Sampling

1. SAMPLING AND
SAMPLING TECHNIQUES

2. INTRODUCTION
• Sampling is the motherboard or core of any research. Sampling is a process of
selecting representative units from an entire population of a study.
• In order to answer the research questions, it is doubtful that researcher should be
able to collect data from all cases. Thus, there is a need to select a sample. The
entire set of cases from which researcher sample drawn is called the population.
Since, researchers neither have time nor the resources to analysis the entire
population so they apply sampling technique to reduce the number of cases.

4. TERMINOLOGY USED IN SAMPLING
• Population
The aggregate of all the units pertaining to a study is called the “population” or the “universe”.
Population is the target group to be studied.
• Sample
A sample is the part of the population or universe selected for the purpose of investigation.
• Sampling
Sampling is the process of drawing a sample from a larger population or universe.
The following three elements are in the process of sampling.
i. Selecting the sample;
ii. Collecting the information;
iii. Making an inference about the population.
• Element
A member or an object of the population is an element.

5. Contd.
• Sample size
The sample size refers to the number of sampling units selected from the population for exploration.
• Sample Frame
The list of sampling units from which sample is taken is called the sampling frame.
• Sampling error
There may be fluctuation in the values of the statistics of characteristics from one sample to another, or
even those drawn from the same population.
• Sampling bias
Distortion that arises when a sample is not representative of the population from which it was drawn.

6. PRINCIPLES OF SAMPLING
1. Selection of sample must be systematic and objective manner
2. Sample unit must be clearly define and easily identifiable
3. Sample units must be independent of each other
4. Same units of sample must be used through out the study
5. The selection process must be on sound criteria.
6. It should avoid error, bias

7. PURPOSES OF SAMPLING
i. Economy
ii. Less time consuming
iii. Reliability
iv. Detailed study
v. Scientific technique
vi. Greater suitability

8. OBJECTIVES OF SAMPLING
i. To make an inference about an unknown parameter from a
measurable sample statistic.
ii. To test the hypothesis relating to population.
iii. To avoid the vast study about the entire population.
iv. To obtain quick result.

9. CHARACTERISTICS OF A GOOD SAMPLE
i. Representativeness
ii. Independence
iii. Adequacy
iv. Homogeneity

10. ADVANTAGES OF SAMPLING
1. Reduce time and cost to collect data
2. More comprehensive data is obtained than in a census.
3. Administrative control
4. Better motivation
5. Reliability of data
6. Less non response error
7. Conclusion

12. SAMPLING TECHNIQUES
Sampling techniques or methods may be classified into the
following two broad types.
I. Probability Sampling (or) Random Sampling
II. Non-Probability Sampling (or) Non-Random Sampling

14. I. PROBABILITY SAMPLING
• Probability sampling is also known as ‘random sampling.
• Probability sampling is a sampling technique in which researchers choose samples from a
larger population using a method based on the theory of probability. This sampling method
considers every member of the population and forms samples based on a fixed process.
• For example, in a population of 1000 members, every member will have a 1/1000 chance of
being selected to be a part of a sample. Probability sampling eliminates bias in the
population and gives all members a fair chance to be included in the sample.

15. 1. Simple Random Sampling/Unrestricted
Random Sampling
• Simple random sampling refers to the technique of sampling in
which each and every item of population or universe has an equal
independent chance of being included in the sample. Thus the
unit in the population under simple random sampling is provided
an equal chance of being selected.
• The unrestricted random samples are usually obtained by using
the following two methods.
i. Lottery method
ii. Random number method

16. STAGES IN RANDOM SAMPLING
Define
Population
Develop
sampling
Frame
Assign
each
unit a
number
Randomly
select the
required
amount of
random
numbers
Systematically
select random
numbers until it
meets the
sample size
requirements

17. Merits
• A good representative of the universe
• A less expensive method
• Prior knowledge of the characteristics of population is not necessary.
• Human bias and influences are eliminated.
• Accuracy of the result can be assessed by standard error of estimation.
• A suitable method for small population.
Limitations
• Sampling is likely to be biased at the survey stage due to non-response or non-availability of the sample units.
• It is not suitable in case of large population.

