Sampling

SAMPLING
AND
SAMPLE SIZE
DR. AMITABH MISHRA 1

Sample
• “A Sample is a subset of the population that should
represent the entire group”.
• “Sampling is simply a process of learning about population
on the basis of sample drawn from it”
• Sample Survey: “A sample survey is carried out using a
sampling method”
i.e. in which “a portion only and not a whole population is
surveyed”.

Census
• “Census is an investigation of all the individual
elements that make up a population”.
• “Census is an accounting of the complete population”
• A census study is preferred over sample study when-
– Population is small
– Variability within population is high.
DR. AMITABH MISHRA 12–3

Sample Vs. Census
Conditions Favoring the Use of
Type of Study Sample Census
1. Budget Small Large
2. Time available Short Long
3. Population size Large Small
4. Variance in the characteristic Small Large
5. Cost of sampling errors Low High
6. Cost of nonsampling errors High Low
7. Attention to individual cases Yes No

Basic Concepts in Sampling

Population/ Universe
•“The universe is the entire group of items the researcher
wish to study”.
•“The target population is the collection of elements or
objects that possess the information sought by the
researcher and about which inferences are to be made”.

• For a given project universe might consist-
– Women older than 40 yrs residing in India.
– All the families within the city of Noida.
– All grocery stores in Gr. Noida.
• Information about the population parameter may be obtained
by taking a census or sample.

Sample Unit
• “Sampling unit is basic unit containing the elements of target
population”.
• A sampling unit is an element, or a unit containing the
element, that is available for selection at some stage of the
sampling process.
• Sample unit may be-
• A geographical one, such as-states, district, village etc.
• A construction unit, such as-house, flat, etc.
• A social unit, such as- family, club , school, etc.

Sampling Frame
• “The Sampling Frame (Working Population) is a list of
target population elements from which a sample
may be drawn”.
• “Sampling Frame is a master list of the entire
population”
• The researcher take sample from sample frame not
from population.

• Popularly known sample frame are-
– Census report
– Telephone book
– City directory

Sample design
• Sample design is determined before data is
collected.
• “Sample design refers to the technique or the
procedure the researcher would adopt in
selecting some sample unit from which
inferences about the population is drawn.”

Sample size
• “Sample size refers to the number of items to
be selected from the sample frame to
constitute a sample”.
• The size of sample should neither be
excessively large nor too small.

Sampling Error
• Sampling give rise to certain errors known as sampling errors
(sampling fluctuations).
• “Any error in a survey that occurs because a sample is used”.
• Sampling errors are-
– Biased sampling errors.
– Unbiased sampling errors.
• Biased errors are those which arises from any biasness in
selection, estimation etc. of the sample.

Sample Frame Error
• “Sample frame error is the degree to which the
sample frame fails to account for all of the
population”.
• Ex- A telephone book listing does not contain
unlisted numbers

Advantages of
Sampling/
Why Sample?/
Need for Sampling

1. Budget and time constraints (Sampling reduces the costs
of research in finite populations.)
2. Limited access to total population.
3. Samples can yield reasonably accurate information.
4. Strong similarities in population elements makes
sampling possible.
5. Sampling may be more accurate than a census.
6. Inability of researcher to analyze huge amounts of data
generated by census.

Sampling process
Or
Sample design
process/
Stages in the Selection
of a Sample

Define the Population
Determine the Sampling Frame
Select Sampling Technique(s)
Determine the Sample Size
Execute the Sampling Process

1. Define the Target Population/Universe
• Population/universe is any complete group of entities
that share some common set of characteristics”.
•“The target population is the collection of elements or
objects that possess the information sought by the
researcher and about which inferences are to be made”.

•The target population should be defined in
terms of-elements, sampling units, extent, and
time.
– An population element is the object about which or from
which the information is desired, e.g., the respondent,
product.
– A sampling unit is an element, or a unit containing the
element, that is available for selection at some stage of the
sampling process. E.g. retail outlet, supermarket

– Sample unit may be
• A geographical one, such as-states, district, village etc.
• A construction unit, such as-house, flat, etc.
• A social unit, such as- family, club , school, etc.
– Extent refers to the geographical boundaries. Such as- New Delhi,
Noida, Faridabad etc
– Time is the time period under consideration. Ex- 12faburary 2013
to 25 July 2013.

SAMPLING TECHNIQUES
OR
METHODS

• “Sampling method indicate, how a sample
unit is selected from the sample frame”.

