Sampling is based on two premises. One is that there is enough similarity among the elements in a population that a few of these elements will adequately represent the characteristics of the total population. The second premise is that while some elements in a sample underestimate a population value, others overestimate this value. The result of these tendencies is that a sample statistic such as the arithmetic mean is generally a good estimate of a population mean.
A good sample has both accuracy and precision. An accurate sample is one in which there is little or no bias or systematic variance. A sample with adequate precision is one that has a sampling error that is within acceptable limits for the study's purpose.
In developing a sample, five procedural questions need to be answered:
What is the target population?
What are the parameters of interest?
What is the sampling frame?
What is the appropriate sampling method?
What size sample is needed?
A variety of sampling techniques are available. They may be classified by their representation basis and element selection techniques as shown in the accompanying table.
Representation Basis
Element Selection
Probability
Nonprobability
Unrestricted
Simple random
Convenience
Restricted
Complex random
Purposive
Systematic
Cluster
Stratified
Double
Judgment
Quota
Snowball
Probability sampling is based on random selection—a controlled procedure that ensures that each population element is given a known nonzero chance of selection. The simplest type of probability approach is simple random sampling. In this design, each member of the population has an equal chance of being included in a sample. In contrast, nonprobability selection is "not random." When each sample element is drawn individually from the population at large, this is unrestricted sampling. Restricted sampling covers those forms of sampling in which the selection process follows more complex rules.
Complex sampling is used when conditions make simple random samples impractical or uneconomical. The four major types of complex random sampling discussed in this chapter are systematic, stratified, cluster, and double sampling. Systematic sampling involves the selection of every kth element in the population, beginning with a random start between elements from 1 to k. Its simplicity in certain cases is its greatest value.
Stratified sampling is based on dividing a population into subpopulations and then randomly sampling from each of these strata. This method usually results in a smaller total sample size than would a simple random design. Stratified samples may be proportionate or disproportionate.
In cluster sampling, we divide the population into convenient groups and then randomly choose the groups to study. It is typically less efficient from a statistical viewpoint than the simple random because of the high degree of homogeneity within the clusters. Its great advantage is its savings in cost—if the population is dispersed geographically—or in time. The most widely used form of clustering is area sampling, in which geographic areas are the selection elements.
At times it may be more convenient or economical to collect some information by sample and then use it as a basis for selecting a subsample for further study. This procedure is called double sampling.
Nonprobability sampling also has some compelling practical advantages that account for its widespread use. Often probability sampling is not feasible because the population is not available. Then, too, frequent breakdowns in the application of probability sampling discount its technical advantages. You may find also that a true cross section is often not the aim of the researcher. Here the goal may be the discovery of the range or extent of conditions. Finally, nonprobability sampling is usually less expensive to conduct than is probability sampling.
Convenience samples are the simplest and least reliable forms of nonprobability sampling. Their primary virtue is low cost. One purposive sample is the judgmental sample, in which one is interested in studying only selected types of subjects. The other purposive sample is the quota sample. Subjects are selected to conform to certain predesignated control measures that secure a representative cross section of the population. Snowball sampling uses a referral approach to reach particularly hard-to-find respondents.
