Sampling Methods

Dr. KANUPRIYA CHATURVEDI
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SAMPLING
METHODS

LEARNING OBJECTIVES
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Learn the reasons for sampling
Develop an understanding about different
sampling methods
Distinguish between probability & non probability
sampling
Discuss the relative advantages & disadvantages
of each sampling methods

What is research?
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• “Scientific research is systematic, controlled,
empirical, and critical investigation of natural
phenomena guided by theory and hypotheses
about the presumed relations among such
phenomena.”
– Kerlinger, 1986
• Research is an organized and systematic way of
finding answers to questions

Important Components of Empirical Research
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Problem statement, research questions, purposes,
benefits
Theory, assumptions, background literature
Variables and hypotheses
Operational definitions and measurement
Research design and methodology
Instrumentation, sampling
Data analysis
Conclusions, interpretations, recommendations

SAMPLING
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A sample is “a smaller (but hopefully
representative) collection of units from a
population used to determine truths about that
population” (Field, 2005)
Why sample?
Resources (time, money) and workload
Gives results with known accuracy that can be
calculated mathematically
The sampling frame is the list from which the
potential respondents are drawn
Registrar’s office
Class rosters
Must assess sampling frame errors

SAMPLING……
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What is your population of interest?
To whom do you want to generalize your
results?
All doctors
School children
Indians
Women aged 15-45 years
Other
Can you sample the entire population?

SAMPLING…….
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3 factors that influence sample representative-
ness
Sampling procedure
Sample size
Participation (response)
When might you sample the entire population?
When your population is very small
When you have extensive resources
When you don’t expect a very high response

SAMPLING…….
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TARGET POPULATION
STUDY POPULATION
SAMPLE

Types of Samples
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Probability (Random) Samples
Simple random sample
Systematic random sample
Stratified random sample
Multistage sample
Multiphase sample
Cluster sample
Non-Probability Samples
Convenience sample
Purposive sample
Quota

Process
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The sampling process comprises several stages:
Defining the population of concern
Specifying a sampling frame, a set of items or
events possible to measure
Specifying a sampling method for selecting
items or events from the frame
Determining the sample size
Implementing the sampling plan
Sampling and data collecting
Reviewing the sampling process

Population definition
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A population can be defined as including all
people or items with the characteristic one
wishes to understand.
 Because there is very rarely enough time or
money to gather information from everyone
or everything in a population, the goal
becomes finding a representative sample (or
subset) of that population.

Population definition…….
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Note also that the population from which the sample
is drawn may not be the same as the population about
which we actually want information. Often there is
large but not complete overlap between these two
groups due to frame issues etc .
Sometimes they may be entirely separate - for
instance, we might study rats in order to get a
better understanding of human health, or we might
study records from people born in 2008 in order to
make predictions about people born in 2009.

SAMPLING FRAME
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In the most straightforward case, such as the
sentencing of a batch of material from production
(acceptance sampling by lots), it is possible to
identify and measure every single item in the
population and to include any one of them in our
sample. However, in the more general case this is not
possible. There is no way to identify all rats in the
set of all rats. Where voting is not compulsory, there
is no way to identify which people will actually vote at
a forthcoming election (in advance of the election)
As a remedy, we seek a sampling frame which has the
property that we can identify every single element
and include any in our sample .
The sampling frame must be representative of the
population

PROBABILITY SAMPLING
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A probability sampling scheme is one in which every
unit in the population has a chance (greater than zero)
of being selected in the sample, and this probability
can be accurately determined.
. When every element in the population does have the
same probability of selection, this is known as an
'equal probability of selection' (EPS) design. Such
designs are also referred to as 'self-weighting'
because all sampled units are given the same weight.

