RESEARCH METHODOLOGY - ISP-Infinite Possibilities · 2016. 8. 17. · LECTURE 12 SAMPLING &...
Transcript of RESEARCH METHODOLOGY - ISP-Infinite Possibilities · 2016. 8. 17. · LECTURE 12 SAMPLING &...
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LECTURE 12
SAMPLING & PROBABILITY
DISTRIBUTIONS
Mazhar Hussain
Dept of Computer Science
ISP,Multan
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RESEARCH
METHODOLOGY
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ROAD MAP
Introduction
Chosing your research problem
Chosing your research advisor
Literature Review
Plagiarism
Variables in Research
Construction of Hypothesis
Research Design
Writing Research Proposal
Writing your Thesis
Data Collection
Data Representation
Sampling and Distributions
Paper Writing
Ethics of Research
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SAMPLING
How to find average student age in the
university?
Ask each student and compute the average
Randomly select 3 to 4 students from each discipline
and find their average age – Estimation of the
average age of student in the university
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SAMPLING
Why sampling?
Efforts and resources required to carry out the study
on the population
Examples
Average income of families living in a city
Results of an election
Opinion about the a problem
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SAMPLING
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Sampling is the process of selcetion 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
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RECAP – MEAN & STANDARD DEVIATION
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Mean/Average
Standard Deviation
On the average, how far the data values are from the
mean
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POPULATION VS SAMPLE
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Karl Friedrich Gauss 1777-1855
Gaussian
Distribution
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GAUSSIAN/NORMAL PROBABILITY
DISTRIBUTION
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Most of the naturally occurring processes can be
modeled by a bell shaped curve
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GAUSSIAN/NORMAL PROBABILITY
DISTRIBUTION
The Gaussian probability distribution is perhaps
the most used distribution in all of science.
Sometimes it is called the ―bell shaped curve‖ or
normal distribution.
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2
2
( )
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( )2
x
p x e
= mean of distribution
= standard deviation of distributionx is a continuous variable (-∞x ∞
2( , )N
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GAUSSIAN/NORMAL PROBABILITY
DISTRIBUTION
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The area within +/- σ is ≈ 68%
The area within +/- 2σ is ≈ 95%
The area within +/- 2σ is ≈ 99.7%
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GAUSSIAN/NORMAL PROBABILITY
DISTRIBUTION
Probability (P) of x being in the range [a, b] is
given by an integral:
12
2
2
( )
21
( ) ( )2
xb b
a a
P a x b p x dx e dx
95% of area within 2 Only 5% of area outside 2
Gaussian pdf with =0 and =1
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GAUSSIAN/NORMAL PROBABILITY
DISTRIBUTION
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Standard Normal Distribution
http://en.wikipedia.org/wiki/Image:Normal_Distribution_PDF.svg
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STANDARD NORMAL DISTRIBUTION
Normal distribution with mean of zero and
standard deviation of one
Since mean and standard deviation define any
normal distribution…
Standard normal distribution can be used for any
normally distributed variable by converting mean
to zero and standard deviation to one—z scores
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Z SCORES
By itself, a raw score or X value provides very little
information about how that particular score
compares with other values in the distribution.
A score of X = 53, for example, may be a relatively
low score, or an average score, or an extremely
high score depending on the mean and standard
deviation for the distribution from which the score
was obtained.
If the raw score is transformed into a z-score,
however, the value of the z-score tells exactly
where the score is located relative to all the other
scores in the distribution. 15
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Z SCORES
The process of changing an X value into a z-score
involves creating a signed number, called a z-
score, such that
The sign of the z-score (+ or –) identifies whether the
X value is located above the mean (positive) or below
the mean (negative).
The numerical value of the z-score corresponds to the
number of standard deviations between X and the
mean of the distribution.
Thus, a score that is located two standard deviations
above the mean will have a z-score of +2.00
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Z SCORES
In addition to knowing the basic definition of a z-
score and the formula for a z-score, it is useful to
be able to visualize z-scores as locations in a
distribution.
