Introduction
Previous lessons focused on the relationship
between samples and populations, and on using
random sampling to select a representative sample
and reduce sampling bias. This lesson introduces the
idea that simple random sampling is not the only
method for selecting representative samples, and
that the sampling method used often depends on the
goal of the research being conducted as well as
practical considerations.
1
1.3.3: Other Methods of Random Sampling
Introduction, continued
Different sampling methods can be helpful tools for a
wide variety of research situations. Furthermore,
familiarity with these methods allows you to
understand the methods used by other researchers
who often need to mix and match methods in order to
meet practical challenges without compromising the
representative nature of their samples.
2
1.3.3: Other Methods of Random Sampling
Key Concepts
• Additional sampling methods include cluster
sampling, systematic sampling, and stratified
sampling.
• All of these methods involve random assignment,
although none meet the criteria of simple random
sampling.
3
1.3.3: Other Methods of Random Sampling
Key Concepts, continued
• With a cluster sample, naturally occurring groups of
population members are chosen for the sample. This
method involves dividing the population into groups by
geography or other practical criteria. Some of the
groups are randomly selected, while others are not.
This method allows each member of the population to
have a nearly equal chance of selection. Cluster
sampling is usually chosen to eliminate excessive travel
or reduce the disruption that a study may cause.
4
1.3.3: Other Methods of Random Sampling
Key Concepts, continued
• A systematic sample is a sample drawn by selecting
people or objects from a list, chart, or grouping at a
uniform interval. This method involves using a natural
ordering of population members, such as by arrival
time, location, or placement on a list. Once the order is
established, every nth member (e.g., every fifth
member) is chosen. If the starting number is randomly
selected, then each member of the population has a
nearly equal chance of selection. Systematic sampling
is usually chosen when relative position in a list may be
related to key variables in a study, or when it is useful to
a researcher to space out data gathering.
1.3.3: Other Methods of Random Sampling
5
Key Concepts, continued
• For a stratified sample, the population is divided into
subgroups so that the people or objects within the
subgroup share relevant characteristics. This method
involves grouping members of the population by
characteristics that may be related to parameters of
interest. Once the groups are formed, members of each
group are randomly selected so that the number of
members in the sample with given characteristics is
approximately proportional to the number of members
in the population with the same characteristics.
Stratified sampling has been used for many years to
predict the results of state and national elections.
1.3.3: Other Methods of Random Sampling
6
Key Concepts, continued
• A convenience sample is a sample for which members
are chosen in order to minimize time, effort, or expense.
Convenience sampling involves gathering data quickly
and easily. The advantage of convenience sampling is
that, in some cases, preliminary estimates of population
parameters can be obtained quickly. The main
disadvantage of convenience sampling is that the
samples are prone to serious biases. As a result, the
estimates obtained are seldom accurate and the
statistics are difficult to interpret.
7
1.3.3: Other Methods of Random Sampling
Key Concepts, continued
• While simple random samples provide unbiased
estimates, there are situations in which the goal of
the research is better served by other forms of
sampling. These include situations in which the
goal is to count all members of a population and
situations in which the sample provides a
comparison group.
• It is unwise to use a sampling method simply
because it is the most convenient. Unless the
sample is representative of the population of
interest, the statistics that are produced may be
misleading.
1.3.3: Other Methods of Random Sampling
8
Key Concepts, continued
• A larger sample is not always a better sample.
There is less variability in measures taken from a
large sample, but if the large sample is biased, the
researcher will likely obtain estimates that are
inaccurate.
9
1.3.3: Other Methods of Random Sampling
Common Errors/Misconceptions
• mistakenly believing that a larger sample is always a
better sample
• ignoring bias when making estimates regarding the
entire population
10
1.3.3: Other Methods of Random Sampling
Guided Practice
Example 2
Pearce wants to conduct a survey of shoppers at the local
mall. He obtains a list of the major stores, restaurants,
and other establishments and creates the following table
that includes each destination’s name, location (zone),
category, and category rank. The category rank
represents where the mall destination falls in a list of all
the establishments in the same category; for example,
Aéropostale is second in the list of clothing stores, so its
category rank is 2.
11
1.3.3: Other Methods of Random Sampling
Use the table (shown on the following slides) and two
methods to choose a cluster sample of 5 establishments
at which Pearce can interview shoppers.
• Method 1: Give each zone an equal chance of
selection.
• Method 2: Give each establishment an equal
chance of selection.
