Francis Galton: Pioneer of Heredity and Biometry

6. The Charms of Statistics

168 6 The Charms of Statistics The Charms of Statistics.—It is difficult to understand why statisticians commonly limit their inquiries to Averages, and do not revel in more comprehensive views. Their souls seem as dull to the charm of variety as that of the native of one of our flat English counties, whose retrospect of Switzerland was that, if its mountains could be thrown into its lakes, two nuisances would be got rid of at once. An Average is but a solitary fact, whereas if a single other fact be added to it, an entire Normal Scheme, which nearly corresponds to the observed one, starts potentially into existence . Some people hate the very name of statistics, but I find them full of beauty and interest.... They are the only tools by which an opening can be cut through the formidable thicket of difficulties that bars the path of those who pursue the Science of man. Galton, Natural Inheritance Historians of science have recognized that there was a “probability revolution ” in the period 1830–1930, which led to the application of probability theory and statistical models to a wide range of problems in the natural and social sciences (Porter 1986; Krüger, Daston, and Heidelberger 1987; Gigerenzer et al. 1989; Hacking 1990). The revolution began with the demonstration of statistical regularities in social data by Quetelet, on which he built a science of “social physics”; Quetelet’s work inspired both Galton’s statistical theory of heredity and Maxwell’s statistical interpretation of the kinetic theory of gases. This growing range of applications reflects the increasing acceptance of statistical laws as valid scientific explanations. It was accompanied by a reinterpretation of the meaning of probability, from rational degree of belief to relative frequency in the long run. These statistical applications were accompanied by the development of the corresponding statistical theory. Of particular importance were the invention of the concepts of regression and correlation by Francis Galton, and their development on a sound mathematical basis by Karl Pearson, which are described in this chapter; their attempt to construct a statistical The Charms of Statistics 169 theory of heredity based on these ideas is discussed in the next two chapters . The normal distribution played a key role in these developments. It was usually represented in the nineteenth century by the function f x c x c ( ) exp ( )/ = − − [ ] 1 2 π μ . [1] This formula defines a family of distributions with the same bell shape but depending on two parameters, μ and c, the mean and the modulus, which respectively determine its location and dispersion. (The square of the modulus is twice the variance, σ2 .) The importance of the normal distribution is due to the central limit theorem, which states that the sum of a large number of independent random variables of individually small effect follows a normal distribution , almost regardless of their individual distributions. This theorem was formulated as a general result by Laplace about 1810 and was applied by him and others to explain why errors of measurement, particularly in astronomy, were approximately normal; for this reason, it was often called the “law of error.” It was applied to the human sciences by Quetelet, with whose work Galton became familiar from his book Letters on Probabilities, published in 1846 and translated into English in 1849. (It was written in the form of letters to the Grand Duke of Saxe Coburg and Gotha, the father of Prince Albert.) It was not called the “normal distribution” until the 1870s, when this term was independently used by three men, Charles S. Peirce, Francis Galton, and Wilhelm Lexis; since the same date it has also been called the “Gaussian distribution” after the great mathematician Carl Friedrich Gauss, who associated it with the method of least squares in 1809 (Stigler 1999). Quetelet and the Average Man Adolphe Quetelet (1796–1874) was a Belgian mathematician who made his career as an astronomer and meteorologist at the Royal Observatory in Brussels. On a visit to Paris to learn the practical side of these subjects, he found out about probability and its applications and was struck by the statistical regularity of observations on large numbers of individuals. For example, he found that the stillbirth rate in Belgium was consistently higher in towns than in the country; about 6 per cent of the urban babies and only 3 percent of the rural babies were stillborn. He went on to show 170 Francis...