Sampling Theory- Definition, Target and accessible population, Factors effecting sampling, sampling frame, Sampling technique, Sampling Process, Sample size, sampling error, sampling bias

1. Prof Suja Santosh
RVS College of Nursing, Sulur, Coimbatore

2. Is one grain of rice or one teaspoon of rice to conclude the rice is boiled?

3. Checking Hemoglobin and blood glucose
Is One drop is enough for the conclusion?

4. SAMPLING

5. Sampling

6. Sampling
process of selecting
a small number of elements
(samples)
from a larger defined
target group
of elements (Population) such tha
the information gathered
from the samples
will allow judgments
to the population

7. Sampling
• Sampling is used for more than just survey
research
– All forms of research
• Quantitative research – Probability and
Non Probability Sampling
• Qualitative research – Non Probability
Sampling

8. Census Method
•Complete Enumeration Survey Method - Each and every
item in the universe is selected for the data collection
•Whenever the entire population is studied to collect the
detailed data about every unit, then the census method is
applied.

10. Sample vs. Census

11. Purpose of Sampling
1. Economical
2. Improved quality of data
3. Quick study results
4. Precision and accuracy of data

12. Basics of Sampling Theory
Population
Element
Defined target
population
Sampling unit
Sampling frame

14. Defining Population of Interest
• Population of interest is entirely dependent on
Research Problems, and Research Design.
• Some Bases for Defining Population:
– Geographic Area
– Demographics
– Usage/Lifestyle
– Awareness
Population : A complete set of elements (persons/objects)
that possess some common characteristic defined by the
sampling criteria established by the researcher
Eg: study to be conducted among female teachers in India

15. Target Population
The entire group of people or objects to which the
researcher wishes to generalize the study findings
EG: All low birth weight infants, all people with AIDS

16. Accessible Population
The portion of the population to which the researcher
has reasonable access may be a subset of the target
population
EG: All people with AIDS in Tamilnadu, All low birth weight infants
admitted to the neonatal ICUs in Tamilnadu

18. ELEMENT
A single member of
the population or
sample

19. • SAMPLING UNIT : It may be geographical
one such as state, district, village or it may
be social unit like family, school or
construction unit like house or it may be
an individual and from which data is
collected
• SAMPLE DESIGN: It is a definite plan for
obtaining sample from a given population.
It refers to the technique / procedure the
researcher would adapt in selecting items
for the sample in the research

20. Factors to Consider in Sample Design
Research objectives Degree of accuracy
Statistical analysis needs
Time frame
Knowledge of
target population
Resources
Research scope

21. Sampling Frame
• A list of population elements
(people, companies, houses,
cities, etc.) from which units to
be sampled can be selected.
• Difficult to get an accurate list.
• Sample frame error occurs
when certain elements of the
population are accidentally
omitted or not included on the
list.
• Eg: A list of All low birth weight
infants admitted to the neonatal ICUs
in Tamilnadu

22. CHARACTERISTICS OF GOOD SAMPLE
• Representativeness
• Accuracy – degree to which bias is absent
from the sample
• Precision – amount of error can be tolerate
• Size – adequate in size and in order to be
reliable
• Not have any substitution of originally selected
unit by some other unit
• Free from bias and errors
• Appropriate Sample size

24. Sampling Process
Identifying and defining the Target Population
Describing Accessible Population
Determine Sampling Frame
Specifying Sampling Unit
Select Sampling Technique
Determine the Sample size
Specifying the Sampling Plan
Selecting a Desired Sample

25. FACTORS INFLUENCING SAMPLING PROCESS
Nature of the Researcher
•Inexperienced investigator
•Lack of interest
•Lack of honesty
•Intensive workload
• Inadequate Supervision
Nature of the Sample
•Inappropriate Sampling Technique
•Sample size
•Defective Sampling frame
Circumstances
•Lack of Time
•Large Geographic area
•Lack of cooperation
•Natural Calamities
Target
Accessible

26. Classification of Sampling Techniques
Sampling
Techniques
Non probability
Sampling Techniques
Probability
Sampling Techniques
Convenience
Sampling
Purposive
Sampling
Quota
Sampling
Snowball
Sampling
Systematic
Sampling
Stratified
Sampling
Cluster
Sampling
Sequential
Sampling
Simple
Random
Sampling

27. Probability Sampling
• representativeness
is most important
• equal chances to
all individuals in the
population to be
selected as sample

28. Advantages Disadvantages
Easy to conduct Identification of all
members of the
population can be
difficult
High representativeness
of including sample
Heterogeneous
population cannot apply
Meet assumptions of
many statistical
procedures

29. Simple Random Sampling
Every member of population
has an equal
chance of being selected
as sample

30. Simple Random
Sampling (SRS)
• Population should be Homogeneous and finite
• As sample size increases, sample becomes more
and more representative of population.
• Sampling is generally without replacement
• Problem: Very costly if population is large.
Choices come from a list (sampling frame )

31. Simple Random Sampling
• Lottery method
•Random Number table
•Use of Computer Generation for selection

35. Simple Random Sampling

36. Simple Random
Sampling
1. Select a suitable sampling frame
2. Each element is assigned a number from 1 to N
(pop. size)
3. Generate n (sample size) different random
numbers between 1 and N
4. The numbers generated denote the elements that
should be included in the sample

37. ADVANTAGES
• Most reliable & unbiased
method
• Requires minimum
knowledge of study
population
• Free from sampling errors &
bias
DISADVANTAGES
• Needs up-to-date complete
list of all the members of
the population
• Expensive and time
consuming
Simple Random Sampling

38. Stratified Random Sampling
method of
probability sampling
in which the population
is divided into
different subgroups (strata)
and samples
are selected from each by SRS

39. • A two-step process in which the population is
partitioned into subpopulations, or strata.
• The strata should be mutually exclusive and
collectively exhaustive in that every population
element should be assigned to one and only one
stratum and no population elements should be
omitted.
• Next, elements are selected from each stratum by
a random procedure, usually SRS.
• A major objective of stratified sampling is to
increase precision without increasing cost.
Stratified Sampling

40. Stratified Sampling
• The elements within a stratum should be as
homogeneous as possible, but the elements in
different strata should be as heterogeneous as
possible.
• The stratification variables should also be closely
related to the characteristic of interest.

41. Stratified Sampling
Number of
samples selected
based on the
proportionate to
the relative size of
that stratum in the
total population.
Proportionate
stratified sampling
Disproportionate
stratified sampling
Equal number of samples from each
stratum

42. Disproportionate
stratified sampling

43. ADVANTAGES
• Ensures representative
sample in heterogeneous
population
• Comparison is possible in
two groups
DISADVANTAGES
• Requires complete
information of population
• Large population is
required
• Chances of faulty
classification of strata
Stratified Sampling

44. 44
Systematic Sampling
• Homogeneous and Finite population

45. Systematic Sampling
1. Select a suitable sampling frame
2. Each element is assigned a number from 1 to N
(Population size)
3. Determine the sampling interval i; i=N/n. If i is a fraction,
round to the nearest integer
4. Select a random number, r, between 1 and i, as explained
in simple random sampling
5. The elements with the following numbers will comprise
the systematic random sample: r, r+i,r+2i,r+3i,r+4i,...,r+(n-1)i

46. Systematic Random Sampling
method of probability sampling in which the defined
target population is ordered and the sample is selected
according to position using a skip interval

47. ADVANTAGES
• Convenient and simple to
carry out
• Distribution of sample over
entire population
DISADVANTAGES
• Less representative sample
if subjects are non randomly
distributed
• Sometimes may result in
biased sample
Systematic Sampling

48. Cluster (area) Random Sampling

49. Cluster Sampling
• The target population is first divided into non overlapping and
collectively exhaustive subpopulations, or clusters.
• Then a random sample of clusters is selected, based on a probability
sampling technique such as SRS.
• For each selected cluster, either all the elements are included in the
sample (one-stage) or a sample of elements is drawn probabilistically
(two-stage).
• Elements within a cluster should be as heterogeneous as possible,
but clusters themselves should be as homogeneous as possible.
Ideally, each cluster should be a small-scale representation of the
population.

50. Types of Cluster Sampling
Cluster Sampling
One-Stage
Sampling
Multistage
Sampling
Two-Stage
Sampling
sample all
members of the
cluster
random
sampling
within the
clusters

51. One stage Cluster Sampling
Examples:
• There are 420 nurses working at
the 22 hospitals in Coimbatore
Region
• We wish to interview a sample of
these nurses for the research
study about the workload of nurses
- select a simple random of
samples of 3 hospitals
- interview all nurses employed at
the 3 selected hospitals

52. Two stage Cluster Sampling
• From above
example
- interview only 30
nurses from the 3
selected hospitals
using Simple
random

53. Multi stage Cluster Sampling
COIMBATORE CITY
Panchayat

54. ADVANTAGES
• Less Cost, quick and easy
for a large population
• More no of samples
included in small time
period
• Large Coverage of samples
from Population
DISADVANTAGES
• Possibility of high sampling
error
• Chances of least
representative sample due
to over-represented or
under represented cluster
Cluster Sampling

55. 55
Difference Between Cluster and Stratified Sampling
Population of L strata, stratum l contains nl units Population of C clusters
Take simple random sample in every stratum Take srs of clusters, sample
every unit in chosen clusters

56. A B C D E
F G H I J K
L M N O P
Q R S T U
V W X Y Z
D H
L P
T X
Systematic
Sampling

57. SEQUENTIAL SAMPLING
The investigator initially select small sample
and tries to make inferences, if not able to
draw result, he then adds subjects until
clear cut inferences can be drawn

58. Non Probability Sampling
• Each elements in the population
does not guarantee equal chance
to be a sample

59. Non Probability sampling
• Qualitative researchers are not as
concerned about representativeness
– Relevance to the research topic
– Importance of context
• Sample size does not have to be
determined in advance.
– Selection of cases gradually over time
• Important: many statistics assume random
sampling

60. Non Probability Sampling Methods
Convenience sampling
Purposive sampling
Quota sampling
Snowball sampling
Consecutive Sampling

61. Convenience Sampling
Convenience sampling attempts to obtain a sample
of convenient elements.
Investigator pick up all the available sample who
are meeting the preset inclusion and exclusion
criteria

63. Convenience Sampling
- sample whoever is available.
– use of students, and members of social
organizations
– department stores using charge account lists
– “people on the street” interviews

64. •Used by both quantitative
and qualitative
researchers
•Used when limited
availability of time and
resources
Convenience Sampling

65. Convenience Sampling
ADVANTAGE
• Easiest method
• Helps in saving time,
money and resources
• Used in pilot study
DISADVANTAGES
• Chances of sampling
bias
• Non representative
sample
• Findings cannot be
generalized

66. Purposive Sampling
 Subjects are chosen
to be part of sample
with a specific
purpose in mind

67. Purposive Sampling
 Requires in-depth
knowledge about
accessible population
 Used when limited number
of individuals possess the
trait of interest

68. Purposive Sampling

69. Purposive Sampling
ADVANTAGE
• Simple to draw a
sample
• Saves resources as it
requires less field
work
DISADVANTAGES
• Requires
considerable
knowledge about
the population
• Conscious biases
may occur

70. Quota Sampling
The researcher ensures equal or proportionate representation
of subjects, depending on which trait is considered as the basis
of the quota

71. Quota Sampling
Quota sampling may be viewed as two-stage
– The first stage consists of dividing population into non
overlapping subgroups or quotas
– In the second stage, sample elements are selected based on
convenience or purposive.

72. Quota Sampling
The bases of the quota are usually age, gender, education, race,
religion, socio-economic status etc
ADVANTAGES
• Economically cheap
•Suitable where the
field has to be done
like studies related to
market and public
opinion polls
DISADVANTAGES
• Always does not
guarantee
representative sample
•Chances of sampling
bias

73. Snowball Sampling
• In snowball sampling,
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 referrals.

74. – Locating the initial subject and then taking
assistance from the subject to identify people with
a similar trait of interest

75. Used by the researchers to identify potential
subjects in studies where subjects are hard to
locate
Snowball Sampling

76. - Subject refers only one other subject
- Subject gives multiple referrals and
each referral gives some more until
required sample size reached
- Subject refers multiple people but
only one is chosen as sample
Snowball Sampling

77. The bases of the quota are usually age, gender, education, race,
religion, socio-economic status etc
ADVANTAGES
• Facilitates sampling
for people difficult to
locate
• Cheap, Simple and
cost-efficient
• Needs little planning
and lesser workforce
DISADVANTAGES
• Little control of
researcher over the
sampling method
• Representativeness of the
sample is not guaranteed
• Changes of poor
coverage of entire
population
Snowball Sampling

78. Consecutive Sampling
• More like convenient sampling
• Picks up all the available subjects who are
meeting the preset inclusion and exclusion
criteria
• Used for continuously changing population,
such as hospital patients