12
1.3.3: Other Methods of Random Sampling
Establishment
Abercrombie &
Fitch
Aéropostale
Amato’s
American Eagle
Arby’s
Zone
Category
Category rank
D
Clothing
1
D
A
B
A
Clothing
Food
Clothing
Food
Technology/electronic
s
2
1
3
2
AT&T
C
babyGap
D
Clothing
4
Banana Republic
E
Clothing
5
Barton’s Couture
D
Clothing
6
Bath & Body Works
B
Bath/beauty
1
The Body Shop
D
Bath/beauty
1.3.3: Other Methods of Random Sampling
1
2
(continued)
13
Establishment
Build-A-Bear
Workshop
Bureau of Motor
Vehicles
Charley’s Subs
Zone
Category
Category rank
B
Toys/hobbies
1
D
Services
2
A
Food
3
Chico’s
D
Clothing
7
The Children’s Place
B
Clothing
8
Claire’s
A
Accessories
1
Coach
B
Accessories
2
Coldwater Creek
dELiA*s
Dube Travel
C
B
A
Clothing
Clothing
Services
9
10
1
(continued)
1.3.3: Other Methods of Random Sampling
14
Establishment
Zone
Category
Category rank
Eddie Bauer
Express
D
D
11
12
f.y.e.
A
Foot Locker
Francesca’s
G.M. Pollack &
Sons
GameStop
Gap
Gloria Jean’s Coffee
Go Games
Gymboree
B
B
Clothing
Clothing
Technology/electronic
s
Clothing
Clothing
C
Jewelry
4
A
D
C
C
E
Toys/hobbies
Clothing
Food
Toys/hobbies
Clothing
1.3.3: Other Methods of Random Sampling
2
13
14
2
15
4
3
16
(continued)
15
Establishment
Zone
Hannoush Jewelers
Hometown Buffet
Hot Topic
Icing by Claire’s
J.Crew
J.Jill
Johnny Rockets
Just Puzzles
Kamasouptra
Kay Jewelers
La Biotique
A
C
A
A
E
B
A
B
A
D
A
Category
Jewelry
Food
Clothing
Accessories
Clothing
Clothing
Food
Toys/hobbies
Food
Jewelry
Bath/beauty
Category rank
1
5
17
3
18
19
6
4
7
2
3
(continued)
1.3.3: Other Methods of Random Sampling
16
Establishment
Zone
Category
Lane Bryant
D Clothing
LensCrafters
A Services
Lids
A Accessories
LOFT
D Clothing
LUSH
E Bath/beauty
MasterCuts
A Bath/beauty
Mayflower Massage
A Services
Mrs. Field’s Cookies
A Food
Olympia Sports
D Toys/hobbies
On Time
A Accessories
Origins
B Bath/beauty
Category rank
20
3
4
21
4
5
4
8
5
5
6
(continued)
1.3.3: Other Methods of Random Sampling
17
Establishment
PacSun
Panda Express
The Picture People
Piercing Pagoda
Pretzel Time/TCBY
Pro Vision
Qdoba
Radio Shack
Red Mango
Regis Salon
Sarku Japan
Zone
A
A
A
E
C
A
A
C
A
A
A
Category
Category rank
Clothing
22
Food
9
Services
5
Jewelry
3
Food
10
Services
6
Food
11
Technology/electronics
3
Food
12
Bath/beauty
7
Food
13
(continued)
1.3.3: Other Methods of Random Sampling
18
Establishment
Sbarro
Sephora
Starbucks
Sunglass Hut
Super Hearing Aids
Swarovski
T & C Nails
T-Mobile
Teavana
Verizon Wireless
Zone
A
E
A
B
A
D
A
B
D
A
Category
Category rank
Food
14
Bath/beauty
8
Food
15
Accessories
6
Services
7
Jewelry
5
Bath/beauty
9
Technology/electronics
4
Food
16
Technology/electronics
5
19
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 2, continued
Method 1: Give each zone an equal
chance of selection.
1. Number the zones.
The mall is divided into 5 zones, so assign each
zone a number 1 through 5.
Let A = 1, B = 2, C = 3, D = 4, and E = 5.
20
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 2, continued
2. Select a zone of the mall.
Randomly select 1 of the 5 zones using 5 cards from
a standard deck or a random number generator.
Suppose that a 4 is chosen. This corresponds to
Zone D.
21
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 2, continued
3. Label the businesses in the chosen zone.
There are 16 establishments in Zone D, so label each one
with a number from 1 to 16.
