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Chapter 11
Sampling Design
Chapter Objectives
• define sampling, sample, population, element, subject
and sampling frame
• describe and discuss the different probability and nonprobability sampling designs
• identify the use of appropriate sampling designs for
different research purposes
• discuss precision and confidence
• estimate sample size
• discuss efficiency in sampling
• discuss generalisability in the context of sampling
designs
The Principles of Sampling Design
Population, Element, Sampling Frame,
Sample and Subject
• Population (or target population)
• entire group of people, events or things of interest that
the researcher wishes to investigate
• Element
• a single member of the population
• Sampling Frame
• a listing of all the elements in the population from which
the sample is drawn
• Sample
• a subset of the population
• Subject
• a single member of the sample
Relationship between Population,
Sampling Frame and Sample
Relationship between Sample Statistics
and Population Parameters
Advantages of Sampling
• Less costs
– cheaper than studying whole population
• Less errors due to less fatigue
– better results
• Less time
– quicker
• Destruction of elements avoided
– eg bulbs
Normal Distibution in a Population
As the sample size n increases, the means of the
random samples taken from practically any
population approach a normal distribution with mean
μ and standard deviation 
Representativeness of Samples
• If the sample mean is much > than the
population mean μ then the sample would
overestimate the true population mean
• If the sample mean is much < than the
population mean μ then the sample would
underestimate the true population mean
• The more representative the sample is of the
population, the more generalisable are the
findings of the research.
Preparing a Sampling Design
Probability & Non-probability Sampling
• Probability Sampling
– the elements in the population have some known
chance or probability of being selected as sample
subjects
• Non-probability Sampling
– the elements do not have a known or
predetermined chance of being selected as
subjects
Probability Sampling
• Simple random sampling
– every element in the population has a known and
equal chance of being selected as a subject
• Complex (or restricted) probability sampling
– procedures to ensure practical viable alternatives
to simple random sampling, at lower costs, and
greater statistical efficiency
Simple Random Sampling
• Is the most representative of the population
for most purposes
• Disadvantages are:
– Most cumbersome and tedious
– The entire listing of elements in population
frequently unavailable
– Very expensive
– Not the most efficient design
Complex Probability Sampling
•
•
•
•
•
Systematic sampling
Stratified random sampling
Cluster sampling
Area sampling
Double sampling
Systematic Sampling
• Every nth element in the population starting
with a randomly chosen element
• Example:
– Want a sample of 35 households from a total of 260
houses. Could sample every 7th house starting from
a randomly chosen number from 1 to 10. If that
random number is 7, sample 35 houses starting with
7th house (14th house, 21st house, etc)
– Possible problem is that there could be systematic
bias. eg every 7th house could be a corner house,
with different characteristics of both house and
dwellers.
Stratified Random Sampling
• Comprises sampling from populations
segregated into a number of mutually exclusive
sub-populations or strata. Eg
– University students divided into juniors, seniors, etc
– Employees stratified into clerks, supervisors,
managers, etc
• Homogeneity within stratum and heterogeneity
between strata
• Statistical efficiency greater in stratified samples
• Sub-groups can be analysed
• Different methods of analysis can be used for
different sub-groups.
Stratified Random Sampling Example
Stratum
Clerks
Middle Managers
Top Managers
Motivation Level
Low
Very high
Medium
Combined X would not discrimate among
groups
• Stratified Sampling
– Proportionate sampling
– Disproportionate sampling
Proportionate & Disproportionate
Stratified Random Sampling
Cluster Sampling
• Take clusters or chunks of elements for study
– Eg, sample all students in MGMT 303 and MGMT
304 to study the characteristics of Management
Science majors
• Advantage of cluster sampling is lower costs
• Statistically it is less efficient than other
probability sampling procedures discussed so
far
Area Sampling:
• Cluster sampling confined to a particular area
– Eg, sampling residents of a particular locality,
county, etc
Double Sampling
• Collect preliminary data from a sample,
and choose a sub-sample of that
sample for more detailed investigation.
• Example:
– Conduct unstructured interviews with a
sample of 50.
– Repeat a structured interview with 30 from
the 50 originally sampled.
Non-probability Sampling
• Convenience sampling
– Survey whoever is easily available
– Used for quick diagnosis of situations
• Simplest and cheapest
• Least reliable
• Purposive sampling
– Judgement sampling
– Snowball sampling
– Quota sampling
Judgement Sampling
• Involves the choice of subjects who are
in the best position to provide the
information required
• Experts’ opinions could be sought
– Eg, Doctors surveyed for cancer causes
Snowball Sampling
• Used when elements in population have
specific characteristics or knowledge, but are
very difficult to locate and contact.
• Initial sample group can be selected by
probability or non-probability methods, but
new subjects are selected based on
information provided by initial subjects.
– Eg, used to locate members of different
stakeholder groups regarding their opinions of a
new public works project.
Quota Sampling
•
•
Quotas for numbers or proportion of
people to be sampled, established.
Examples:
1) survey for research on dual career
families: 50% working men and 50%
working women surveyed.
2) Women in management survey: 70%
women surveyed and 30% men
surveyed.
Choice Points in Sampling Design
Precision and Confidence
• Precision
– refers to how close the sample estimate eg X is to
the true population characteristic( ) depends on the
variablity in the sampling distribution of the mean, ie
the standard error ( SS X )
– indicates the confidence interval within which the
population mean can be estimated (= X + KS X )
X
• Confidence
– reflects the level of certainty that the sample
estimates will actually hold true for the population
– bias is absent from the data
– accuracy is reflected by the confidence level ( K )
Standard Error
SX  S
S
n
SX
n
= standard deviation of the sample
= sample size
= standard error or standard deviation
of the sample mean
Characteristics of the Standard Error
SX  S
n
• The smaller the standard deviation of
the population, the smaller the standard
error and the greater the precision
• The standard error varies inversely with
the square root of the sample size.
Hence the larger the n, the smaller the
standard error, and the greater the
precision.
Confidence Interval for the Mean
  X  KS X

