This document discusses key concepts in sampling including: - Probability and non-probability sampling designs such as simple random sampling, stratified random sampling, cluster sampling, and convenience sampling. - Determining appropriate sample size based on desired precision, confidence level, and population variability. - The differences between sampling error and non-sampling error, where sampling error is due to an unrepresentative sample and non-sampling error is from other issues like poor question design. - Advantages of probability sampling include being cost-effective, simple, and non-technical compared to non-probability sampling which is faster and cheaper but provides less accuracy.

1. Major Areas Covered
• Sampling concepts
• Sampling vs Non-sampling error
• Probability sampling design
• Non- probability sampling design
• Determination of sample size

2. SAMPLING CONSIDERATION

3. Sampling concepts

11. • Basic Laws and principles of sampling
•
1. Law of statistical regularity
2. Principle of inertia of large numbers
3. Principle of Validity
4. Principle of persistent of small numbers
5. Principle of optimization

17. SAMPLING VS NON SAMPLING
ERROR

18. INTRODUCTION
Sampling error is one which occurs due to unrepresentative ness of the
sample selected for observation.
Conversely, non-sampling error is an error arise from human error, such
as error in problem identification, method or procedure used, etc.
An ideal research design seeks to control various types of error, but there
are some potential sources which may affect it. In sampling theory, total
error can be defined as the variation between the mean value of population
parameter and the observed mean value obtained in the research. The total
error can be classified into two categories, i.e. sampling error and non-
sampling error.

19. Definition of Sampling Error
Sampling Error denotes a statistical error arising out of a certain sample selected
being unrepresentative of the population of interest. In simple terms, it is an error
which occurs when the sample selected does not contain the true characteristics,
qualities or figures of the whole population.
The main reason behind sampling error is that the sampler draws various
sampling units from the same population but, the units may have individual
variances. Moreover, they can also arise out of defective sample design, faulty
demarcation of units, wrong choice of statistic, substitution of sampling unit done
by the enumerator for their convenience. Therefore, it is considered as the
deviation between true mean value for the original sample and the population.

20. Definition of Non-Sampling Error
Non-Sampling Error is an umbrella term which
comprises of all the errors, other than the sampling error.
They arise due to a number of reasons, i.e. error in
problem definition, questionnaire design, approach,
coverage, information provided by respondents, data
preparation, collection, tabulation, and analysis.

21. There are two types of non-sampling error:
Response Error: Error arising due to inaccurate answers were given by respondents, or their answer is misinterpreted or
recorded wrongly. It consists of researcher error, respondent error and interviewer error which are further classified as under.
Researcher Error
 Surrogate Error
 Sampling Error
 Measurement Error
 Data Analysis Error
 Population Definition Error
Respondent Error
 Inability Error
 Unwillingness Error
Interviewer Error
 Questioning Error
 Recording Error
 Respondent Selection Error
Non-Response Error: Error arising due to some respondents who are a part of the sample do not respond.

22. BASIS FOR
COMPARISON
SAMPLING ERROR NON SAMPLING ERROR
Meaning Sampling error is a type of error,
occurs due to the sample
selected does not perfectly
represents the population of
interest.
An error occurs due to sources other than
sampling, while conducting survey activities
is known as non sampling error.
Cause Deviation between sample
mean and population mean
Deficiency and analysis of data
Types Random Random or Non random
Occurs Only when sample is selected. Both in sample and census.
Sample size Possibility of error reduced with
the increase in sample size.
It has nothing to do with the sample size.

23. Key Differences Between Sampling and Non-Sampling Error
The significant differences between sampling and non-sampling error are
mentioned in the following points:
 Sampling error is a statistical error happens due to the
sample selected does not perfectly represents the
population of interest. Non-sampling error occurs due to
sources other than sampling while conducting survey
activities is known as non-sampling error.
 Sampling error arises because of the variation between the
true mean value for the sample and the population. On the
other hand, the non-sampling error arises because of
deficiency and inappropriate analysis of data.

24.  Non-sampling error can be random or non-random whereas
sampling error occurs in the random sample only.
 Sample error arises only when the sample is taken as a
representative of a population. As opposed to non-sampling
error which arises both in sampling and complete
enumeration.
 Sampling error is mainly associated with the sample size,
i.e. as the sample size increases the possibility of error
decreases. On the contrary, the non-sampling error is not
related to the sample size, so, with the increase in sample
size, it won’t be reduced.

25. PROBABILITY SAMPLING DESIGN

26. INTRODUCTION
DEFINITION: Probability sampling is defined as a sampling technique in
which the researcher chooses samples from a larger population using a
method based on the theory of probability. For a participant to be
considered as a probability sample, he/she must be selected using a
random selection.
Types of probability sampling design
1.Simple Random sampling
Simple Random sampling,as the name suggests, is an entirely random
method of selecting the sample. This sampling method is as easy as assigning
numbers to the individuals (sample) and then randomly choosing from those
numbers through an automated process. Finally, the numbers that are chosen
are the members that are included in the sample.

27. 2.Stratified Random Sampling
■Statified Random Sampling involves a
method where the researcher divides
a more extensive population into
smaller groups that usually don’t
overlap but represent the entire
population. While sampling, organize
these groups and then draw a sample
from each group separately.
■A standard method is to arrange or
classify by sex, age, ethnicity, and
similar ways. Splitting subjects into
mutually exclusive groups and then
using simple random sampling to
choose members from groups.
■Members of these groups should be
distinct so that every member of all
groups get equal opportunity to be
selected using simple probability. This
sampling method is also called
“random quota sampling.”

28. 3.Random cluster Sampling
■Random cluster Sampling is a way to select
participants randomly that are spread out
geographically. For example, if you wanted to
choose 100 participants from the entire
population of the U.S., it is likely impossible
to get a complete list of everyone. Instead,
the researcher randomly selects areas (i.e.,
cities or counties) and randomly selects from
within those boundaries.
■Cluster sampling usually analyzes a
particular population in which the sample
consists of more than a few elements, for
example, city, family, university, etc.
Researchers then select the clusters by
dividing the population into various smaller
section.

29. 4.Systematic sampling
■ Systematic sampling iswhen you
choose every “nth” individual to be a
part of the sample. For example, you
can select every 5th person to be in
the sample. Systematic sampling is
an extended implementation of the
same old probability technique in
which each member of the group is
selected at regular periods to form a
sample. There’s an equal opportunity
for every member of a population to
be selected using this sampling
technique.

30. Advantages of Probability Sampling
1.It’s Cost-effective: This process is both cost and time effective, and a larger sample
can also be chosen based on numbers assigned to the samples and then choosing
random numbers from the more significant sample.
2. It’s simple and straightforward: Probability sampling is an easy way of sampling as
it does not involve a complicated process. It’s quick and saves time. The time saved
can thus be used to analyze the data and draw conclusions.
3. It is non-technical: This method of sampling doesn’t require any technical
knowledge because of its simplicity. It doesn’t require intricate expertise and is not at
all lengthy.

31. NON PROBABILITY SAMPLING DESIGN

32. INTRODUCTION
Non-probability sampling is Define sampling method in which not all members of the population have an
equal chance of participating in the study, unlike probability
sampling. Each member of the population has a known chance of being selected.
Non-probability sampling is most useful for exploratory studies like a pilot survey
(deploying a survey to a smaller sample compared to predetermined sample size).
Researchers use this method in studies where it is impossible to draw random
probability sampling due to time or cost considerations.
Definition
Non-probability sampling is defined as a sampling technique in which the
researcher selects samples based on the subjective judgment of the researcher
rather than random selection. It is a less stringent method. This sampling
method depends heavily on the expertise of the researchers. It is carried out by
observation, and researchers use it widely for qualitative research.

33. TYPES OF NON PROBABILITY SAMPLING
1.Convenience sampling:Convenience sampling is a non-probability sampling technique where samples are
selected from the population only because they are conveniently available to the researcher. Researchers choose
these
samples just because they are easy to
recruit, and the researcher did not consider
selecting a sample that represents the entire
population.
■Ideally, in research, it is good to test a
sample that represents the population. But,
in some research, the population is too large
to examine and consider the entire
population. It is one of the reasons why
researchers rely on convenience sampling,
which is the most common non-probability
sampling method, because of its speed, cost-
effectiveness, and ease of availability of the
sample.