18. i. Lottery Method
• Lottery method of sampling refers to the process of drawing a lot from among the
population or universe. Under this method, the required number of samples are selected
from the total population by blindfold from the drum or urn.
For Example:
 To take a sample of ten persons out of a population of 100 persons, the researcher writes
the names of 100 persons on separate slips of paper, folds them and, mix them thoroughly
and then make a blindfold selection of 10 slips.

19. ii. Random number method
• This method is an alternative to lottery method. Under this method, samples are drawn by using
the table of random numbers. The random numbers are generally obtained by some mechanism
that could be expected in a random sequence of the digits from 0 to 9.
Some of the standard tables of random sample are:
a. Tippett’s (1927) random number tables consisting of 41600 random digits.
b. Fisher and Yates (1938) table of rando numbers with 15000 random digits.
c. Kendall and Babington Smith (1939) table of random numbers consisting of 100000 random
digits.
d. C.R. Rao, Mitra and Mathai (1966) table of random numbers.

21. 2. RESTRICTED RANDOM SAMPLING
• As the size of population or universe is not restricted under unrestricted
method of sampling, it consumes much expense and time. Hence,
restricted sample is used in order to increase the efficiency of sampling
techniques. Under this method the size of the population is restricted to
normal size on the basis of certain characteristics.
• The restricted random samples are usually obtained by using the
following methods, namely,

22. i. Stratified random sampling:
• Under this method, the population is divided into some groups or classes (stratum) based on their
homogeneity. Samples are drawn from each stratum at random. It is a method used for effecting the
precision of sampling. If some proportion of sampling units is drawn from each stratum, then it is known
as proportional stratified sampling. Otherwise, it is known as disproportional stratified sampling.
Suitability
The stratified random sampling method is appropriate for a large population.

24. Advantages
• More precise than other methods
• Avoids bias to some extent
• Saves time and money
• A good representation of population
• As it is geographically concentrated, it is convenient for data collection.
Disadvantages
• Sometimes the results have to be weighed according to the size of strata, which is a difficult task.
• It requires the knowledge of the traits of population.
• Sometimes stratification becomes difficult.

25. ii. Systematic sampling:
• Under this method the universe or population is arranged on the basis of some systems like
alphabetical, numerical, geographical etc. The samples are drawn from these lists. For instance, if
the universe has been ordered as 10th, 20th or 100th items are selected as samples.
• Sampling interval (or) K = Size of Population/Size of Sample

26. Suitability
• While simple random sampling can’t be adopted for some reason, this method serves as an alternative method.
Systematic selection can be applied to various population.
Merits
• It is a simple method. The execution also leads simple.
• Randomness and probability features are present in the sampling which mark good representation.
• A good system always yields fruitful results.
Limitations
• This method leads to repetition of the same work at every stage.
• It is difficult to apply the systems in grouping, when the population is large.

27. iii. Cluster sampling
• Cluster sampling refers to the procedure of dividing the population into groups called clusters and samples are
drawn from these clusters (to represent the entire population).
• A cluster may consist of either the primary sample units or secondary sample units. From the selected cluster, either all
sample units or few of them are chosen for any sampling method.
• For instance, if the study is to be made on the industrial workers of a district, the industrial units are the primary sample
units.
• primary sample units clustering in one particular locality is selected it forms the first stage cluster, and when workers
employed in one or two firms are selected, that forms the second stage cluster. Thus the various clusters are formed from
which the sampling units are drawn.
• Sometimes, the clusters will be selected from among other clusters, which is called multi-stage cluster sampling. A cluster
may refer to anything, a school, a company, an industry or a society.

29. Suitability
• This method is suitable if the sampling units have to
be selected from various clusters.
Advantages
• It is an easy and more practical method.
• Less expensive when compared to other methods.
• This method of sampling gives a good representation.
Disadvantages
• Sometimes clustering of population affects the
representativeness of the sample.
• Results are also likely to be less precise and
accurate.

30. Difference between Stratification and Clustering

31. iv. Area Sampling
• This is an important form of cluster
sampling.
• In larger field surveys, clusters
consisting of specific geographical
areas like districts, taluks, villages or
blocks in a city are randomly drawn as
the geographical areas and selected for
sampling.

