CHAPTER 1

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CHAPTER 1

SOLUTIONS TO PROBLEMS

The first step the student must take in order to obtain a simple random sample is to specify the population. In this case, the population is all full-time sophomore students enrolled at their university. If they were going to generalize to all sophomores attending all universities, they would have to obtain enrollment lists from other universities, select a sample of the lists, and then select a sample of sophomores from within each selected list.

The next step for the student is to assign a number to every element, in this case student, on the population list. After all individuals are numbered, they can begin their sample selection by entering a random numbers table at any place to make the first selection. By definition, it does not matter where they enter the table since it is a random numbers table; there is no inherent order to the numbers. After they have entered the table, however, they should systematically move within the table, selecting elements that correspond to the random number selected. They should continue this selection process until the entire sample of 60 students has been obtained.

Using these random sampling techniques, every element in the population, that is, every student in the sophomore class, has an equal and known probability of being selected for the sample. By selecting a sample in this way, the student has maximized the probability that their sample of 60 sophomores will be representative of the entire population of sophomores at their university.

In systematic sampling, the student begins with a random starting point but systematically select elements thereafter. The general rule for systematic sampling is to begin with the kth (any number selected randomly) element in the population, and select every kth element thereafter. The kth element is the only element which is truly selected at random; it can be selected from a random numbers table or by some other random method. Systematic sampling eliminates the process of deriving a new random number for every element selected. For example, if a student selected the number 7 to begin systematic sampling from the list of sophomores, the first student selected would be number 7. They would continue to select every 7th student thereafter until they had the entire sample of 60 students selected.
When lists of a population are not complete, or more often, not available, we must utilize other sampling techniques. In such cases, the sampling procedures become a little more complex. We usually end up working toward the sample we want through successive approximations; first by extracting a sample from lists of groups or clusters that are available, and then sampling the elements of interest from these selected clusters. Sampling procedures of this nature are typically called Multistage Cluster Sampling.
One of the primary problems we face when generalizing information obtained from a sample to a population is uncertainty. How accurately does our sample reflect the true population? This uncertainty is inherent in any sample because by definition, we only have a part of the population. The goal when obtaining a sample, then, is to select elements from the population in a way that increases the chances of this sample being representative. Probability sampling techniques increase the likelihood of accomplishing this goal. The fundamental element in probability sampling is random selection. When a sample is randomly selected from the population, this means every element (e.g. individual) has an equal and independent chance of being selected for the sample.
When a sample is randomly selected from the population, it means every element (e.g. individual) has a known and independent chance of being selected for the sample. The notion of randomness implies "no bias" within the selection process.
Weighted or Quota sampling techniques.
Unlike probability samples, when collecting a sample using nonprobability sampling techniques, elements within the population do not have a known probability of being selected. Because the chance of one individual being selected versus another remains unknown, we cannot be certain the selected sample actually represents our population. Since we are generally interested in making inferences to a population, this uncertainty can represent a major problem.
Nonprobability sampling techniques are often the only way of obtaining samples from particular populations or for certain types of research questions. The example used in the chapter of shoplifters is one example. It would be hard to technically define a population of shoplifters since we don't have a list of shoplifters to randomly select from. In other cases, we may want to over-sample certain subsets of the population. Nonprobability sampling techniques allows us the flexibility to obtain samples for these types of research problems.

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