1 Introduction
Ken Brewer
One of the most difficult problems I struck in writing this paper was in knowing where to begin. Initially I had intended to start with Laplace as I had in an earlier paper (Brewer and Gregoire 2009), which incorrectly described him as being unable to fulfill his ambition to estimate the population of France by using what we would now describe as survey sampling. He had, in fact, achieved that using a sample of the small administrative districts known as communes as early as September 22, 1802 (Cochran 1978). In later accounts, I had read of him struggling to repeat that performance while the boundaries of France were in a constant state of flux, and I had jumped to the incorrect conclusion that he had never achieved it at all.
However, I soon found myself being pulled further back into history. No, Laplace had not been the first person to use a ratio estimator, not even the first Frenchman (Stephan 1948). The Englishman John Graunt had used the ratio estimator in his estimation of the population of London (Graunt 1662). Well, perhaps he had not really used the ratio estimator (he probably hadn't used anything that would be recognized as a ratio estimator today, certainly not by a finicky survey statistician like me!), but he had admittedly used the Rule of Three.
I had not come across that Rule before, but apparently it was well-known to be this: "If AB = CD and D is unknown, then D = AB/C.� Obviously the present-day ratio estimator was a particular case of that Rule of Three. In fact, the Rule of Three must have predated the 17th Century by a considerable margin, so it might genuinely be of interest when searching for a survey-sampling start date.
It soon occurred to me that the Rule of Three was bound to have been known to Hammurabi's astronomers, getting on for 4,000 years ago, because they were very arithmetically minded, having invented a sexagesimal system of counting that still survives today in the using of "hours� (and also of "degrees�) "minutes� and "seconds�, and also of 300-600-900 ["30-60-90�] triangles.
That realization encouraged me to start to look for a more recent starting point for this paper, and I eventually concluded that a good choice would be to start with "modern survey sampling�, a topic that had been suggested to me before. The paper is structured as follows. Section 2 discusses the first controversy which is Anders Kiaer's "Representative Method.� Section 3 provides a discussion on the second controversy, which is the exclusive use of randomization as a means for selecting samples, as advocated by Neyman (1934). The arguments for using the model-assisted or the model-based approach as a means for inference in survey sampling is described in Section 4. Section 5 provides a middle ground that incorporates both procedures. The paper ends with a summary given in Section 6.
- Date modified: