Sampling

1. Prof Tauseef Irfan

2. Definition
Sampling: is the process of selecting a few (a sample)
from a bigger group, the sampling population, to
become the basis for estimating or predicting the
prevalence of an unknown piece of information,
situation or outcome regarding the bigger group.
Sample: is a subgroup of population you are interested
in.

3. Adv. & Disad. Of Sampling Process
Advantages
Saves time
Saves financial and human resources
Disadvantages
Unable to find out the information about the
population’s characteristics of interest to you but you
only estimate or predict them
The possibility of an error in your estimation exists

4. Sampling Terminology
Term Definition
Population/stud The large general group of many cases from which a researcher draw a
y population sample and are usually denoted by the letter (N)
Sample A smaller set of cases a researcher selects from a larger group and
generalizes to the population
Sample size The number of selected cases from larger population from who you obtain
the required information and is usually denoted by the letter (n)
Sampling The method you use to select your sample
design/strategy
Sampling unit/ The name for a case or single unit to be selected
sampling
element
Sampling frame The list of units composing a population from which a sample is selected
Sample statistics Information obtained from your respondents
Population A characteristic of the entire population that is estimated from a sample
parameters/pop
ulation mean

5. Principles of Sampling
 Average age of four people: A, B, C
Principle One: & D.
In a majority of cases of  A is 18 yrs, B is 20, C is 23 & D is 25
sampling there will be a  Average age is : 21.5 (18+20+23+25
difference between the
sample statistics and the true = 86 divided by 4)
population mean, which is  By selecting a sample of two we
attributable to the selection can estimate their average age.
of the units in the sample  And we can have six possible
combinations of two:
1. A & B
2. A & C
3. A & D
4. B & C
5. B & D
6. C & D

6. Difference between Sample average &
population Average (2 cases)
Sample Sample Population Difference bet 1
average mean &2
1. A & B
2. A & C 1 19.0 21.5 -2.5
3. A & D
4. B & C 2 20.5 21.5 -1.5
5. B & D
6. C & D
3 21.5 21.5 0.0
4 21.5 21.5 0.0
5 22.5 21.5 +1.0
6 24.0 21.5 +2.5

7.  Average age of four people: A, B, C
Principle Two: & D.
The greater the  A is 18 yrs, B is 20, C is 23 & D is 25
 Average age is : 21.5 (18+20+23+25 =
sample size, the more 86 divided by 4)
accurate will be the  By selecting a sample of three we
estimate of the true can estimate their average age.
 And we can have four possible
population mean combinations of three:
1. A + B+C
2. A + B+D
3. A + C+D
4. B + C+D

8. Difference between Sample
& Population Average (3 cases)
Sample Sample average Population Difference bet 1 &
mean 2
1. A +
1 20.33 21.5 --1.17
B+C
2. A +
B+D
3. A + 2 21.00 21.5 -0.5
C+D
4. B +
C+D
3 22.00 21.5 +0.5
4 22.67 21.5 +1.17

9. Principle Three:
The greater the difference A is 18 yrs, B is 26, C is 32
in the variable under study & D is 40
in a population for a given Average age is: 29
sample size, the greater (18+26+32+40 = 116
will be the difference divided by 4)
between the sample
statistics and the true
population mean

10. Difference between Sample Statistics &
Population Mean (2 cases)
Sample Sample Population Difference bet
1. A & B average mean 1&2
2. A & C
3. A & D 1 22 29.00 -7.00
4. B & C
5. B & D
2 25 29.00 -4.00
6. C & D
3 29 29.00 0.00
4 29 29.00 0.00
5 33 29.00 +4.00
6 36 29.00 +7.00

11. Difference between Sample and
Population Average (3 cases)
Sample Sample Population Difference bet 1 &
average mean 2
1 25.33 29.00 --3.67
2 28.00 29.00 -1.00
3 30.00 29.00 +1.00
4 32.66 29.00 +3.66
1. A + B+C
2. A + B+D
3. A + C+D
4. B + C+D

12. Factors affecting the inferences of sample
The size of the sample
The extent of variation in the sampling population

13. Aims in selecting a sample
To achieve maximum precision in your estimates
within a given sample size
To avoid bias in the selection of your sample
Bias in the selection of a sample can occur if:
Sampling is done by a non-random method
The sampling frame does not cover the sampling
population accurately and completely
A section of a sampling population is impossible
to find or refuses to cooperate

15. Random/probability sampling Designs
 Each element in the population has an equal and independent chance
of selection in the sample.
Equal : means the probability of selection of each element in the
population is the same.
 That is, the choice of an element in the sample is not influenced by
other considerations such as personal preference.
Independent : means that the choice of one element is not dependent
upon the choice of another element in the sampling
 That is, the selection or rejection of one element does not affect the
inclusion or exclusion of another.
A sample can only be considered a random/probability sample and
representative of the population under study if these conditions are
met. If not, bias can be introduced into the study.

16. Advantages of Random/Probability Samples
As they represent the total sampling population, the
inferences drawn from such samples can be
generalized to the total sampling population.
Some statistical tests based upon the theory of
probability can be applied only to data collected from
random samples. Some of these tests are important
for establishing conclusive correlations.

