Random Sampling

Random sampling refers to SURVEY sampling designs that meet the criteria necessary to permit the use of randomization-based methods of STATISTICAL INFERENCE. The term probability sampling is synonymous. The defining characteristics of a random sampling design are the following:

1.
The study population is fully defined.
2.
The design is specified.
3.
The design is objective.
4.
The design is replicable.
5.
Every unit in the population has a known probability of being selected.
6.
All selection probabilities are nonzero.

These criteria warrant a little further explanation. The first seems straightforward but is often overlooked. It is necessary to define precisely the units of interest to the survey and the boundaries of the population. For example, it is not sufficient to say “all adults.” The definition should encompass geography, time, civil status, age range, and other relevant factors. A better definition might be “All people aged 18 or over whose sole or main residence as of 10 July 2003 was a private household in one of the 48 mainland states of the USA.” If the survey is carried out over a long period of time, we should also specify how we deal with the distinction between stock and flow.

Specification (Criterion 2) necessitates a clear and full description of the process that resulted in the selection of the sample.

Objectivity requires that each selection—and each stage in the selection process, because many designs are multistage—is governed by a random chance mechanism. It is not permissible for any subjective judgment to influence the selection of sample units. This is perhaps the heart of the definition of random sampling. A number of studies have shown that both experts and nonexperts produce samples that are seriously in error in terms of important characteristics if asked purposively to select a sample that they believe to be representative. Teachers of sampling also observe this phenomenon regularly in class exercises. Selection by means of a chance mechanism is the only way to avoid SYSTEMATIC ERROR (while also being able to measure variable error).

REPLICABILITY requires that another researcher, given identical circumstances, would be able to implement exactly the same design. This does not mean that he or she would necessarily replicate the selected sample (in fact, this would be extremely unlikely), but that he or she could replicate the design, that is, [Page 913]reproduce the stages in the process and reapply the random mechanisms where appropriate.

Criterion 5 states that it is necessary to know the selection probability of every unit in the population. In fact, for purposes of estimation, it is necessary to know the probabilities of only those units that were actually selected—not of the ones that were not selected. The point is that it must, in principle, be possible to calculate the selection probability of any unit in the population. To meet this requirement, it is necessary first to have a design that is specified and objective, and, additionally, to have collected and recorded necessary information during the course of sample selection. For example, if the design involves selecting residential addresses from a list and subsequently selecting one person at random to interview at each address, it is necessary to record the number of eligible people at each sample address.

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