6 The rise of statistical thinking in the 19 th century
6.3 Discovery of social phenomena and their stability
People working in the statistical offi ces were civil servants, and statistical socie-ties were manned by more or less ordinary citizens whose knowledge of statistics was limited. The large amount of numbers appeared incoherent – even chaotic – because there was nothing that tied them together (see Hacking 1990). It was necessary that scientists with vision develop a theory before social research and statistics could gain plausibility and become widely accepted. Characteristic to that era was disbelief that human populations could include such regularities.
Theory building became possible when statistical offi ces and societies began to publish comparable statistics.
6.3.1 Early examples of social research
Before the avalanche of printed numbers started, there were only few examples of social research. William Petty’s Political Arithmetic was practiced in some
form up to the middle of the 19th century. Political arithmetic was a discipline of empirical collection of population records and preparation of accurate life ta-bles. Its idea was bookkeeping of the population facts, not research. For example, Halley’s life tables were mainly used for actuarial purposes. However, there are two famous examples of early investigations in the 18th century by Arbuthnot and Süssmilch.
In 1712, John Arbuthnot (1667–1735) published a paper which discussed the slight excess of male births over female births from a statistical point of view (Ar-buthnot 1712). This paper is generally considered as the fi rst application of prob-ability to social statistics (Hacking 1975). Arbuthnot took 82 consecutive years of data on registered births in London and observed that on every recorded year more boys were born than girls. Arbuthnot argues that if there is an even chance for male and female births, the distribution of births should be like outcomes from tosses of a fair coin. He calculated that if his hypothesis were true, there would be an extremely small chance of getting 82 consecutive male years, i.e., (½)82.
The fi rst infl uence of enlightenment philosophy on statistical thinking is claimed to be seen in the works of Johann Peter Süssmilch (1707–1767). Süssmilch pub-lished a book in which he gave an extensive presentation of demographic mate-rial from a great number of sources, mainly from Germany, but also some from other countries (Süssmilch 1741). The leading motif in Süssmilch’s work was the regularity that could be observed in the statistical fi gures, which were composed of material from larger areas or population groups. The interpretation Süssmilch gave to the statistical regularity has been considered a turning point in the gradual liberation of science from religious infl uence (see also Hacking 1975).
6.3.2 Quetelet’s contribution to statistics
Adolphe Quetelet’s impact on the emergence of statistics and statistical science was vital in two different areas: as an energetic organizer, he was a key person in forming the statistical institutions in Europe; and as a social scientist, he es-tablished a new branch of research which essentially was based on statistics. He appears to have been more innovative, energetic, and infl uential than any of his contemporaries. In addition, Quetelt’s impact on the intellectual atmosphere in Europe was profound.
In the beginning the 19th century, a human population was considered a cha-otic mass of individuals. An illustrative example is the reception to Quetelet’s attempt to apply Laplace’s estimation method. Approximately 25 years after Laplace had estimated the population of France, Quetelet wanted to attempt a similar estimation for the population of the Low Countries (Stigler 1986, p.163). When he had published his plans, baron de Keverberg55 objected the plans (De Keverberg 1827). De Keverberg was afraid that the sample could never reach full “representativeness” because of the fundamental heterogeneity of the population. He writes
55 Only little is known about baron de Keverberg (1768-1841). According to Stigler (1986), he apparently was serving as an offi cial advisor on state matters in Low Countries.
“The law regulating mortality is composed of a large number of elements: it is dif-ferent for towns and for the fl atlands, for large opulent cities and for smaller and less rich villages, and depending on whether the locality is dense or sparsely popu-lated. This law depends on the terrain (raised or depressed), on the soil (dry or marshy), on the distance to the sea (near or far), on the comfort or distress of the people, on their diet, dress, and general manner of life, and on a multitude of local circumstances that would elude any a priori enumeration.” (see Stigler 1986)
Laplace’s estimation and inference had been based on the assumption that the birth and death rates were relatively homogeneous and stable. In essence, de Ke-verberg argues that the rates were not constant, or more generally, the stability of statistical ratios could not be assumed and hence the urn model could not be ap-plied. Mathematically, it meant that binomial distribution could not be apap-plied.
