Download Probability Sampling

Chapter Eleven
Sampling Fundamentals 1
Sampling Fundamentals
• Population
• Sample
• Census
• Parameter
• Statistic
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 Is Sample Appropriate?
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, Non-response Error
Sampling Process: Identify Population
• Question: For a toy store in Charlotte (be as
specific as possible)
• Question: For a small bookstore in RH
specializing in romance novels
Sampling Process: Determine sampling frame
• List and contact information 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
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 has equal, non-zero
probability of being selected
• Equivalent to choosing with replacement
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
– Size of group in population
• Increases accuracy at a faster rate than cost
Stratified Sampling – what strata are naturally
present
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
• Knowledge of credit amongst all freshman 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
Random sampling in each group
Census within the group
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