PROBABILITY SAMPLING…….
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Probability sampling includes:
Simple Random Sampling,
Systematic Sampling,
Stratified Random Sampling,
Cluster Sampling
Multistage Sampling.
Multiphase sampling

NON PROBABILITY SAMPLING
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 Any sampling method where some elements of population
have no chance of selection (these are sometimes
referred to as 'out of coverage'/'undercovered'), or
where the probability of selection can't be accurately
determined. It involves the selection of elements based
on assumptions regarding the population of interest, which
forms the criteria for selection. Hence, because the
selection of elements is nonrandom, nonprobability
sampling not allows the estimation of sampling errors..
 Example: We visit every household in a given street, and
interview the first person to answer the door. In any
household with more than one occupant, this is a
nonprobability sample, because some people are more
likely to answer the door (e.g. an unemployed person who
spends most of their time at home is more likely to
answer than an employed housemate who might be at work
when the interviewer calls) and it's not practical to
calculate these probabilities.

NONPROBABILITY SAMPLING…….
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• Nonprobability Sampling includes:
Accidental Sampling, Quota Sampling and
Purposive Sampling. In addition, nonresponse
effects may turn any probability design into a
nonprobability design if the characteristics of
nonresponse are not well understood, since
nonresponse effectively modifies each
element's probability of being sampled.

SIMPLE RANDOM SAMPLING
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• Applicable when population is small, homogeneous &
readily available
• All subsets of the frame are given an equal
probability. Each element of the frame thus has an
equal probability of selection.
• It provides for greatest number of possible samples.
This is done by assigning a number to each unit in the
sampling frame.
• A table of random number or lottery system is used
to determine which units are to be selected.

SIMPLE RANDOM SAMPLING……..
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 Estimates are easy to calculate.
 Simple random sampling is always an EPS design, but not all
EPS designs are simple random sampling.
 Disadvantages
 If sampling frame large, this method impracticable.
 Minority subgroups of interest in population may not be
present in sample in sufficient numbers for study.

REPLACEMENT OF SELECTED UNITS
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Sampling schemes may be without replacement
('WOR' - no element can be selected more than once
in the same sample) or with replacement ('WR' - an
element may appear multiple times in the one
sample).
For example, if we catch fish, measure them, and
immediately return them to the water before
continuing with the sample, this is a WR design,
because we might end up catching and measuring the
same fish more than once. However, if we do not
return the fish to the water (e.g. if we eat the fish),
this becomes a WOR design.

SYSTEMATIC SAMPLING
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Systematic sampling relies on arranging the target
population according to some ordering scheme and then
selecting elements at regular intervals through that
ordered list.
Systematic sampling involves a random start and then
proceeds with the selection of every kth element from
then onwards. In this case, k=(population size/sample
size).
It is important that the starting point is not
automatically the first in the list, but is instead
randomly chosen from within the first to the kth
element in the list.
A simple example would be to select every 10th name
from the telephone directory (an 'every 10th' sample,
also referred to as 'sampling with a skip of 10').

SYSTEMATIC SAMPLING……
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As described above, systematic sampling is an EPS method, because all
elements have the same probability of selection (in the example
given, one in ten). It is not 'simple random sampling' because
different subsets of the same size have different selection
probabilities - e.g. the set {4,14,24,...,994} has a one-in-ten
probability of selection, but the set {4,13,24,34,...} has zero
probability of selection.

SYSTEMATIC SAMPLING……
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 ADVANTAGES:
 Sample easy to select
 Suitable sampling frame can be identified easily
 Sample evenly spread over entire reference population
 DISADVANTAGES:
 Sample may be biased if hidden periodicity in population
coincides with that of selection.
 Difficult to assess precision of estimate from one survey.

STRATIFIED SAMPLING
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Where population embraces a number of distinct
categories, the frame can be organized into separate
"strata." Each stratum is then sampled as an
independent sub-population, out of which individual
elements can be randomly selected.
Every unit in a stratum has same chance of being
selected.
Using same sampling fraction for all strata ensures
proportionate representation in the sample.
Adequate representation of minority subgroups of
interest can be ensured by stratification & varying
sampling fraction between strata as required.

