Probability Sampling

Simple random sampling With simple random sampling, every member of the population has an equal probability of being selected for the sample. If the population has 1,000 members, each has one chance out of a thousand of being selected. Suppose you want to sample students who attend your school. A list of all students would be needed; from that list, students would be chosen at random to form the sample.

When conducting telephone interviews, researchers commonly have a computer randomly generate a list of telephone numbers with the dialing prefixes used for residences in the city or area being studied. This will produce a random sample of the population because most residences have telephones (if many people do not have phones, the sample would be biased). Some companies will even provide researchers with a list of telephone numbers for a survey in which the phone numbers of businesses and numbers that phone companies do not use have been removed. You might note that this procedure results in a random sample of households rather than individuals. Survey researchers use other procedures when it is important to select one person at random from the household.

Stratified random sampling A somewhat more complicated procedure is stratified random sampling. The population is divided into subgroups (also known as strata), and random sampling techniques are then used to select sample members from each stratum. Any number of dimensions could be used to divide the population, but the dimension (or dimensions) chosen should be relevant to the problem under study. For instance, a survey of sexual attitudes might stratify on the basis of age, gender, and amount of education because these factors are related to sexual attitudes. Stratification on the basis of height or hair color would be ridiculous for this survey.

Stratified random sampling has the advantage of a built-in assurance that the sample will accurately reflect the numerical composition of the various subgroups. This kind of accuracy is particularly important when some subgroups represent very small percentages of the population. For instance, if African Americans make up 5% of a city of 100,000, a simple random sample of 100 people might not include any African Americans; a stratified random sample would include five African Americans chosen randomly from the population. In practice, when it is important to represent a small group within a population, researchers will “oversample” that group to ensure that a representative sample of the group is surveyed; a large enough sample must be obtained to be able to Page 151make inferences about the population. Thus, if your campus has a distribution of students similar to the city described here and you need to compare attitudes of African Americans and Whites, you will need to sample a large percentage of the African American students and only a small percentage of the White students to obtain a reasonable number of respondents from each group.

Cluster sampling It might have occurred to you that obtaining a list of all members of a population might be difficult. What if officials at your school decide that you cannot have access to a list of all students? What if you want to study a population that has no list of members, such as people who work in county health care agencies? In such situations, a technique called cluster sampling can be used. Rather than randomly sampling from a list of individuals, the researcher can identify “clusters” of individuals and then sample from these clusters. After the clusters are chosen, all individuals in each cluster are included in the sample. For example, you might conduct the survey of students using cluster sampling by identifying all classes being taught—the classes are the clusters of students. You could then randomly sample from this list of classes and have all members of the chosen classes complete your survey (making sure, of course, that no one completes the survey twice).

Most often, use of cluster sampling requires a series of samples from larger to smaller clusters—a multistage approach. For example, a researcher interested in studying county health care agencies might first randomly determine a number of states to sample and then randomly sample counties from each state chosen. The researcher would then go to the health care agencies in each of these counties and study the people who work in them. Note that the main advantage of cluster sampling is that the researcher does not have to sample from lists of individuals to obtain a truly random sample of individuals.