MODULE R7 - SAMPLING

Random sampling as suggested by Van Dalen (1979) often means chance or a haphazard method of assignment to many people, but in reality it is a carefully controlled process. Randomization is used to eliminate bias, both conscious and unconscious, that researchers might introduce while selecting a sample. Kerlinger (1986) described randomization as the assignment of objects (subjects, treatments, groups, etc.) of a population to subsets (sample) of the population in such a way that, for any given assignment to a subset (sample), every member of the population has an equal probability of being chosen for that assignment. Randomization is essential for probability samples which are the only samples that can generalize results back to the population. Kerlinger (1986) reported that random sampling is important because it is required by inferential statistics. If the researcher desires to make inferences about populations based on the behavior of samples, then random sampling must be used.

Stratified sampling is a procedure for selecting a sample that includes identified subgroups from the population in the proportion that they exist in the population. This method can be used to select equal numbers from each of the identified subgroups if comparisons between subgroups is important. A good example of stratified sampling would be to divide the population into men and women. The different strata to use for each study would be determined in part by the review of literature of previous research. The purpose of stratified sampling is to guarantee the desired distribution among the selected subgroups of the population.

Proportional sampling (Van Dalen, 1979) provides the researcher a way to achieve even greater representativeness in the sample of the population. This is accomplished by selecting individuals at random from the subgroup in proportion to the actual size of the group in the total population. Proportional sampling is used in combination with stratified and cluster sampling.

The most used method in educational research according to Kerlinger (1986) is cluster sampling. Groups of elements (clusters) instead of individuals from the population are used for the sample. Cluster sampling often is more convenient when the population is very large. It often isn’t possible to randomly select from the entire population but is more manageable when using clusters because of time, expense, and convenience. A cluster sampling is using schools as clusters and randomly selecting from the list of schools instead of randomly selecting individuals from a list that includes all schools. This can help the researcher cut down on travel expense, time, etc. One problem with cluster sampling is that it usually produces a larger sampling error than a simple random sample of the same size because the clusters tend to be more similar within the cluster, reducing the representativeness of the sample (Van Dalen, 1979).

In some cases when the population of a study is available as a list, a sample is drawn from certain intervals on the list. The starting point is randomly chosen and then every so many numbers another individual is chosen from the list and added to the sample. This method can be equal to random selection only if the names were randomized at the beginning. Van Dalen (1979) cautions us to be wary of departure from randomness of the list because of structure, some trend, or cyclical fluctuation.

Kerlinger (1986) explained purposive sampling as another type of non-probability sampling, which is characterized by the use of judgment and a deliberate effort to obtain representative samples by including typical areas or groups in the sample. In other words, the researcher attempts to do what proportional clustering with randomization accomplishes by using human judgment and logic. As a result, there are many opportunities for error. In addition, nonprobability samples do not use random sampling which makes them unacceptable for generalizing back to the population.

 In random sampling each object has an equal and independent opportunity of being chosen. Stratified sampling involves the identification of the variable and subgroups (strata) for which you want to guarantee appropriate representation (either proportional or equal). To use cluster sampling, you must list and identify all clusters that comprise the population and estimate the average number of population members per cluster to determine the number of clusters needed for the sample. Proportional sampling determines the ratio of individuals in subgroups for which you want proportional representation. Once the strata, cluster, or ratio has been determined, individual objects, clusters, or individuals in a subgroup are randomly selected. Systematic sampling takes every nth name (n=size of population divided by desired sample size) on a list of the population until the desired sample size is reached.

The first thing that is needed is to identify or define the population. Jaccard (1983) defined population as the aggregate of all cases to which one wishes to generalize. At this time, it is necessary to determine if your research requires the identification of subgroups and if so define the subgroups within the population. To have a sample that is of use it needs to be as close as possible to being representative of the complete population. Popham and Sirotnik (1973) contend that in order to draw legitimate inferences about populations from samples that the sample has to be representative of the population and randomly selected.

Van Dalen (1979) lists three factors that he considers to determine the size of an adequate sample as (l) the nature of the population, (2) the type of investigation, and (3) the degree of precision desired. The formula for estimating the sample size and a table for determining the sample size based on confidence level needed from a given population was provided by Krejcie and Morgan (1970).

where

TABLE FOR DETERMINING NEEDED SIZE S OF A RANDOMLY CHOSEN SAMPLE FROM A GIVEN FINITE POPULATION OF N CASES SUCH THAT THE SAMPLE PROPORTION p WILL BE WITHIN ± .05 OF THE POPULATION PROPORTION P WITH A 95 PERCENT LEVEL OF CONFIDENCE