STRATIFIED SAMPLING……
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Finally, since each stratum is treated as an
independent population, different sampling
approaches can be applied to different strata.
Drawbacks to using stratified sampling.
 First, sampling frame of entire population has to
be prepared separately for each stratum
Second, when examining multiple criteria,
stratifying variables may be related to some, but
not to others, further complicating the design,
and potentially reducing the utility of the strata.
 Finally, in some cases (such as designs with a
large number of strata, or those with a specified
minimum sample size per group), stratified
sampling can potentially require a larger sample
than would other methods

STRATIFIED SAMPLING…….
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Draw a sample from each stratum

POSTSTRATIFICATION
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Stratification is sometimes introduced after the
sampling phase in a process called "poststratification“.
This approach is typically implemented due to a lack of
prior knowledge of an appropriate stratifying variable
or when the experimenter lacks the necessary
information to create a stratifying variable during the
sampling phase. Although the method is susceptible to
the pitfalls of post hoc approaches, it can provide
several benefits in the right situation. Implementation
usually follows a simple random sample. In addition to
allowing for stratification on an ancillary variable,
poststratification can be used to implement weighting,
which can improve the precision of a sample's
estimates.

OVERSAMPLING
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Choice-based sampling is one of the stratified
sampling strategies. In this, data are
stratified on the target and a sample is taken
from each strata so that the rare target class
will be more represented in the sample. The
model is then built on this biased sample. The
effects of the input variables on the target
are often estimated with more precision with
the choice-based sample even when a smaller
overall sample size is taken, compared to a
random sample. The results usually must be
adjusted to correct for the oversampling.

CLUSTER SAMPLING
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Cluster sampling is an example of 'two-stage
sampling' .
 First stage a sample of areas is chosen;
 Second stage a sample of respondents within
those areas is selected.
 Population divided into clusters of homogeneous
units, usually based on geographical contiguity.
Sampling units are groups rather than individuals.
A sample of such clusters is then selected.
All units from the selected clusters are studied.

CLUSTER SAMPLING…….
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Advantages :
Cuts down on the cost of preparing a sampling
frame.
This can reduce travel and other
administrative costs.
Disadvantages: sampling error is higher for a
simple random sample of same size.
Often used to evaluate vaccination coverage in
EPI

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• Identification of clusters
– List all cities, towns, villages & wards of cities with
their population falling in target area under study.
– Calculate cumulative population & divide by 30, this
gives sampling interval.
– Select a random no. less than or equal to sampling
interval having same no. of digits. This forms 1st
cluster.
– Random no.+ sampling interval = population of 2nd
cluster.
– Second cluster + sampling interval = 4th
cluster.
– Last or 30th
cluster = 29th
cluster + sampling interval

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Two types of cluster sampling methods.
One-stage sampling. All of the elements within
selected clusters are included in the sample.
Two-stage sampling. A subset of elements
within selected clusters are randomly selected
for inclusion in the sample.

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• Freq c f cluster
• I 2000 2000 1
• II 3000 5000 2
• III 1500 6500
• IV 4000 10500 3
• V 5000 15500 4, 5
• VI 2500 18000 6
• VII 2000 20000 7
• VIII 3000 23000 8
• IX 3500 26500 9
• X 4500 31000 10
• XI 4000 35000 11, 12
• XII 4000 39000 13
• XIII 3500 44000 14,15
• XIV 2000 46000
• XV 3000 49000 16
• XVI 3500 52500 17
• XVII 4000 56500 18,19
• XVIII 4500 61000 20
• XIX 4000 65000 21,22
• XX 4000 69000 23
• XXI 2000 71000 24
• XXII 2000 73000
• XXIII 3000 76000 25
• XXIV 3000 79000 26
• XXV 5000 84000 27,28
• XXVI 2000 86000 29
• XXVII 1000 87000
• XXVIII 1000 88000
• XXIX 1000 89000 30
• XXX 1000 90000
• 90000/30 = 3000 sampling interval

Difference Between Strata and Clusters
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Although strata and clusters are both non-
overlapping subsets of the population, they
differ in several ways.
All strata are represented in the sample; but
only a subset of clusters are in the sample.
With stratified sampling, the best survey
results occur when elements within strata are
internally homogeneous. However, with cluster
sampling, the best results occur when elements
within clusters are internally heterogeneous

MULTISTAGE SAMPLING
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 Complex form of cluster sampling in which two or more levels of
units are embedded one in the other.
 First stage, random number of districts chosen in all
states.
 Followed by random number of talukas, villages.
 Then third stage units will be houses.
 All ultimate units (houses, for instance) selected at last step are
surveyed.

