Sampling

Sampling
 Concept of sample and sampling
 Sampling process and problems
 Types of samples: Probability and non-
probability sampling
 Determination and sample size
 Sampling and non-sampling errors

Why Sampling is ?
 In any statistical investigation complete
enumeration of the population is rather impractical.
If the population is infinite, complete enumeration is
not possible.
 And, even if the population is finite, 100%
enumeration is not taken because of administrative
and financial implications, time factor, resource
available etc. So there is a need to take the help of
sampling.
 The foremost purpose of sampling is to gather
maximum information about the population under
consideration at minimum cost, time and human

Why and in what situation sampling is
inevitable ?
 When population is infinite
 When the items or units destroyed under
investigation
 When the results are required in a short time
 When the resources for a survey are limited
particularly money and trained persons
 When area of survey is wide

Population:
 Population is a group of items, units or subjects which is under
reference of study. Population may consist of finite and infinite
number of units. Population can be classified into four
categories.
 Finite Population: If the population consists of fixed and limited
number of items or units, it is known as finite population.
Example, the workers in a factory, students in a college etc.
 Infinite Population: If the population consists of an infinite
number of items or units, it is called infinite population.
Example, the population of stars in the sky, water in a pond etc.
 Real population: Population consisting of the items which are
all present physically is termed as real population. Example, no
of court case in a day, no of snake bite patients admitted in the
hospital etc.
 Hypothetical Population: Population consisting of the results
of repeated trials is named as hypothetical population. The
tossing of coin, rolling of a dice again and again are some

Sample
 Sample is a part or fraction of a population selected in some
basis. It consists of a few representative items of a population.
 Or, it is a finite subset of statistical individual in a population
and the number of individuals in sample is called the sample
size (n) (if B is a sub set of A fig..) if A
={1,2,3,4,5,6,………….100} and B
={3,7,9,10,45,51,55,72,91,96} Here, BcA then, A is pop. And B
is sample
 In principle a sample should be such that it is a true
representative of the population or universe
 Different sampling techniques are used to select sample units
according to the nature of the population (Homogeneous or
heterogeneous, geographical variation etc.)
Populatio
n
Sample

Related terminologies use in sampling
 Sampling frame: It is a list or a map of population identifying
each sampling unit by a number. It is essential for adopting
any sampling procedure.
 Parameter and statistics : The values that described the
characteristics of the population are called Parameters and the
values that described the characteristics of samples are called
Statistics.
For examples:
Population Size = (N)
Population Mean = ( ) Population
Parameters
Population Variance =
And,
Sample Size =
Sample Mean = Sample Statistics

 2

 n
 x
 2
s

Sampling Process
 It is the procedures or steps of selecting final sample units
.These steps are in sequential order which are given below in
the chart (Seven steps sampling design)
Define the population
Specify the sampling frame
Specify sampling units
Selection of sampling method
Determine of the sample size
Specify the sampling plan
Select the sample

Type of
sampling:
Sampling Method
Non-Probability
Sampling
Judgment Sampling
Quota Sampling
Convenience
Sampling
Snowball Sampling
Probability
Sampling
Simple random
sampling
Stratified Sampling
Systematic Sampling
Cluster Sampling

Non-Probability and probability Sampling
 In this sampling technique, all items or units in the
population do not have equal chance of being
selected. The sample selected in this method is
mostly based on the investigators own views or
ideas.
 In probability sampling each and every element in
the population has equal chance of being selected.
This sampling technique attained through some
mathematical operation of randomization.

Judgment or purposive sampling
 In this method of sampling the choice of sample
items depends exclusively on the judgment of the
investigators. That is, the investigators exercises
their judgment in the choice and includes those
items in the sample.
 For example, if sample of 25 students is to be
selected from a class of 90 students for analyzing
the smoking habits of tobacco, the investigators
would select 25 students who, in his opinion, are
representative of the class.

Quota Sampling
 Quota sampling is a type of judgment sampling and
is perhaps the most commonly used sampling
technique in non-probability category. In a quota
sample, quotas are set up according to the some
specified characteristics.
 For example, in radio listening survey, the
interviewers may be told to interview 500 people
living in a certain areas and that out of every 100
parsons interviewed 60 are housewife, 25 farmers
and 15 children under the age of 18.With in these
quotas the interviewer is free to select the people to
be interviewed.

Convenience Sampling:
 Convenience sampling is obtained by selecting
'convenient' population units.
 If a person is to submit a project report on marketing
management in textile industry and he/she takes a
textile industry close to his/her house or area and
interviews some people over there and submit the
report. Then, it is known that he/she is following the
convenience sampling method.

Snowball Sampling
 Snowball ball sampling is known as network or
chain referral sampling.
 In this sampling technique, first one or two persons
in the population are contacted and ask them to
identify further persons.
 Accordingly, new person are identified until there are
as large as manageable sample. The selection
process is stopped when either no new people are
identified or start to repeat the same people again
and again.

Simple Random Sampling:
 Simple random sampling refers to that
sampling technique in which each and
every unit of the population has equal
chances of being selected in the sample.
 Personal bias of the investigator does not
influence the selection.
 For examples: blood tests in laboratory,
tottery method, selection of sample units
from random numbers chart/table are some
examples of SRS.

