Week 7:
Sampling
Lessons of Life
Slide 1
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.
• The two categories of sampling techniques and the variety of
sampling techniques within each category.
• The various sampling techniques and when each is used.
Slide 2
Idea of Sampling
The basic idea of sampling is that
by selecting several elements
from a population, we can make
an inference about the entire
population.
Slide 3
Population and Sampling
Slide 4
Population and Sampling
Slide 5
The Nature of Sampling
• Population
• Population Element
• Sample
• Sample subject
• Sampling frame
• Census
• Parameter
• Statistics
Slide 6
Statistics
Slide 7
Inference Process
Population
Sample
Sample
Statistics
Estimation &
Hypothesis
Testing
),( spX
Slide 8
Parameter and Statistics: Example
“Average height of 2nd year students is
150 centimeters”
Parameter
“Average height of 2nd year students in
Mr Ali’s class is 150 centimeters”
Statistic
Population
Sample
Slide 9
Inference
Slide 10
Why Sampling is Needed?
• Cost
• Time
• Destruction of Test unit
• More accurate
▪ Better interviewing
▪ Checking for missing, suspicious
information
▪ Better supervision
▪ Better processing
Slide 11
When Is a Census Appropriate?
NecessaryFeasible
Slide 12
What Is a Valid Sample?
Accurate Precise
Slide 13
Accuracy (Unbiased)
Presidential poll In 1936, 2 million people participated,
Alfred Landon was predicted to defeat Franklin Roosevelt.
Problem was they drew the sample from telephone owners
who were mostly middle and upper class.
True Mean
2.5 3 3.5 4 4.5
S1
S2
Slide 14
Sampling Design within the Research Process
Slide 15
Types of Sampling Designs
Element Selection Probability Nonprobability
Unrestricted Simple random Convenience
Restricted Complex random Purposive
Systematic Judgment
Cluster Quota
Stratified Snowball
Double
Slide 16
Some basic terms
• Representativeness
• Probability Sampling
▪ Randomly selected, each element has a known probability of
being chosen which is not equal to 0
• Non-Probability Sampling
▪ Non-random, unknown probability of being chosen
Slide 17
14-105
Steps in Sampling Design
1. What is the target population?
2. What are the parameters of interest?
4. What is the appropriate sampling method?
5. What size sample is needed?
3. What is the sampling frame?
Slide 18
Formula – Infinite Population
Where:
n = Sample Size for infinite population
Z = Z value (e.g. 1.96 for 95% confidence level)
p = population proportion (expressed as decimal)
(assumed to be 0.5 (50%)
M = Margin of Error at 5% (0.05)
n =൯z2 ∗ p(1 − p
M2
Slide 19
Formula – Finite Population
Where:
S = Required Sample size
X = Z value (e.g. 1.96 for 95% confidence level)
N = Population Size
P = Population proportion (expressed as decimal)
(assumed to be 0.5 (50%)d = Degree of accuracy (5%), expressed as a
proportion (.05); It is margin of error
S =൯X2NP(1 − p
ሻd2 N − 1 + X2P(1 − P
Slide 20
Sample Sizes – Rules of Thumb
• Rules of Thumb
▪ 5 sample per item
▪ 10 sample per item
Slide 21
Sample Sizes – Krejcie & Morgan
Slide 22
Gpower
Slide 24
Gpower
14-25 Slide 25
Power
Slide 26
Sales Profit
Gender Grades
Ethnicity Grades
Slide 27
Sample Sizes – Raosofthttp://www.raosoft.com/samplesize.html
Slide 28
When to Use Larger Sample Sizes?
Population variance
Small error range
Desired Precision
Number of Subgroups
Confidence Level
Slide 29
Selecting a random sample
• Numbered paper/ball
• Random number tables
• Computer generated
Slide 30
Numbered paper/ball
Slide 31
Random Number Tables
57613 55089 10233 28076 57112 50531
85765 78648 49879 69624 64138 91376
91297 12918 71506 21698 10908 34550
77602 13397 52530 77171 42623 76675
5215 36596 1273 30562 73009 59435
40421 19973 75608 1754 91815 78997
1625 85425 55401 41762 68540 25339
71816 15535 77156 98915 95654 70585
64313 47684 63308 80079 54648 13211
87164 13605 30983 77390 57604 54092
68575 38111 95346 24386 59240 44034Slide 32
Random Number Tables
57613 55089 10233 28076 57112 50531
85765 78648 49879 69624 64138 91376
91297 12918 71506 21698 10908 34550
77602 13397 52535 77171 42623 76675
15215 36596 11273 30562 73009 59435
40421 19973 75608 11754 91815 78997
11625 85425 55401 41762 68540 25339
71816 15535 77156 98915 95654 70585
64313 47684 63308 80079 54648 13211
87164 13596 30983 77390 57604 54092
68575 38111 95346 24386 59240 44034Slide 33
Computer Generated
Slide 34
Computer Generated
Slide 35
Computer Generated
Slide 36
Computer Generated
Slide 37
Simple Random
• In the unrestricted probability sampling design, more commonly
known as simple random sampling, every element in the population
has a known and equal chance of being selected as a subject.
