poor and the concentration of mercury in the fish will reflect the

# Poor and the concentration of mercury in the fish

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poor, and the concentration of mercury in the fish will reflect the concentration of mercury in the lake. Thus, we do not obtain as much information about all nursing home residents in the United States by sampling two residents in the same home as by sampling two residents in different homes, because the two residents in the same home are likely to have more similar opinions. By sampling everyone in the cluster, we partially repeat the same information instead of obtaining new information, and that gives us less precision for estimates of population quantities. Cluster sampling is
f0) Chapter 5: Cluster Sampling with Equal Probabilities 133 FIGURE 5.1 Similarities and differences between cluster sampling and stratified sampling Stratified Sampling Each element of the population is in exactly one stratum. Population of H strata; stratum It has Nh elements: I i Take an SRS from ever, stratum: I Cluster Sampling Each element of the population is in exactly one cluster. One-stage cluster sampling; population of N clusters: Take an SRS of clusters; observe all elements within the clusters in the sample: I I m 0 I Variance of the estimate o f ' U depends on the variability of values within strata. For greatest precision, individual elements within each stratum should have similar values, but stratum means should differ from each other as much as possible. The cluster is the sampling unit; the more clusters we sample, the smaller the variance. The variance of the estimate of -)'U depends primarily on the variability between cluster means. For greatest precision, individual elements within each cluster should be heterogeneous, and cluster means should be similar to one another. used in practice because it is usually much cheaper and more convenient to sample in clusters than randomly in the population. Almost all large household surveys carried out by the U.S. government, or by commercial or academic institutions, use cluster sampling because of the cost savings. One of the biggest mistakes made by researchers using surveys is to analyze a cluster sample as if it were an SRS. Such confusion usually results in the researchers
CAD C... (-A 'L3 A.. 134 Chapter 5: Cluster Sampling with Equal Probabilities EXAMPLE 5.1 reporting standard errors that are much smaller than they should be; this gives the impression that the survey results are much more precise than they really are. Basow and Silberg (1987) report results of their research on whether students evaluate female college professors differently than they evaluate male college professors. The authors matched 16 female professors with 16 male professors by subject taught, years of teaching experience, and tenure status, and then gave evaluation questionnaires to students in those professors' classes. The sample size for analyzing this study is n = 32, the number of faculty studied; it is not 1029, the number of students who returned questionnaires. Students' evaluations of faculty reflect the different styles of

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