STATISTICS

The invention of statistics involved the recognition of a distinct and widely applicable set of procedures based on mathematical probability for studying mass phenomena.

theoretical debates

Pierre-Simon Laplace (1749–1827) is generally considered one of the fathers of (inverse) probabilities, mainly applied to astrophysics. He exploited the previous works of Abraham de Moivre (1667–1754) and Jakob Bernoulli (1654–1705). The development of mathematical probability, although motivated by problems in insurance, the social sciences, and astronomy, was actually linked to the analysis of games of chance. But, instead of adopting the law of large numbers (according to which the larger the sample, the less the conclusion will be liable to error), Laplace further developed an intuition of Thomas Bayes (1701–1761), who replaced the ordinary assumption of equally likely causes with the principle of a priori probabilities, which holds that each of the different causes of an event may occur. A direct probability is the chance that a fair coin tossed ten times will yield six heads and four tails; the inverse probability is the probability that the coin is unfair once it is known that six heads and four tails appeared in ten tosses. This conclusion allowed Laplace to indicate, for example, the most likely causes (climate, biology, etc.) of the higher rate of male births in London than in Paris.

The application of probability to the social sciences centered around the work of the Belgian Adolphe Quetelet (1796–1874). As a follower of the large numbers law, he supported general censuses rather than sample studies, whose selection he considered arbitrary. He was reluctant to group together as homogenous data that which he believed were not. Social scientists were thus encouraged to gather as much data as possible. Quetelet's name is tightly bound to the notion of the average person, with the statistical average turned into an ideal social type, for example, the average height of the soldier, the average income, age, and so on of a criminal or a drunk. He used probabilities to estimate the propensity of the average person to commit a crime. Quetelet saw in the regularity of crime the proof that statistical-social laws are true when applied to the whole society, although they may be false for a single individual. This approach reflected the nineteenth-century positivistic ideal of a science able to manage society. The liberal notion of equality is also reflected in the average person: in principle no a priori distinctions are made between individuals, but their social attitudes, as "scientifically" proved, can prevent society from deviance. Deviations from the average (and normality, as Émile Durkheim added later [1895]) cancel themselves out when a large enough number of cases is considered. In this view, statistics confirmed the stability of bourgeois society (Quetelet was writing in the immediate aftermath of the 1848 revolution) while trying to identify regularities in the apparent chaos that accompanied the fall of the ancien régime and the onset of the Industrial Revolution.

The judgment of homogeneity, however, could be made either on external grounds or on internal evidence. One solution consisted in developing a test of homogeneity internal to data (accomplished, for example, by the German statistician Wilhelm Lexis (1837–1914); another solution was to develop a methodology that acted as a surrogate for experimental control in social sciences. The three main contributors to the latter approach were Francis Galton, Francis Ysidro Edgeworth, and Karl Pearson. Galton (1822–1911), a romantic English traveler with a medical background, is known principally for his Hereditary Genius (1869). Unlike Quetelet, Galton seemed more interested in the exceptional than in the average. In his approach, the homogeneity of data was the starting tool and not the aim, as in Quetelet; in fact, once a stable homogenous group had been identified, Galton raised the question of identifying deviation from the average. For example, he classified how well hundreds of people performed a particular talent as evaluated according to a pre-settled scale. On this ground he identified the probability that certain characteristics of peas could be reproduced according to hereditary laws, and he extended this conclusion to human beings.

Edgeworth (1845–1926) corrected Galton's approach using Laplacés analysis of inverse probability. Edgeworth divided a population into subgroups and tested their homogeneity. By doing so, he anticipated the modern t-test and variance analysis. Pearson (1857–1936) went beyond Edgeworth's conclusions by considering homogenous groups and corresponding curves to be mental constructs rather than real phenomena. Pearson's philosophy of science, as expressed in his Grammar of Science (1892), constituted the ground on which he developed his analysis of skew curves, which were outside the bounds of the "normal distribution" studied by his predecessors.

The social and political implications of this new generation's studies were important. Galton is generally considered the founder of eugenics, the evolutionary doctrine holding that the condition of human beings can be improved through a scientific process of breeding rather than through education. Galton concluded that the upper classes hold their rank based not on greater economic means but on superior biological characteristics. Pearson further developed this approach in what became a form of social Darwinism: on the ground of a "real scientific knowledge" the state had to promote efficient reproduction of individuals, beyond personal beliefs and market competition.

