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  The selection of a subset from a defined population to provide needed information (as in a survey analysis), used when the population is too large for a complete enumeration of all individuals (i.e. a census).

Sampling theory has been developed by statisticians so that conclusions about a population\'s characteristics can be inferred from those of the selected sample; the inferred values lie within error limits, whose size is known from the theory. The selection of the sample members must follow certain rules if valid inferences regarding the population characteristics are to be drawn; if these rules are violated the sample is likely to be biased and the conclusions unreliable. In general, the larger the sample (in absolute terms, not as a percentage of the population) the greater its likely accuracy as a representation of the population.

The most common selection procedure is random sampling: the population is enumerated and a sample of predetermined size taken, usually employing a table of random numbers. To reduce effort, and also to counter problems if the size of the population is unknown, a systematic sample may be taken (e.g. of every tenth person entering a shopping centre). The investigator must be sure that this will not introduce bias because of some periodicity in the population (e.g. every tenth shopper is more likely to be a male than are the other nine!). Stratified sampling is used when the researcher wants to ensure a representative selection from two or more subgroups within the population. (If it is known that 20 per cent of all theatre-goers are male, for example, then to get an equal number of male and female respondents every fourth male and every sixteenth female entering the theatre might be questioned.) A quota sample (frequently used in opinion polling) is a variant on the stratified form: the investigator uses either random or systematic sampling procedures to obtain a set of respondents with a particular profile of characteristics and selection continues until the desired profile is achieved, with unneeded respondents discarded. (For example, a sample of ten may have to include six females, five individuals aged under 40, seven in white-collar occupations etc. Once the sampling procedure delivers five persons aged under 40 in a survey of shoppers, that part of the profile will be complete. It may be necessary to interview more than ten persons before all of the criteria are met, however, so that more than five respondents aged under 40 are interviewed in order to obtain a satisfactory sample on the other variables.)

In geographical studies, the standard procedures may be varied to ensure spatial coverage. Methods of random, systematic and stratified sampling of points on a map have been devised using coordinate systems, for example, as have methods of selecting transects (line samples) across an area.

Analyses of sample data make statements about the population as a whole, using significance tests based on theoretical frequency distributions. They involve statements regarding the range of values around the sample statistic within which the population characteristic will probably be found at a specified significance level: the most frequently used of these is the standard error. For example, the standard error around a sample mean may be four percentage points: thus if the observed percentage of shoppers purchasing shoes at a suburban centre is 23, then in 67 per cent of all samples the population value will lie between 19 and 27 per cent. The size of the standard error is a function of the sample size (cf. quantitative methods). (RJJ)

Suggested Reading Berry, B.J.L. and Baker, A.M. 1968. Methods of spatial sampling. In B.J.L. Berry and D.F. Marble, eds, Spatial analysis: a reader in statistical geography. Englewood Cliffs, NJ and London: Prentice-Hall, 91-100. Dixon, C.J. and Leach. B. 1977: Sampling methods for geographical research. Concepts and Techniques in Modern Geography 17. Norwich: Geo Books. Walford, N. 1995: Geographical data analysis. Chichester and New York: John Wiley.



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