1 = Abercrombie & Fitch
9 = Express
2 = Aéropostale
10 = Gap
3 = babyGap
11 = Kay Jewelers
4 = Barton’s Couture
12 = Lane Bryant
5 = The Body Shop
13 = LOFT
6 = Bureau of Motor Vehicles
14 = Olympia Sports
7 = Chico’s
15 = Swarovski
8 = Eddie Bauer
16 = Teavana
22
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 2, continued
4. Randomly select 5 of the establishments in
the selected zone.
Using 16 cards or a random number generator,
randomly select 5 establishments from Zone D. Discard
repeats.
Results will vary, but suppose the numbers 1, 4, 7, 8,
and 12 are randomly chosen.
23
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 2, continued
These numbers correspond to the following
establishments:
1 = Abercrombie & Fitch
4 = Barton’s Couture
7 = Chico’s
8 = Eddie Bauer
12 = Lane Bryant
The corresponding cluster sample of 5
establishments at which Pearce can interview
shoppers consists of Abercrombie & Fitch, Barton’s
Couture, Chico’s, Eddie Bauer, and Lane Bryant.
1.3.3: Other Methods of Random Sampling
24
Guided Practice: Example 2, continued
Method 2: Give each establishment an equal
chance of selection.
1. Label each establishment.
There are 75 establishments, so label each of them
with a number from 1 to 75.
25
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 2, continued
2. Randomly select a number from 1 to 75.
Randomly select one of the 75 establishments using
75 cards or a random number generator.
Suppose a 10 is chosen. This corresponds to
Barton’s Couture.
26
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 2, continued
3. Since this is a cluster sample, choose
4 other establishments in the same zone.
Barton’s Couture is in Zone D.
There are 16 establishments in Zone D, so label each
one with a number from 1 to 16, as shown on the next
slide.
27
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 2, continued
1 = Abercrombie & Fitch
2 = Aéropostale
3 = babyGap
4 = Barton’s Couture
5 = The Body Shop
6 = Bureau of Motor Vehicles
7 = Chico’s
8 = Eddie Bauer
9 = Express
10 = Gap
11 = Kay Jewelers
12 = Lane Bryant
13 = LOFT
14 = Olympia Sports
15 = Swarovski
16 = Teavana
28
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 2, continued
4. Randomly select 4 other establishments in
Zone D.
Using 16 cards or a random number generator,
randomly select 4 additional establishments from
Zone D. Discard repeats.
Results will vary, but suppose the numbers 1, 9, 13,
and 15 are randomly chosen.
29
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 2, continued
These numbers correspond to the following stores:
1 = Abercrombie & Fitch
9 = Express
13 = LOFT
15 = Swarovski
The corresponding cluster sample of 5
establishments at which Pearce can interview
shoppers consists of Barton’s Couture, Abercrombie
& Fitch, Express, LOFT, and Swarovski.
30
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 2, continued
Note: Method 1 will probably be more convenient
because the smaller zones (Zone C and Zone E)
have an equal chance of selection. Since small
zones have fewer establishments, the
establishments in a small zone will probably be
closer together, on average, than the
establishments in a large zone, making it easier on
Pearce to conduct his survey. Using Method 2
means that the establishments in smaller zones
have less chance of being selected.
✔
31
1.3.3: Other Methods of Random Sampling
Guided Practice
Example 3
Kylie wants to estimate the total number of times
customers enter different establishments at the same
mall described in Example 2. Kylie has 10 electronic
devices that can count the number of customers
entering a given establishment. Use the tables provided
in Example 2 to select a stratified sample (by category)
of 10 establishments at which Kylie can install her
counting devices.
32
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 3, continued
1. Construct a table that shows the number
of establishments in each category.
Refer to the table in Example 2 to determine the
number of establishments in each category.
Organize the results in a new table (shown on the
next slide).
33
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 3, continued
Category
Number of
establishments
Clothing
22
Food
16
Bath/beauty
9
Services
7
Accessories
6
Jewelry
5
Technology/electronics
5
Toys/hobbies
5
Total
75
1.3.3: Other Methods of Random Sampling
34
Guided Practice: Example 3, continued
2. Determine the number of establishments
to select from each category.
Since Kylie needs to select 10 establishments from
only 8 categories, select 2 establishments from the
largest 2 categories, and 1 from each remaining
category. Two stores each from the Clothing and
Food categories will be selected, since these are the
largest categories.
