Chapter Sampling.pptx

SAMPLING
Dr. NISHIKANT C. WARBHUWAN
Ph. D. MBA (HRM) BE (IT)
School of Management Sciences,
S.R.T.M. University, Sub centre, Latur, India.
Email: nishikant.warbhuwan@srtmun.ac.in
nishikant.warbhuwan@srtmun.ac.in

Sr.
No.
Name of the
District in
Marathwada
Region
Block Selected
based on lowest rate
of Literacy
Total
Number of
Villages in
the District
Appropriate
sample from
the Block
1 Aurangabad Soygaon 1372 140
2 Beed Wadvani 1376 140
3 Jalna Ghansawangi 971 100
4 Parbhani Sonpeth 851 90
5 Hingoli Aundha Nagnath 714 70
6 Nanded Biloli 1620 160
7 Latur Jalkot 955 100
8 Osmanabad Paranda 741 70
Total 8600 870

Population is the target group to be studied
A part of population is a sample
The Factors of Making Decision Sampling or
Census
1. The size of the population
2. Amount of funds budgeted for the study
3. Facilities
4. Time

Sampling
The process of drawing a sample from a larger
population is called sampling.
A well selected sampling may reflect fairly
accurately the characteristics of the population.
The Factors of Making Decision Sampling or
Census
1. The size of the population
2. Amount of funds budgeted for the study
3. Facilities
4. Time nishikant.warbhuwan@srtmun.ac.in

Aims of Sampling
To make an inference about an unknown parameter
from a measurable sample statistics.
Test a statistical hypothesis relating to population

Sr. No. State/Union Seats
Sr.
No. State/Union Seats
1 Andhra Pradesh 25 19 Nagaland 1
2 Arunachal Pradesh 2 20 Odisha 21
3 Assam 14 21 Punjab 13
4 Bihar 40 22 Rajasthan 25
5 Chhattisgarh 11 23 Sikkim 1
6 Goa 2 24 Tamil Nadu 39
7 Gujarat 26 25 Telangana 17
8 Haryana 10 26 Tripura 2
9 Himachal Pradesh 4 27 Uttar Pradesh 80
10 Jammu and Kashmir 6 28 Uttarakhand 5
11 Jharkhand 14 29 West Bengal 42
12 Karnataka 28 30 Andaman and Nicobar 1
13 Kerala 20 31 Chandigarh 1
14 Madhya Pradesh 29 32 Dadra and Nagar Haveli 1
15 Maharashtra 48 33 Daman and Diu 1
16 Manipur 2 34 Lakshadweep 1
17 Meghalaya 2 35 NCT of Delhi 7
18 Mizoram 1 36 Puducherry 1

No. Constituency No. Constituency
1 Nandurbar 25 Thane
2 Dhule 26 Mumbai North
3 Jalgaon 27 Mumbai North West
4 Raver 28 Mumbai North East
5 Buldhana 29 Mumbai North Central
6 Akola 30 Mumbai South Central
7 Amravati 31 Mumbai South
8 Wardha 32 Raigad
9 Ramtek 33 Maval
10 Nagpur 34 Pune
11 Bhandara–Gondiya 35 Baramati
12 Gadchiroli–Chimur 36 Shirur
13 Chandrapur 37 Ahmednagar
14 Yavatmal–Washim 38 Shirdi
15 Hingoli 39 Beed
16 Nanded 40 Osmanabad
17 Parbhani 41 Latur
18 Jalna 42 Solapur
19 Aurangabad 43 Madha
20 Dindori 44 Sangli
21 Nashik 45 Satara
22 Palghar 46 Ratnagiri–Sindhudurg
23 Bhiwandi 47 Kolhapur
24 Kalyan 48 Hatkanangle

88 Loha Nanded 41 Latur
234 Latur Rural Latur 41 Latur
235 Latur City Latur 41 Latur
236 Ahmadpur Latur 41 Latur
237 Udgir Latur 41 Latur
238 Nilanga Latur 41 Latur
239 Ausa Latur 40 Osmanabad
Maharashtra Constituency= 288

