The document discusses different sampling methods and terminology used in sampling theory. It defines key terms like population, sample, parameter, and statistics. It then describes four main sampling methods - simple random sampling, stratified random sampling, systematic sampling, and cluster sampling. For each method it provides examples, advantages, limitations and the procedures used to select samples.

1. UNIT-2: Sampling (Theory Only):
Points to be covered:
• Terminology: population, Sample, Parameter,
Statistics.
• Characteristics of ideal sample, population
survey, sample survey, sampling errors,
• Sampling methods: procedure, merits and
demerits of
• (i) Simple Random Sampling (ii) Stratified
Random Sampling (iii) Systematic Sampling
(iv) Cluster sampling

2. Population
• A population is any entire collection of people,
animals, plants or things from which we may
collect data.
• It is the entire group we are interested in, which
we wish to describe or draw conclusions about.
• It is important that the investigator carefully and
completely defines the population before
collecting the sample, including a description of
the members to be included.

3. Sample:
• A sample is a group of units selected from a larger
group (the population). By studying the sample it is
hoped to draw valid conclusions about the larger
group.
• A sample is generally selected for study because the
population is too large to study in its entirety.
• The sample should be representative of the general
population.
• Also, before collecting the sample, it is important
that the researcher carefully and completely defines
the population, including a description of the
members to be included.

4. Parameter:
• A parameter is a value, usually unknown (and
which therefore has to be estimated), used to
represent a certain population characteristic.
• For example, the population mean is a parameter
that is often used to indicate the average value of
a quantity.

5. Statistics
• A statistic is a quantity that is calculated from a
sample of data. It is used to give information about
unknown values in the corresponding population.
• For example, the average of the data in a sample is
used to give information about the overall average in
the population from which that sample was drawn.
• Statistics are often assigned Roman letters (e.g. m
and s), whereas the equivalent unknown values in
the population (parameters ) are assigned Greek
letters (e.g. µ and ).

6. Characteristic of good sample:
1. The sample must be representative of the
population. i.e. all the characteristics of the
population should be in the sample.
2. Each unit of the population must be independent.
3. All units of the sample should be selected during
the same period of time.
4. No unit of the population should be favoured at
the time of selecting a sample.
5. All the units of the sample should be adequate. If
less number of units are selected, better accuracy
cannot be achieved. If more number of units are
selected, the expenditure, time etc. Will be more.

7. Population Survey and Sample Survey
Sr. No. Population Survey Sample Survey
1. In population study all units are
examined and hence it requires more
time
In sample study few units are examined
and hence it requires less time
2. The cost of survey is more. The cost of survey is less
3. As more observations are to be
studied, the accuracy cannot be
maintained.
As less no. of observations are to be
studied, the desired accuracy can be
maintained.
4. As more persons are to be employed in
the survey work, experts may not be
available.
As few persons are to be employed the
experts can be appointed.
5. As all observations are to be studied,
detail study cannot be done.
As few observations are to be studied
detail study can be done.
6. When the field of inquiry is very large
this method is lengthy and difficult.
The sample survey is less lengthy and
relatively easy.
7. When complete information is needed
this method is to be used.
When the complete information of all
units is required, this method cannot be
used.

8. Sampling Error
• “Sampling error is the error that arises in a data
collection process as a result of taking a sample from a
population rather than using the whole population.
• Sampling error is one of two reasons for the difference
between an estimate of a population parameter and the
true, but unknown, value of the population parameter.
• The sampling error for a given sample is unknown but
when the sampling is random, for some estimates (for
example, sample mean, sample proportion) theoretical
methods may be used to measure the extent of the
variation caused by sampling error.”

9. Sampling Methods
(A)Simple Random Sampling:
• If each and every unit of the population is given
equal chance to enter into the sample, the method
of sampling is known as simple random sampling.
• If the given population is homogeneous, this
method of sampling gives very reliable results,
but if the population is not homogeneous, the
method does not give a representative sample.
• Random sampling plays a very important role in
higher studies.

10. Methods of Drawing a random sample
(1) Lottery Method:
• Very popular method of drawing a random sample.
• In this method the names or numbers of all the units of the
population are written on different slips of paper.
• These slips should be identical in shape, size and color.
• The slips are folded up and placed in a container and are
mixed up.
• From the container, the number of slips equal to the desired
size of the sample are chosen at random.
• The names or numbers in the slips constitute e a random
sample.
• In this method there is no partiality or prejudice against the
selection of any unit of the population.

11. (2) Using random numbers tables:
• The lottery method of selecting a random sample
becomes tedious when the population is very large.
• In such cases a random sample can be drawn by
using tables of random numbers.
• Ransom numbers tables are scientifically prepared
and they are free from personal bias.
• Commonly used random numbers tables are (i)
Tippet’s random numbers table (ii) Fisher’s and
Yates's random numbers (iii) Tables of random
numbers by Rend corporation.

12. Advantages of random sampling:
1. As all the members of the population have equal
chance of being selected in the sample, the
selection is without any partiality or prejudice.
2. Random sample is a representative sample. As the
size of the sample increase, the reliability of the
result also increase.
3. The error committed about the result of the
population from the results of the sample can be
estimated.
4. The reliability of the results can also be checked
by this method.

