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SAMPLING
Chapter 10
It is often said that without water,
life would be impossible.
Similarly, without sampling, marketing research
as we know it would be impossible.
Feinberg, Kinnear, & Taylor (2008, p. 290)
Probability vs. Nonprobability Sampling
• Probability Sampling
• Each sampling unit has a known probability of being
included in the sample
• Nonprobability sampling
• When the probability of selecting each sampling unit is
unknown
Probability Sampling Procedures
• Simple Random Sampling
• A sampling approach in which each sampling unit in a target
population has a known and equal probability of being included
• Advantage: Good generalizability and unbiased estimates
• Disadvantage: must be able to identify all sampling units within
a given population; often, this is not feasible
• Systematic Random Sampling
• Similar to random sampling, but work with a list of sampling
units that is ordered in some way (e.g., alphabetically).
• Select a starting point at random, then survey each nth person
where the “skip interval” = (population size/desired sample size)
• Advantage: quicker and easier than SRS
• Disadvantage: may be hidden “patterns” in the data
Probability Sampling Procedures
• Stratified Random Sampling
• Break up population into meaningful groups (e.g., men, women),
then sample within each “strata”, then combine
• Proportionate stratified sampling: here you sample based on the
size of the populations (i.e., sample more from the bigger strata:
e.g., Caucasians)
• Disproportionate stratified sampling: sample the same number of
units from each strata, regardless of the strata’s size in the pop.
• A variant is optimal allocation: here you use smaller sample
sizes for strata within which there is low variability (as the lower
variability will give you more precision with lower N).
• Advantages: more representative; can compare strata
• Disadvantages: Can be hard to figure out what to base strata on
(Gender? Ethnicity? Political party?)
Probability Sampling Procedures
• Cluster Sampling
• Similar to stratified random sampling, but with stratified random
sampling, the strata are thought to possibly differ between strata
(men vs. women), but be homogeneous within strata.
• In cluster sampling, you divide overall population into
subpopulations (like SRS), but each of those subpopulations (called
“clusters”) are assumed to be mini-representations of the
population (e.g., survey customers at 10 Red Robins in WA).
• Area sampling: clusters based on geographic region
Probability Sampling Procedures
• Cluster Sampling
• One-step clustering: just select one cluster (e.g., one store);
problem = may not be representative of population
• Two-step cluster sampling: break into meaningful subgroups (Red
Robins in big cities vs. Red Robins in suburbs), then randomly
sample within each of those clusters
• Advantages: easy to generate sampling frame; cost efficient;
representative; can compare clusters
• Disadvantages: must be careful in selecting the basis for clusters;
also, within clusters, often little variability (they’re homogeneous),
and this lack of variability leads to less precise estimates
Nonprobability Sampling Procedures
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Convenience Sample
Survey people based on convenience (e.g., college students)
Advantage: is fast and easy
Disadvantage: may not be representative
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Judgment Sampling
Use your judgment about who is best to survey
Advantage: Can be better than convenience if judgment is right
Disadvantage: but if judgment wrong, may not be
representative/generalizable
Nonprobability Sampling Procedures
• Quota Sampling
• Sample fixed number of people from each of X categories, possibly
based on their relative prevalence in the population
• Advantage: Can ensure that certain groups are included
• Disadvantage: but b/c you aren’t using random sampling,
generalizability may be questionable
• Snowball Sampling
• You contact one person, they contact a friend (e.g., one cancer
survivor is in contact with other survivors, and so recruits them)
• Advantages: can make it easier to contact people in hard to reach
groups
• Disadvantage: there may be bias in the way people recruit others
Factors Affecting Choice of Sampling Procedure
• Use some type of random sampling if:
• You are collecting quantitative data that you want to use to arrive at
accurate generalizations about population
• You have sufficient resources and time
• You have a good sense for the population
• You are sampling over a broader range (e.g., of states, nations)
Computing the Sample Size Based on Usable Rates
• Several factors can reduce your sample size
• Thus, you may want to plan for more than your final sample size
(i.e., use a higher “number of contacts” to achieve your final sample
size). You adjust using the following three factors:
• RR = reachable rate (e.g., how many people on a telephone list
will you actually be able to reach?)
• OIR = overall incidence rate (i.e., % of target population that will
qualify for inclusion; e.g., can’t use people over 40)
• ECR = expected completion rate (i.e., some folks won’t complete
your survey)
• For example 
Computing the Sample Size Based on Usable Rates
• You want a sample size of n = 500
• You figure you can reach 95% of the folks on your list (RR = .95)
• You think 60% will be 40 or younger (OIR = .60)
• You predict that 70% will complete your survey (ECR = .70)
• Based on these numbers, you should contact 1,253 people
Number of contacts 
n
500

