and detailed enumeration; that is to say, the formation of nominative states of all the inhabitants, with indication of their age and occupation. Only by this mode of operation can reliable documents be obtained on the actual number of inhabitants of a country, and at the same time on the statistics of the ages of which the population is composed, and the branches of industry in which it finds the means of comfort and prosperity.1
In one of his letters to the Duke of Saxe‐Coburg Gotha, Quételet (1846, p. 293) also advocates for an exhaustive statement:
La Place had proposed to substitute for the census of a large country, such as France, some special censuses in selected departments where this kind of operation might have more chances of success, and then to carefully determine the ratio of the population either at birth or at death. By means of these ratios of the births and deaths of all the other departments, figures which can be ascertained with sufficient accuracy, it is then easy to determine the population of the whole kingdom. This way of operating is very expeditious, but it supposes an invariable ratio passing from one department to another. [
It is interesting to examine the argument used by Quételet (1846, p. 293) to justify his position.
To not obtain the faculty of verifying the documents that are collected is to fail in one of the principal rules of science. Statistics is valuable only by its accuracy; without this essential quality, it becomes null, dangerous even, since it leads to error.3
Again, accuracy is considered a basic principle of statistical science. Despite the existence of probabilistic tools and despite various applications of sampling techniques, the use of partial data was perceived as a dubious and unscientific method. Quételet had a great influence on the development of official statistics. He participated in the creation of a section for statistics within the British Association of the Advancement of Sciences in 1833 with Thomas Malthus and Charles Babbage (see Horvàth, 1974). One of its objectives was to harmonize the production of official statistics. He organized the International Congress of Statistics in Brussels in 1853. Quételet was well acquainted with the administrative systems of France, the United Kingdom, the Netherlands, and Belgium. He has probably contributed to the idea that the use of partial data is unscientific.
Some personalities, such as Malthus and Babbage in Great Britain, and Quételet in Belgium, contributed greatly to the development of statistical methodology. On the other hand, the establishment of a statistical apparatus was a necessity in the construction of modern states, and it is probably not a coincidence that these personalities come from the two countries most rapidly affected by the industrial revolution. At that time, the statistician's objective was mainly to make enumerations. The main concern was to inventory the resources of nations. In this context, the use of sampling was unanimously rejected as an inexact and fundamentally unscientific procedure. Throughout the 19th century, the discussions of statisticians focused on how to obtain reliable data and on the presentation, interpretation, and possibly modeling (adjustment) of these data.
1.3 Controversy on the use of Partial Data
In 1895, the Norwegian Anders Nicolai Kiær, Director of the Central Statistical Office of Norway, presented to the Congress of the International Statistical Institute of Statistics (ISI) in Bern a work entitled Observations et expériences concernant des dénombrements représentatifs (Observations and experiments on representative enumeration) for a survey conducted in Norway. Kiær (1896) first selected a sample of cities and municipalities. Then, in each of these municipalities, he selected only some individuals using the first letter of their surnames. He applied a two‐stage design, but the choice of the units was not random. Kiær argues for the use of partial data if it is produced using a “representative method”. According to this method, the sample must be a representation with a reduced size of the population. Kiær's concept of representativeness is linked to the quota method. His speech was followed by a heated debate, and the proceedings of the Congress of the ISI reflect a long dispute. Let us take a closer look at the arguments from two opponents of Kiær's method (see ISI General Assembly Minutes, 1896).
Georg von Mayr (Prussia)[
Guillaume Milliet (Switzerland). I believe that it is not right to give a congressional voice to the representative method(which can only be an expedient) an importance that serious statistics will never recognize. No doubt, statistics made with this method, or, as I might call it, statistics, pars pro toto, has given us here and there interesting information; but its principle is so much in contradiction with the demands of the statistical method that as statisticians, we should not grant to imperfect things the same right of bourgeoisie, so to speak, that we accord to the ideal that scientifically we propose to reach.5
The content of these reactions can again be summarized as follows: since statistics is by definition exhaustive, renouncing complete enumeration denies the very mission of statistical science. The discussion does not concern the method proposed by Kiaer, but is on the definition of statistical science. However, Kiaer did not let go, and continued to defend the representative method in 1897 at the congress of the ISI at St. Petersburg (see Kiær, 1899), in 1901 in Budapest, and in 1903 in Berlin (see Kiær, 1903, 1905). After this date, the issue is no longer mentioned at the ISI Congress. However, Kiær obtained the support of Arthur Bowley (1869–1957), who then played a decisive role in the development of sampling theory. Bowley (1906) presented an empirical verification of the application of the central limit theorem to sampling. He was the true promoter of random sampling techniques, developed stratified designs with proportional allocations, and used the law of total variance. It will be necessary to wait for the end of the First World War and the emergence of a new generation of statisticians for the problem to be rediscussed within the ISI. On this subject, we cannot help but quote Max Plank's reflection on the appearance of new scientific truths: “a new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it” (quoted by Kuhn, 1970, p. 151).
In 1924, a commission (composed of Arthur Bowley, Corrado Gini, Adolphe Jensen, Lucien March, Verrijn Stuart, and Frantz Zizek) was created to evaluate the relevance of using the representative method. The results of this commission, entitled “Report on the representative method of statistics”, were presented at the 1925 ISI Congress in Rome. The commission accepted the principle of survey sampling as long as the methodology is respected. Thirty years after Kiær's communication, the idea of sampling was officially accepted. The commission laid the foundation for future research. Two methods are clearly distinguished: “random selection” and “purposive selection”. These two methods correspond to two fundamentally different scientific approaches. On the one hand, the validation of random methods is based on the calculation of probabilities that allows confidence intervals to be build for certain parameters. On the other hand, the validation of the purposive selection method can only be obtained through experimentation by comparing the obtained estimations to census results. Therefore, random methods are validated by a strictly mathematical argument while purposive methods are validated by an experimental approach.
1.4
