Purposive Sampling as an Optimal Bayes Sampling Design

Year: 2012       Vol.: 61       No.: 2      

Authors: Jacqueline M. Guarte

Abstract:

Purposive sampling takes place when the researcher’s knowledge about the population is used to handpick the units to be included in the sample. This is hinged on the experienced researcher’s belief that the handpicked sampling units will provide “enough” information to characterize the population. Bayesian analysis makes explicit use of prior information as part of the model to satisfy some optimality criteria. Hence, purposive rather than purely random locations of design points need to be chosen. This paper presents a proof that purposive sampling is an optimal Bayes sampling design. Purposive sampling satisfies the sufficient condition for an optimal Bayes sampling design set by Zacks (1969) for single-phase designs. It is shown that the posterior Bayes risk of the population parameter ? given the sample observations is independent of the observed values under purposive sampling. The parameter of interest is the population mean. The normal distribution is used for the sampling distribution and the prior distribution of the population mean due to its universal significance and mathematical maneuverability. The squared error loss function is used in determining the posterior Bayes risk associated with estimating the population mean, with the sample mean as estimator. The posterior Bayes risk under simple random sampling is also determined for comparison purposes. It is shown that the risk levels under purposive sampling are lower than those under simple random sampling when important model parameters are made to vary.

Keywords: purposive sampling; optimal Bayes sampling design; posterior Bayes risk

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