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Chapter Eleven
Sampling Fundamentals
Sampling Fundamentals
• Population
– The set of all objects that possess a common set of
characteristics w.r.t. a marketing research problem
• Sample
– A subset of the population of interest
• Census
– When the entire population is surveyed
• Parameter
– A statistic generated from a census
• Statistic
– A statistic generated from the sample
• Question: What would you survey if you wanted zero
sampling error?
The One and Only Goal in Sampling!!
Select a sample
that is as
representative
as possible.
So that an accurate inference about the population
can be made – goal of marketing research
Sampling Fundamentals
• When Is Census Appropriate?
– when the population size is small
– when the cost of making a sampling error is
unacceptable
• When Is Sample Appropriate?
– when the population size is large and cannot be
accessed in a reasonable amount of time and cost
– when the population is reasonably homogeneous
Error in Sampling
• Total Error
– Difference between the true value (in the population) and the
observed value (in the sample) of a variable
• Sampling Error
– Error due to sampling (depends on how the sample is
selected, and its size)
• Non-sampling Error (dealt with in chapter 4)
– Measurement Error, Data Recording Error, Data Analysis Error, Nonresponse Error
• Trade-off decision between sampling and non-sampling
errors to decide sample size
Sampling Process: Identify Population
• Example: For a toy store – all households with
children living in Charlotte
• Ambiguous with respect to sampling units
(children’s ages) and geographical coverage (MSA
or just metro area)
• Who in the HH will provide information
• Be as specific as possible
• Question: For a small bookstore in RH
specializing in romance novels, define the
population.
Sampling Process: Determine sampling frame
• List of population members used to obtain the
sample from
• Example – to address a population of all
advertising agencies in the US, the sampling
frame would be the Standard Directory of
Advertising Agencies
• Availability of lists is limited, lists may be obsolete
and incomplete
Problems with sampling frames
• Subset problem
– The sampling frame is smaller than the population
– Another sampling frame needs to be tapped
• Superset problem
– Sampling frame is larger than the population
– A filter question needs to be posed
• Intersection problem
– A combination of the subset and superset problem
– Most serious of the three
Problems with sampling frames
• Population: all RH residents. Sampling frame:
Phone book. Which problem do we have?
• Population: all advertising agencies with annual
billings over $1 million. Sampling frame: The
Standard Directory of Advertising Agencies.
Which problem do we have? If all ad agencies
are not required to register with the Directory,
which problem do we have?
Sampling Process: Sampling Procedure
Probability Sampling
• Each member of the population stands an
equal chance of getting into the sample
• Preferred due to greater representativeness
Nonprobability Sampling
• Convenience sampling – some members
stand a better chance of being sampled than
others
Sampling Procedure
Probability Sampling
Sampling Procedures
-Simple Random Sampling
-Systematic Sampling
-Stratified Sampling
-Cluster Sampling
Here’s the
difference!
Non-Probability
Sampling
-Convenience Sampling
-Judgmental Sampling
-Snowball Sampling
-Quota Sampling
Probability Sampling: Each subject has the same non-zero
probability of getting into the sample!
Probability Sampling Techniques
Simple Random Sampling
• Each population member, and each possible
sample, has equal probability of being
selected
• Using a random numbers table can help
– Computer generated
– Knowledge of a string of ten numbers gives no
indication of what the eleventh number could be
Probability Sampling Techniques
• Accuracy – cost trade off
• Sampling Efficiency = Accuracy/Cost
– Sampling efficiency can be increased by
either reducing the cost, increasing the
accuracy or doing both
– This has led to modifying simple random
sampling procedures
Probability Sampling Techniques
Stratified Sampling
• The chosen sample is forced to contain units from each of
the segments or strata of the population
• Sometimes groups (strata) are naturally present in the
population
• Between-group differences on the variable of interest are
high and within-group differences are low
• Then it makes better sense to do simple random sampling
within each group and vary within-group sample size
according to
– Variation on variable of interest
– Cost of generating the sample
Stratified Sampling – what strata are naturally
present
• Winthrop students: their attitudes towards
romance novels
• Winthrop students: their attitude towards
marketing
• Winthrop students: their knowledge about
football
• Winthrop students: their attitudes towards the
food in Thompson Hall
• Increases accuracy at a faster rate than cost
Directly Proportionate Stratified Sampling
Consumer type
Group size
Brand-loyal
400
10 Percent
directly
proportional
stratified sample
size
40
Variety-seeking
200
20
Total
600
60
Inversely Proportional Stratified Sampling
• 600 consumers in the population:
• 200 are heavy drinkers
• 400 are light drinkers.
