22 CHAPTER 1 Introduction to Statistics TRY IT YOURSELF 3 A company employs 79 people. Choose a simple random sample of five to survey. Answer: Page A35 When you choose members of a sample, you should decide whether it is acceptable to have the same population member selected more than once. If it is acceptable, then the sampling process is said to be with replacement. If it is not acceptable, then the sampling process is said to be without replacement. There are several other commonly used sampling techniques. Each has advantages and disadvantages. • Stratified Sample When it is important for the sample to have members from each segment of the population, you should use a stratified sample. Depending on the focus of the study, members of the population are divided into two or more subsets, called strata, that share a similar characteristic such as age, gender, ethnicity, or even political preference. A sample is then randomly selected from each of the strata. Using a stratified sample ensures that each segment of the population is represented. For instance, to collect a stratified sample of the number of people who live in West Ridge County households, you could divide the households into socioeconomic categories and then randomly select households from each category. In using a stratified sample, care must be taken to ensure that all strata are sampled in proportion to their actual percentages of occurrence in the population. For instance, if 40% of the people in West Ridge County belong to the low-income group, then the proportion of the sample should have 40% from this group. Group 1: Low income Group 2: Middle income Group 3: High income Stratified Sampling • Cluster Sample When the population falls into naturally occurring subgroups, each having similar characteristics, a cluster sample may be the most appropriate. To select a cluster sample, divide the population into groups, called clusters, and select all of the members in one or more (but not all) of the clusters. Examples of clusters could be different sections of the same course or different branches of a bank. For instance, to collect a cluster sample of the number of people who live in West Ridge County households, divide the households into groups according to zip codes, then select all the households in one or more, but not all, zip codes and count the number of people living in each household. In using a cluster sample, care must be taken to ensure that all clusters have similar characteristics. For instance, if one of the zip code clusters has a greater proportion of high-income people, the data might not be representative of the population. Zone 1 Zone 3 Zone 4 Zone 2 Zip Code Zones in West Ridge County Cluster Sampling Study Tip Be sure you understand that stratified sampling randomly selects a sample of members from all strata. Cluster sampling uses all members from a randomly selected sample of clusters (but not all, so some clusters will not be part of the sample). For instance, in the figure for “Stratified Sampling” at the right, a sample of households in West Ridge County is randomly selected from all three income groups. In the figure for “Cluster Sampling,” all households in a randomly selected cluster (Zone 1) are used. (Notice that the other zones are not part of the sample.)
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