Sampling Techniques
Non probability
Sampling Techniques
Probability
Sampling Techniques
Convenience
Sampling
Judgmental
Sampling
Quota
Sampling
Snowball
Sampling
Systematic
Sampling
Stratified
Sampling
Cluster
Sampling
Other Sampling
Techniques
Simple Random
Sampling

NON PROBABILITY
SAMPLING
• “Non probability sampling method is any
sampling method in which, the
chance/probability of choosing a particular
universe element is unknown”.
• The selection of units within the sample involves
human judgment rather than pure chance.

• In non probability sampling there is a great
opportunity for bias to enter the selection procedure
and to distort the finding of the study.

TYPES OF
NON PROBABILITY
SAMPLING
Sampling
Techniques
Non probability
Sampling
Techniques
Probability
Sampling
Techniques
Convenience
Sampling
Judgmental
Sampling
Quota
Sampling
Snowball
Sampling

Convenience Sampling or
Accidental Sampling
• “In Convenience sampling the selection of the
sample is left to the researcher who is to select
the sample”.
• Often, respondents are selected because they
happen to be in the right place at the right time.

• Data collection time and sample cost is minimum.
• Data quality and accuracy is low.
• It is suitable in Exploratory research.
• Example-
• Mall intercept interviews without qualifying the respondents
• Department stores using charge account lists
• “People on the street” interviews

A Graphical Illustration of Convenience
Sampling
A B C D E
1 6 11 16 21
2 7 12 17 22
3 8 13 18 23
4 9 14 19 24
5 10 15 20 25
Group D happens to
assemble at a
convenient time and
place. So all the
elements in this
Group are selected.
The resulting sample
consists of elements
16, 17, 18, 19 and 20.
Note, no elements are
selected from group
A, B, C and E.

Judgmental Sampling
• “Judgmental sampling is a form of convenience
sampling in which the population elements are selected
based on the judgment and opinion of the researcher”.
• Specialist in the subject matter of the survey choose
what they believe to be best sample for that particular
study.

• This method may be useful when total sample size
is very small.
• This method produce unsatisfactory result.
• It lacks accuracy
• Ex- a group of sales managers might select a sample of
grocery stores in the city that they regarded as
representative.

Graphical Illustration of Judgmental Sampling
A B C D E
1 6 11 16 21
2 7 12 17 22
3 8 13 18 23
4 9 14 19 24
5 10 15 20 25
The researcher considers
groups B, C and E to be
typical and convenient.
Within each of these
groups one or two
elements are selected
based on typicality and
convenience. The
resulting sample
consists of elements 8,
10, 11, 13, and 24. Note,
no elements are selected
from groups A and D.

Quota Sampling
• “Quota samples use a specific quota of certain types of individuals to be
interviewed”
• Quota sampling uses the principle of stratification.
• it may be viewed as two-stage restricted judgmental sampling.
– The first stage consists of developing control categories, or quotas, of
population elements.
– In the second stage, sample elements are selected based on
convenience or judgment.

• Bases of stratification in consumer survey are commonly
demographic. As- age, gender, income etc.
Control Variable
Population
Composition
Quota Sample
Composition
Gender
Total
Number
Percentage Percentage
Total
Number
Male 480 48% 48% 48
Female 520 52% 52% 52
1000 100% 100% 100

• Often compound stratification is used.
– Ex- A food manufacturer wishes to sample current users of company’s
brand to obtain their reactions to proposed new packaging. a quota
sample of brand users stratified by age with gender was designed with
the following quota
Stratum Quota
Men 18-34 50
Men 35-49 50
Women 18-34 100
Women 35-49
100

A Graphical Illustration of Quota Sampling
A B C D E
1 6 11 16 21
2 7 12 17 22
3 8 13 18 23
4 9 14 19 24
5 10 15 20 25
A quota of one
element from each
group, A to E, is
imposed. Within each
group, one element is
selected based on
judgment or
convenience. The
resulting sample
consists of elements 3,
6, 13, 20 and 22. Note,
one element is
selected from each
column or group.

Snowball Sampling or
Referral Sampling
• “Snowball sampling is a non probability sampling method
in which a set of respondent is chosen & and they help
the researcher to identify additional people to be included
in the study”

• In snowball sampling, an initial group of respondents
is selected, usually at random.
– After being interviewed, these respondents are asked to identify
others who belong to the target population of interest.
– Subsequent respondents are selected based on the referrals.

• Snowball sampling is used in a situation-
– The defined target population is small and unique.
and
– Compiling a complete list of sampling units is very difficult.