32. Suitability
• This method is useful in marketing research.
Advantages:
• It is an easy method.
• It is less expensive
• It gives a good representation
Disadvantages
• Sometimes clustering of population affects the representativeness of the sample.
• Results are also likely to be less precise and accurate.

33. v. Multi-stage Sampling
• Multi-stage sampling is a type of sample design in which some information is collected from the
whole sample and additional information is also collected from sub-sample of the full sample.
• For example, for the study on the working efficiency of nationalized banks in India, the sample units
(banks) are selected, from large primary sampling unit such as states in the country, at first. Again
out of certain districts chosen, some units of samples are selected. This would represent a two stage
sampling design. Thus sampling units are selected at different stages based on certain traits.
• Suitability
This method is suitable where the population is scattered cover a wider geographical area and no list is
available for sampling. It is also useful when a survey has to be made within a limited time and cost.

34. Merits
• It is an appropriate sampling plan in finding out
the variability of groups
• As greater probability of selection is stressed,
the sampling units becomes a good
representative.
• Multi-stage sampling is used to estimate the
effect of non-response in the sub-sample.
Limitations
• It involves elaborate work
• It is appropriate only in two-stage or multi-stage
sampling plan.

35. vi. Sequential Sampling
• Under this method, the size of the sample units is not determined in
advance, but fixed according to mathematical decision rules based on
the survey.
• This is usually adopted in case of acceptance sampling plan in
context of statistical quality control. Thus in sequential sampling, the
sampling units are selected one after another, so long as one desires
to do so.

36. vii. Random sampling with probability proportional
to size
• The procedure of selecting clusters with probability proportional to size is widely
followed. If one primary cluster has twice as large a population as another, it is given
twice the chance of being selected. If the same number of persons is then selected
from each of the selected clusters, the overall probability of any person will be the same.
• Suitability
Random sampling with probability proportional to size is used in all multistage
sampling

37. Advantages
• Cluster of various sized gets proportionate representations.
• It leads to greater precision than a simple random sample of cluster and a constant sampling fraction
at the second stage.
• Equal-sized samples from each selected primary cluster are convenient for field work.
• If one interviewer is assigned to each cluster, the interviewers have equal workloads.
Limitation
• This method cannot be used if the size of the primary sampling clusters are not known.

38. viii. Multiphase Sampling
• In this method, a sample is taken for the first phase of research
from which some simple and general information is gathered.
Then, a sub-sample from this large sample is taken for a detailed
enquiry in the second phase of the study.

39. ix. Replicated or Interpenetrating Sampling
• Replicated or Interpenetrating sampling involves selection of a
certain number of sub-samples rather than one fully drawn, using
the same sampling techniques and each is a self-contained and
adequate sample of the population.
• Suitability
This method can be used with any basic sampling technique.

40. Advantages
• It provides a simple means of resolving replicated sampling error.
• It is practical, if the size of the total sample is too large.
• If a different set of interviewers is used, an estimation of inter-interviewer
variation for each of the sub-samples can be obtained.
Disadvantages
• It limits the amount of stratification that can be employed.

41. Uses of probability sampling
• Reduce Sample Bias: Using the probability sampling method, the bias in the sample derived from a population is
negligible to non-existent. The selection of the sample mainly depicts the understanding and the inference of the
researcher. Probability sampling leads to higher quality data collection as the sample appropriately represents the
population.
• Diverse Population: When the population is vast and diverse, it is essential to have adequate representation so that
the data is not skewed towards one demographic. For example, if Square would like to understand the people that
could make their point-of-sale devices, a survey conducted from a sample of people across the US from different
industries and socio-economic backgrounds helps.
• Create an Accurate Sample: Probability sampling helps the researchers plan and create an accurate sample. This
helps to obtain well-defined data.

42. II. NON-PROBABILITY /NON-RANDOM SAMPLING
METHOD
• Non-probability or Non-random sampling method is not based on the
theory of probability. Under this method of sampling the researcher cannot
assure that every element has an equal chance of being chosen.

