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
Why Sample?
• Sampling
– Cuts costs
– Reduces labor requirements
– Gathers vital information quickly
• Most properly selected samples give sufficiently
accurate results
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
Target Population
• Relevant population
• Operationally define
– All women still capable of bearing children vs.
– All women between the ages of 12 and 50
• Comic book reader?
– Does this include children under 6 years of age
who do not actually read the words?
Sampling Frame
• A list of elements from which the sample may be
drawn
• A.K.A., the working population
• Mailing lists - data base marketers
– Sampling services or list brokers
• Sampling frame error
– Error that occurs when certain sample elements are
excluded from or overrepresented in a sampling
frame
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
Judgment
Quota
Snowball
Convenience Sampling
• Also called haphazard or accidental
sampling
• The sampling procedure of obtaining the
people or units that are most conveniently
available
Judgment Sampling
• Also called purposive sampling
• An experienced individual selects the
sample based on his or her judgment about
some appropriate characteristics required of
the sample member
Quota Sampling
• Ensures that the various subgroups in a
population are represented on pertinent sample
characteristics to the exact extent that the
investigators desire
• It should not be confused with stratified
sampling.
Snowball Sampling
• A variety of procedures
• Initial respondents are selected by probability
methods
• Additional respondents are obtained from
information (or referrals) 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
•Subjective
•Does not allow
generalizations
Quota Sampling
•Can control sample
characteristics
•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
Stratified
Sampling
Simple Random Sampling
• A sampling procedure that ensures that each
element in the population will have an equal
chance of being included in the sample
Systematic Sampling
• A simple process
• Every nth name from the list will be drawn
• Periodicity
– Problem that occurs in systematic sampling
when the original list has a systematic pattern
(I.e., the original list is not random in character)
Stratified Sampling
• Probability sample
• Subsamples are drawn within different
strata using simple random sampling
• Each stratum is more or less equal on some
characteristic
• Do not confuse with quota sample
Comparing the Probability Techniques
Technique
Strengths
Simple Random Sampling •Easily understood
•Can project results
Weaknesses
•Expensive
•Difficult to construct
sampling frame
•No assurance of
representativeness
Systematic Sampling
•Easier to implement than •Can decrease
SRS
representativeness
•Increased
representativeness
•Sampling frame not
necessary
Stratified Sampling
•Precision
•Includes all important
subpopulations
•Selection of stratification
variables difficult
•Expensive
What is the
Appropriate Sample Design?
•
•
•
•
•
•
Degree of accuracy
Resources
Time
Advanced knowledge of the population
National versus local
Need for statistical analysis
Choosing Between Nonprobability &
Probability Sampling
Factor
Nonprobability
Probability
Nature of Research
Exploratory
Conclusive
Relative Magnitude of Sampling &
Nonsampling Errors
Nonsampling errors larger
Sampling errors larger
Population Variability
Homogeneous
(low variability)
Heterogeneous
(high variability)
Statistical Considerations
Unfavorable
Favorable
Operational Considerations
Favorable
Unfavorable
Internet Samples
• Recruited Ad Hoc Samples
• Opt-in Lists
Information Needed to Determine
Sample Size
• Variance (standard deviation)
– Get from pilot study or rule of thumb (managerial
judgment)
• Magnitude of error
– Managerial judgment or calculation
• Confidence level
– Managerial judgment
Sample Size Formula for
Questions Involving 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 a Proportion
2
Z pq
n
E
2
z2pq
n
2
E
Where:
n = Number of items in samples
Z2 = The square of the confidence interval in standard error units.
p = Estimated proportion of success
q = (1-p) or estimated the proportion of failures
E2 = The square of the maximum allowance for error between the
true proportion and sample proportion or zsp squared.
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 )