 1,253
(RR) x (OIR) x (ECR) (.95)(.60)(.70)
Some Key Terms
•
•
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•
•
•
Sampling
• Selection of a small number of elements from a larger defined target group of
elements and expecting that the information gathered from the small group
will allow judgments to be made about the larger group
Population
• The identifiable set of elements of interest to the researcher and pertinent to
the information problem
Defined Target Population
• The complete set of elements identified for investigation
Element
• A person or object (e.g., a firm) from the defined target population from
which information is sought
Sampling Units
• The target population elements available for selection during the sampling
process
Sampling Frame
• The list of all eligible sampling units
Some Key Terms
• Total Error = Sampling Error + Nonsampling Error
• Sampling Error
• Any type of bias that is attributable to mistakes in either drawing a
sample or determining the sample size
• Nonsampling Error (controllable)
• A bias that occurs in a research study regardless of whether a sample
or a census is used (recall all the different types of errors we
discussed)
• Respondent Errors (non response, response errors)
• Researcher’s measurement/design errors (survey, data analysis)
• Problem definition errors
• Administrative errors (data input errors, interview errors, poor
sample design)
Central Limit Theorem
• A theory that states that, regardless of the shape of the
population from which we sample (e.g., positively skewed), as
long as our sample size is > 30, the sampling distribution of
the mean (x-bar) will be normally distributed with the
following characteristics:
x  
sx 
The mean of the sampling distribution of the mean
will equal the mean in the population.
s
n
The standard error of the sampling distribution of
the mean will equal sample standard deviation (s)
divided by sample size (n). This is a sample
estimate of the true standard error in population.
The larger the sample size, the more precise we can
get about our estimate of the true mean in the
population (e.g., in our confidence interval).
variance
Note: Dr. Joireman does not put
a “bar” above s or s2.
Computing Standard Deviation
Assume your data are continuous
(i.e., are not just yes/no data).
For example, let’s say we want to know how much
people would be willing to pay for a tennis racquet.
We sample 7 folks and wish to generalize to the
population….
Results 
Formulas for
Variance and Standard Deviation
Sum of Squared
Deviations
POPULATION
SS
Population Variance   
N
2
Population Standard Deviation   
SS
N
SAMPLE
Sample Variance  s 2 
SS
N 1
Sample Standard Deviation  s 
SS
N 1
The Sum of Squared Deviations (SS)
Conceptual Formula
SS  ( X i  X ) 2
Highlights Concept
Tells a Story
Raw Score Formula
SS  X
2
(X ) 2

N
“Crank it Out”
Faster, Less Meaningful
• Both Formulas Give Identical Answers!
• SS = NUMERATOR of the Variance
• Examples on board…
Example of Computing Standard Deviation (for a Sample)
Xi
Mean
Xi-Mean
(Xi-Mean)2
X2
60
75
-15
225
3600
65
75
-10
100
4225
70
75
-5
25
4900
75
75
0
0
5625
80
75
5
25
6400
85
75
10
100
7225
90
75
-15
225
8100
Σ(X-M) = 0 !
Σ(X-M)2 = 700
ΣX2 = 40075
ΣX = 525
Conceptual Formula for SS
SS  ( X i  X ) 2  700
Raw Score Formula for SS
 (X ) 2 
 (525) 2 
SS  X  
  40075  
  40075  39375  700
 N 
 7 
2
Sample Variance  s 2 
SS
700

 116.67
N 1 7 1
Sample Standard Deviation  s 
Standard Error of Mean  s X 
SS
700

 10.82
N 1
7 1
s
10.82

 4.09
n
7
This is the “standard deviation” of the sampling distribution of means.
This (4.09) will naturally be smaller than our sample standard deviation (10.82)
based on our single sample of scores, and it will become smaller as n increases.
Confidence Intervals
A confidence interval is the statistical range of
values within which the true value of the
target population parameter is expected to lie.
Computing Confidence Intervals
• 95% Confidence Interval:
• We are 95% confident that the mean of the population from which we
took our sample has a mean between these lower and upper limits.
• To compute, we need:
Mean of our sample
Standard error
of mean
Critical Z-value for our
desired level of confidence
(see next page for Z-critical values)
Confidence Interval .95  CI  x  ( sx )( Zb, cl )  75  (4.09)(1.96)  75  8.02
Restated, Confidence Interval .95  66.98  X  83.02
Based on these results, we are 95% confident that the mean in the population
from which we sampled is between 66.98 and 83.02. Cool beans!
Common Z-Critical Values
• To be 90% confident, you use a z-critical value of 1.65
• To be 95% confident, you use a z-critical value of 1.96
• To be 99% confident, you use a z-critical value of 2.58
An example…
Z-critical values for 95% confidence
(put ½ of .05 on each side)
.025
.025
-1.96
+1.96
What if my data are Yes/No?
Here we want to estimate the
population percentage.
For example, a CNN poll (9/25/08) asked
whether readers believed Obama and
McCain should continue with their plans to
debate on Friday (9/26/08).
Results 
Recent Poll on Presidential Debate
Yes = 75% (or yes, but debate on economy)
No = 25% No (wait till bailout is taken care of)
N = 9782
Let’s compute standard error and 95% confidence interval
Here, p = % yes, q = (1-p) or % no
Estimated Standard Error of Sample Percentage 
sP 
( p )( q )

n
(75)( 25)
 .44%
9782
Confidence Interval .95  CI  p  ( s p )( Zb, cl )  75%  (.44)(1.96)  75%  0.86
Confidence Interval .95  CI  74.14  P  75.86