43. i. Convenience sampling
• This method is also called Chunk method. A chunk refers to the fraction of the population to
be investigated. This chunk is not selected by probability but selected by judgment or by
convenience.
• For example
• Sample obtained from readily available list such as car booking, telephone directories, etc.,
is a convenient sample.
• The results obtained in this method can hardly be representative of the population. They
are generally biased and unsatisfactory. However, it is often used for pilot studies.

44. Suitability
• This method is suitable for simple purposes like testing
ideas or rough impressions about a subject of interest.
Advantages
• It is the cheapest and the simplest method.
• It does not require a list of population
• It does not require any statistical expertise.
Disadvantages
• It is highly biased
• It is the least reliable sample method.
• The findings cannot be generalized.

45. ii. Judgement or Purposive Sampling
• It is that method of sampling, in which the samples are drawn on the basis of personal judgement of a
person. Generally, the researcher uses his judgement in the choice of the samples which he thinks
most suitable for his study. While choosing the samples only the average items are considered and
extreme items are omitted.
• Selection of the sample is adjusted in accordance with the object of the survey. This method is suitable
only when small number of samples are required.
• Suitability
This method is appropriate when what is important is the typicality and specific relevance of the
sampling units to the study and not their over all representatives of the population.

46. Advantages
• It is less costly and more convenient
• It guarantees inclusion of relevant elements in
the sample.
Disadvantages
• This method does not ensure the
representativeness of the sample.
• This method is less efficient than random
sampling for generalization.

47. iii. Quota Sampling
• It is one of the commonly used methods of sampling in market surveys
and opinion polls. Though it is a non-random sampling it combines the
technique of probability sampling and purposive selection. This
method is convenient and economical.
• Suitability
This method is suitable for marketing surveys, opinion polls and
leadership survey.

48. Advantages
• It is considerably less costly than probability sampling
• It consumes less time
• There is no need for a list of population
• Field work can easily be organized
Disadvantages
• It may not yield a representative sample
• It is impossible to estimate the sampling error
• The finding is not generalizable to any significant extent
• Strict control of field work is difficult.
• It is difficult to sample more than three variable dimensions.

49. iv. Snowball Sampling
• Snowball sampling is a special type of non-probability sampling technique through which a respondent list is
built up by using an initial set of its members as informants.
• For example:
If a researcher wants to study the problems faced by the SriLankan refugees (or) Refugees from Bangaladesh or
Burma, he may identify an initial group of refugees through some Government sources like collectorate, embassy
and from a list of camp officer. Then he can ask each one of them to supply names of other refugees known to
them and continue this procedure until he gets an exhaustive list from which he can draw a sample.
• Suitability
This method is suitable for a study for which no sample frames are readily available.

50. Merits
• It is useful for smaller populations for which no frames are
readily available.
• It is very useful in studying social groups of various kinds.
Demerits
• It is difficult to apply this method when the population is
large.
• It does not ensure the inclusion of all elements in the list.
• This method does not allow the use of probability statistical
methods.
• Elements included are dependent on the subjective choice
of the originally selected respondents.

51. Uses of non-probability sampling
• Create a hypothesis: Researchers use the non-probability sampling method to create an
assumption when limited to no prior information is available. This method helps with the immediate
return of data and builds a base for further research.
• Exploratory research: Researchers use this sampling technique widely when conducting
qualitative research, pilot studies, or exploratory research.
• Budget and time constraints: The non-probability method when there are budget and time
constraints, and some preliminary data must be collected. Since the survey design is not rigid, it is
easier to pick respondents at random and have them take the survey or questionnaire.

