Sampling involves selecting a subset of a population to make inferences about the whole population. Common sampling techniques include probability sampling, where every unit has a known chance of selection, and non-probability sampling, where the probability of selection cannot be determined. Some specific sampling methods are systematic sampling, stratified sampling, cluster sampling, simple random sampling, convenience sampling, judgement sampling, snowball sampling, and quota sampling. Sampling error, the difference between the sample and the true population, can be reduced by using a large, randomly selected sample.

1. Prepared by:-
M.S.SaHiR
A.R.Nadaf
Yaseen K.
Saleem N.
Shaheen S.
Shahin M.

2. Sampling Concept:-
Though sampling is not new, the sampling theory has been developed
recently. People knew or not but they have been using the sampling
technique in their day to day life.
1. For example a house wife tests a small quantity of rice to see
whether it has been well-cooked and gives the generalized result
about the whole rice boiling in the vessel. The result arrived at is
most of the times 100% correct.
2. In another example, when a doctor wants to examine the blood for
any deficiency, takes only a few drops of blood of the patient and
examines. The result arrived at is most of the times correct and
represent the whole amount of blood available in the body of the
patient. In all these cases, by inspecting a few, they simply believe
that the samples give a correct idea about the population. Most of
our decision are based on the examination of a few items only i.e.
Sample studies.

3. Concept:-
Sampling is that part of statistical practice concerned
with the selection of a subset of individual observations
within a population of individuals intended to yield some
knowledge about the population of concern, especially
for the purposes of making predictions based on
statistical inference.

4. Sample Survey:-
A sample design is a definite plan for obtaining a sample from a
given population (Kothari, 1988). Sample constitutes a certain
portion of the population or universe. Sampling design refers to the
technique or the procedure the researcher adopts for selecting items
for the sample from the population or universe. A sample design
helps to decide the number of items to be included in the sample,
i.e., the size of the sample. The sample design should be
determined prior to data collection. There are different kinds of
sample designs which a researcher can choose. Some of them are
relatively more precise and easier to adopt than the others. A
researcher should prepare or select a sample design, which must be
reliable and suitable for the research study proposed to be
undertaken.

6. Types of Sampling:-
1. Probability sampling -
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. The combination of these traits
makes it possible to produce unbiased estimates of
population totals, by weighting sampled units according to
their probability of selection.

7. 2. Non probability sampling-
Non probability sampling is any sampling method
where some elements of the population have no definite
chance of selection, or where the probability of selection
can't be accurately determined. Probability sampling
may be of the following types:

8. Systematic sampling
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').

9. Stratified sampling
Where the population embraces a number of distinct
categories, the frame can be organized by these categories
into separate "strata." Each stratum is then sampled as an
independent sub-population, out of which individual
elements can be randomly selected. Dividing the
population into distinct, independent strata can enable
researchers to draw inferences about specific subgroups
that may be lost in a more generalized random sample.

10. Cluster sampling
It is an example of 'two-stage sampling' or 'multistage
sampling': in the first stage a sample of areas is chosen; in
the second stage a sample of respondents within those areas
is selected. When the total area of research interest is large,
a convenient way in which a sample can be selected is to
divide the area into a number of smaller non-overlapping
areas and then randomly selecting a number of such smaller
areas. In the process, the ultimate sample would consist of
all the units in these small areas or clusters. Thus in cluster
sampling, the total population is sub-divided into numerous
relatively smaller subdivisions, which in themselves
constitute clusters of still smaller units. And then, some of
such clusters are randomly chosen for inclusion in the
overall sample.

11. Simple random sampling:-
In a simple random sample ('SRS') of a given size,
all such subsets of the frame are given an equal
probability. Each element of the frame thus has an equal
probability of selection: the frame is not subdivided or
partitioned. This minimizes bias and simplifies analysis of
results.

12. Convenience sampling
(sometimes known as grab or opportunity sampling) is a type of
non probability sampling which involves the sample being drawn
from that part of the population which is close to hand. That is, a
sample population selected because it is readily available and
convenient. It may be through meeting the person or including a
person in the sample when one meets them or chosen by finding them
through technological means such as the internet or through phone.
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 such 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.

13. Judgement Sampling
This is a form of convenience sampling otherwise called as
purposive sampling because the sample elements are chosen
since it is expected that they can serve the research purpose.
The sample elements are chosen based on the judgement
that prevails in the researcher‟s mind about the prospective
individual. The researcher may use his wisdom to conclude
that a particular individual may be a representative of the
population in which one is interested.The distinguishing
feature of judgment sampling is that the population elements
are purposively selected. Again, the selection is not based on
that they are representative, but rather because they can offer
the contributions sought.

14. In judgement sampling, the researcher may be well
aware of the characteristics of the prospective
respondents, in order that, he includes the
individual in the sample. It may be possible that the
researcher has ideas and insights about the
respondent‟s requisite experience and knowledge to
offer some perspective on the research question.

15. Snowball Sampling
This is another popular non-probability technique widely used,
especially in academic research. In this technique, 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 information provided by the selected group members.
The group members may provide information based on their
understanding about the qualification of the other prospective
respondents. This method involves probability and non-probability
methods. The initial respondents are chosen by a random method
and the subsequent respondents are chosen by non-probability
methods.

16. Quota sampling,
In 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 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.

17. Errors in sampling
Sampling error is the deviation of the selected sample from
the true characteristics, traits, behaviors, qualities or figures
of the entire population.
Sample Size and Sampling Error
Given two exactly the same studies, same sampling
methods, same population, the study with a larger sample
size will have less sampling process error compared to the
study with smaller sample size. Keep in mind that as the
sample size increases, it approaches the size of the entire
population, therefore, it also approaches all the
characteristics of the population, thus, decreasing sampling
process error.

18. Ways to Eliminate Sampling Error
There is only one way to eliminate this error. This solution is to
eliminate the concept of sample, and to test the entire population. In
most cases this is not possible; consequently, what a researcher must
to do is to minimize sampling process error. This can be achieved by a
proper and unbiased probability sampling and by using a large sample
size.

19. Sampling errors occur primarily due to the following reasons:
1. Faulty selection of the sample:
Some of the bias is introduced by the use of defective
sampling technique for the selection of a sample e.g.
Purposive or judgment sampling in which the investigator
deliberately selects a representative sample to obtain certain
results. This bias can be easily overcome by adopting the
technique of simple random sampling.
2. Substitution:
When difficulties arise in enumerating a particular sampling
unit included in the random sample, the investigators usually
substitute a convenient member of the population. This
obviously leads to some bias since the characteristics
possessed by the substituted unit will usually be different from
those possessed by the unit originally included in the sample.

20. 3. Faulty demarcation of sampling units:
Bias due to defective demarcation of sampling units is particularly
significant in area surveys such as agricultural experiments in the field
of crop cutting surveys etc. In such surveys, while dealing with border
line cases, it depends more or less on the discretion of the investigator
whether to include them in the sample or not.
4. Error due to bias in the estimation method:
Sampling method consists in estimating the parameters of the
population by appropriate statistics computed from the sample.
Improper choice of the estimation techniques might introduce the
error.
5. Variability of the population:
Sampling error also depends on the variability or heterogeneity of the
population to be sampled.
Sampling errors are of two types: Biased Errors and Unbiased
Errors