MULTISTAGE SAMPLING……..
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 This technique, is essentially the process of taking random
samples of preceding random samples.
 Not as effective as true random sampling, but probably
solves more of the problems inherent to random sampling.
 An effective strategy because it banks on multiple
randomizations. As such, extremely useful.
 Multistage sampling used frequently when a complete list
of all members of the population not exists and is
inappropriate.
 Moreover, by avoiding the use of all sample units in all
selected clusters, multistage sampling avoids the large,
and perhaps unnecessary, costs associated with traditional
cluster sampling.

MULTI PHASE SAMPLING
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 Part of the information collected from whole sample & part from
subsample.
 In Tb survey MT in all cases – Phase I
 X –Ray chest in MT +ve cases – Phase II
 Sputum examination in X – Ray +ve cases - Phase III
 Survey by such procedure is less costly, less laborious & more
purposeful

MATCHED RANDOM SAMPLING
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A method of assigning participants to groups in which
pairs of participants are first matched on some
characteristic and then individually assigned randomly to
groups.
The Procedure for Matched random sampling can be
briefed with the following contexts,
Two samples in which the members are clearly paired, or
are matched explicitly by the researcher. For example,
IQ measurements or pairs of identical twins.
Those samples in which the same attribute, or variable, is
measured twice on each subject, under different
circumstances. Commonly called repeated measures.
 Examples include the times of a group of athletes for
1500m before and after a week of special training; the
milk yields of cows before and after being fed a
particular diet.

QUOTA SAMPLING
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 The population is first segmented into mutually exclusive
sub-groups, just as in stratified sampling.
Then judgment used to select subjects or units from
each segment based on a specified proportion.
For example, an interviewer may be told to sample 200
females and 300 males between the age of 45 and 60.
It is this second step which makes the technique one of
non-probability sampling.
 In quota sampling the selection of the sample is non-
random.
For example interviewers might be tempted to interview
those who look most helpful. The problem is that these
samples may be biased because not everyone gets a
chance of selection. This random element is its greatest
weakness and quota versus probability has been a matter
of controversy for many years

CONVENIENCE SAMPLING
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 Sometimes known as grab or opportunity sampling or accidental
or haphazard sampling.
 A type of nonprobability sampling which involves the sample being
drawn from that part of the population which is close to hand.
That is, readily available and convenient.
 The researcher using such a sample cannot scientifically make
generalizations about the total population from this sample
because it would not be representative enough.
 For example, if the interviewer was to conduct a survey at a
shopping center early in the morning on a given day, the people
that he/she could interview would be limited to those given there
at that given time, which would not represent the views of other
members of society in such an area, if the survey was to be
conducted at different times of day and several times per week.
 This type of sampling is most useful for pilot testing.
 In social science research, snowball sampling is a similar technique,
where existing study subjects are used to recruit more subjects
into the sample.

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CONVENIENCE SAMPLING…….
 Use results that are easy to get
42

Judgmental sampling or Purposive
sampling
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- The researcher chooses the sample based on
who they think would be appropriate for the
study. This is used primarily when there is a
limited number of people that have expertise
in the area being researched

PANEL SAMPLING
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 Method of first selecting a group of participants through a
random sampling method and then asking that group for the same
information again several times over a period of time.
 Therefore, each participant is given same survey or interview at
two or more time points; each period of data collection called a
"wave".
 This sampling methodology often chosen for large scale or nation-
wide studies in order to gauge changes in the population with
regard to any number of variables from chronic illness to job
stress to weekly food expenditures.
 Panel sampling can also be used to inform researchers about
within-person health changes due to age or help explain changes in
continuous dependent variables such as spousal interaction.
 There have been several proposed methods of analyzing panel
sample data, including growth curves.