• If heavy drinkers opinions are valued more and a sample
size of 60 is desired, a 10 percent inversely proportional
stratified sampling is employed. Selection probabilities are computed as
follows:
Denominator
600/200 + 600/400 = 3 + 1.5 = 4.5
Heavy Drinkers
proportion and
sample size
3/ 4.5 = 0.667; 0.667 * 60 = 40
Light drinkers
proportion and
sample size
1.5 / 4.5 = 0.333; 0.333 * 60 = 20
Probability Sampling Techniques
Cluster Sampling
• Involves dividing population into subgroups
• Random sample of subgroups/clusters is selected
and all members of subgroups are interviewed
• Advantages
– Decreases cost at a faster rate than accuracy
– Effective when sub-groups representative of the
population can be identified
Cluster Sampling
• Geography knowledge of all middle school
children in the US
• Attitudes to cell phones amongst all college
students in the US
• Attitudes to football amongst all college students
in the US
• Combine cluster and stratified sampling
A Comparison of Stratified and Cluster Sampling
Stratified sampling
Cluster sampling
Homogeneity within group
Homogeneity between groups
Heterogeneity between groups
Heterogeneity within groups
All groups are included
Random selection of groups
Sampling efficiency improved by
increasing accuracy at a faster
rate than cost
Sampling efficiency improved by
decreasing cost at a faster rate
than accuracy.
Probability Sampling Techniques
• Systematic Sampling
– Systematically spreads the sample through the entire list of
population members
– E.g. every tenth person in a phone book
– Bias can be introduced when the members in the list are
ordered according to some logic. E.g. listing women members
first in a list at a dance club.
– If the list is randomly ordered then systematic sampling
results closely approximate simple random sampling
– If the list is cyclically ordered then systematic sampling
efficiency is lower than that of simple random sampling
Non-Probability Sampling
• Benefits
– Driven by convenience
– Costs may be less
• Common Uses
– Exploratory research
– Pre-testing questionnaires
– Surveying homogeneous populations
– Operational ease required
Non-Probability Sampling Techniques
• Judgmental
– Selected according to ‘expert’ judgment
• Snowball
– Each sample member is asked to recommend another
– Used when populations are highly specialized / niched
• Convenience
– ‘whosoever
is convenient to find’
• Quota
– Judgment sampling with a stipulation that the sample
include a minimum number from each specified sub-group
Sampling Process
Identify Target Population
Determine Sampling Frame
Select Sampling Procedure
Determine Sample Size
Determining Sample Size – Ad Hoc Methods
• Rule of thumb
– Each group should have at least 100 respondents
– Each sub-group should have 20 – 50 respondents
• Budget constraints
– The question then is whether the study can be
modified or cancelled
• Comparable studies
– Find similar studies and use their sample sizes as
guides
Factors determining sample size
• Number of groups and sub-groups in the sample
that are to be analyzed
• Value of the study and accuracy required
• Cost of generating the sample
• Variability in the population
Revisit definitions
• Mean: the arithmetic average of scores on a
variable
– Only interval / ratio level data
– Categorical data - Mode
• Variance: the average value of the dispersion
(spread) of squared scores on a variable. Based
on how a response differs from the average
response
• Standard deviation: Square root of the variance
Basic Statistics
Mean
Variance
Standard Deviation
Sample Size
Population

2

N
1 n
C = S Ci
n i =1
n
1
2
2
=
S
C
C
s
(
)
i
n - 1 i =1
Sample
X
s2
s
n
Sampling distribution of the means
• In most MR problems we are interested in
knowing the mean. (e.g. mean attitude
scores, mean sales, etc.).
• We want an good estimate of the
population mean
• Since the population mean is generally
unknown, we must select the sample with
care so that the sample mean will be the
closest approximation to the population
mean
Sampling distribution of means
• E(X bar) = µ
– Sampling distribution of means
– Larger sample sizes give a better approximation of the
sampling distribution of means to the normal
distribution
Sampling distribution of means
• ơ(X bar) = ơ / sq. root of n
– I.e. standard deviation of the sampling distribution of
means (a.k.a. standard error of the mean) will equal
the standard deviation of the population divided by the
square root of the sample size
– I.e. the greater the n, the smaller the ơ of the
sampling distribution and more closer the
approximation to the population standard deviation
• Therefore random sampling with a larger sample
size gives a more accurate estimate
Normal Distribution
The entire area under
the curve adds up to 100%
Example Histogram
40
30
20
Percent
10
0
1.00
Q11ATRAN
2.00
3.00
4.00
5.00
6.00
7.00
Interval Estimation
• X bar varies from sample to sample
• The difference between the sample mean (X
bar) and the population mean (µ) is the
sampling error
• X + sampling error = interval estimate of
population mean
Interval Estimate of the Population Mean
• X + sampling error
Or
x + z x / n
n - sample size
Size of Interval Estimate
• Confidence level (e.g. 90%, 95%, 99%, etc.)
– The number of times the population mean must fall
within the confidence interval after repeated samplings
– Lower confidence levels mean smaller sample sizes
and smaller intervals; Higher confidence levels mean
larger sample sizes and larger intervals
• Population standard deviation
– Generally unknown
– Estimated from a previous study, a pilot, judgment or a
worst case scenario
Sample - Size Question
• Size of the sampling error that is desired
• Confidence level
• Sample size n = Z2 2 /(sampling error)2