Probability Sample

Underlying Concepts

The concepts behind probability sampling underlie statistical theory. From the finite population of N elements, all possible samples of size n are identified. For example, if the population consisted of 6 elements, and samples of size 2 are to be chosen, there would be 15,

Reliability And Validity

From a probability sample, the quantities that are estimated, such as population totals, means, proportions, and variances, have certain properties that can be evaluated. For instance, over repeated sampling, estimators from the probability sample can be evaluated for how reproducible or reliable they are (variance) and if, on average, the estimates from the sample are similar to the true value of the population quantity (unbiasedness or validity). Combining the ideas of reliability and validity, the accuracy, or how far away on average the estimator is from the true value (mean squared error), can also be evaluated on the sample estimator.

None of these desirable properties can be determined from estimates derived from nonprobability samples. Nonprobability samples are used in many unscientific surveys, market research, and public opinion polls, often because they are easier and less expensive to conduct. These types of surveys include purposive or deliberate, quota, and snowball samples. As an example, imagine that interviewers are attempting to question shoppers as to their political views at a local supermarket in order to describe future poll results for a city. In quota sampling, the interviewer may be asked to "find" a certain number of individuals in various demographic groups, such young women, older women, black men, and white men. The individuals that are found by the interviewer may be of only one political leaning or of [Page 622]one socioeconomic group simply because they are easy to find and shop at the particular market. Without a systematic plan for sampling, the decision about whom to interview is left up to the interviewer, likely creating bias in the sample. In certain circumstances, such as in populations that are hard to reach, probability samples may not be feasible. Thus, as long as they are not used to make inference to a larger population, some non-probability samples are useful.

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