34. 2.Consecutive Sampling
This non-probability sampling method is very similar to convenience sampling, with a
slight variation. Here, the researcher picks a single person or a group of a sample,
conducts research over a period, analyzes the results, and then moves on to another
subject or group if needed. Consecutive sampling technique gives the researcher a
chance to work with many topics and fine-tune his/her research by collecting results
that have vital insights.
3.Quota sampling
Hypothetically consider, a researcher wants to study the career goals of male and
female employees in an organization. There are 500 employees in the organization, also
known as the population. To understand better about a population, the researcher will
need only a sample, not the entire population. Further, the researcher is interested in
particular strata within the population. Here is where quota sampling helps in dividing
the population into strata or groups.

35. 4.Judgmental Or Purposive sampling
In the judgmental sampling method, researchers select the samples based purely on the
researcher’s knowledge and credibility. In other words, researchers choose only those
people who they deem fit to participate in the research study. Judgmental or purposive
sampling is not a scientific method of sampling, and the downside to this sampling
technique is that the preconceived notions of a researcher can influence the results.
Thus, this research technique involves a high amount of ambiguity.
5.Snowball sampling:
Snowball sampling helps researchers find a sample when they are difficult to locate.
Researchers use this technique when the sample size is small and not easily available.
This sampling system works like the referral program. Once the researchers find suitable
subjects, he asks them for assistance to seek similar subjects to form a considerably good
size sample.

36. ADVANTAGES OF NON PROBABILITY SAMPLING
■ Non-probability sampling techniques are a more conducive and practical
method for researchers deploying surveys in the real world. Although statisticians
prefer probability sampling because it yields data in the form of numbers,
however, if done correctly, it can produce similar if not the same quality of
results.
■ Getting responses using non-probability sampling is faster and more cost-
effective than probability sampling because the sample is known to the
researcher. The respondents respond quickly as compared to people randomly
selected as they have a high motivation level to participate.

37. DIFFERENCE BETWEEN NON-PROBABILITY SAMPLING AND PROBABILITY SAMPLING
DESIGN
Non-probability Sampling Design
■ Sample selection based on the
subjective judgment of Researcher.
■ Not every one has an equal chance to
participate.
■ The researcher does not consider
sampling bias.
■ The sample does not accurately
represent the population.
Probability sampling design
■ The sample is selected at random.
■ Everyone in the population has an
equal chance of getting selected.
■ Used when sampling bias has to be
reduced.
■ Used to create an accurate sample.

38. DETERMINATION OF SAMPLE SIZE

39. Sample size definition and concept :-
The no of objects or items is called as sample size. If the sample size is too
small, it may not serve to achieve the objectives and if it is too large, we may incur huge
cost and waste resources. As a general rule, one can say that the sample must be of an
optimum size I.e.it should neither be excessively be large nor too small.

40. TYPES OF SAMPLE SIZE:
There are two types of sample size

41. Quantitative :- It is based on quantity . It is finite sample ,then it is countable
to some amount of numbers. The formula of quantitative sample size are as
follows
Quantitative :- It is based on quantity . It is finite sample ,then it is countable
to some amount of numbers. The formula of quantitative sample size are as
follows

42. BASIC FACTOR OF DETERMINING SAMPLE SIZE
There are three statistical consideration in determining the appropriate
sample size.
1)Degree of level of precision
2) Desired confidence level
3) Degree of variability

43. 1.DEGREE OF LEVEL OF PRECISION
Level of precision is the “Margin of Error” between the estimate of
sample value and population value.
It Is also known as “Margin of permissible error” or “Sampling error.”
The margin of error is usually expressed in percentage.

44. 2. DESIRED CONFIDENCE LEVEL
While calculating sample size the desire confidence levels is specified by
the z value .
Now from the central limit theorem we know that if

46. 3. DEGREE OF VARIABILITY
The “dregee of variability” describes the distribution of attributes in the
population
 The more homogenous a population , the smaller the sample size
required
 The more heterogeneous a population, the larger the sample size
required to obtain a given level of precision (or margin of error)

47. The value of e is known as the margin of error or the error of estimate

48. Reference:-
1. Israel Glenn D. (1992) Determining sample size
2. Internet materials :- https://www.wikihow.com/calculate-
samplesize
3. Kothari ,C.R.(2004),research methodology : methods and
techniques,(2nd edition), new age international publishers.
4. http://www.shcollege.ac.in
5. http://epgp.inflibnet.ac.in
6. https://www.questionpro.com
7. https://keydifferences.com/difference-between-sampling-and-non-
sampling-error.html

49. THANK YOU