the Invention of Least Squares	55	(7)
Probabilists and the Measurement of Uncertainty	62	(37)
Jacob Bernoulli	63	(7)
De Moivre and the Expanded Binomial	70	(7)
Bernoulli's Failure	77	(1)
De Moivre's Approximation	78	(7)
De Moivre's Deficiency	85	(3)
Simpson and Bayes	88	(1)
Simpson's Crucial Step toward Error	88	(6)
A Bayesian Critique	94	(5)
Inverse Probability	99	(40)
Laplace and Inverse Probability	100	(5)
The Choice of Means	105	(4)
The Deduction of a Curve of Errors in 1772-1774	109	(4)
The Genesis of Inverse Probability	113	(4)
Laplace's Memoirs of 1777-1781	117	(3)
The Error Curve of 1777	120	(2)
Bayes and the Binomial	122	(9)
Laplace the Analyst	131	(4)
Nonuniform Prior Distributions	135	(1)
The Central Limit Theorem	136	(3)
The Gauss-Laplace Synthesis	139	(20)
Gauss in 1809	140	(3)
Reenter Laplace	143	(5)
A Relative Maturity: Laplace and the Tides of the Atmosphere	148	(9)
The Situation in 1827	157	(2)
PART TWO The Struggle to Extend a Calculus of Probabilities to the Social Sciences	159	(104)
Quetelet's Two Attempts	161	(60)
The de Keverberg Dilemma	163	(6)
The Average Man	169	(5)
The Analysis of Conviction Rates	174	(8)
Poisson and the Law of Large Numbers	182	(4)
Poisson and Juries	186	(8)
Comte and Poinsot	194	(1)
Cournot's Critique	195	(6)
The Hypothesis of Elementary Errors	201	(2)
The Fitting of Distributions: Quetelismus	203	(18)
Attempts to Revive the Binomial	221	(18)
Lexis and Binomial Dispersion	222	(3)
Arbuthnot and the Sex Ratio at Birth	225	(1)
Buckle and Campbell	226	(3)
The Dispersion of Series	229	(4)
Lexis's Analysis and Interpretation	233	(1)
Why Lexis Failed	234	(3)
Lexian Dispersion after Lexis	237	(2)
Psychophysics as a Counterpoint	239	(24)
The Personal Equation	240	(2)
Fechnner and the Method of Right and Wrong Cases	242	(12)
Ebbinghaus and Memory	254	(9)
PART THREE A Breakthrough in Studies of Heredity	263	(100)
The English Breakthrough: Galton	265	(35)
Galton, Edgeworth, Pearson	266	(1)
Galton's Hereditary Genius and the Statistical Scale	267	(5)
Conditions for Normality	272	(3)
The Quincunx and a Breakthrough	275	(6)
Reversion	281	(2)
Symmetric Studies of Stature	283	(7)
Data on Brothers	290	(3)
Estimating Variance Components	293	(1)
Galton's Use of Regression	294	(3)
Correlation	297	(3)
The Next Generation: Edgeworth	300	(26)
The Critics' Reactions to Galton's Work	301	(1)
Pearson's Initial Response	302	(3)
Francis Ysidro Edgeworth	305	(2)
Edgeworth's Early Work in Statistics	307	(4)
The Link with Galton	311	(4)
Edgeworth, Regression, and Correlation	315	(4)
Estimating Correlation Coefficients	319	(3)
Edgeworth's Theorem	322	(4)
Pearson and Yule	326	(37)
Pearson the Statistician	327	(2)
Skew Curves	329	(4)
The Pearson Family of Curves	333	(5)
Pearson versus Edgeworth	338	(4)
Pearson and Correlation	342	(3)
Yule, the Poor Law, and Least Squares: The Second Synthesis	345	(13)
The Situation in 1900	358	(5)
Appendix A. Syllabus for Edgeworth's 1885 Lectures	363	(4)
Appendix B. Syllabus for Edgeworth's 1892 Newmarch Lectures	367	(3)
Suggested Readings	370	(4)
Bibliography	374	(25)
Index	399