QUALITATIVE AND QUANTITATIVE SAMPLINGWe draw several samples in stages in cluster
sampling. In a three-stage sample, stage 1 is a ran-
dom sampling of large clusters; stage 2 is a random
sampling of small clusters within each selected
large cluster; and the last stage is a sampling of ele-
ments from within the sampled small clusters. For
example, we want a sample of individuals from
Mapleville. First, we randomly sample city blocks,
then households within blocks, and then individu-
als within households (see Chart 2). Although there
is no accurate list of all residents of Mapleville, there
is an accurate list of blocks in the city. After select-
ing a random sample of blocks, we count all house-
holds on the selected blocks to create a sample
frame for each block. Then we use the list of house-
holds to draw a random sample at the stage of
sampling households. Finally, we choose a specific
individual within each sampled household.
Cluster sampling is usually less expensive than
simple random sampling, but it is less accurate.
Each stage in cluster sampling introduces sampling
errors, so a multistage cluster sample has more
sampling errors than a one-stage random sample.^8
When we use cluster sampling, we must decide
the number of clusters and the number of elements
within clusters. For example, in a two-stage cluster
sample of 240 people from Mapleville, we could
randomly select 120 clusters and select 2 elements
from each or randomly select two clusters and select
120 elements in each. Which is better? A design
with more clusters is better because elements within
clusters (e.g., people living on the same block) tend
to be similar to each other (e.g., people on the same
block tend to be more alike than those on different
blocks). If few clusters are chosen, many similar
elements could be selected, which would be less
representative of the total population. For example,
we could select two blocks with relatively wealthy
people and draw 120 people from each block. This
would be less representative than a sample with 120
different city blocks and 2 individuals chosen from
each.
When we sample from a large geographical
area and must travel to each element, cluster
sampling significantly reduces travel costs. As
usual, there is a trade-off between accuracy and cost.
For example, Alan, Ricardo, and Barbara each
personally interview a sample of 1,500 students
who represent the population of all college stu-
dents in North America. Alan obtains an accurate
sampling frame of all students and uses simple
random sampling. He travels to 1,000 different
locations to interview one or two students at each.
Ricardo draws a random sample of three colleges
from a list of all 3,000 colleges and then visits the
three and selects 500 students from each. Barbara
draws a random sample of 300 colleges. She visits
the 300 and selects 5 students at each. If travel costs
average $250 per location, Alan’s travel bill is
$250,000, Ricardo’s is $750, and Barbara’s is
$75,000. Alan’s sample is highly accurate, but
Barbara’s is only slightly less accurate for one-third
the cost. Ricardo’s sample is the cheapest, but it is
not representative.
Within-Household Sampling.Once we sample a
household or similar unit (e.g., family or dwelling
unit) in cluster sampling, the question arises as to
whom we should choose. A potential source of bias
is introduced if the first person who answers the
telephone, the door, or the mail is used in the
sample. The first person who answers should be
selected only if his or her answering is the result of
a truly random process. This is rarely the case. Cer-
tain people are unlikely to be at home, and in some
households one person (e.g., a husband) is more
likely than another to answer the telephone or door.
Researchers use within-household sampling to
ensure that after a random household is chosen, the
individual within the household is also selected
randomly.
We can randomly select a person within a
household in several ways.^9 The most common
method is to use a selection table specifying whom
you should pick (e.g., oldest male, youngest female)
after determining the size and composition of the
household (see Table 2). This removes any bias that
might arise from choosing the first person to answer
the door or telephone or from the interviewer’s
selection of the person who appears to be friend-
liest.
Probability Proportionate to Size (PPS).There are
two ways we can draw cluster samples. The method
just described is proportionate or unweighted