Characteristics of Good Sample:
1. Representativeness
2. Accuracy-bias is absent
3. Precision
4. Size
Advantages of Sampling:
1. Reduce time and cost- Poverty Survey, Marketing Survey
2. Save Labour
3. Better Quality- better interviewing, investigation, supervision, processing
4. Quicker Results
5. Only Procedure Possible if the population is infinite- Consumer
behavior Survey

आपल्याकडे कोरोना संसर्ाा च्या बाबतीत वेर् वेर्ळे ननष्कर्ा काढले जात आहेत. उदाहरणार्ा आपण अजून
स्टेज 2 नक
ं वा स्टेज 3 मध्ये नाहीत? आपल्याकडे अजून कम्युनीटी संसर्ा सुरू झाला आहे नक
ं वा नाही? की
सध्या आपण फक्त क्लस्टर संसर्ाातून जातोय? आपले तापमान जास्त असल्यामुळे , लोकांची रोर् प्रनतकार
शक्ती उत्तम असल्याने नक
ं वा BCG लस घेतल्याने आपल्याकडे रुग्ांची संख्या कमी आहे वर्ैरे वर्ैरे...
अर्दी ररसचा मेर्डॉलाॅजी च्या शास्त्रीय भार्ेत सांर्ायचे तर असले क
ु ठलेही अनुमान आत्ता लर्ेच काढणे
र्ोडे धाडसाचे होईल. कारण आपण जे अनुमान काढतोय, generalizations करतोय त्यासाठी जो डेटा
वापरतोय नक
ं वा जो आपला Sample आहे तो पुरेसा आहे का...? नवनवध अनधक
ृ त रीपोटास् नुसार हेच समोर
येत आहे की जेवढ्या प्रमाणात टेस्ट्स व्हायला पानहजेत तेवढ्या भारतात होत नाहीत आनण अजून जास्त
टेस्ट्स झाल्या तरच खरे नचत्र स्पष्ट होईल... म्हणजेच आपल्या क
े लेल्या टेस्ट्स म्हणजेच सम्पल ह्या पूणा
पॉप्युलेशन च्या प्रमाणात अत्यल्प आहेत आनण या नठकाणी the sample is not representing the total
population adequately hence it can not exactly describe or generalize the total population आनण
म्हणुन inadequate data वापरून आपन inferences काढ
ू शकत नाही..
या आठवड्यात सरकारने जास्तीत जास्त टेस्ट्स सुरू क
े ल्या आहेत तसेच येणार्या काळात Rapid
Antibody Tests सुरु होणार आहेत.. तेव्हा आपल्याकडे sufficient डेटा येईल तो कदानचत पूणा पॉप्युलेशन
चे प्रनतनननधत्व करू शक
े ल... आनण मर्च आपण क
ु ठल्यातरी ननष्कर्ाापयंत पोचू शकतो.
Lastly.... A sample should represent the population as a whole and not reflect any bias toward a
specific attribute.
डॉ नननशकांत वारभुवन 7 April 2020

Sampling Methods/ Designs/ Types
Probability Sampling Non-Probability Sampling
A. Simple Designs
i) Simple Random Sampling
ii) Stratified Random Sampling
iii) Systematic random Sampling
i) Convenience or Accidental
Sampling
ii) Purposive or Judgment
Sampling
B. Complex Design
i) Cluster and Area Sampling
ii) Multi-stage and sub-Sampling
iii) Probability proportional to size Sampling
iv) Double Sampling
v) Replicated Sampling
i) Quota Sampling
ii) Snow-ball Sampling

1. Probability or Random Sampling
 It is based on the theory of probability.
It provides a known non-zero chance of selection for each population
element.
Every population has a chance of being selected
Such chance is known probability
It yields a representative sample and hence the findings can be
generalized
Used when generalization is the objective of the study
Used when greater degree of accuracy of estimation of population
parameters is required