The proportions could not be interpreted as probabilities because there were no homogeneous groups. In the absence of homogeneous groups, there could be no reliable inferences or inductive generalizations from a part to the whole. De Ke-verberg argued that the only solution was to take a complete enumeration and to describe the entire population. Quetelet accepted de Keverberg’s argument about the lack of homogeneity and lost interest in partial investigations.
The debate about stability of statistical ratios, either biological or social, con-tinued throughout the 19th century. Some, for example Poisson, argued that the laws of probability could be applied to human population and its social condi-tions, implying that he believed in the existence of homogeneous groups (see Stigler 1986). However, many were in favour of de Keverberg’s argument that there were an unlimited number of ways of classifying social data after selection, and that homogeneous groups did not exist (Stigler ibid.). For example, in 1843, Cournot argued that there are countless ways to categorize social data.
“Even a scientist of only average curiosity could classify births by birth order, by parent’s age, profession, wealth, or religion, by season of the year, by whether it was a fi rst marriage for both parents, and so forth.” (Stigler 1986)
By that argument, striving for full coverage, a sample is simply impossible. It would ultimately mean that the only sample that would fulfi l such a require-ment would be the population itself. Underlying this debate was the deeper question: are there any stable regularities, or laws, in social science?
Quetelet and social research
Quetelet’s interest in social phenomena and statistics grew after his visit to study in Paris in 1824, where Joseph Fourier56 introduced him to Laplacian mathemat-ics57. In the 1820s, Fourier had noticed that statistics on the number of births, deaths, marriages, suicides, and various crimes in the city of Paris had remarkably stable averages from year to year (see Porter 1986). This led Quetelet to think that
56 Jean Baptiste Joseph Fourier (1768 – 1830) was a French mathematician and physicist probably best known for initiating the investigation of Fourier series. He was a student of Lagrande.
57 There has been controversy on how much Quetelet met with Laplace. It has been documen-ted that they met few times but Laplace was an old man at that time, and not very actively taking part in research anymore. Obviously, Laplace’s direct infl uence was not noteworthy.
social phenomena are governed by laws as is nature. Poisson’s Law of Large Num-bers was the direct inspiration and indication of the social laws for Quetelet.
Quetelet was convinced that probability infl uenced the course of human affairs more than earlier generations had believed and more than his contempo-raries did. He believed the law of error could also apply to human beings. If the phenomena were part of human nature, Quetelet concluded that it was possible to determine the average physical and intellectual features of a population. He believed that it was possible to identify the underlying regularities for both nor-mal and abnornor-mal behaviour.
Quetelet utilized the outburst of statistics, and in 1835 he published the book “physique sociale”, or Social Physics, with a large number of tables on vital data, moral and criminal statistics, and anthropometry (Quetelet 1835). He did not confi ne only to presentation of the facts; he also derived new variables58. The tables included many different measures, but the most important point was that Quetelet described the distributions of both observed and derived variables – which without exception was the Normal Distribution – and showed that these variables were stable between countries and over time.
In Social Physics, Quetelet argued that it was necessary to go beyond the observation of singularities, since they were obstacles to perceiving “the laws of the human species”:
“Above all, we need to lose sight of man taken in isolation, and view him as merely a fraction of the species. By stripping him of his individuality, we will eliminate all that is merely accidental; and the individual particularities that have little or no effect on the mass will disappear by themselves, enabling us to apprehend the general results.” (Quetelet 1835)
Quetelet noted that if things are examined at too close a range, it is possible to see only diversity, and observation limited to individual cases does not allow us to identify the “admirable laws”. It is important to find the right observational distance to exclude what is accidental. Quetelet argued that this distance makes it possible to develop a science of collective phenomena: by losing sight of in-dividuals, one can unravel, through the social phenomena that dominate the masses, a set of laws. (Quetelet 1835)
Quetelet demonstrated that there existed stability within social phenom-ena and that there existed regularity, or invariance, which could be called social law59. Quetelet’s ideas were partly based on his own interpretation of Laplace’s error law. Its importance was due to the Central Limit Theorem that Laplace derived mainly to analyze errors of measurements in astronomy. Quetelet was one of the fi rst to apply the error law to human sciences.