13. Limitations of Random Sampling
1. A list of all the units of the population is required.
In absence of such a list, the method cannot be
used.
2. S.R.S. can give reliable results only when the
population is homogeneous.
3. The work of preparing slips or giving numbers is
tedious and tiresome particularly when the
population is large.
4. At times, the results obtained by the method are
biased.
5. When the population is very small, this method
fails to give reliable results

14. (2) Stratified Random Sampling:
• If the population is not homogeneous, i.e. there are more
variations among the units of population, simple random
sampling cannot be a representative sample.
• In this case, the population is divided into different parts,
such that each part is internally homogeneous.
• These homogenous parts of the population are known as
strata.
• Simple random samples are independently drawn from
different strata and are combined into a single sample
known as a Stratified Random Sample.
• The method of taking a sample in this way is called
Stratified Random Sampling.

15. For example:
• Determining the standard of English of the
students of a commerce college we can divide
the students into three different strata, viz,
students of F.Y. class, S.Y. class and students
of T.Y. class.
• From each class i.e. from each stratum random
sample is drawn independently.
• When these samples are combined into a
single sample we get a stratified random
sample.

16. Advantages:
1. As the population is divided into different strata,
all the parts of the population are adequately
represented.
2. Administrative convenience increases in this type
of sampling.
3. Each stratum is being internally homogenous even
a small sample from that stratum will give reliable
information about the stratum.
4. Sampling problems differ in different parts of the
population.
5. If different standards of accuracy are required for
different strata, this method is convient.

17. Limitation:
1. It is always difficult to divide the population into
homogenous strata.
2. The results obtained by this method cannot be
reliable if stratification is not proper.
3. The mathematics involved in estimating the
population characteristics from the sample results
is difficult in this method.
4. Simple random samples are to be drawn from
different strata. In absence of required number of
efficient persons, the desired standard of accuracy
cannot be attained.

18. (3) Systematic Sampling
• Systematic sampling is a random sampling technique
which is frequently chosen by researchers for its
simplicity and its periodic quality.
• In systematic random sampling, the researcher first
randomly picks the first item or subject from the
population. Then, the researcher will select each n'th
subject from the list.
• The procedure involved in systematic random sampling
is very easy and can be done manually.
• The results are representative of the population unless
certain characteristics of the population are repeated for
every n'th individual, which is highly unlikely.

19. • The process of obtaining the systematic sample is
much like an arithmetic progression.
• Starting number:
The researcher selects an integer that must be less
than the total number of individuals in the
population. This integer will correspond to the
first subject.
• Interval:
The researcher picks another integer which will
serve as the constant difference between any two
consecutive numbers in the progression.
• The integer is typically selected so that the
researcher obtains the correct sample size

20. Advantages of Systematic Sampling
• The main advantage of using systematic sampling
over simple random sampling is its simplicity.
• It allows the researcher to add a degree of system
or process into the random selection of subjects.
• Another advantage of systematic random
sampling over simple random sampling is the
assurance that the population will be evenly
sampled.
• There exists a chance in simple random sampling
that allows a clustered selection of subjects.
• This is systematically eliminated in systematic
sampling.

21. Disadvantage of Systematic Sampling
• The process of selection can interact with a
hidden periodic trait within the population.
• If the sampling technique coincides with the
periodicity of the trait, the sampling technique
will no longer be random and representativeness
of the sample is compromised.

22. (4) Cluster Sampling:
• The population is divided into N groups, called clusters.
• The researcher randomly selects n clusters to include in the
sample.
• The number of observations within each cluster Mi is known,
and M = M1 + M2 + M3 + ... + MN-1 + MN.
• Each element of the population can be assigned to one, and
only one, cluster.
• This tutorial covers 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.

23. When to Use Cluster Sampling
• Cluster sampling should be used only when it is
economically justified - when reduced costs can be
used to overcome losses in precision. This is most
likely to occur in the following situations.
• Constructing a complete list of population elements
is difficult, costly, or impossible.
• For example, it may not be possible to list all of the
customers of a chain of hardware stores.
• However, it would be possible to randomly select a
subset of stores (stage 1 of cluster sampling) and
then interview a random sample of customers who
visit those stores (stage 2 of cluster sampling).

24. • The population is concentrated in "natural"
clusters (city blocks, schools, hospitals, etc.).
• For example, to conduct personal interviews of
operating room nurses, it might make sense to
randomly select a sample of hospitals (stage 1 of
cluster sampling) and then interview all of the
operating room nurses at that hospital.
• Using cluster sampling, the interviewer could
conduct many interviews in a single day at a
single hospital.
• Simple random sampling, in contrast, might
require the interviewer to spend all day traveling
to conduct a single interview at a single hospital.

25. Advantages and Disadvantages of Cluster Sampling
• This sampling technique is cheap, quick and easy.
Instead of sampling an entire country when using
simple random sampling, the researcher can allocate
his limited resources to the few randomly selected
clusters or areas when using cluster samples.
• Related to the first advantage, the researcher can
also increase his sample size with this technique.
Considering that the researcher will only have to
take the sample from a number of areas or clusters,
he can then select more subjects since they are more
accessible.

26. • From all the different type of probability
sampling, this technique is the least representative
of the population.
• The tendency of individuals within a cluster is to
have similar characteristics and with a cluster
sample, there is a chance that the researcher can
have an overrepresented or underrepresented
cluster which can skew the results of the study.
• This is also a probability sampling technique with
a possibility of high sampling error.
• This is brought by the limited clusters included in
the sample leaving off a significant proportion of
the population unsampled.

27. The Difference Between Strata and Clusters
• 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.

28. REFERENCES
• http://www.stats.gla.ac.uk/steps/glossary/bas
ic_definitions.html
• http://stattrek.com/survey-research/cluster-
sampling.aspx
• https://explorable.com/cluster-sampling