17. Method of drawing
a random sample
1.

18. Procedure for using a table of random
numbers
 Identify the total number of elements in the study population.
 The total number of elements in a study population may run up to
four or more digits.
 Number each element starting from 1.
 If the table for random numbers is on more than one page, choose the
starting page by a random procedure.
 Again select a column or row that will be your starting point with a
random procedure and proceed from there in a predetermined
direction
 Corresponding to the number of digits to which the total population
runs, select the same number, randomly, of columns or rows of digits
from the table
 Decided on your sample size
 Select the required number of elements for your sample from the
table
 If you happen to select the same number twice, discard it and go to

21. Difference Systems of Drawing a Random
Sample
Sampling without replacement
Sampling with replacement

22. Type of Specific Random/Probability
Sampling Designs
Simple random sampling (SRS)
Stratified random sampling
Cluster sampling

23. Procedure for Selecting Simple Random
Sampling
1. Identify by a number all elements or sampling units
in the population
2. Decide on the sample size (n)
3. Select (n) using either the fishbowl draw, the table
of random numbers or a computer program

24. Stratified Random Sampling
In this sampling the researcher attempts to stratify the
population in such a way that population within a stratum
is homogeneous with respect to the characteristic on the
basis of which it is being stratified.
It is important that the characteristics chosen as the basis
of stratification are clearly identifiable in the study
population
For example, it is much easier to stratify a population on
the basis of gender than on the basis of age, income or
attitude.
Once the sampling population has been separated into
non-overlapping groups you select the required number of
elements from each stratum, using the simple random
sampling technique.

25. Types of stratified Random Sampling
Proportionate stratified sampling : the number of
elements from each stratum in relation to its proportion
in the total population is selected.
Disproportionate stratified sampling: consideration is not
given to the size of the stratum.

26. Cluster Sampling
Based on the ability of the researcher to divide
the sampling population into groups, called
cluster, and then to select elements within each
cluster, using the SRS technique.
Depending on the level of clustering, sometimes
sampling may be done at different levels. These
levels constitute the different stages (single,
double or multi-stage cluster sampling).

27. Non-random/non-probability Sampling
Designs
These are used when the number of elements in a
population is either unknown or cannot be
individually identified.
In such situations the selection of elements is
dependent upon other considerations.

28. Types of Non-random/non-probability
Sampling Designs
1. Quota sampling
2. Accidental sampling
3. Judgmental or purpose sampling
4. Snowball sampling

29. Quota Sampling
The researcher is guided by some visible
characteristic, such as gender or race, of the study
population
The sample is selected from a location convenient
to the researcher, and whenever a person with
this visible relevant characteristic is seen that
person is asked to participate in the study.
The process continues until the researcher has
been able to contact the required number of
respondents (quota).

30. Quota Sampling
 Advantages:
It is the least expensive way of selecting a sample
You do not need any information, such as a sampling frame,
the total number of elements, their location, or other
information about the sampling population
It guarantees the inclusion of the type of people you need
 Disadvantages:
 The resulting sample is not a probability one, the findings
cannot be generalized to the total sampling population
The most accessible individuals might have characteristics
that are unique to them and hence might not be truly
representative of the total sampling population

31. Accidental sampling
Whereas quota sampling attempts to include
people possessing an obvious/visible
characteristic, accidental sampling makes no such
attempt.
The method of sampling is common among
market research and newspaper reporters.
It has same advantages and disadvantages as
quota sampling.
As you are guided by any obvious characteristics,
some people contact may not have the required
information

32. Judgmental or purpose sampling
Is the judgment of the researcher as to who can
provide the best information to achieve the
objectives of the study.
The researcher only goes to those people who in
his/her opinion are likely to have the required
information and be willing to share it.
This type of sampling is extremely useful when
you want to construct a historical reality, describe
phenomenon or develop something about which
only a little is known.

33. Snowball sampling
Is the process of selecting a sample using networks.
To start with, a few individuals in a group or
organization are selected and the required
information is collected from them.
They are then asked to identify other people in the
group or organization, and the people selected by
them become a part of the sample.
This process continued until the required number
or a saturation point bas been researched.
This method is useful for studying communication
patterns, decision making or diffusion of knowledge
within a group.

35. Mixed Sampling Design :
Systematic Sampling Design
Systematic Sampling has the characteristics of both
random and non-random sampling designs
In systematic sampling the sampling frame is first
divided into a number of segments called intervals.
If the first interval is the fifth element, the fifth
element of each subsequent interval will be chosen

36. Procedure for Selecting a Systematic
Sample
Prepare a list of all the elements in the study
population (N)
Decide on the sample size (n)
Determine the width of the interval (k)
= total population
sample size
Using the SRS, select an element from the first
interval (nth order)
Select the same order element from each
subsequent interval

38. Calculation of sample Size
Depends on what you want to do with the findings
and what type of relationships you want to establish.
In qualitative research the question of sample size is
less important as the main focus is to explore or
describe a situation, issue, process or phenomenon.

39. Calculation of sample Size
 In qantative research and particularly for cuase-
and-effect studies, you need to consider the
following:
1. At what level of confidence do you want to test your
results, findings or hypotheses?
2. With what degree of accuracy do you wich to
estimate the population parameters?
3. What is the estimated level of variation (standard
deviation, with respect to the main variable you are
studying, in the study population?

40. Calculation of Sample Size
 The size of the sample is important for testing a
hypothesis or establishing an association, but for
other studies the general rule is the larger the sample
size, the more accurate will be your estimates.
 In practice, your budget determines the size of your
sample.
 Your skills in selecting a sample, within the
constraints of your budget, lie in the way you select
your elements so that they effectively and adequately
represent your sampling population.