Sampling

Maxim #1: Survey sampling is an applied discipline and is not a branch of mathematical statistics

Survey sampling as we know it today originated in a proposal presented in Berne in 1895 to a meeting of the International Statistical Institute (ISI) by the director of the Norwegian Central Bureau of Statistics, Anders Kiaer.1 His audience was composed primarily of senior government statisticians, whose preference and inclination was for complete enumerations of populations, either through Censuses or from administrative records.

The objective of sampling was to identify a miniature of the population that mirrored important aspects of the population, but on a smaller scale. The prerequisites for selecting a sample were knowledge of the population and its important parameters. There is no reference in Kiaer's presentation or in the discussion of it to any statistical or mathematical theory, apart from the pejorative [Page 295]comment of von Mayr who disparaged the whole enterprise by declaring ‘pas de calcul là où l’ observation peut être faite' (Kiaer, 1897, p. 52). This notion that sampling and estimation is a form of guesswork legitimated by mathematical sleight of hand is still prevalent today, as we can see from the controversy that still surrounds the use of sampling in the decennial Population Census.

As a mental exercise, think about choosing a real population about which there is substantial information. Next, consider how to design a sample to use to collect data from this population. The population might be all residents of a country who are aged 18 and over, voters in an election, adults in a city, consumers of a company's products, households in a legislative district, or readers of a newspaper.

As an example I will suggest possible reasoning for a national sample in the US measuring attitudes to the war in Iraq.

Every real population has diversity, and almost certainly a researcher would want to represent that diversity in a sample. This means that the (ideal) sample should contain elements (people) that represent that diversity. For the national attitude survey, that means (at the very least) that it should represent proponents and opponents of the war, and the ambivalent. On the issue of the Iraq war there has been strong disagreement between the Democrat and Republic an political parties. Thus, this might be built into the sample design by classifying the population into blue (Republican) states and red (Democrat) states and ensuring that the sample is drawn from each in proportion to their population. [These segments are called strata in the sampling literature.] The more the researcher knows about the population and about factors that might be related to the target variable, the more it will be possible to structure the sample to represent these dimensions of the population.

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