Stratified Random Sampling:
(restricted)
 In this type of sampling method first the whole
population is divided into relatively homogenous
groups under certain criterion. These groups are
terms as strata.
 Then the sample is drawn randomly from each
stratum independently. The estimate is calculated
from the data obtained from all the stratum.
 Proper classification of the population into various
strata and a suitable sample size from each
stratum are the two major points need to be
considered in stratified random sampling.

Systematic Sampling:
 In systematic sampling, sample units are selected from a
population at a uniform interval that could measure in time,
order or space. It is formed by selecting one unit at random
and then selecting additional units at an equal interval of its
measurement.
 i.e. [(j), (j+k), (j+2k), (j+3k),…………,{j+(n-1)k}], [1,2,3,4,
5,6,7,8,9,10,11,12,13,14,15,………………..1000]
 In systematic sampling, N = nK, and K= N/n, where K is a
sampling interval, n is sample size and N is the population
size. Such a selection procedure is known as linear
systematic sampling. This sampling technique need a well
defined sampling frame.
 This procedure fails if the population size N is not a multiple
of n. i.e ( N≠ nK) and need to introduce circular systematic
sampling which takes as rounded to the nearest integer.

Cluster Sampling:
 In many situations, the sampling frame for elementary units of
the population is not available; moreover it is not easy to
prepare it.
 However, the information is available for groups of elements.
In such case, cluster sampling can be applied to study the
population characteristics.
 In this sampling tchnique the population is divided into groups
so called clusters. The cluster include all types of
characteristics in the population. Therefore, the characteristics
within the cluster are heterogeneous and between the cluster
are homogeneous. The size of cluster may or may not be
equal.
 The sampling efficiency of cluster is likely to decrease with the
increase in cluster size. This sampling is extensively used, if
the population characteristics are heterogeneous and
geographically varied.
 Each and every elementary unit of the selected cluster are

Contd…
 For instance, the list of college may be available
but not the students studying over there,
 The list of individual farms may not be available
but the list of villagers is generally available.
 Hence, in these situation college or villages are
known as clusters and selection has to be made of
college or villages as of samples. And, each and
every element of the selected sample will be
studied to estimate the population characteristics.

Determination of sample size
 Different opinion have been expressed by experts for the selection
of sample size (i.e 5%,10% or 25% of the universe). There are no
hard and fast rule can be laid down. However, according to the law
of large number, the largest the sample size, the better the
estimation, or the larger the sample, the closer the ‘true’ value of
the population. It may also be pointed out that the sample size
should neither be too large nor too small. It should be 'optimum'
(efficiency, representativeness, reliability and flexibility).
The following factor should be considered while deciding the
sample size:
 The size of the universe, the resource available
 Desired degree of accuracy or precision
 Homogeneity or Heterogeneity of the universe, Nature of study
 Method of sampling adopted and, the Nature of respondents

Formula for the determination of the sample size,
Here,
where,
n = Sample size
z = Value at a specified level of confidence or
desired degree of precision.
= Standard deviation of the population.
d = Different between population mean and
sample mean. Or desired error in estimation of
pop. Mean
Example: 1) Determine the sample size if = 6, Population mean is
25, sample mean is 23 and the desired degree of precision is 99% (
z at 1% level of significance is 2.58)
2) Let us suppose the value of population mean is 45 and s.d = 8, N =
460 and the desired error in the estimation of this value is 10%, and
the desired degree of precision is 95% ( z at 5% level of significance
is 1.96). Determine the size of ‘n’ .
2







d
z
n




If population size is given then, n can
be determine by,
Example: A survey is to be conducted to investigate the characteristics
of a factor in a population of size 500, having variance 85.
Determine the sample required for error of 2 in estimation of
population mean.
Level of
significanc
e
Z œ/2 Variance
(sigma sq.)
error n0 n
1% 2.58 85 2 141 110
5% 1.96 85 2 82 70
10% 1.64 85 2 58 52

Sampling and Non-sampling
Errors
 The errors involved in the collection, processing and analysis of data may
be broadly classified under two categories such as
 i) Sampling errors ii) Non- sampling errors
 Sampling errors: Even if utmost care has been made in selecting a
sample, the result derive from a sample study may not be exactly equal to
the true value in the population.
 The reason is that the estimate is based on a part and not on the whole.
Hence sampling rise certain errors known as sampling error or sampling
fluctuations. This error would not present in a complete enumeration.
 Sampling error are primarily exist due to the following reasons:
1. Faulty selection of sample (e.g bias or defective sampling technique –
Judgment or purposive, quota, convenience sampling technique)
2. Substitution (if difficulties arise in enumerating, the investigator usually
substitute a convenient number of population)
3. Faulty demarcation of sampling unit ( Prevailing in area sampling)
4. Constant error due to improper choice of the statistics for estimating
the population parameter, that is,
Where , the given variance are bias and unbiased estimate of population
variance.


Non-sampling errors
 Non sampling errors mainly arise at the stage of observation and
processing of the data and thus present in both the complete
and enumeration survey and the sample survey. It can occur at
ever stage of the planning or execution of census or sample
survey.
Non-sampling error may exist due to the following reasons:
 Faulty planning or definition (definition of employment, literacy,
labour etc.)
 Response errors ( response error may be accidental or prestige
bias)
 Self-interest
 Bias due to interviewer
 Non-response bias
 Errors in coverage (inclusion or exclusion of certain items which
are not to be included and not to be excluded )
 Compiling Errors (Cleaning, coding, data entry )
 Publication errors (errors committed in presentation and printing)

Sampling

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Sampling