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Sampling Design
Sampling Terminology
• Sample
– A subset, or some part, of a larger population
• Population or universe
– Any complete group of entities that share some
common set of characteristics
• Population element
– An individual member of a population
• Census
– An investigation of ALL the individual elements that
make up a population
A puzzle is a sample until it’s done.
The sample allows one to guess at the picture.
Why Sample?
• Pragmatic Reasons
– Budget & time constraints.
– Limited access to total population.
• Accurate and Reliable Results
– Samples can yield reasonably accurate information.
– Strong similarities in population elements makes sampling
possible.
– Sampling may be more accurate than a census.
• Destruction of Test Units
– Sampling reduces the costs of research in finite populations.
Sample vs. Census
CONDITIONS FAVORING THE USE OF
Sample
Census
1. Budget
Small
Large
2. Time available
Short
Long
3. Population size
Large
Small
4. Variance in the characteristic
Small
Large
5. Cost of sampling error
Low
High
6. Cost of nonsampling errors
High
Low
7. Nature of measurement
Destructive
Nondestructive
8. Attention to individual cases
Yes
No
Stages in Sample Selection
Identifying a Relevant Population
• Defining the Target Population
– What is the relevant population?
– Whom do we want to talk to?
• Population is operationally defined by specific &
explicit tangible characteristics.
• If you want to target “Women”, do you mean
– All women still capable of bearing children or,
– All women between the ages of 12 and 50?
Identifying a Sampling Frame
• A list of elements from which a sample may be drawn
• Also called the working population.
– Sampling Frame Error occurs when certain sample elements
• are not listed, or
• are not accurately represented in a sampling frame.
– Sampling services (list brokers)
• Provide lists or databases of the names, addresses, phone numbers, & e-mail
addresses of specific populations.
• Reverse directory
– A directory similar to a telephone directory except that listings are by city & street
address or by phone number rather than alphabetical by last name.
– Online Panels
• Lists of respondents who have agreed to participate in marketing research via e-mail.
– International Research
• Availability of sampling frames varies dramatically around the world.
Sampling Units
• Sampling Unit
– A single element or group of elements subject to
selection in the sample.
• Primary Sampling Unit (PSU)
– A unit selected in the first stage of sampling.
• Secondary Sampling Unit
– A unit selected in the second stage of sampling.
• Tertiary Sampling Unit
– A unit selected in the third stage of sampling.
Random Sampling & Nonsampling Errors
• Random Sampling Error
– The difference between the sample result & the result of a
census conducted using identical procedures.
– A statistical fluctuation that occurs because of chance variations
in the elements selected for a sample.
– Probability of such error increases as sample size decreases.
• Systematic Sampling Error
– Systematic (nonsampling) error results from nonsampling
factors, primarily the nature of a study’s design & the
correctness of execution.
• It is not due to chance fluctuation.
• Probability of such error increases as sample size increases.
Errors Associated with Sampling
Two Major Categories of Sampling
• Probability sampling
•Known, nonzero, & equal
probability of selection for every
population element
• Nonprobability sampling
•Probability of selecting any
particular member is unknown
Nonprobability Sampling
• Convenience Sampling
– Obtaining people or units that are most conveniently available.
• Judgment (Purposive) Sampling
– Experienced individual selects sample based on personal judgment about
some appropriate characteristic of the sample member.
• Quota Sampling
– Ensures that various subgroups of a population will be represented on
pertinent characteristics to the exact extent that the investigator desires.
• Snowball Sampling
– A sampling procedure in which initial respondents are selected by probability
methods and additional respondents are obtained from information provided
by the initial respondents.
Comparing the Nonprobability Techniques
Technique
Strengths
Weaknesses
Convenience Sampling
•Least expensive
•Least time needed
•Most convenient
•Selection bias
•Not representative
Judgmental Sampling
•Low expense
•Little time needed
•Convenient
• Highly Subjective
•Does not allow
generalizations
Quota Sampling
•Can control sample
characteristics
•Greatest probability of
representative sample
•Selection bias
•Most likely not
representative
Snowball Sampling
•Can estimate rare
characteristics
•Time consuming
•Most likely not
representative
Most Commonly-Used
Probability Sampling Techniques
Probability Sampling Techniques
Simple Random
Sampling
Systematic
Sampling
Proportional vs.
Disproportional
Sampling
Stratified
Sampling
Cluster
Sampling
Probability Sampling
• Simple Random Sampling
– Assures each element in the population of an equal
chance of being included in the sample.
• Systematic Sampling
– A starting point is selected by a random process and
then every nth number on the list is selected.
• Stratified Sampling
– Simple random subsamples that are more or less equal
on some characteristic are drawn from within each
stratum of the population.
Systematically Sampling from a List
Proportional vs. Disproportional Sampling
• Proportional Stratified Sample
– Number of sampling units drawn from each
stratum is in proportion to population size of
that stratum.
• Disproportional Stratified Sample
– Sample size for each stratum is allocated
according to analytical considerations.
Disproportional Sampling:
Hypothetical Example
Cluster Sampling
• Economically efficient sampling
technique in which primary sampling
unit is not the individual element in the
population but a large cluster of
elements.
• Clusters are selected randomly.
Examples of Clusters
What is the Appropriate Sample Design?
It Depends
Degree of accuracy
Resources
Time
Advanced knowledge of the population
National versus local
Need for statistical analysis
Internet Samples
• Recruited Ad Hoc Samples
– Potential subjects unaware they might be asked to participate
in a study
– Less expensive
– Lower selection bias
• Opt-in Lists
– Potential subjects know they might be asked to participate in
studies as they have previously agreed to receive such
invitations.
– More expensive
– Greater chance of selection bias
– “Much Better” response rates (????)
Sample Size
Bigger Is Better — Right?
• One study indicates that 60%
of consumers believe that there
is too much violence in video
games, but another study
suggests that 75% of parents do
not believe it harms children.
• Another shows that 40% of
Nintendo owners are highly
likely to buy a new game that
has been concept tested.
• How good are these descriptive
statistics?
Consider the sample!
Information Needed to Determine Sample Size
• Variance (standard deviation)
– A heterogeneous population has more variance (a larger standard deviation)
which will require a larger sample.
– A homogeneous population has less variance (a smaller standard deviation)
which permits a smaller sample.
– Get from pilot study or rule of thumb (managerial judgment)
• Magnitude of error
– How precise must the estimate be?
– Managerial judgment or calculation
• Confidence level
– How much error will be tolerated?
– Managerial judgment
– Most commonly used standards are a 95% confidence level (Z score = 1.96),
or 99% confidence level (Z score = 2.57).
Sample Size Formula for Questions
Involving an Analysis of Means
zs 

