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Chapter 14
Sampling
McGraw-Hill/Irwin
Copyright © 2011 by The McGraw-Hill Companies, Inc. All Rights Reserved.
Learning Objectives
Understand . . .
• The two premises on which sampling theory is
based.
• The accuracy and precision for measuring
sample validity.
• The five questions that must be answered to
develop a sampling plan.
14-2
Learning Objectives
Understand . . .
• The two categories of sampling techniques and
the variety of sampling techniques within each
category.
• The various sampling techniques and when
each is used.
14-3
Small Samples Can Enlighten
“The proof of the pudding is in the eating.
By a small sample we may judge of the
whole piece.”
Miguel de Cervantes Saavedra
author
14-4
PulsePoint:
Research Revelation
80
The average number of text
messages sent per day by
American teens.
14-5
The Nature of Sampling
•Population
•Population Element
•Census
•Sample
•Sampling frame
14-6
Why Sample?
Availability of
elements
Greater
speed
Lower cost
Sampling
provides
Greater
accuracy
14-7
What Is a Sufficiently
Large Sample?
“In recent Gallup ‘Poll on polls,’ . . . When asked
about the scientific sampling foundation on which
polls are based . . . most said that a survey of 1,500 –
2,000 respondents—a larger than average sample
size for national polls—cannot represent the views of
all Americans.”
Frank Newport
The Gallup Poll editor in chief
The Gallup Organization
14-8
When Is a Census
Appropriate?
Feasible
Necessary
14-9
What Is a Valid Sample?
Accurate
Precise
14-10
Sampling Design
within the Research Process
14-11
Types of Sampling Designs
Element
Probability
Selection
•Unrestricted • Simple random
•Restricted
Nonprobability
• Convenience
• Complex random • Purposive
• Systematic
• Judgment
•Cluster
•Quota
•Stratified
•Snowball
•Double
14-12
Steps in Sampling Design
What is the target population?
What are the parameters of interest?
What is the sampling frame?
What is the appropriate sampling
method?
What size sample is needed?
14-13
When to Use Larger Sample?
Population
variance
Number of
subgroups
Confidence
level
Desired
precision
Small error
range
14-14
Simple Random
Advantages
• Easy to implement
with random dialing
Disadvantages
• Requires list of
population elements
• Time consuming
• Larger sample
needed
• Produces larger
errors
• High cost
14-15
Systematic
Advantages
Disadvantages
• Simple to design
• Easier than simple
random
• Easy to determine
sampling distribution
of mean or proportion
• Periodicity within
population may skew
sample and results
• Trends in list may
bias results
• Moderate cost
14-16
Stratified
Advantages
Disadvantages
• Control of sample size in
strata
• Increased statistical
efficiency
• Provides data to represent
and analyze subgroups
• Enables use of different
methods in strata
• Increased error if
subgroups are selected at
different rates
• Especially expensive if
strata on population must
be created
• High cost
14-17
Cluster
Advantages
• Provides an unbiased
estimate of population
parameters if properly
done
• Economically more
efficient than simple
random
• Lowest cost per sample
• Easy to do without list
Disadvantages
• Often lower statistical
efficiency due to
subgroups being
homogeneous rather than
heterogeneous
• Moderate cost
14-18
Stratified and Cluster Sampling
Stratified
• Population divided into
few subgroups
• Homogeneity within
subgroups
• Heterogeneity between
subgroups
• Choice of elements
from within each
subgroup
Cluster
• Population divided into
many subgroups
• Heterogeneity within
subgroups
• Homogeneity between
subgroups
• Random choice of
subgroups
14-19
Area Sampling
14-20
Double Sampling
Advantages
• May reduce costs if first
stage results in enough
data to stratify or cluster
the population
Disadvantages
• Increased costs if
discriminately used
14-21
Nonprobability Samples
No need to
generalize
Feasibility
Limited
objectives
Time
Cost
14-22
Nonprobability
Sampling Methods
Convenience
Judgment
Quota
Snowball
14-23
Key Terms
•
•
•
•
•
Area sampling
Census
Cluster sampling
Convenience sampling
Disproportionate
stratified sampling
• Double sampling
• Judgment sampling
• Multiphase sampling
• Nonprobability
sampling
• Population
• Population element
• Population parameters
• Population proportion
of incidence
• Probability sampling
14-24
Key Terms
• Proportionate stratified
sampling
• Quota sampling
• Sample statistics
• Sampling
• Sampling error
• Sampling frame
• Sequential sampling
• Simple random
sample
• Skip interval
• Snowball sampling
• Stratified random
sampling
• Systematic sampling
• Systematic variance
14-25
Appendix 14a
Determining
Sample Size
McGraw-Hill/Irwin
Copyright © 2011 by The McGraw-Hill Companies, Inc. All Rights Reserved.
Random Samples
14-27
Increasing Precision
14-28
Confidence Levels & the
Normal Curve
14-29
Standard Errors
Standard Error
(Z score)
% of Area
Approximate
Degree of
Confidence
1.00
68.27
68%
1.65
90.10
90%
1.96
95.00
95%
3.00
99.73
99%
14-30
Central Limit Theorem
14-31
Estimates of Dining Visits
Confidence
Z
score
% of
Area
Interval Range
(visits per
month)
68%
1.00
68.27
9.48-10.52
90%
1.65
90.10
9.14-10.86
95%
1.96
95.00
8.98-11.02
99%
3.00
99.73
8.44-11.56
14-32
Calculating Sample Size for
Questions involving Means
Precision
Confidence level
Size of interval estimate
Population Dispersion
Need for FPA
14-33
Metro U Sample Size for Means
Steps
Information
Desired confidence level
Size of the interval estimate
Expected range in
population
Sample mean
Standard deviation
Need for finite population
adjustment
Standard error of the mean
Sample size
95% (z = 1.96)
 .5 meals per month
0 to 30 meals
10
4.1
No
.5/1.96 = .255
(4.1)2/ (.255)2 = 259
14-34
Proxies of the
Population Dispersion
• Previous research on the
topic
• Pilot test or pretest
• Rule-of-thumb calculation
– 1/6 of the range
14-35
Metro U Sample Size for
Proportions
Steps
Information
Desired confidence level
Size of the interval estimate
Expected range in population
Sample proportion with given
attribute
Sample dispersion
Finite population adjustment
Standard error of the
proportion
Sample size
95% (z = 1.96)
 .10 (10%)
0 to 100%
30%
Pq = .30(1-.30) = .21
No
.10/1.96 = .051
.21/ (.051)2 = 81
14-36
Appendix 14a: Key Terms
•
•
•
•
•
•
Central limit theorem
Confidence interval
Confidence level
Interval estimate
Point estimate
Proportion
14-37
Addendum: Keynote
CloseUp
McGraw-Hill/Irwin
Copyright © 2011 by The McGraw-Hill Companies, Inc. All Rights Reserved.
Keynote Experiment
14-39
Keynote Experiment (cont.)
14-40
Determining
Sample Size
Appendix 14a
McGraw-Hill/Irwin
Copyright © 2011 by The McGraw-Hill Companies, Inc. All Rights Reserved.
Random Samples
14-42
Confidence Levels
14-43
Metro U. Dining Club Study
14-44