35
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 3, continued
3. Organize the list of establishments by
category, then number each item within a
category.
Create tables to organize the 8 categories of
establishments (shown beginning on the next slide).
Number the stores from 1 to n, where n is the number
ranking of a particular establishment in a list of all the
members of the same category. For example,
babyGap is fourth in the list of clothing stores, so its
value for n is 4.
36
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 3, continued
Food
Name
Amato’s
Arby’s
Charley’s Subs
Gloria Jean’s Coffee
Hometown Buffet
Johnny Rockets
Kamasouptra
Mrs. Field’s Cookies
n
1
2
3
4
5
6
7
8
Name
Panda Express
Pretzel Time/TCBY
Qdoba
Red Mango
Sarku Japan
Sbarro
Starbucks
Teavana
n
9
10
11
12
13
14
15
16
37
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 3, continued
Name
Abercrombie & Fitch
Aéropostale
American Eagle
babyGap
Banana Republic
Barton’s Couture
Chico’s
The Children’s Place
Coldwater Creek
dELiA*s
Eddie Bauer
Clothing
n
Name
1
Express
2
Foot Locker
3
Francesca’s
4
Gap
5
Gymboree
6
Hot Topic
7
J.Crew
8
J.Jill
9
Lane Bryant
10
LOFT
11
PacSun
1.3.3: Other Methods of Random Sampling
n
12
13
14
15
16
17
18
19
20
21
22
38
Guided Practice: Example 3, continued
Bath/beauty
Name
Bath & Body Works
The Body Shop
La Biotique
LUSH
MasterCuts
Origins
Regis Salon
Sephora
T & C Nails
n
1
2
3
4
5
6
7
8
9
Services
Name
Dube Travel
Bureau of Motor Vehicles
LensCrafters
Mayflower Massage
The Picture People
Pro Vision
Super Hearing Aids
n
1
2
3
4
5
6
7
39
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 3, continued
Accessories
Name
Claire’s
Coach
Icing by Claire’s
Lids
On Time
Sunglass Hut
n
1
2
3
4
5
6
Jewelry
Name
Hannoush Jewelers
Kay Jewelers
Piercing Pagoda
G.M. Pollack & Sons
Swarovski
n
1
2
3
4
5
40
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 3, continued
Technology/electronics
Name
n
AT&T
1
f.y.e.
2
Radio Shack
3
T-Mobile
4
Verizon Wireless
5
Toys/hobbies
Name
Build-A-Bear Workshop
GameStop
Go Games
Just Puzzles
Olympia Sports
n
1
2
3
4
5
41
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 3, continued
4. Randomly select the appropriate number
of stores in each category.
Using cards or a random number generator, randomly
select 2 of the 22 clothing stores, 2 of the 16 food
stores, 1 of the 9 bath/beauty stores, 1 of the 7
service stores, 1 of the 6 accessories stores, 1 of the
5 jewelry stores, 1 of the 5 technology/electronics
stores, and 1 of the 5 toys/hobbies stores.
42
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 3, continued
Results will vary, but suppose the following numbers
were selected:
• Clothing: The random integers 12 and 9 were
selected.
• Food: The random integers 9 and 16 were selected.
• Bath/beauty: The random integer 5 was selected.
• Services: The random integer 1 was selected.
• Accessories: The random integer 5 was selected.
• Jewelry: The random integer 5 was selected.
• Technology/electronics: The random integer 5 was
selected.
• Toys/hobbies: The random integer 5 was selected.
43
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 3, continued
5. Match each random number with the
establishment that falls in that position in
the category list.
From our tables, we can use the randomly generated
numbers to select a stratified sample.
44
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 3, continued
The following stores represent the stratified sample.
• Clothing: 9 = Coldwater Creek and 12 = Express
• Food: 9 = Panda Express and 16 = Teavana
• Bath/beauty: 5 = MasterCuts
• Services: 1 = Dube Travel
• Accessories: 5 = On Time
• Jewelry: 5 = Swarovski
• Technology/electronics: 5 = Verizon Wireless
• Toys/hobbies: 5 = Just Puzzles
45
1.3.3: Other Methods of Random Sampling
Guided Practice: Example 3, continued
Note: It is possible with a simple random sample that
one or more of the categories will be left out if 10
stores are selected using simple random sampling.
By using stratified sampling, each category
is represented.
✔
1.3.3: Other Methods of Random Sampling
46