Sampling

Sampling design and procedures
• Census
• Sample
• Selection of sampling design
• Sampling frame
• Reference, target and study population
• Determination of sample size
• Sampling techniques
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Why sample?
Save time and money
More effort to ensure high-quality measurement
if smaller sample
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Criteria for a Good Sample
Samples can be selected in two ways
• Purposive Sample
• Random sample
Purposive sample or Non-probability Sample
Sample units are selected from the population to suit a
specific purpose as per the desire of the investigator
These samples serves very limited purpose
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Examples of population and
samples
Situation Population Sample
Sex ratio of births the world’s birth some hospital records
Is my well water safe? Water in well Vial in lab
Medical study people in Nepal some subjects
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Technical Terms
• A sampling frame is a list of sampling units.
• A sample is a collection of sampling units drawn from a
sampling frame.
• Parameter: numerical characteristic of a population
• Statistic: numerical characteristic of a sample
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Sampling
• Sampling is a process of systematically
selecting cases for inclusion in a research
project.
• Sampling involves the selection of a number of
study units from a defined study population.
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What is Sampling?
• Sampling is the process of selecting observations (a sample) to
provide an adequate description and robust inferences of the
population
• It is the process of selecting a sufficient number of elements from
the population so that by studying the sample, and understanding
the properties or characteristics of the sample subjects, it would
be possible to generalise the properties or characteristics to the
population elements.
• The more representative the sample is of the population, the more
generalizable are the findings of the research
10

What is Sampling….
Population
Sample
Using data to say something (make an inference) with confidence, about
a whole (population) based on the study of a only a few (sample).
Sampling
Frame
Sampling Process
What you
want to talk
about
What you
actually
observe in
the data
Inference
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Sampling Frame
• List of population units from which the sample units are to
be selected.
• If Sampling frame - not available, Prepare it –
• From - Telephone Directories, Tax Records, Driver’s
License Records.
• A good sampling frame is crucial to good sampling.
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Steps in Sampling
• Defining the population to be covered
• Defining sampling units
• Acquiring frame / list of the population
elements
• Deciding about the size of the sample
• Deciding about the type of the sample to
be used and
• Testing the reliability of the sample
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Levels of sample selection
Target population(s) - population(s)
to which the results can be applied
Source population - population(s)
from which eligible subjects are drawn
Eligible population - population(s) of
subjects eligible for inclusion in study
Study participants - individuals who
contribute data to the study: results apply
directly only to these subjects
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Factors to be considered in sampling process
* Study Objectives
- Descriptive vs. Analytic
* Selection Criteria
- Inclusion & Exclusion
- Probability vs. Non-probability
* Sampling Frame & Sampling Units
- Unit
- Time & Place
* Strategies in approaching sampling units
- Identification & Classification
- Willing/Consent to Participate
O P D
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Sampling Terms
• Target Population:
– Specific pool of cases or sample that researchers
wants to study.
• Sampling Ratio:
– Size of the sample / size of the target population.
– For example
– The population has 50,000 people, and a researcher
draws a sample of 150 from it. Researchers
sampling ratio is 150/50,000 = 0.03 or 0.3 percent.
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1 ) Is the population from which the sample is drawn
consistent with the population of interest for the study?
(generalizability/external validity)
2) Have the methods for selecting subjects or units
biased the sample? (bias/internal validity)
3) Are the estimates or sample statistics sufficiently
precise for the study purpose? (power/sample size/precision)
Sampling Issues
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Determination of sample size
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TABLE OF RANDOM NUMBERS
53 74 23 99 67 61 32 28 69 84 94 62
63 38 06 86 54 99 00 65 26 94 02 82
35 30 58 21 46 06 72 17 10 94 25 21
63 43 36 82 69 65 51 18 37 88 61 38
98 25 37 55 26 01 91 82 81 46 74 71
02 63 21 17 69 71 50 80 89 56 38 15
64 55 22 21 82 48 22 28 06 00 61 54
85 07 26 13 89 01 10 07 82 04 59 63
58 54 16 24 15 51 54 44 82 00 62 61
34 85 27 84 87 61 48 64 56 26 90 18
03 92 18 27 46 57 99 16 96 56 30 33
62 95 30 27 59 37 75 41 66 48 86 97
08 45 93 15 22 60 21 75 46 91 98 77
07 08 55 18 40 45 44 75 13 90 24 94
01 85 89 95 66 51 10 19 34 88 15 84
72 84 71 14 35 19 11 58 49 26 50 11
88 78 28 16 84 13 52 53 94 53 75 45
45 17 75 65 57 28 40 19 72 12 25 12
96 76 28 12 54 22 01 11 95 25 71 96
43 31 67 72 30 24 02 94 08 63 38 32
50 44 66 44 21 66 06 58 05 62 68 15
22 66 22 15 86 26 63 75 41 99 58 42
96 24 40 14 51 23 22 30 88 57 95 67
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Requirements for estimation of Size of the sample
An approximate idea of the estimate of the characteristic
under observation
Variability of this characteristic from unit to unit in the
population
Initial knowledge of the desired accuracy of the estimate
of the characteristic under study
Probability level within which the desired precision of
estimates is to be maintained
Availability of the experimental material, resources and
other practical considerations
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Calculation of sample size for field surveys
For Field surveys to estimate the prevalence
rates
n = ( 4pq / L2
)
where n is the required sample size
p is the approximate prevalence rate
q= (1-p)
L is the permissible error in the estimate of p
stimates calculated with this sample size
would be true in 95 out of 100 samples 100
samples
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p = 40%
q = (100-40 ) = 60%
L = 5% of 40% = 2%
n = ( 4 x 40 x 60) / ( 22
)
= (4 x 40 x 60 ) / 4
= 2400
2,400 persons are to be examined to estimate the
prevalence rate with 5% error.
