and then the rest are chosen according to some well-defined pattern. For example, if you wanted 100
people in your sample to be chosen from a list of 10,000 people, you could randomly select one of the
first 100 people and then select every 100th name on the list after that.
• stratified random sample : This is a sample in which the population is first divided into distinct
homogenous subgroups called strata (strata in italics) and then a random sample is chosen from each
subgroup. For example, you might divide the population of voters into groups by political party and
then select an SRS of 250 from each group.
• cluster sample: The population is first divided into sections or “clusters.” Then we randomly select
the population is first divided into distinct homogenous subgroups called strata (strata in italics) and
then a random sample is chosen from each subgroup. For example, you might divide the population of
voters into groups by political party and then select an SRS of 250 from each group or clusters, and
include all of the members of the cluster(s) in the sample.
example: You are going to conduct a survey of your senior class concerning plans for graduation.
You want a 10% sample of the class. Describe a procedure by which you could use a
systematic sample to obtain your sample and explain why this sample isn’t a simple random
sample. Is this a random sample?
solution: One way would be to obtain an alphabetical list of all the seniors. Use a random number
generator (such as a table of random digits or a scientific calculator with a random digits
function) to select one of the first 10 names on the list. Then proceed to select every 10th name
on the list after the first.
Note that this is not an SRS because not every possible sample of 10% of the senior class is
equally likely. For example, people next to each other in the list can’t both be in the sample.
Theoretically, the first 10% of the list could be the sample if it were an SRS. This clearly isn’t
possible.
Before the first name has been randomly selected, every member of the population has an
equal chance to be selected for the sample. Hence, this is a random sample, although it is not a
simple random sample.
example: A large urban school district wants to determine the opinions of its elementary schools
teachers concerning a proposed curriculum change. The district administration randomly
selects one school from all the elementary schools in the district and surveys each teacher in
that school. What kind of sample is this?
solution: This is a cluster sample. The individual schools represent previously defined groups
(clusters) from which we have randomly selected one (it could have been more) for inclusion
in our sample.
example: You are sampling from a population with mixed ethnicity. The population is 45%
Caucasian, 25% Asian American, 15% Latino, and 15% African American. How would a
stratified random sample of 200 people be constructed?
solution: You want your sample to mirror the population in terms of its ethnic distribution.
Accordingly, from the Caucasians, you would draw an SRS of 90 (that’s 45%), an SRS of 50
(25%) from the Asian Americans, an SRS of 30(15%) from the Latinos, and an SRS of 30
(15%) from the African Americans.
Of course, not all samples are probability samples. At times, people try to obtain samples by
processes that are nonrandom but still hope, through design or faith, that the resulting sample is