Non-Probability or Non-Random Sampling
Non-Probability or Non-Random Sampling is not based on theory
of probability.
This sampling does not provide a chance of selection to each
population element.
The only merits of this type of sampling are simplicity, convenience
and low cost.
It does not ensure a selection chance to each population unit
The selection probability is unknown
It may not be a representative one
It suffers from sampling bias which will distort the results

i) Simple random Sampling-
 This sample technique gives each element an equal
and independent chance of being selected
 It does not require a prior knowledge of the true
composition of the population.
 It is suitable only for small homogeneous population,
where a complete list of all elements is available or
can be prepared.
 It is not suitable for large heterogeneous population,
as it may not represent the total population

Randomization can be done through

 The population is sub-divided into homogeneous groups or strata
 From each stratum, random sample is drawn
 It is necessary for
 Increasing a sample’s statistical efficiency
 Provide adequate data for analyzing sub population
 Apply different methods to different strata
 It is necessary when researcher is interested to study characteristics
of sub groups
 It enhances the representativeness of the sample by giving proper
representation to all sub groups in the population.

 It gives higher statistical efficiency than simple random sampling
 It is appropriate for a large heterogeneous population

Strata Sample Size
HRM 30*0.4= 12
Finance 30*0.2=6
Marketing 30*0.3=9
Disaster 30*0.1=3
Sample Size 30
Specialization No. of Students Proportion of each
stream
HRM 40 0.4
Finance 20 0.2
Marketing 30 0.3
Disaster 10 0.1
Total 100 1

iii) Systematic Sampling/ Fixed Interval Method
 It consists of taking every Kth item in the population.


iii) Systematic Sampling/ Fixed Interval Method
 It consists of taking every Kth item in the population.
 An interval between sample units is fixed hence it is also called as
fixed interval method
 Actually this method posses characteristics of probability and non
probability traits
 Examples:
 Houses in a street
 Customers of Bank
 Students in the class
 Assembly line output in factory

iv) Cluster Sampling
 It is random selection of sampling units consisting of population elements
 Each such population unit is a cluster of a population elements
 Then from each selected sampling unit, a sample is drawn by random
method or stratified method
 If you have a population dispersed over a wide
 In cluster sampling the sample units contain groups of element (cluster)
instead of individual members or items in the population.
 Rather than listing all elementary school children in a given city and
randomly selecting 15 % of these students for the sample, a researcher lists
all of the elementary schools in the city, selects at random 15 % of these
clusters of units, and uses all of the children in the selected schools as

iv) Cluster Sampling Vs Stratified Sampling

v) Multi-Stage Sampling
 can be a complex form of
cluster sampling. Pardo
Fuccboi refers it to
sampling plans where the
sampling is carried out in
stages using smaller and
smaller sampling units at
each stage.
 Sampling is carried out in two or more stages

Non- Probability Sampling
 i) Convenience Sampling- Selecting whatever sampling units are
conveniently available.

ii) Convenience Sampling-
 Though convenience sampling has no status, it may be used for
simple purpose such as testing ideas or gaining ideas or rough
impression about a subject of interest.
 When a population cannot be defined or a list of population is
not available, there is no other alternative than to use convenient
sampling.
 Highly biased
 Least reliable method
 Findings can not be generalized.

ii) Purposive or Judgment Sampling
 This involves selection of cases which we judge as the most
appropriate ones for the given study.
 It is based on the judgment of the researcher
 Depends on subjective judgment
 Suitable when specific relevance of the sampling units to the study
is important than overall representativeness.
 It guarantee inclusion of relevant elements in the sample
 It does not guarantee the representativeness of the sample

ii) Purposive or Judgment Sampling

• According to the Prime Minister’s Office, the districts chosen for the scheme are those where more than
25,000 migrant workers have returned in the last few months. These districts are estimated to cover about
66 per cent of such migrant workers.
• Numbers obtained by The Indian Express from district authorities show that about 10.8 lakh migrants
have returned to the eight districts in the region with each seeing anywhere between 60,000 to 2.5 lakh
returnees from cities in the last three months.
• said Hingoli Collector Ruchesh Jaywanshi.
• Collector of neighbouring Parbhani, Deepak Mugalikar, said
• Harkal, who hails from Gunj Khurd village in Parbhani district, said
• Pankaj Gajmal, a 30-year-old from Pathri town in the same district, had returned in April from Mumbai
• Experts believe that schemes like GKRA may help migrants survive the pandemic period by providing
them minimum income. But GKRA, like MGNREGA, can’t keep the population of migrant workers back
home, who leave their homes looking for better wages.
• these schemes may not help them stay back in the native districts,” said Nishikant Warbhuvan, assistant
professor at the School of Management Sciences, Swami Ramandand Teerth Marathwada University
(SRTMU), sub-centre, Latur.