If we increase the error percentage to 10%
L=10% of 40% = 4
n = ( 4 x 40 x 60 ) / 16
= 600
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For Quantitative data, the sample size is
calculated from the formula.
n = (tα
2
x s2
) / e2
n is the desired sample size
s is the standard deviation of observations
e is the permissible error in the estimation
of mean difference
tα is the value of t at 5% level from t tables
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In a survey to estimate the haemoglobin level
If mean Hb% level is approximately 12gm%
Standard deviation 1.5gm%
Permissible error 0.5gm%
s=1.5gms
e = 0.5gms
t0.05 can be taken as 2, as it is conventional to use 5% level
of significance
n = { 22
x (1.5) 2
} / (0.52
)
= (4 x 2.25 ) / (2.25 )
= 36 persons
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ERRORS IN RESEARCH
Non-sampling errors
Coverage errors
Response errors
Non-response errors
Processing errors
Measurement errors
Estimation errors
Analysis errors
Sampling errors
Sample size
Population size
Variability of the characteristic of interest
Sample plan
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Sampling techniques
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Sampling
Methods
Probability
samples
Simple
random
Cluster
Stratified
Multi-stage
Non-
probability
samples
Convenienc
e
Judgments
Snowball
Quota
Classification of Sampling Methods
Systemati
c
(mixed)
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Convenience or Haphazard Sampling
• Cheap and quick
• Study units that happen to be available at the time of data
collection are selected in the sample
• Choose when population is not clearly defined, sampling
units are not clear.
• When a researcher haphazardly selects cases that are
convenient researcher can easily get a sample that seriously
misrepresents the population.
– Some units over selected, other under selected or missed altogether
– Causes ineffective, unrepresentative samples.
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Convenience or Haphazard Sampling
• Examples:
• The person-on-the-street interview conducted by television
programs is an example of a haphazard sample. Television
interviewers go out on the street with camera and microphone
to talk to a few people who are convenient to interview.
• A researcher wants to study the attitudes of villagers toward
family planning services provided by MCH clinic. He decides
to interview all adult patients who visit the out-patient clinic
during one particular day. This is more convenient than taking
a random sample of people in the village, and it gives a useful
first impression.
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Purposive or Judgmental Sampling
• Researcher deliberately selects certain units for study
from the population
• Choice of the selection is supreme and nothing is left to
chance
Appropriate in 3 situations:
• For unique cases selection that are especially informative
• For selection of members of difficult to reach, specialized
population
• Another situation for purposive sampling occurs when a
researcher wants to identify particular types of cases for
in-depth investigation.
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Quota Sampling
• Pre plan number of subjects in specified
categories (e.g. 100 men and 100 women)
• Once the quota sample fixes the categories and
number of cases in each category, researcher uses
convenient sampling
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Snowball Sampling
• Selecting the cases in a network
• Begins with one or a few people or cases and
spread out on the basis of links to the initial cases
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Methods of Sampling - Probability Sampling
·
·
1. Simple Random Sampling:
Objective: To select n units out of N such that each NCn has
an equal chance of being selected.
Procedure: Use a table of random numbers, a computer
random number generator, or a mechanical device to select
the sample.
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
N = 50
n = 10 Sampling Frame
1 2
3 4
5 ….. 49 50
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Simple Random Sampling
• Lottery Method
– With replacement (Unrestricted random sampling )
– Without replacement (Restricted random sampling)
• Random number table method
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Mixed Sampling
• Notice that from the first interval the choice of an
element is on a random basis but the choice of the
elements from subsequent intervals is dependent upon
the choice from the first, and hence cannot be classified
as a random sample. For this reason it has been
classified here as mixed sampling.