n 
E
2
Sample Size Formula - Example
Suppose a survey researcher is studying
expenditures on lipstick
Wishes to have a 95 percent confident level
(Z) and
Range of error (E) of less than $2.00.
The estimate of the standard deviation is
$29.00.
Sample Size Formula - Example
 zs 
n  
E
2
 1.9629.00 


2.00


2
2
 56.84 
2




28
.
42

 2.00 
 808
Sample Size Formula - Example
Suppose, in the same example as the one
before, the range of error (E) is acceptable at
$4.00 (rather than the original $2.00), sample
size is reduced.
Sample Size Formula - Example
 zs 
 1.9629.00
n    

4.00 
E

2
2
2
56.84
2




14
.
21

 4.00 
 202
Calculating Sample Size
99% Confidence


(
2
.
57
)(
29
)
n

2


74.53 


 2 
2
 [37.265]
1389
2
2


(
2
.
57
)(
29
)
n

4




74
.
53


 4 
2
 [18.6325]
 347
2
2
Sample Size for an Analysis of
Proportions
2
Z pq
n
E
2
Sample Size for a Proportion:
Example
• A researcher believes that a simple random sample will
show that 60 percent of a population (p = .6) recognizes
the name of an automobile dealership.
• Note that 40% of the population would not recognize
the dealership’s name (q = .4)
• The researcher wants to estimate with 95% confidence
(Z = 1.96) that the allowance for sampling error is not
greater than 3.5 percentage points (E = 0.035)
Calculating Sample Size
at the 95% Confidence Level
p
q
 . 6
 . 4
n

( 1.
96
(.

2
) (. 6 )(. 4 )
035
( 3.
8416
)2
)(.
001225
.

.

922
001225
753
24 )