What sampling method u recommend?
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Determining proportion of undernourished five year
olds in a village.
Investigating nutritional status of preschool children.
Selecting maternity records for the study of previous
abortions or duration of postnatal stay.
In estimation of immunization coverage in a province,
data on seven children aged 12-23 months in 30
clusters are used to determine proportion of fully
immunized children in the province.
Give reasons why cluster sampling is used in this
survey.

Probability proportional to size
sampling
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In some cases the sample designer has access to an "auxiliary variable"
or "size measure", believed to be correlated to the variable of
interest, for each element in the population. This data can be used to
improve accuracy in sample design. One option is to use the auxiliary
variable as a basis for stratification, as discussed above.
Another option is probability-proportional-to-size ('PPS') sampling,
in which the selection probability for each element is set to be
proportional to its size measure, up to a maximum of 1. In a simple
PPS design, these selection probabilities can then be used as the basis
for Poisson sampling. However, this has the drawbacks of variable
sample size, and different portions of the population may still be
over- or under-represented due to chance variation in selections. To
address this problem, PPS may be combined with a systematic
approach.

Contd.
48
Example: Suppose we have six schools with populations of 150,
180, 200, 220, 260, and 490 students respectively (total 1500
students), and we want to use student population as the basis for a
PPS sample of size three. To do this, we could allocate the first
school numbers 1 to 150, the second school 151 to
330 (= 150 + 180), the third school 331 to 530, and so on to the
last school (1011 to 1500). We then generate a random start
between 1 and 500 (equal to 1500/3) and count through the school
populations by multiples of 500. If our random start was 137, we
would select the schools which have been allocated numbers 137,
637, and 1137, i.e. the first, fourth, and sixth schools.
The PPS approach can improve accuracy for a given sample size by
concentrating sample on large elements that have the greatest
impact on population estimates. PPS sampling is commonly used
for surveys of businesses, where element size varies greatly and
auxiliary information is often available - for instance, a survey
attempting to measure the number of guest-nights spent in hotels
might use each hotel's number of rooms as an auxiliary variable. In
some cases, an older measurement of the variable of interest can be
used as an auxiliary variable when attempting to produce more
current estimates.

Event sampling
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Event Sampling Methodology (ESM) is a new form of
sampling method that allows researchers to study ongoing
experiences and events that vary across and within days in its
naturally-occurring environment. Because of the frequent
sampling of events inherent in ESM, it enables researchers to
measure the typology of activity and detect the temporal and
dynamic fluctuations of work experiences. Popularity of ESM as a
new form of research design increased over the recent years
because it addresses the shortcomings of cross-sectional research,
where once unable to, researchers can now detect intra-individual
variances across time. In ESM, participants are asked to record
their experiences and perceptions in a paper or electronic diary.
There are three types of ESM:# Signal contingent – random
beeping notifies participants to record data. The advantage of this
type of ESM is minimization of recall bias.
Event contingent – records data when certain events occur

Contd.
50
Event contingent – records data when certain events occur
Interval contingent – records data according to the passing of a
certain period of time
ESM has several disadvantages. One of the disadvantages of ESM is
it can sometimes be perceived as invasive and intrusive by
participants. ESM also leads to possible self-selection bias. It may
be that only certain types of individuals are willing to participate
in this type of study creating a non-random sample. Another
concern is related to participant cooperation. Participants may not
be actually fill out their diaries at the specified times.
Furthermore, ESM may substantively change the phenomenon
being studied. Reactivity or priming effects may occur, such that
repeated measurement may cause changes in the participants'
experiences. This method of sampling data is also highly
vulnerable to common method variance.[6]

contd.
51
Further, it is important to think about whether or not an
appropriate dependent variable is being used in an ESM design.
For example, it might be logical to use ESM in order to answer
research questions which involve dependent variables with a great
deal of variation throughout the day. Thus, variables such as
change in mood, change in stress level, or the immediate impact
of particular events may be best studied using ESM methodology.
However, it is not likely that utilizing ESM will yield meaningful
predictions when measuring someone performing a repetitive task
throughout the day or when dependent variables are long-term in
nature (coronary heart problems).

Sampling Methods

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