79. Non Probability Sampling Methods
Convenience sampling relies
upon convenience and access
Purposive sampling relies upon belief
that participants fit characteristics
Quota sampling emphasizes representation
of specific characteristics
Snowball sampling relies upon respondent
referrals of others with like characteristics

80. Difference between probability &
Non probability Sampling
Comparison
Factors
Probability Sampling Non-probability Sampling
List of Population Complete list necessary Complete list not necessary
Information about Sampling
Units
Each unit identified Need detail on Habits,
Activities, Traits etc
Sampling skill Skill required Little skill required
Time Time consuming Low time consuming
Cost Moderate to high Low
Estimates of population
parameters
Unbiased Biased
Sample Representativeness Good, Assured Suspect, Undeterminable
Accuracy & Reliability Computed with Confidence
interval
Unknown
Measurement of Sampling
error
Statistical measures No true measures available

81. How big should your
sample be?
• Rule of thumb: Bigger is better

82. Factors affecting Sample Size
• Size of population
• Nature of study
• Type of Sampling techniques
• Homogeneity
• Degree of Accuracy (or Errors)
• Availability of time, money and resources
• Effect size
• Variability (SD) –Pilot study, Literature
• Margin of error
• Power of study
• Level of Significance
• Dropout Rate

83. Common Methods for Determining
Sample Size
Common Methods:
–Budget/time available
–Executive decision
–Statistical methods
–Historical data/guidelines

84. Qualitative studies – Sample size
• Depends upon
- purpose of study
- quality of informants
- type of sampling
- Variety of characteristics
• Thumb rule estimation
(In ethnography studies -25-50 samples
In phenomenology studies- minimum 10 samples
In grounded theory – 20-30 samples)

85. Quantitative studies – Sample size
• Large sample chosen is good
• Power analysis used to estimate accurate sample size
• Thumb rule estimation
(In health science,
For small sized trial /PG research- atleast 30 subjects
For medium sized trial /PG research- atleast 100
For Large sized trial /PG research- atleast 300 subjects
Descriptive studies – 200 subjects)
• Sample size determination using sample size calculation formula
- using tables, through computer

86. Determining Sample size
• Used for estimating adequate number of samples to
be included in the study
• Part of designing a High Quality study
• To allow appropriate analysis
• Provide desired level of accuracy
• To allow validity of significance test

90. Sample Size for two Population Mean

92. Sample Error
How close the
sample size is to
the population
size, or how
well a sample of
that size
approximates a
given
population.

93. Sampling Error
Difference between a
sample result
and the true population
result,
such an error results
From chance sampling
fluctuations

94. • The standard deviation of a sampling distribution is
referred to as the standard error or sampling error.
• It is the deviation of the selected sample from the
true characteristics, traits, behaviours, qualities or
figures of entire population
• The greater your sample size, the smaller the
standard error.
Sampling Error

97. Types of Sampling Errors
Sampling Errors Non Sampling Errors
Any type of bias that
results from mistakes in
either the selection
process of sampling
units, sampling
techniques or in
determining sample size
Bias that occurs in a research
study regardless of whether a
sample or census is used.
Bias caused by measurement
errors, response errors,
coding errors etc.

98. Difference between sampling and non
sampling errors
Sampling Errors Non Sampling Errors
Occurs in any project involving
sampling
Poorly worded Questions
Because only a sample of the
population is studied
Inadequate responses
Interviewer interview the wrong
respondents
Non response of individuals
selected to the study –
Behavioural effects
Bias error, where only interested
respondents respond
Coding error
Poor Sampling methods Bias in the selection of
individuals for the study

99. Sampling Bias
The error resulting from taking a non-random
sample of a population

100. Sampling Bias
• Based on sampling method used, some members of a
population are less likely to be included in the sample.
• Reduces the ability for results to be generalized to a larger
population.
• Some studies might deliberately take a biased sample in
order to produce misleading results.
• More often, sampling bias occurs because of difficulty in
obtaining a truly representative sample of a complex
population.

101. Types of Sampling Bias
• Self-selection bias- Selection from only a specific area
of the population (intentional (“purposive”), or accidental
“convenience sample”)
• Information bias – due to systematic measurement
error or misclassification of subjects on one or more variables,
either risk factors or disease status
• Confounding bias – results when the risk factor being
studied is so mixed up with other possible risk factors that its
single effect is very difficult to distinguish
• Response bias- subjects gives an incorrect response or
the question is misleading

103. Avoid Bias
• Select individuals for the sample at Random