A Graphical Illustration of Snowball
Sampling
A B C D E
1 6 11 16 21
2 7 12 17 22
3 8 13 18 23
4 9 14 19 24
5 10 15 20 25
Elements 2 and 9 are selected
randomly from groups A and B.
Element 2 refers elements 12
and 13. Element 9 refers
element 18. The resulting
sample consists of elements 2,
9, 12, 13, and 18. Note, there are
no elements from group E.
Random Selection
Referrals

• “Probability sampling technique methods are those in
which every items in the universe has a known
chance or probability of being chosen for sample”
• Sampling elements are chosen by chance.
• Every potential sample need not have the same
probability of selection, but it is possible to specify
the probability of selecting any particular sample of
given size.

CLASSIFICATION
OF
PROBABILITY
SAMPLING
Sampling Techniques
Non probability
Sampling Techniques
Probability
Sampling Techniques
Systematic
Sampling
Stratified
Sampling
Cluster
Sampling
Other
Sampling
Techniques
Simple
Random
Sampling

Simple Random Sampling
• “In SRS each element in the population has a known and equal
probability of selection”.
• This implies that every element is selected independently of
every other element.
• It is easiest probability sampling method.
• Personal bias of investigator does not influence the selection.

Probability of selection =sample size/ population size
Ex- If population size = 20000, sample size = 300
Then,
Probability of selection =300/ 20000
=.015
=1.5%

Types
of
Simple Random
Sample

1.Lottery Method
or
Blind Draw Method

• Under this method all the items of the universe are
numbered or named on a separate slip of paper of
identical size and shape. These slips are then folded
and mixed in a drum or container.
• A blind fold selection is then made of the no. of
slips required to constitute the desired sample size.

2. Table of
Random Numbers

• Various statisticians like Tippetts, Fisher and Yates have
prepared the table of random numbers.
• Generally, Tippetts table of random no. is used for the
purpose.
• Tippetts table of random no. contains 10400, four digit
numbers.

Random number table

Advantage of SRS
• Known and equal chance of selection.
• EVERYONE has a chance!
Disadvantages of SRS:
• It requires population list (sample frame) that is often
not available.
• For small population SRS is appropriate, but for
population large it is cumbersome.

Procedures for Drawing
Simple Random Samples
1. Select a suitable sampling frame.
2. Each element is assigned a number from 1 to N
(pop. size).
3. Generate n (sample size) different random numbers
between 1 and N.
4. The numbers generated denote the elements that
should be included in the sample.

Stratified Random
Sampling

• In Stratified Random sampling the universe is
divided (or stratified) in to groups that are mutually
exclusive and include all the items in the universe.
• A simple random sample is chosen independently
from each group or stratum.

• The strata should be mutually exclusive and collectively exhaustive
in that every population element should be assigned to one and
only one stratum and no population elements should be omitted.
• The elements within a stratum should be as homogeneous as
possible, but the elements in different strata should be as
heterogeneous as possible.
• A major objective of stratified sampling is to increase precision
without increasing cost.

• The variables used to partition the population in to strata are referred as
stratification variables.
• The variables commonly used for stratification are
– Demographic variables.
– Type of consumers.
– Size of firm
– Type of industry.
• The no. of strata to use is a matter of judgment, but experienced researcher do not
use more than 6 strats

Stratification Of MBA 2nd Semester Students on the Basis of
their Educational Background

Stratified Random Samples
1. Select a suitable frame.
2. Select the stratification variable(s) and the number of strata, H.
3. Divide the entire population into H strata. Based on the classification variable,
each element of the population is assigned to one of the H strata.
4. In each stratum, number the elements from 1 to Nh (the pop. size of stratum h ).
5. Determine the sample size of each stratum, nh, based on
proportionate or disproportionate stratified sampling.
6. Select a simple random sample of size nh

• Suppose a researcher wish to study retail sales of the product
such as wheat in a universe of 10000 grocery stores.
• The researcher might first sub divide universe in to three
strata, based on store size as-
Store Size /Stratum No. of Stores % of Stores
Large Stores 2000 20%
Medium Stores 3000 30%
Small Stores 5000 50%
Total 10000 100

Types of Stratified Random Sampling

• In Proportionate Stratified random sampling, each stratum is
properly represented so the sample drawn from it is
proportionate to the stratum’s share of total population.
• If a proportionate sample of 1000 is taken-
Store Size /Stratum No. of Stores % of Stores
Sample
Size
Large Stores 2000 20% 200
Medium Stores 3000 30% 300
Small Stores 5000 50% 500
Total 10000 100% 1000

A Graphical Illustration of
Stratified Sampling
Fig. 11.4
A B C D E
1 6 11 16 21
2 7 12 17 22
3 8 13 18 23
4 9 14 19 24
5 10 15 20 25
Randomly select a number
from 1 to 5
for each stratum, A to E. The
resulting
sample consists of
population elements
4, 7, 13, 19 and 21. Note, one
element
is selected from each
column.

