## The History of Statistics

Statistics is one of those disciplines, relatively rare, which leads an unconfined existence. Unlike zoology or geometry, statistics ministers to an immense variety of needs, both academic and practical. The techniques and skills of statistical science serve the quantum physicist, the economist, the sociologist, the psychologist; they are to be found at work in virtually all government departments, bureaucracies, and corporations which shape and control the modern world. How many people poring in puzzlement over complex numerical tabulations have paused to wonder where and when the characteristic ideas and methods of this powerful and pervasive discipline originated and grew to maturity?

Stephen Stigler has the answers to such questions in this lengthy, technical, and learned history of statistics. The story he tells is a European one, with a specifically English finale. It covers the two centuries between 1700 and 1900, that period in which the discipline of statistics was formed out of the concepts and requirements of several diverse fields. His guiding theme is the notion of uncertainty, which is the main preoccupation of modern statistical thinking. All scientific activities which engage with and depend upon measurement have to be concerned with uncertainty, the degree to which measured quantities and the propositions based upon them are accurate. Uncertainty, technically speaking, is the name of the concepts and techniques which estimate quantitative accuracy, and is at the heart of the statistical enterprise.

Stigler partly discerns the origins of this science of uncertainty within the problems encountered by astronomers in the eighteenth century. The elimination of potential errors was of vital importance for astronomy, because crucial theoretical issues, notably those of planetary and lunar motion, depended on the degrees of accuracy which could be brought to bear computationally upon observations of complex dynamical systems. This line of origin traced by Stigler therefore runs through a tradition of mathematician-astronomers, such as Pierre-Simon Laplace, culminating with Adrien Legendre’s formulation of the method of least squares of 1805. The other route he follows is the sequence of efforts made by mathematicians to produce an effective probability calculus; first, by showing how the chances of error decrease as the number of observations increase and, second, by performing calculations based upon the mean value of results produced by observation. With the following of such methods, it was claimed, large errors would almost certainly be eliminated, and the likelihood of small errors persisting would be considerably diminished.

The motivations for such work, and the store of empirical materials upon which it drew, indicate a largeness and complexity to the question of the origins of statistical science that is not immediately apparent in Stigler’s opening chapters. By the eighteenth century, astronomy was a long-established and thoroughly mathematicized discipline, and it is therefore unremarkable that astronomers in their pursuit of theoretical accuracy should contribute significantly to the design of mathematical techniques for the elimination of error. Nevertheless, equally striking in the eighteenth century was the drive, both general and profound, to submit the whole observable world to number and measure where at all possible. This drive was apparent not merely where one might have expected it, in experimental physical sciences such as electricity and chemistry. It was equally present in attempts to formulate a viable social science which might prove as successful for the understanding, prediction, and control of the social world as physics and astronomy had proved for the natural world. The eighteenth century was in this sense a scientistic age, and mathematicians such as Laplace, who pursed the possibility of a genuine social science, were by no means untypical in their pursuit.

Stigler, in his close and necessary focus on technical mathematical advances, is by no means unaware of these larger features of eighteenth century development, but in his account, for the eighteenth century at least, the quest for social science remains in the background, and statistics moves into the nineteenth century armed with its technical achievements in probability theory and error distribution.

With the advent of Adolphe Quetelet’s work in the 1820’s, the issue of the historical relationship of statistics to social science became more pressing, and Stigler presents Quetelet’s project as a definitive step toward incorporating probability theory within practical social science. The first half of the nineteenth century was a period of great expansion for practical statistics, with work going forward especially in the study of population and of public health. Quetelet’s early...

(The entire section is 1981 words.)