iii) Quota Sampling
• The population is first segmented into mutually exclusive sub-groups,
just as in stratified sampling.
• Then judgment is used to select the subjects or units from each
segment based on a specified proportion.
• It is a method of stratified sampling in which selection within strata is
no-random.
• Used in Marketing Surveys, Opinion Polls and leadership Surveys
which do not aim at precision but to get quickly some crude results

iv) Snow-ball Sampling
 In snowball sampling, you start by identifying a few respondents
that match the criteria for inclusion in your study, and then ask them
to recommend others they know who also meet your selection
criteria.
 Useful in studying social groups
 Useful for smaller populations for which no frames are readily
available.
 Dependent on the subjective choice of the original selected
respondents

Sample Size
 Misconception about required size of a sample
 Sample should not be less than 10% of the population. But its not relevant to large
populations
 When a probability sample reaches a certain size, such as 1000 its efficiency for
estimating population parameters is not much different than probability sample of
10,000 or even 1,00,000
 Larger the sample does not mean greater the accuracy.
 Large sample size does not guarantee the accuracy of the results.
 The sample size can be statistically estimated by deciding the required
level of accuracy.
 Making a sample too big wastes resources, making it too small diminishes
the value of findings – a dilemma resolved only with the effective use of
sampling theory.

Sample Size
• Several qualitative factors should also be taken into
consideration when determining the sample size.
• These include the importance of the decision, the nature of
the research, the number of variables, the nature of the
analysis, sample sizes used in similar studies, incidence
rates (the occurrence of behaviour or characteristics in a
population), completion rates and resource constraints.
• The statistically determined sample size is the net or final
sample size.

Sample Size
 The concept of statistical inference relates the sample characteristics to
population characteristics..
 Our real interest is to draw conclusions about the population.
 We have to draw conclusions about the population based upon the
sample results.
 From sample we are computing statistic, which is a characteristic of
sample and this becomes an estimate of the similar characteristics of
the population.
 An important task in research is to calculate statistics, such as the
sample mean and sample proportion, and use them to estimate the
corresponding true population values. This process of generalizing the
sample results to a target population is referred to as statistical
inference.

Sample Size
• Population Size — How many total people fit your demographic?
• Confidence Interval — No sample will be perfect, so you need to
decide how much error to allow. The confidence interval determines
how much higher or lower than the population mean you are willing
to let your sample mean fall.
• Confidence Level — How confident do you want to be that the actual
mean falls within your confidence interval? The most common
confidence intervals are 90% confident, 95% confident, and 99%
confident.
• Population Mean — 4,9,5,6 is= 6
• Sample Mean- For 4 &6 is=5 For 5 & 6 is= 5.5

Sample size determination
Normal distribution: A basis for classical statistical inference that
is bell shaped and symmetrical in appearance. Its measures of
central tendency are all identical.

Sample size determination : Means
• Steps:
• 1 Specify the level of precision.
• 2 Specify the level of confidence.
• 3 Determine the z value associated with the confidence level.
• 4 Determine the standard deviation of the population.
• 5 Determine the sample size using the formula for the standard
error of the mean

• Steps:
• 1 Specify the level of precision.
• 2 Specify the level of confidence.
• 3 Determine the z value associated with the confidence level.
• 4 Determine the standard deviation of the population.
• 5 Determine the sample size using the formula for the standard
error of the mean