58 An example of the derived variables is the so-called Quetelet index, which in modern form is called the Body Mass Index, indicating obesity. The Body Mass Index, or Quetelet Index, is weight divided by the square of the height of a person (BMI = W / H2).
59 Behind Quetelet’s idea was his aim to show that there were similar laws as the laws of nature that govern social life. However, many Quetelet’s contemporaries did not accept the idea that regularities could be interpreted as laws.
The law of error
The error law, which was later named the Normal Distribution60, became a central concept in Quetelet’s analysis. His initial contribution was to show that nearly all features – biological, social, and moral – of human population fol-lowed this distribution. In the 1830s, Quetelet invented the concept of “l’homme moyen”, the average man. Quetelet justifi ed this idea of the typical by saying,
“If we do observe a [normal distribution] in nature, it is because nature was aim-ing for a target and missed due to random errors.”
The target, the average man, represents the centre of the population. Quetelet interpreted the normal distribution as evidence that departures from the mean were like errors of measurements, so that the mean value was a ‘true mean’
which represented a real underlying value or type. The importance that Quete-let (and his followers) gave to the normal distribution led to an exaggerated idea of its prevalence, which was nicknamed “Queteletismus” or “Quetelism”.
Eventually, the mean values in a “normal distribution” actually took on the prestige of a social law. Especially Quetelet thought that these statistical regular-ities were evidence of determinism. Individuals might think marriage was their decision, but since the number of total marriages was relatively stable from year to year, Quetelet claimed that the individuals were determined to marry.
Throughout his work, Quetelet held to the notion that there was no such thing as a chance event. He thought that all phenomena were ‘caused’ and relat-ed. If events have causes that persist through time periods, then the same events can be expected to reoccur. Quetelet claimed that “so long as the same causes exist, we must expect a repetition of the same effects” (Quetelet 1848).
General social conditions infl uencing the greater part of the social group re-sult in suffi ciently constant social phenomena. The study of large numbers sug-gests that general causes dominate the numerous infl uences of trivial ones. “The greater the number of individuals, the more the individual is effaced and allows to predominate the series of general facts which depend on general causes accord-ing to which society exists and is maintained” (Quetelet 1849). This ‘doctrine of probabilities’ has been regarded as the essence of Quetelet’s statistical analysis.
The emergence of modern social research has been regarded beginning with the Quetelet’s works. His social physics is often held as the origin of modern empirical sociology61. Quetelet published several books touching on the same topic (e.g., Quetelet 1848 and 1869), which subsequently inspired many scien-tists to develop new theories, thus generating a tradition of statistical research of social affairs. For example, Block devotes a considerable part of his textbook on statistics, Traité théoretique et pratique de Statistique, (Block 1886) in explaining the (statistical) regularities observed in different societies.
In addition, Quetelet had a strong infl uence on criminology. He showed that there was a relationship between crime and social factors. Among his fi ndings
60 The term”normal distribution” was coined by Galton at the end of the 19th century. Before that, the distribution was called the error law.
61 Sociology is usually held a creation of the French philosopher August Comte (1798–1857), but he did not accept the statistical approach. Therefore empirical sociology is usually dedi-cated to Quetelet.
was the relationship between crime and age, as well as the relationship between crime and gender (and poverty, education, and alcohol consumption, etc.).
Quetelet’s statistical analysis of crimes had far-reaching consequences, especially on social research in German states and in France.
Quetelet also contributed to probability theory, but he did not make epoch-making discoveries. In 1849, he published a book that was in the form of letters, often cited later as Quetelet’s Letters on Probability (Quetelet 1849). In this book, he outlined the use of probability in statistical research. The probability analysis of Quetelet was based on Laplace’s and Poisson’s ideas and he was one of the persons who strongly fostered adherence to the Laplace–Bayes paradigm.