• If we have 1000 elements in the population, and we need a sample
of 100. The probability would be 100/1000 = 0.1.
Slide 38
Simple Random
Advantages
• Easy to implement with random
dialing
Disadvantages
• Requires list of population elements
• Time consuming
• Uses larger sample sizes
• Produces larger errors
• High cost
Slide 39
Systematic Sampling
• The systematic sampling design involves drawing every nth element
(denoted as k) in the population starting with a randomly chosen element
between 1 and n.
• Let’s say we want to sample n = 10 from a population of N = 30.
• First, we will calculate the: k = N/n = 30/10 = 3
• Then we will need to select the first respondent randomly from 1-3, then
the subsequent respondent will follow the step number k which is +3.
• Let’s say we selected the first number as 2, then the next number will be 5
and the next number will be 8 and so on until we get the 10 samples.
Slide 40
Systematic Sampling
Slide 41
Systematic Sampling
Advantages
• Simple to design
• Easier than simple random
• Easy to determine sampling
distribution of mean or proportion
Disadvantages
• Periodicity within population may
skew sample and results
• Trends in list may bias results
• Moderate cost
Slide 42
Stratified Random Sampling
Slide 43
Stratified Sampling
• Population is divided into sub-
population or stratum and the
subjects selected randomly.
▪ Proportionate
▪ Disproportionate
All Students
Off Campus On Campus
Sample
Slide 44
Stratified Sampling
• Population is N = 10,000
• Sample size needed is n = 500
Stratum Population % Proportionate Disproportionate (%) Selected
Small 95 475 50 250
Medium 3 15 25 124
Large 2 10 25 125
Total 100 500 100 500
Slide 45
Stratified Sampling
Advantages
• Control of sample size in strata
• Increased statistical efficiency
• Provides data to represent and
analyze subgroups
• Enables use of different
methods in strata
Disadvantages
• Increased error will result if
subgroups are selected at different
rates
• Especially expensive if strata on
population must be created
• High cost
Slide 46
Cluster Sampling
Population is divided
into clusters, the cluster
is randomly selected
All Students in
Malaysia
Kuala Lumpur Johor
Sample
Malacca
Slide 47
Cluster Sampling
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
Slide 48
Comparing 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
Slide 49
Area Sampling
• Area sampling is a method of sampling used when no complete frame of
reference is available. The total area under investigation is divided into
small sub-areas which are sampled at random or according to a restricted
process (stratification of sampling).
• Clusters consist of geographic areas such as counties, city blocks, or
particular boundaries within a locality.
• It is a low-cost and frequently used method.
Slide 50
Area Sampling
Slide 51
Double Sampling
Advantages
• May reduce costs if first stage
results in enough data to stratify
or cluster the population
Disadvantages
• Increased costs if indiscriminately
used
Slide 52
Nonprobability Samples
• In nonprobability sampling designs, the elements in the population
do not have any probabilities attached to their being chosen as
sample subjects.
• This means that the findings from the study of the sample cannot be
confidently generalized to the population.
Slide 53
When to be Used
Cost
No need to generalize
Limited Objectives
Time
Feasibility
Slide 54
Nonprobability Sampling Methods
Convenience
Snowball
Quota
Judgement
Slide 55
Convenience Sampling
• Convenience sampling refers to the collection of information from
members of the population who are conveniently available to provide it.
• Convenience sampling is most often used during the exploratory phase
of a research project and is perhaps the best way of getting some basic
information quickly and efficiently.
Slide 56
Convenience Sampling
Slide 57
Advantages
1. Collect data quickly: In situations where time is a constraint, many researchers choose
this method for quick data collection.
2. Inexpensive to create samples: The money and time invested in other probability
sampling methods are quite large compared to convenience sampling. It allows
researchers to generate more samples with less or no investment and in a brief period.
3. Easy to do research: The name of this surveying technique clarifies how samples are
formed. Elements are easily accessible by the researchers and so, collecting members
for the sample becomes easy.
4. Low cost: Low cost is one of the main reasons why researchers adopt this technique.
When on a small budget, researchers – especially students, can use the budget in other
areas of the project.
