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

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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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