However, Quetelet did not touch on inverse probability, as he did not undertake any partial investigations.
Monograph surveys
Based on Quetelet’s idea of the average man, a new type of survey research was introduced at the end of the 19th century by the French mineralogist and engineer Frederic LePlay. The method was called the Monograph study or the LePlay method. In the second half of the 19th century, the Monograph stud-ies, or surveys, became popular, especially in exploring family budgets62. In the monograph method, it suffi ces to collect information only about typical cases, and investigation of extreme cases was to be avoided. Compared to complete enumeration, in a monograph survey, the amount of collected information per household was enormous. Sometimes the enumerators or observers stayed in the household for many days. Therefore, monograph studies were sometimes called in-depth surveys. The method was partly motivated by Quetelet’s propagation of the normal distribution and his idea of the average man (see Desrosiéres 1998 and Hacking 1990).
The monograph design was widely applied at the end of the 19th century, and at the beginning of the 20th century it was still an offi cially accepted method used by the International Statistical Institute. Especially in Russia, the monographic method was very popular. For example, more than one-third of Tchuprov’s text-book on statistical methods dealt directly or indirectly with monograph surveys (see Tchuprov 1910). Also in France, it was still frequently used in the beginning of the 20th century.
6.3.3 Statistics in German states
Statistics was taught at many German universities since the late 18th century.
Statistical investigations were originally undertaken by individual scholars in search of the laws of social events, but soon statistical-topographical bureaus took over and statistics assumed a more purposeful orientation to solve prob-lems of policy and crime control (see Tönnies 1925). Operated by professional
62 Those surveys were the forerunners of the modern Household Budget Surveys, which most national statistical institutes conduct even today. In some countries, the current sampling design still has traces of the method that was applied at the end of the 19th century. For example, the sample is composed of households that have been purposefully selected to be typical households of specifi c socio-economic classes of that region.
statisticians, the offi ces collected information regardless of the specifi c needs of the political and legal administration. Statistical material was considered to benefi t the public administration because the topics of information were not determined beforehand.
6.3.3.1 Engel and the fi rst social law
It has been claimed that the fi rst social law was discovered by Ernst Engel63. While studying in Paris, he came under the infl uence of Frederic LePlay who is a pioneer in the study of fam ily budgets. Later, Engel stayed in Belgium for some time and became acquainted with Quetelet, who instilled in him the faith that it was possible to discover quantitative social laws. Hacking (1990) gives a compre-hensive account and analysis of Engel’s and Quetelet’s collaboration.
The basis of Engel’s investigations was family budget surveys in which data was collected using the monograph method. Engel’s law deals with the relationship of expenditures for consump tion in households to the income available. It states that the proportion of a consumer’s budget spent on food tends to decline as the consumer’s income goes up (Engel 1883). Engel’s law has been confi rmed in many surveys in all parts of the world. The signifi cant point is that Engel demonstrated that general re sults in social statistics can be obtained from these individual data.
Engel had a strong interest in the development of international statistics, and he was an active participant in the International Statistical Congresses. After the International Statistical Congresses had faded away, Engel was one of the active founding members of the International Statistical Institute (see Hacking 1990).
Engel has been said to be one of the fi rst who conceived statistics in the modern sense as a science on its own, as a struc tural theory of human societies which he called “demology” (Engel 1871). He was convinced that this science serves to recognize and analyze problems arising from the formation of societies.
Sometimes Engel has been called the fi rst statistician, and he has been claimed to point the way to the future of statistics as a science and as an essential tool of applied research (Porter 1986).
He was a prolifi c writer but his statistical papers are mostly published in the periodicals which he himself established, namely, Preußisch Statistik; Zeitschrift des Statistischen Bureaus, and Zeitschrift des Statistischen Bureaus des Königreichs
He was a prolifi c writer but his statistical papers are mostly published in the periodicals which he himself established, namely, Preußisch Statistik; Zeitschrift des Statistischen Bureaus, and Zeitschrift des Statistischen Bureaus des Königreichs