If the information you need is not already available from a previous study, you might acquire it by conducting a census – that is, by obtaining information for the entire population of interest. However, conducting a census may be time consuming, costly, impractical, or even impossible.
Two methods other than a census for obtaining information are sampling and experimentation. If sampling is appropriate, you must decide how to select the sample; that is, you must choose the method for obtaining a sample from the population. Because the sample will be used to draw conclusions about the entire population, it should be a representative sample – that is, it should reflect as closely as possible the relevant characteristics of the population under consideration.
For instance, using the average weight of a sample of professional football players to make an inference about the average weight of all adult males would be unreasonable. Nor would it be reasonable to estimate the median income of California residents by sampling the incomes of Beverly Hills residents.
Most modern sampling procedures involve the use of probability sampling. In probability sampling, a random device – such as tossing a coin, consulting a table of random numbers, or employing a random-number generator – is used to decide which members of the population will constitute the sample instead of leaving such decisions to human judgment.
PS: Probability sampling is based on the fact that every member of a population has a known and equal chance of being selected. For example, if you had a population of 100 people, each person would have odds of 1 out of 100 of being chosen. With non-probability sampling, those odds are not equal. For example, a person might have a better chance of being chosen if they live close to the researcher or have access to a computer. Probability sampling gives you the best chance to create a sample that is truly representative of the population.
The use of probability sampling may still yield a nonrepresentative sample. However, probability sampling helps eliminate unintentional selection bias and permits the researcher to control the chance of obtaining a nonrepresentative sample. Furthermore, the use of probability sampling guarantees that the techniques of inferential statistics can be applied.
Simple Random Sampling
The inferential techniques considered most often are intended for use with only one particular sampling procedure: simple random sampling. A simple random sampling is a sampling procedure for which each possible sample of a given size is equally likely to be the one obtained. And simple random sample is a sample obtained by simple random sampling.
There are two types of simple random sampling. One is simple random sampling with replacement (SRSWR), whereby a member of the population can be selected more than once; the other is simple random sampling without replacement (SRS), whereby a member of the population can be selected at most once. Unless we specify otherwise, assume that simple random sampling is done without replacement. Technologies to do a simple random sampling include random-number tables and random-number generators.
Systematic Random Sampling
Simple random sampling is the most natural and easily understood method of probability sampling – it corresponds to our intuitive notion of random selection by lot. However, simple random sampling does have drawbacks. For instance, it may fail to provide sufficient coverage when information about subpopulations is required and may be impractical when the members of the population are widely scattered geographically.
One method that takes less effort to implement than simple random sampling is systematic random sampling. Proceudre 1.1 presents a step-by-step method for implementing systematic random sampling.
Systematic random sampling is easier to execute than simple random sampling and usually provides comparable results. The exception is the presence of some kind of cyclical pattern in the listing of the members of the population (e.g., male, female, male, female, …), a phenomenon that is relatively rare.
Another sampling method is cluster sampling, which is particularly useful when the members of the population are widely scattered geographically. Procedure 1.2 provides a step-by-step method for implementing cluster sampling.
Many years ago, citizens' groups pressured the city council of Tempe, Arizona, to install bike paths in the city. The council members wanted to be sure that they were supported by a majority of the taxpayers, so they decided to poll the city's homeowners. Their first survey of public opinion was a questionnaire mailed out with the city's 18,000 homeowner water bills. Unfortunately, this method did not work very well. Only 19.4% of the questionnaires were returned, and a large number of those had written comments that indicated they came from avid bicyclists or from people who stronglye resented bicyclists. The city council realized that the questionnaire generally had not been returned by the average homeowner.
An employee in the city's planning department had sample surveyt experience, so the council asked her to do a survey. She was given two assistants to help her interview 300 homeowners and 10 days to complete the project. The planner first considered taking a simple random sample of 300 homes: 100 interviews for herself and for each of her two assistants. However, the city was so spread out that an interviewer of 100 randomly scattered homeowners would have to drive an average of 18 minutes from one interview to the next. Doing so would require approximately 30 hours of driving time for each interviewer and could delay completion of the report. The planner needed a different sampling design.
Although cluster sampling can save time and money, it does have disadvantages. Ideally, each cluster should mirror the entire population. In practice, however, members of a cluster may be more homogeneous than the members of the entire population, which can cause problems.
Another sampling method, known as stratified sampling, is often more reliable than cluster sampling. In stratified sampling, the population is first divided into subpopulations, called strata, and then sampling is done from each stratum. Ideally, the members of each stratum should be homogeneous relative to the characteristic under consideration.
In stratified sampling, the strata are often sampled in proportion to their size, which is called proportional allocation. Procedure 1.3 presents a step-by-step method for implementing stratified (random) sampling with proportional allocation.
Most large-scale surveys combine one or more of simple random sampling, systematic random sampling, cluster sampling, and stratified sampling. Such multistage sampling is used frequently by pollsters and government agencies.