Chapter One
Data Collection
1.4
Other Types of Sampling
Objective(s)



Obtain a stratified sample.
Obtain a systematic sample.
Obtain a cluster sample.
Warm-up
Explain in your own words what a simple
random sample is.
Give one pro and one con of using a simple
random sample.
Simple Random Sampling
Pros:
 Almost Easiest
 Requires little
knowledge of pop
Cons:
 Possibly larger
sampling error [more
variation] from
sample to sample
 Need to have a listing
of population
elements in some
form
Definition
A stratified sample is one obtained by
separating the population into homogeneous,
non-overlapping groups called strata, and
then obtaining a simple random sample from
each stratum.
Stratified Sampling
EXAMPLE
Obtaining a Stratified Sample
The 107th Congress of the United States (2001 - 2003)
had 435 members in the House of Representatives
(221 Republicans, 212 Democrats, and 2 Others). The
president wants to have a luncheon with 4
Republicans, 4 Democrats and 1 Other. Obtain a
stratified sample in order to select members who will
attend the luncheon.
Stratified Random Sample
Pros:
 Less sampling error
[variability from
sample to sample]
 Able to analyze more
about groups with
small proportions in
the population
Cons:
 For each element you
need to have a list of
characteristics for
which you want to
stratify
 May cost more and
not be worth it…just
take a larger SRS
Definition
A systematic sample is obtained by
selecting every kth individual from the
population. The first individual selected is a
random number between 1 and k.
Systematic Sampling
EXAMPLE
Obtaining a Systematic Sample
A quality control engineer wants to obtain a
systematic sample of 25 bottles coming off a
filling machine to verify the machine is working
properly. Design a sampling technique that can
be used to obtain a sample of 25 bottles.
STEPS IN SYSTEMATIC SAMPLING,
POPULATION SIZE KNOWN
Step 1: Determine the population size, N.
Step 2: Determine the sample size desired, n.
Step 3: Compute N/n and round down to the nearest
integer. This value is k.
Step 4: Randomly select a number between 1 and k. Call
this number p.
Step 5: The sample will consist of the following
individuals:
p, p + k, p + 2k,…, p + (n – 1)k
Systematic Random Sampling
Pros
 Easiest
Cons
 Possible periodicity
 Need a list or
mapping of
population
Definition
A cluster sample is obtained by selecting
all individuals within a randomly selected
collection or group of individuals.
Useful when a sampling frame (a list) of elements
is not available like with large populations that
are spread out across a wide geographic area or
across many different organizations
Cluster Sampling
EXAMPLE
Obtaining a Cluster Sample
A school administrator wants to obtain a sample
of students in order to conduct a survey. She
randomly selects 10 classes and administers the
survey to all the students in the class.
EXAMPLE
Obtaining a Cluster Sample
You want to conduct face-to-face interviews
with people.
To save on travel expenses, you may consider
“clusters” of neighborhoods or city blocks.
Cluster samples often involve multiple stages, with
clusters within clusters, as when a national study of
middle school students might involve first sampling
states, then counties, then schools, and finally
students within each selected school .
Cluster Sampling
Pros
 Saves time
 Saves money
 Should allow for
closer supervision in
the field
 Requires
enumerating only part
of the population
Cons
 Larger sampling error
[variation in score
form sample to
sample]
 Typically “requires”
larger sample
Definition
A convenience sample is one in which the
individuals in the sample are easily obtained.
Definition
A convenience sample is one in which the
individuals in the sample are easily obtained.
Any studies that use this type of sampling generally have
results that are suspect. Results should be looked upon
with extreme skepticism.
EXAMPLE
•Interviewing people on a •Magazine surveys
street corner or at the
•Observing conversations
mall
in an on-line chat room
•Surveying students in a
classroom
Convenience Sampling
a.k.a. Availability sampling
Pros
 Easiest
Cons
 Least information
Objective(s)



Obtain a stratified sample.
Obtain a systematic sample.
Obtain a cluster sample.
To estimate the percentage of defects in a
recent manufacturing batch, a qualitycontrol manager at Intel selects every 8th
chip that comes off the assembly line
starting with the 3rd until she obtains a
sample of 140 chips
1.
2.
3.
4.
Simple Random Sample
Stratified Sample
Systematic Sample
Cluster Sample
25%
25%
25%
25%
To determine the prevalence of human growth
hormone (HGH) use among high school varsity
baseball players, the State Athletic Commission
randomly selects 50 high schools. All member
of the selected high schools’ varsity baseball
teams are tested for HGH
1.
2.
3.
4.
Simple Random Sample
Stratified Sample
Systematic Sample
Cluster Sample
25%
25%
25%
25%
To determine customer opinion of its boarding
policy, Southwest Airlines randomly selects 60
flights during a certain week and surveys all
passengers on the flights
1.
2.
3.
4.
Simple Random Sample
Stratified Sample
Systematic Sample
Cluster Sample
25%
25%
25%
25%
A member of Congress wishes to determine her
constituency’s opinion regarding estate taxes.
She divides her constituency into three income
classes: low-income households, middleincome households, and upper-income
households. She then takes a simple random
sample of households from each income class.
1.
2.
3.
4.
Simple Random Sample
Stratified Sample
Systematic Sample
Cluster Sample
25%
25%
25%
25%
In an effort to identify if an advertising
campaign has been effective, a marketing firm
conducts a nationwide poll by randomly
selecting individuals form a list of known users
of the product.
1.
2.
3.
4.
Simple Random Sample
Stratified Sample
Systematic Sample
Cluster Sample
25%
25%
25%
25%
A radio station asks its listeners to call in their
opinion regarding the use of U.S. forces in
peacekeeping missions.
1.
2.
3.
4.
Simple Random Sample
Stratified Sample
Systematic Sample
Cluster Sample
25%
25%
25%
25%
A farmer divides his orchard into 50
subsections, randomly selects 4, and samples
all the trees within the 4 subsections to
approximate the yield of his orchard.
1.
2.
3.
4.
Simple Random Sample
Stratified Sample
Systematic Sample
Cluster Sample
25%
25%
25%
25%
A school official divides the student population
into five classes: freshman, sophomores,
junior, senior, and graduate student. The
official takes a simple random sample from
each class and asks the members’ opinions
regarding student services
1.
2.
3.
4.
Simple Random Sample
Stratified Sample
Systematic Sample
Cluster Sample
25%
25%
25%
25%
A survey regarding download time on a certain
website is administered on the Internet by a
market research firm to anyone who would like
to take it
1.
2.
3.
4.
Simple Random Sample
Stratified Sample
Systematic Sample
Cluster Sample
25%
25%
25%
25%
The presider of a guest-lecturer series at a
university stands outside the auditorium before
a lecture begins and hands every fifty person
who arrives, beginning with the third, a speaker
evaluation survey to be completed and returned
at the end of the program
1.
2.
3.
4.
Simple Random Sample
Stratified Sample
Systematic Sample
Cluster Sample
25%
25%
25%
25%
To determine his DSL internet connection
speed, Shawn divides up the day into foru
parts: morning, midday, evening, and late night.
He then measures his internet connection
speed at 5 randomly selected times during each
part of the day.
1.
2.
3.
4.
Simple Random Sample
Stratified Sample
Systematic Sample
Cluster Sample
25%
25%
25%
25%
24 Hour Fitness wants to administer a
satisfaction survey to its current members.
Using its membership roster, the club randomly
selects 40 club members and asks them about
their level of satisfaction with the club
1.
2.
3.
4.
Simple Random Sample
Stratified Sample
Systematic Sample
Cluster Sample
25%
25%
25%
25%