Beginning in the 1860s and particularly during the last quarter of the nineteenth century, however, increasing criticism of positivism led to attacks on social and statistical determinism. Individual free will was opposed to "social laws" and statistical averages; Lexis and Georg Friedrich Knapp (1842–1926) in Germany, their students, and most of the Russian statisticians criticized universal statistical laws. They identified national paths of economic and demographic growth, and, by the same token, they stressed the role of individual freedom in social dynamics. According to Knapp, because every individual is different from every other individual, the notion of variation should replace that of statistical error.

Tightly linked with national specificities, regional and monographic analysis enjoyed increasing success in the last quarter of the nineteenth century. These studies were mostly developed in Germany and Russia where federalism (in the former case) or local governments (the zemstvos, in the latter case) encouraged studies on local economic conditions.

From a theoretical point of view, however, these studies raised a serious problem: in the absence of regular homogenous censuses, academic statisticians were rather skeptical about inference from samples largely gathered by administrative (above all local) statistical offices. Classical histories of statistics have contended that the theory of sampling was roughly constructed by the Norwegian statistician Anders Kiaer (1838–1919) in the 1890s and fully developed by Jerzy Neyman (1894–1981) in 1934. But the practice and theory of sampling were first developed in Russia, where, starting in the 1870s, several statistical bureaus of local self-government organizations (the zemstvos) developed monographic studies on the local population. Most of these studies were "partial" in the sense that they covered only a part of the population. During the following years, the best method of selecting the sample was under discussion in the meetings of the Russian statisticians as well as in their main publications. The first solution considered was that of a completely random selection; unfortunately, this approach required the contemporary achievement of general censuses upon which the test of representativeness could be made. Starting in 1887 a majority of Russian statisticians supported a "reasoned" selection of the sampling based on the investigator's knowledge of the main characteristics of the local economy and society. In the following years and up through the outbreak of World War I, Alexander Chuprov (1874–1926), Pafnuty Chebyshev (1821–1894), and Andrei Markov (1856–1922) strongly contributed to the development of sampling and probability theory in general.

Nevertheless, not only in Russia, but throughout Europe, the use of statistics in local and monographic studies highlighted the difficulty of balancing the reliability of studies and the need to limit their costs. The trade-off between cost–benefit analysis and sampling significance expressed two different notions of the use of scientific knowledge in the public sphere.

statisticians and bureaucrats

Before the nineteenth century, state statistics were limited to state budgeting and demographic concerns. It was only with the increasing economic and social activity of administrations that calculus and statistics acquired major social, political, and organizational roles. The nineteenth century was a period of increasing enthusiasm for statistics as a tool for a scientific management of politics. The positivist ideal and the reformist attitude of most of the European governments contributed to this success. Statistics entered general newspapers, and statistical societies multiplied after the 1830s (an era of social reforms in several European countries) either as sections of broader associations (e.g., the Academy of Sciences in France, the British Association for the Advancement of Science) or as independent associations (e.g., the London or Birmingham Statistical Society, the American Statistical Association). These different outcomes were linked either to the scientific debate (statistics as an independent science or as a general method for other sciences) or had political origins. For example, in Russia, up to World War I, local statisticians were forbidden from gathering as a group and were obliged to find a place in the general meetings of naturalists' associations.

International conferences aimed to offer the image of an international "objective" and homogenous science, and as such, held out the promise of the "scientific." Statisticians complained about the "ignorance" of professional politicians and the differences in the organization of national statistics. In France the statistical apparatus was highly centralized, whereas in Britain, Germany, and Russia, local administrations on the one hand and academicians on the other hand played major roles in the organization of statistical enquiries. Statisticians soon claimed not a mere executive but also a decisional role. In most of the nineteenth-century societies, this problem was deepened by the fact that statisticians mostly came from a different social group than did top-rank bureaucrats and politicians. Statistical analysis thus became a forum for professional, social, and political debates. For example, French and British statisticians focused on health problems in the burgeoning cities, as well as the living and working conditions of workers, and called for social and political reforms. For their part, Russian statisticians stressed the need for agrarian reforms and recommended the redistribution of noble and state lands to the peasants. World War I pushed specialists' ambitions to their apogee, while the ensuing interwar period was marked by the success of administrative bureaucracies.

See alsoDemography; Galton, Francis; Quetelet, Lambert Adolphe Jacques.

bibliography

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Alessandro Stanziani