Download Section 1.2 - USC Upstate: Faculty

Section 1.2
Random Samples
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Sampling techniques
• Simple Random
Sampling
• Stratified Sampling
• Systematic Sampling
• Cluster Sampling
• Convenience
Sampling
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• Simple Random Sample of n measurements
from a population is a subset of the
population selected in a manner such that
• Every sample of size n from the population has
an equal chance of being selected.
• Every item in the population has an equal
chance of being included.
Not random sampling:
Ask for volunteers to respond to a survey.
Choose the next five customers entering a store.
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Random sampling:
• Draw names “from a hat.”
• Use a random number table to select a
sample.
• Use a random number generator.
How to draw a random sample:
Number all members of the population Sequentially
Use a table, calculator or computer to select random
numbers from the numbers assigned to population
members.
Create the sample using population members with
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Simulation
• Provide mathematical imitations of “real”
phenomena.
• May use a random number table to simulate a
process.
• (Good in nuclear reactors, cloud formation,
cardiology etc.)
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Example of Simulation
Use the random-number table to simulate the outcomes
of tossing a balanced (that is, fair) quarter 10 times.
(a) Possible outcomes: 2, heads or tails
(b) Assign an even digit or heads and odd digit for tails.
Then starting at block 3 of row 2 of table 1 in the
appendix, list the 10 single digits 7 1 5 4 9 4 4 8 4 3
(c) The outcomes associated with the
10 digits
T T T H T H H H H T
(d) If you start with different block and row will you get
the same sequence of outcomes? It is possible, but
not very likely
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Sampling Techniques
Sampling with Replacement
• When a number is selected for a sample, it is not removed
from the population.
Stratified Sampling
• Population is divided into groups.
• Random samples are drawn from each group.
Systematic Sampling
• Population is arranged in sequential order.
• Select a random starting point.
• Select every “kth” item.
Cluster Sampling
• Population is divided into sections.
• Some sections are randomly selected.
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• Every item in selected sections is included in sample.
Sampling Techniques
Convenience Sampling
• Use whatever data is readily available.
• Risk severe bias.
Summary of Sampling techniques
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Random Sampling
Stratified Sampling
Systematic Sampling
Cluster Sampling
Convenience Sampling
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Which sampling technique is
described?
College students are waiting in line for
registration. Every eighth person in line is
surveyed.
Systematic sampling
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Which sampling technique is
described?
College students are waiting in line for
registration. Students are asked to
volunteer to respond to a survey.
Convenience sampling
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Which sampling technique is
described?
In a large high school, students from every
homeroom are randomly selected to
participate in a survey
Stratified sampling
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Which sampling technique is
described?
An accountant uses a random number
generator to select ten accounts for audit.
Simple random sampling
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Which sampling technique is
described?
To determine students’ opinions of a
new registration method, a college
randomly selects five majors. All
students in the selected majors are
surveyed.
Cluster sampling
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