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Researchers often face having to reconcile their sample selection method of survey with the costs of collecting the actual sample. An appropriate justification of a sampling strategy is central to ensuring valid, reliable, and generalizable research results. This paper presents a combinatorial optimization method for identification of sample locations. Such an approach is viable when researchers need to identify sites from which to draw a nonprobability sample when the research objective is for comparative purposes. Findings indicate that using a combinatorial optimization method minimizes the population variation assumptions based upon predetermined demographic variables within the context of the research interest. When identifying the location from which to draw a nonprobability sample, an important requirement is to draw from the most homogeneous populations as possible to control for extraneous factors. In comparison to a standard convenience sample with no identified location strategy, results indicate that the proposed combinatorial optimization method minimizes population variability and thus decreases the cost of sample collection.

Academics conducting both survey and experimental research must often weigh the costs and benefits of their sampling strategy. Because sampling can have an impact on the validity of research results, a defensible strategy is necessary (Ferber, 1977). The collection method for the data determines the classification of the sample as either a probability or a nonprobability sample. Probability sampling (e.g., simple random, stratified, or systematic) indicates that every element in the population has a known probability of being chosen in the sample for that survey. Thus, a key benefit of probability sampling is the ability to generalize the results, which allows for an estimate of the sampling error. However, probability sampling can require significant resources in both time and money. Unlike probability sampling, nonprobability sampling (e.g., convenience, quota, or judgmental) indicates that every element in the population does not have a known probability of being chosen in the sample for that survey. Therefore, the results are not as generalizable and the sampling error cannot be estimated. But, nonprobability sampling generally is less costly. The differences between probability and nonprobability sampling are very clear and allow researchers an evaluation criterion to determine an appropriate sampling method. When faced with limited time and money, researchers usually choose the nonprobability sampling method. However, even when a nonprobability sample is the choice, the relation between variability and precision remains. Therefore, if a nonprobability sample comes from a highly variable population, the precision of the results can be in question. If the purpose of the research is for comparison (i.e., to examine the differences between two or more diverse groups of people), homogeneity of the different groups is of utmost importance. Thus, researchers need to minimize demographic differences as much as possible. The purpose of this paper is to demonstrate a combinatorial optimization method for identifying potential data collection locations for a nonprobability sample. The substantive context of this method comes from a research project aimed at understanding the differences between urban and rural residents and their perceptions of a potential transportation tax policy. The next section of the paper describes the importance of an appropriate sampling strategy when handling targeted group comparisons. Following this, the paper presents the sample identification location problem in a substantive context that details the results of the combinatorial optimization method and demonstrates that this method provides a reasonable strategy as opposed to simply selecting a convenient location for a nonprobability sample. Next, the paper concludes with a discussion of the sampling strategy considerations necessary and the practical implications of this method.

The proposed combinatorial optimization method demonstrates a reasonable sample identification strategy for researchers when their research objective is to identify one or more homogeneous group samples using a nonprobability sample. Many studies use nonprobability sampling and indeed in some domains high criticism of the use exists (e.g., international and cross-cultural research) (Reynolds, Simintiras, & Diamantopoulos, 2003), while other domains, such as marketing research, deem the sampling useful (Deville, 1991). The minimization of concerns about nonprobability sampling requires a reasonable justification for the method. Although the combinatorial optimization method can be useful for researchers electing to use a convenience sample and can provide a reasonable justification for selecting the locations for the sample, researchers should consider the following steps prior to using this approach. First, the sampling objective should be for comparative purposes where a need exists to identify distinctive groups in which the desired sampling attributes are to eliminate extraneous factors and maintain homogeneous groups as much as possible. In essence, the homogeneity within the sample reduces the likelihood that the differences among groups are due to extraneous variables and instead are the result of differences between the constructs of interest. Secondly, researchers need to use reasonable demographic variables available within their research context for the combinatorial optimization method to identify the most representative population locations, because the purpose of this method is to minimize the variance for each comparison group. Within the context of the problem this paper presents, the first objective distinguished between rural and urban comparative groups on the basis of government designated commuting codes. Additionally, as identified from the census data, demographic information relating to those who are most likely to work and drive is useful in finding the most homogeneous areas to sample. If the wrong variables are considered, the groups might be homogeneous for the wrong reasons and weaken the interpretation of the results. An appropriate sampling strategy is crucial to the validity of the results. Internal validity can be threatened if any extraneous variables affect or influence the dependent variable. In relation to sampling, two methods for controlling or minimizing the threat of extraneous variables are suggested: (1) the selection of homogeneous groups; or (2) the random selection of a sample (Kerlinger, 1986). The combinatorial optimization method presented provides a strategy for justifying the sample locations selected to encourage homogeneity. This paper demonstrates a solution for identifying sample locations when the research is for comparative purposes, and a probability sample is prohibitively costly and impractical. Much marketing and social sciences research uses nonprobability samples; however, the approach this paper presents helps strategize sample location identification and provides additional justification as to the technique and method for increasing the homogeneity of the comparative samples.