= population mean
X
= sample mean
SX
K
= standard error
= z statistic for large samples ≥ 30
= t statistic for small samples < 30
Confidence Levels
  X  KS X
• For large samples, K = z score
= 1.65 for 90% confidence level
= 1.96 for 95% confidence level
= 2.58 for 99% confidence level
• Example: a 95% confidence interval for mean
purchases (μ) by customers based on a sample
mean of $105 with a standard error of $1.43 is:
μ = 105 ± 1.96*1.43 = 105 ± 2.80
Hence μ would fall between $102.20 and
$107.80
Trade-off between Precision and Confidence
Determining the Sample Size
Example: Suppose a manager wants to be 95%
confident that withdrawals from a bank will be within
a confidence level of ± $500. From a sample of
customers the standard deviation S was calculated
as $3500. What sample size is needed?
  X  KS X
The expression KS X is equivalent to the precision or
admissible margin of error. Let this be E.
E  KS X
or
E  K *S
n
Determining the Sample Size (cont’d)
Rearranging these terms, a formula for the sample size n is:
 K *S
n

 E 
2
Substituting K=1.96 (95% confidence), S=3500, and
E=500 into this equation, provides the sample size n:
n

1.96*3500
500
n  13.72
n  188
2

2
Roscoe’s Rules of Thumb for
Determining Sample Size
• Sample sizes larger than 30 and smaller than
500 are appropriate for most research
• Minimum sample size of 30 for each subcategory is usually necessary
• In multivariate research, the sample size should
be several times as large as the number of
variables in the study
• For simple experimental research, successful
research is possible with samples as small as 10
to 20
Efficiency in Sampling
If n is constant, you should get a smaller S X
or
For the same S X , you should use a
smaller n
Review of Sample Size Decisions
• How much precision is wanted in estimating the
population characteristics, ie what is the margin of
admissible error or confidence interval?
• How much confidence is really needed. How much
risk can we take of making errors in estimating the
population parameters (ie confidence level)?
• How much variability is in the population? The
greater the variability, the larger the sample size
needed.
• Cost and time constraints
• The size of the population (N) itself