5. Readily available sample: Data collection is easy and accessible. Most convenience
sampling considers the population at hand. Samples are readily available to the
researcher. They do not have to move around too much for data collection. Slide 58
Disadvantages
1. Convenience samples do not produce representative results. If you need to
extrapolate to the target population, convenience samples aren't going to
get you there.
2. The natural tendency is to extrapolate from convenience samples.
3. The results of convenience samples are hard to replicate.
4. Highly vulnerable to selection bias and influences beyond the control of
the researcher
5. High level of sampling error.Slide 59
Purposive Sampling
• Instead of obtaining information from those who are most readily or
conveniently available, it might sometimes become necessary to obtain
information from specific target groups.
• The sampling here is confined to specific types of people who can
provide the desired information, either because they are the only ones who
have it, or they conform to some criteria set by the researcher.
Slide 60
Purposive - Judgement Sampling
• Judgment sampling involves the choice of subjects who are most
advantageously placed or in the best position to provide the
information required.
• For instance, if a researcher wants to find out what it takes for women
managers to make it to the top, the only people who can give first‐hand
information are the women who have risen to the positions of presidents,
vice presidents, and important top‐level executives in work
organizations.
Slide 61
Purposive - Quota
• Quota sampling, a second type of purposive sampling, ensures that
certain groups are adequately represented in the study through the
assignment of a quota.
• The population is first subdivided into stratum.
• Then from each stratum and % is selected.
• Reason to ensure representativeness or numbers in each group.
• Useful if you want to do sub-group analysis.
Slide 62
Purposive - Quota
• Population is N = 1,000
• Sample size needed is n = 200
Stratum Population % Selected Selection Quota Selected Quota
Malay 60 120 30 60
Chinese 25 50 30 60
Indian 10 20 20 40
Others 5 10 20 40
Total 100 200 100 200
Slide 63
Advantages
1. Saves time: Because of the involvement of a quota for sample creation, this sampling
process is quick and straightforward.
2. Research convenience: By using quota sampling and appropriate research questions,
interpreting information and responses to the survey is a much convenient process for a
researcher.
3. Accurate representation of the population of interest: Researchers effectively
represent a population using this sampling technique. There is no room for over-
representation as this sampling technique helps researchers to study the population using
specific quotas.
4. Saves money: The budget required for executing this sampling method is minimalistic.Slide 64
Disadvantage
• Vulnerability to errors in judgment by researcher.
• Low level of reliability and high levels of bias.
• Inability to generalize research findings.
Slide 65
Snowball Sampling
Slide 66
When to be Used
1. No official list of names of the members: This sampling technique can be used for a
population, where there is no easily available data like their demographic information. For
example, homeless or list of members of an elite club, whose personal details cannot be
obtained easily.
2. Difficulty to locate people: People with rare diseases are quite difficult to locate. However, if
a researcher is carrying out a research study similar in nature, finding the primary data source
can be a challenge. Once he/she is identified, they usually have information about more such
similar individuals.
3. People who are not willing to be identified: If a researcher is carrying out a study which
involves collecting information/data from sex workers or victims of sexual assault or
individuals who don’t want to disclose their sexual orientations, these individuals will fall
under this category.
4. Secretiveness about their identity: People who belong to a cult or are religious extremists or
hackers usually fall under this category. A researcher will have to use snowball sampling to
identify these individuals and extract information from them.
Slide 67
Advantages
1. It’s quicker to find samples: Referrals make it easy and quick to find subjects as they come
from reliable sources. An additional task is saved for a researcher, this time can be used in
conducting the study.
2. Cost effective: This method is cost effective as the referrals are obtained from a primary data
source. It’s is convenient and not so expensive as compared to other methods.
3. Sample hesitant subjects: Some people do not want to come forward and participate in
research studies, because they don’t want their identity to be exposed. There are some sections
of the target population which are hard to contact. For example, if a researcher intends to
understand the difficulties faced by HIV patients, other sampling methods will not be able to
provide these sensitive samples. Slide 68
Disadvantages
1. Sampling bias and margin of error: Since people refer those whom they know and
have similar traits this sampling method can have a potential sampling bias and margin
of error. This means a researcher might only be able to reach out to a small group of
people and may not be able to complete the study with conclusive results.
2. Lack of cooperation: There are fair chances even after referrals, people might not be
cooperative and refuse to participate in the research studies. Oversampling can be
done; respondents may be hesitant to answer all questions.
3. It is not possible to determine the actual pattern of distribution of population.
4. It is not possible to determine the sampling error
Slide 69
What is Important in this chapter?
• Basic terms
• Why sampling is needed?
• Characteristics of a good sample
• Probability and nonprobability samples
• When each should be used
Slide 70
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