Probability Sampling

Sample Selection

In probability sampling, the selection probabilities of individual population elements and the algorithm with which these are randomly selected are specified by a sampling design. In turn, to apply a sampling design requires a device or frame that delineates the extent of the population of interest. A population often can be sampled directly using a list frame that identifies all the elements in that population, as when the names of all students in a district are registered on school records. If a list frame is available, a probability sample can be formed as each of a string of random numbers generated in accordance with a design is matched to an element or cluster of elements in the population. By contrast, some populations can be framed only by their spatial boundaries. For example, many natural resource populations can be delineated only by the tracts of land over (or under) which they are dispersed. Such a population must be surveyed indirectly via a probability sampling of coordinate locations within its spatial domain. Regardless of how a population is framed, however, the frame must be complete in the sense that it includes the entirety of the population. Inasmuch as any fraction of the population omitted from the frame will have zero probability of being selected, the frame ultimately fixes [Page 1110]the population to which probability sampling inferences apply.

In some applications, once a design is chosen, the set of all selectable probability samples can be discerned together with the relative frequency with which each sample will be drawn. In other cases, the size of the population is never known and one cannot calculate even the number of possible samples. Nevertheless, when a valid probability sampling design is employed, at a minimum it is possible to derive the inclusion probabilities of the elements ultimately selected. The inclusion probability of an element is the relative frequency with which it is included in the observation set. Some probability sampling designs prescribe equal inclusion probabilities for all elements, but most allow for variation across the population. Designs of the latter variety intrinsically favor the selection of certain elements or classes of elements, but only to an extent that can be discerned from the relative magnitudes of the elements' inclusion probabilities.

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