52. Difference between Probability Sampling and Non-
probability Sampling Methods
Basis of Difference Probability Sampling Methods Non-Probability Sampling Methods
Definition Probability Sampling is a sampling technique in which samples
from a larger population are chosen using a method based on
the theory of probability.
Non-probability sampling is a sampling technique in which the
researcher selects samples based on the researcher’s
subjective judgment rather than random selection.
Alternatively Known as Random sampling method. Non-random sampling method
Population selection The population is selected randomly. The population is selected arbitrarily.
Nature The research is conclusive. The research is exploratory.
Sample
Since there is a method for deciding the sample, the population
demographics are conclusively represented.
Since the sampling method is arbitrary, the population
demographics representation is almost always skewed.
Time Taken
Takes longer to conduct since the research design defines the
selection parameters before the market research study begins.
This type of sampling method is quick since neither the
sample or selection criteria of the sample are undefined.
Results
This type of sampling is entirely unbiased and hence the
results are unbiased too and conclusive.
This type of sampling is entirely biased and hence the results
are biased too, rendering the research speculative.
Hypothesis
In probability sampling, there is an underlying hypothesis
before the study begins and the objective of this method is to
prove the hypothesis.
In non-probability sampling, the hypothesis is derived after
conducting the research study.

53. Selection of suitable Sampling Techniques
• For any research, it is essential to choose a sampling method accurately to meet the goals
of your study. The effectiveness of your sampling relies on various factors. Here are some
steps expert researchers follow to decide the best sampling method.
• Jot down the research goals. Generally, it must be a combination of cost, precision, or
accuracy.
• Identify the effective sampling techniques that might potentially achieve the research goals.
• Test each of these methods and examine whether they help in achieving your goal.
• Select the method that works best for the research.

54. Sampling and Non-Sampling Errors
• While using sampling, errors are
committed. These errors are
broadly classified as sampling
errors and non-sampling errors.

56. Sampling Errors
• Sampling errors arise due to drawing
inferences about the population on the basis of
a few observations. That is, when the sample
size is not a true representative of the
population.
• Such errors may be due to the bias of the
investigator or due to wrong operational
aspects of sampling process.
• Two types of sampling errors
• Biased Errors
• Unbiased Errors / Random sampling errors

57. Types of Sampling Errors
• Biased Errors:
Due to selection of sampling techniques; size of sample.
• Unbiased Errors / Random Sampling
Differences between the members of the population included or
not included.

58. Methods of reducing sampling errors
• Specific problem selection.
• Systematic documentation of related research.
• Effective enumeration.
• Effective pre testing.
• Controlling methodological bias.
• Selection of appropriate sampling techniques.

59. Non-sampling Errors
• Non-sampling errors refers to biases and mistakes in selection of sample.
• CAUSES FOR NON-SAMPLING ERRORS
 Sampling operations
 Inadequate of response
 Misunderstanding the concept
 Lack of knowledge
 Concealment of the truth
 Loaded questions
 Processing errors
 Sample size

60. Determination of Sample Size
• Sample Size refers to the number of items to be selected from
the universe to constitute a sample.
• Inadequate, or excessive sample sizes influence the quality and
accuracy of research.

61. • If sample is too large….
 Good precision
 Less errors
 Less bias
But,
– Wastage of time, money and resources
– Resources could be as well be deviated
to other projects.
– Not cost-effective
• If sample is too small…..
 Inaccurate results
 More source of bias
 Power of the study comes down
 Study fails to give meaningful information
 Waste of resources on a inaccurate study
 Ethical issues about recruiting patients
into meaningless study.
 Hence, optimum sample size must be determined before commencement of a study.
 Optimum sample size determination is required for the following reasons:
• To allow for appropriate analysis
• To provide the desired level of accuracy
• To allow validity of significance test

62. • Sample size determination is the mathematical estimation of the number of subjects/units to be
included in a study.
• When a representative sample is taken from a population, the finding are generalized to the population.
• Mathematical formula is used to determine the sample size.
n = ( zσ / d )
Where,
• n is the sample size
• Z is the degree of accuracy desired (specified level of confidence)
• σ is the standard deviation of the population
• d is the difference between the population mean and sample mean

63. Factors determining the size of sample
• The size of the population
• The resources available
• The extent of accuracy desired
• Nature of population
• Method of sampling adopted
• Nature of respondents

64. CONCLUSION
Sampling helps a lot in research. It is one of the most important
factors which determines the accuracy of your research/survey
result. If anything goes wrong with your sample then it will be directly
reflected in the final result. There are lot of techniques which help us
to gather sample depending upon the need and situation.