• Although the general procedure for selecting a sample
by the systematic sampling technique is described
above, one can deviate from it by selecting a different
element from each interval with the Simple Random
Sampling technique. By adopting, systematic sampling
can be classified under probability sampling design.
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Mixed Sampling
·
·
Systematic Sampling
Procedure:
1. Number the units in the population from 1 to N;
2. Decide on the n (sample size) that you want or need;
3. Calculate the interval size k = N/n;
4. Randomly select an integer between 1 to k
5. Take every kth unit
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
N = 50
n = 10
k = 50/10 = 5
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
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Systematic Sampling
Advantages:
1) Do not need to know the entire sampling frame in
advance, just the total number of sampling units;
can be constructed as the study progresses, so ordering
is by time of accrual
2) Often simpler to implement under field conditions than
other sampling methods (e.g. easier to have interviewer
to visit every 5th house on the block rather than to
determine which houses are to be visited by means of a
table of random numbers)
3) If a trend is present in the sampling frame, units will
small values to units with large values, than a systematic
sample will ensure coverage of the spectrum of units
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Systematic Sampling
Disadvantage:
1) If cyclical trends exist in the data, a poor estimate of
the mean will be obtained
(e.g., the prevalence of bronchitis would be considerable
higher if one sampled every 12th month starting in January
than every 12th month starting in July)
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·
·
2. Stratified Random Sampling,
(quota random sampling)
Procedure:
1. Divide the population into non-overlapping homogeneous
subgroups (i.e., strata) N1, N2, N3, ... Ni, such that N1 + N2 + N3
+ ... + Ni = N.
2. Do a simple random sample of f = n/N in each strata.
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
Sampling Frame
.. 12 ….. 20 ..
1
30
31 … 50
N = 50 (N1 30; N2 =20)
n = 10
f = 10/50 = 0.2
thus
n1 = 0.2 x 30 = 6
n2 = 0.2 x 20 = 4
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Stratified Sampling
Advantages:
1) Investigator can make certain that each subgroup in the
population is represented; guarantees mean heights of each
subgroup can be estimated separately in addition to the
overall mean
2) When population divided into subgroups that are more
homogeneous than population as a whole, a more
precise
estimate of population parameters are obtained than
when
a simple random sample is taken, because variance
computed from the entire sample is based on each
within-stratum variance
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Stratified Sampling
Advantages:
3) Strata can be constructed so that those that are least
expensive to study or have the largest variances or largest
number of individuals can be sampled most heavily
4) Administratively it may be easier to deal with strata
Disadvantage:
Loss of precision can occur if very small numbers of units a
sampled within individual strata; although under most
circumstances, greater precision is attained by stratum-spec
estimates of a homogeneous group
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·
4. Cluster (or Area) Random Sampling
Procedure:
1. Divide population into clusters (usually geographic boundaries)
2. Randomly sample clusters
3. Measure all units within sampled clusters
1 2 3 4 5
6 7 8 9 10
N = 50
n = 22
35 36 37 38 39
40 41 42 43 44
45
11 12 13 14 15 16
17 18 19 20 21 22
23 24 25 26 27
28 29 30 31 32 33 34
46 47 48 49 50
1 2 3 4 5
6 7 8 9 10
28 29 30 31 32 33 34
46 47 48 49 50
·
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Cluster Sampling
• A researcher first samples clusters, each of which contains
elements, then draws a second sample from within the clusters
selected in the first stage of sampling. Clusters are often
geographic units (e.g. districts, villages) or organizational units
(e.g. clinics, training groups).
• Cluster sampling is usually less expensive than simple random
sampling, but it is less accurate. A researcher who uses cluster
sampling must decide the numbers of clusters and the number of
elements within clusters.
• For example
– In a study of the KAP related to family planning in rural communities of a
region, a list is made of all the villages. Using this list, a random sample
of villages is chosen and all the adults in the selected villages are
interviewed.
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Cluster Sampling
Advantages:
1) One need not enumerate the entire population in
advance, just the total number of clusters; then just
the units of selected clusters
2) More economical than simple random sampling
Disadvantage:
Factor representing cluster effect must be accounted for
in analysis, complex (violates assumption of independence)
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Multistage Sampling
Primary (larger) sampling units are first selected from a population
Secondary (smaller) sampling units (e.g. city blocks) are sampled
from within each chosen primary unit
Can be extended so that tertiary units (e.g. households) or further
(e.g. individuals) are selected within these secondary units
Differs from clustering in that secondary units are sampled,
whereas in cluster sampling all secondary units are included.
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Sampling

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