2 The First Controversy: Anders Kiaer and the "Representative Method�
Ken Brewer
Anders Kiaer (1838-1919), was the founder and first director of Statistics Norway. Although many now claim him to be the first modern survey statistician, his contribution to statistics did not go unchallenged at the time. It was claimed, for instance, that his approaches to sampling lacked a theoretical description. In addition, there was also a serious lack of references in Kiaer's papers. Most of the charges made against him by his contemporaries have merit, but it is also true that with the first publication of his ideas in 1895 he started a process that ended in the development of modern survey sampling theory. Kiaer was also the first to use a sample survey on its own, as opposed to a by-product from a full enumeration.
By 1895, Kiaer had been conducting sample surveys successfully in his own country for fifteen years or more, finding to his own satisfaction that it was not always necessary to enumerate an entire population to obtain useful information about it. He decided that it was time to convince his peers of this fact, and he attempted to do so at the session of the International Statistical Institute (ISI) being held in Berne that year. Kaier there argued that what he called a "partial investigation�, based on a subset of the population units, could indeed provide such information, provided only that the subset in question had been carefully chosen to reflect the whole of that population in miniature. He described this process as his "representative method�, and he was able to gain some support for it, notably from his Scandinavian colleagues. Unfortunately, his idea of "representation� was too subjective and (in hindsight) too lacking in probabilistic rigour, to make headway against the then universally held belief that only complete enumerations, "censuses�, could provide any useful information (Wright 2001, Lie 2002).
Moreover, all Kiaer's innovations, and in particular his idea of a sample being "representative�, were controversial enough to create serious opposition to his ideas among his contemporaries, and this was particularly evident in the seriously unfavourable reactions to the paper that he presented at that 1895 meeting. However, he persisted and continued to present papers about his surveys and the methods he used in them at later ISI meetings.
Eight years later, at the ISI's Berlin meeting in 1903, Lucien March suggested that randomization might provide an objective basis for the use of "partial investigations� (Wright 2001, Lie 2002).
This idea was further developed by Sir Arthur Lyon Bowley, first in a theoretical paper (Bowley 1906) and later by a practical demonstration of its feasibility in a survey conducted in Reading, England (Bowley 1912).
By 1925, the ISI at its Rome meeting was sufficiently convinced (largely by the report of a study that it had itself commissioned!) to adopt a resolution giving acceptance to the idea of sampling. However it was left to the discretion of the investigators whether they should use randomized or purposive sampling. With the advantage of hindsight we may conjecture that, however vague their awareness of the fact, the writers of that report were intuiting that while purposive sampling was sometimes capable of presenting useful estimates, the underpinning of randomization was also desirable.
In the following year, Bowley himself published a substantial monograph (Bowley 1926) in which he presented what was then known concerning the purposive and randomizing approaches to sample selection, and also made suggestions for further developments in both of them. These included the notion of collecting similar units into groups called "strata,� including the same proportions of units from each stratum in the sample. Furthermore, there was an attempt to make purposive sampling more rigorous by taking into account the correlations between the variables of interest for the survey and any other auxiliary variables that might be helpful in the estimation process.
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