Sample Size Estimating for Multiple Parameters

Sampling Distribution
 Objective of statistical analysis is to know the true value or
actual values of different parameters of the population.
 The ideal situation would be to take the entire population into
consideration in determining true value but it is not possible.
 In general, a single random sample is taken from a given
population.
 Sample mean x’ is considered to represent population mean µ
 This sample mean may or may not represent population mean
 Example: Excel Sheet Class Test Marks (Closeness to population mean)

Sampling Distribution
Child (X) Age
X1 2
X2 4
X3 6
X4 8
X5 10
Population
Mean (µ)
6
N= 5
Selected
Samples (2)
Values Sample Mean
(X’)
X1, X2 2,4 3
X1, X3 2,6 4
X1, X4 2,8 5
X1, X5 2,10 6
X2, X3 4, 6 5
X2, X4 4, 8 6
X2, X5 4, 10 7
X3, X4 6,8 7
X3, X5 6, 10 8
X4, X5 8,10 9
All Possible simple random samples of size 2
POPULATION

Sources of error Or
Sampling And Non-Sampling Error
The research results may differ from the ‘true
values’ of the parameters under study. Such differences
are known as errors and biases.
Classification of Error
1. Sampling Errors
2. Sampling Biases
3. Non-Sampling Errors
4. Non-Sampling Biases

https://www.wisdomjobs.com/e-university/research-methodology-tutorial-
355/some-fundamental-definitions-
11511.html#:~:text=Universe%2FPopulation%3A%20From%20a%20statistica
l,about%20which%20information%20is%20desired.

Sampling Fundamentals in Research Methodology
Before we talk sampling fundamentals and uses of sampling, it seems appropriate that we should be familiar with some fundamental definitions concerning sampling concepts and principles.
1.Universe/Population: From a statistical point of view, the term ‘Universe’refers to the total of the items or units in any field of inquiry, whereas the term ‘population’ refers to the
total of items about which information is desired. The attributes that are the object of study are referred to as characteristics and the units possessing them are called as
elementary units. The aggregate of such units is generally described as population. Thus, all units in any field of inquiry constitute universe and all elementary units (on the basis
of one characteristic or more) constitute population. Quit often, we do not find any difference between population and universe, and as such the two terms are taken as
interchangeable. However, a researcher must necessarily define these terms precisely.
The population or universe can be finite or infinite. The population is said to be finite if it consists of a fixed number of elements so that it is possible to enumerate it in its totality.
For instance, the population of a city, the number of workers in a factory are examples of finite populations. The symbol ‘N’ is generally used to indicate how many elements (or
items) are there in case of a finite population. An infinite population is that population in which it is theoretically impossible to observe all the elements. Thus, in an infinite
population the number of items is infinite i.e., we cannot have any idea about the total number of items. The number of stars in a sky, possible rolls of a pair of dice are examples
of infinite population. One should remember that no truly infinite population of physical objects does actually exist in spite of the fact that many such populations appear to be very
large. From a practical consideration, we then use the term infinite population for a population that cannot be enumerated in a reasonable period of time. This way we use the
theoretical concept of infinite population as an approximation of a very large finite population.
2.Sampling frame: The elementary units or the group or cluster of such units may form the basis of sampling process in which case they are called as sampling units. A list
containing all such sampling units is known as sampling frame. Thus sampling frame consists of a list of items from which the sample is to be drawn. If the population is finite and
the time frame is in the present or past, then it is possibe for the frame to be identical with the population. In most cases they are not identical because it is often impossible to
draw a sample directly from population. As such this frame is either constructed by a researcher for the purpose of his study or may consist of some existing list of the population.
For instance, one can use telephone directory as a frame for conducting opinion survey in a city. Whatever the frame may be, it should be a good representative of the
population.
3.Sampling design: A sample design is a definite plan for obtaining a sample from the sampling frame. It refers to the technique or the procedure the researcher would adopt in
selecting some sampling units from which inferences about the population is drawn. Sampling design is determined before any data are collected. Various sampling designs have
already been explained earlier in the book.
4.Statisitc(s) and parameter(s): A statistic is a characteristic of a sample, whereas a parameter is a characteristic of a population. Thus, when we work out certain measures
such as mean, median, mode or the like ones from samples, then they are called statistic(s) for they describe the characteristics of a sample. But when such measures describe
the characteristics of a population, they are known as parameter(s). For instance, the population mean bmg is a parameter,whereas the sample mean ( X ) is a statistic. To obtain
the estimate of a parameter from a statistic constitutes the prime objective of sampling analysis.
5.Sampling error: Sample surveys do imply the study of a small portion of the population and as such there would naturally be a certain amount of inaccuracy in the information
collected. This inaccuracy may be termed as sampling error or error variance. In other words, sampling errors are those errors which arise on account of sampling and they
generally happen to be random variations (in case of random sampling) in the sample estimates around the true population values. The meaning of sampling error can be easily
understood from the following diagram:

5. Sampling error = Frame error + Chance error + Response error(If we add measurement
error or the non-sampling error to sampling error, we get total error).
Sampling errors occur randomly and are equally likely to be in either direction. The
magnitude of the sampling error depends upon the nature of the universe; the more
homogeneous the universe, the smaller the sampling error. Sampling error is inversely
related to the size of the sample i.e., sampling error decreases as the sample size
increases and vice-versa. A measure of the random sampling error can be calculated for a
given sample design and size and this measure is often called the precision of the
sampling plan. Sampling error is usually worked out as the product of the critical value at a
certain level of significance and the standard error.
As opposed to sampling errors, we may have non-sampling errors which may creep in
during the process of collecting actual information and such errors occur in all surveys
whether census or sample. We have no way to measure non-sampling errors.
6. Precision: Precision is the range within which the population average (or other parameter)
will lie in accordance with the reliability specified in the confidence level as a percentage of
the estimate ± or as a numerical quantity. For instance, if the estimate is Rs 4000 and the
precision desired is ± 4%, then the true value will be no less than Rs 3840 and no more
than Rs 4160. This is the range (Rs 3840 to Rs 4160) within which the true answer should
lie. But if we desire that the estimate should not deviate from the actual value by more than
Rs 200 in either direction, in that case the range would be Rs 3800 to Rs 4200.

expected percentage of times that the actual value will fall within the stated precision
limits. Thus, if we take a confidence level of 95%, then we mean that there are 95
chances in 100 (or .95 in 1) that the sample results represent the true condition of the
population within a specified precision range against 5 chances in 100 (or .05 in 1) that it
does not. Precision is the range within which the answer may vary and still be
acceptable; confidence level indicates the likelihood that the answer will fall within that
range, and the significance level indicates the likelihood that the answer will fall outside
that range. We can always remember that if the confidence level is 95%, then the
significance level will be (100 – 95) i.e., 5%; if the confidence level is 99%, the
significance level is (100 – 99) i.e., 1%, and so on. We should also remember that the
area of normal curve within precision limits for the specified confidence level constitute
the acceptance region and the area of the curve outside these limits in either direction
constitutes the rejection regions.*
8.Sampling distribution: We are often concerned with sampling distribution in sampling
analysis. If we take certain number of samples and for each sample compute various
statistical measures such as mean, standard deviation, etc., then we can find that each
sample may give its own value for the statistic under consideration. All such values of a
particular statistic, say mean, together with their relative frequencies will constitute the
sampling distribution of the particular statistic, say mean. Accordingly, we can have
sampling distribution of mean, or the sampling distribution of standard deviation or the
sampling distribution of any other statistical measure. It may be noted that each item in a
sampling distribution is a particular statistic of a sample. The sampling distribution tends
quite closer to the normal distribution if the number of samples is large. The significance
of sampling distribution follows from the fact that the mean of a sampling distribution is
the same as the mean of the universe. Thus, the mean of the sampling distribution can

1. Krishnaswami O.R. and Rangnathan M (2008) Methodology of research in social sciences. Second revised
edition, Himalaya Publishing House, Mumbai
2. Chawla Deepak, Condhi Neen. (2014). Research Methodology Concepts and Cases. Vikas Publication, New
Delhi
3.Malhotra Naresh and Dash Satyabhushan (2009) Marketing Research An Applied Orientation, Fifth Edition,
Pearson Prentice Hall, New Delhi

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