• “Sampling method in which universe items are chosen in
a group (cluster), rather than individually are called
cluster sampling method.”
• Elements within a cluster should be as heterogeneous as
possible, but clusters themselves should be as
homogeneous as possible.

• The target population is first divided into mutually
exclusive and collectively exhaustive subpopulations,
or clusters.
• Then a random sample of clusters is selected, based
on a probability sampling technique such as SRS.

Types of Cluster Sampling
Cluster Sampling
One-Stage
Sampling
Multistage
Sampling
Two-Stage
Sampling
Simple Cluster
Sampling
Probability
Proportionate
to Size Sampling

• For each selected cluster-
• Either all the elements are included in the sample (one-stage) or
• A sample of elements is drawn probabilistically (two-stage).
• If all the elements in each selected cluster are included in the
sample , the procedure is called ‘one-stage cluster sampling’.
• If sample of elements is drawn probabilistically from each selected
cluster, the procedure is called ‘two stage cluster sampling’

• Simple two stage cluster sampling involves simple
random sample.
• In probability proportionate to size sampling, the
clusters are sampled with probability proportional to
size.

Cluster Sampling (2-Stage)
Fig. 11.4
A B C D E
1 6 11 16 21
2 7 12 17 22
3 8 13 18 23
4 9 14 19 24
5 10 15 20 25
Randomly select 3 clusters,
B, D and E.
Within each cluster,
randomly select one
or two elements. The
resulting sample
consists of population
elements 7, 18, 20, 21, and
23. Note, no elements are
selected from clusters A and
C.

Difference between Stratified and Cluster sampling

Systematic Sampling
or
Quasi random
sampling

• This most widely used form of Cluster sampling.
• “A systematic sample is formed by selecting one unit
at random and then selecting units at evenly spaced
intervals until sample has been formed”.

Systematic Probability Samples
STEP 1. Select a suitable sampling frame.
STEP 2. Each element is assigned a number from 1 to N
(population size=N).
STEP 3. Determine the sampling interval
i=N/n.
n=sample size
If i is a fraction, round to the nearest integer.

STEP 4. Select a random number, r, between 1 and i, as
explained in simple random sampling
STEP 5. The elements with the following numbers will
comprise the systematic random sample:
r, r+i,r+2i,r+3i,r+4i,...,r+(n-1)i.

• EXAMPLE-
– Assume one wish to study dentist’s attitude towards dental
insurance and decide to sample 20 dentists from a list of 100
dentists.
1. Sample interval=100/20=5
2. Suppose we selected a random no. between 1 and 5 i.e 2.
3. 2 will be the first element of sample.
4. now 2+5=7
5. Then 7+5=12, 12+5=17, 17+5=22, 22+5=27 ………… 97.
– These will be other elements of sample of size 20.

• The above example will have only five possible
samples.
SAMPLE NO. IDENTIFICATION OF DENTIST IN SAMPLE
1 1,6,11,16,21………………………………………….96
2 2,7,12,17,22……………………………………………97
3 3,8,13,18,23…………………………………………….98
4 4,9,14,19,24…………………………………………….99
5 5,10,15,20,25…………………………………………100

Systematic Sampling
A B C D E
1 6 11 16 21
2 7 12 17 22
3 8 13 18 23
4 9 14 19 24
5 10 15 20 25
Select a random number
between 1 and 5, say 2.
The resulting sample
consists of population 2,
(2+5=) 7, (2+5x2=) 12,
(2+5x3=)17, and (2+5x4=) 22.
Note, all the elements are
selected from a single row.

Double Sampling
Or
Two-phase sampling
or
Multi-phase
sampling

• “Multi phase sampling involves a design where some
information is collected from the entire sample and additional
information is collected from only a part of sample”.
• The process may be extended to three or more phases.

Example
• Suppose a survey is undertaken to determine the nature
and extent of health facilities available in a city and general
opinion of the people.
– In the first phase, a general questionnaire can be sent out to
ascertain who amongst the respondent had at one time or other
used hospital services.
– In the second phase, a comprehensive questionnaire may be
sent to only these respondents to ascertain what they feel
about the medical facilities in the hospital.

Comparison of Sampling Techniques:
Non probability Sampling
vs.
Probability Sampling

Errors Associated with Sampling

SAMPLE SIZE
DETERMINATION

• Sample size: “Sample size refers to the number of
items to be selected from the universe to
constitute the sample”.
• The size of sample should be neither excessively
large nor too small.

Determinants of Sample Size
• Nature of universe
• No. of classes proposed
• Nature of study
• Type of sampling
• Standard of accuracy and accepted confidence level
• Availability of finance

Sampling

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