Remember, z = 0 is in the center (at the mean),
and the extreme tails correspond to z-scores of
approximately –2.00 on the left and +2.00 on the
right.
Although more extreme z-score values are
possible, most of the distribution is contained
between z = –2.00 and z = +2.00.17
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Z SCORES
z-score for a sample value in a data set is obtained by
subtracting the mean of the data set from the value
and dividing the result by the standard deviation of
the data set.
NOTE: When computing the value of the z-score,
the data values can be population values or sample
values. Hence we can compute either a population z-
score or a sample z-score.
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Z SCORES
The Sample z-score for a value x is given by the
following formula:
Where is the sample mean and s is the sample
standard deviation.
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x xz
s
x
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Z SCORES
The Population z-score for a value x is given by
the following formula:
Where is the population mean and is the
population standard deviation.
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xz
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EXAMPLE
Example: What is the z-score for the value of 14
in the following sample values?
3 8 6 14 4 12 7 10
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Thus, the data value of 14 is 1.57 standard deviations above the mean of 8, since the z-score is positive.
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EXAMPLE
Dot Plot of the data points with the location of
the mean and the data value of 14.
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Z SCORE & PROBABILITY
What is the probability of finding a value
between 100 and 110?
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How to calculate
this area using z
scores?
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Z SCORE CHART
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0.9394
Reading area under curve for z=1.55
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Z SCORE & PROBABILITY
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Probability of z>1.55 (Area in tail)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0
1.55
P=.0606
0.9394
P=1-0.9394
P=0.0606
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Z SCORE & PROBABILITY
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0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0
-1.55 1.55
P=.0606+.0606
P=.1212
Probability of z>1.55 + z
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Z SCORE & PROBABILITY
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0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0
1.55
P=.5-.0606=.4394
Probability of z>0 and z
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EXAMPLE: 50 MEASURES OF POLLUTION
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V a l u e F r e q u e n c y
2 0 0
2 5 3
3 0 5
3 5 6
4 0 8
4 5 1 3
5 0 5
5 5 6
6 0 3
6 5 1
M o r e 0
Histogram
0
2
4
6
8
10
12
14
20 25 30 35 40 45 50 55 60 65
Mor
e
Value
Fre
que
ncy
68.40 88.9
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EXAMPLE: 50 MEASURES OF POLLUTION
Probability value > 45
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•
4372.88.9
68.4045
z
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
-3 -2 -1 0 1 2 3
.4372P=.3300
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EXAMPLE: 50 MEASURES OF POLLUTION
Probability from 35 to 45
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•5749.
88.9
68.4035
z
4372.88.9
68.4045
z
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
-3 -2 -1 0 1 2 3
-.5749 .4372
P=.5-.3300=.1700P=.5-.2843=.2157
P=.2157+.1700=.3857
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Sampling
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SAMPLING
Pros
Saves time
Resources – financial, human
Cons
Not exact value for the population
An estimate or prediction
Compromise on accuracy of findings
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SAMPLING – TERMINOLOGY
Examples
Average student age in the university
Average income of families living in a city
Results of an election
Population or study population (N)
The university students, families living in the city,
electors
Sample
The small group of students, families or electors you
chose to collect the required information33
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SAMPLING – TERMINOLOGY
Sample size (n)
The number of entities in your sample
Sampling design or strategy
The way you select the students, families or electors
Sampling unit or sampling element
Each student, family or elector in your study
Sample statistics
Your findings based on infomration obtained from
your sample34
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SAMPLING – TERMINOLOGY
Population Parameters
Aim of research – find answers to research question
for study population not the sample
Use sample statistics to estimate answers to research
questions in study population
Estimates arrived at from sample statistics –
population parameters
Saturation Point
When no new information is coming from your
respondents
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SAMPLING – TERMINOLOGY
Sampling Frame
A list identifying each student, family or elector in
the study population
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PRINCIPLES OF SAMPLING
Example – Four individuals A,B,C, D
A = 18 years
B = 20 years
C = 23 years
D = 25 years
Average age
(18+20+23+25) / 4 = 21.5 years
Use a sample of two indivudals to estimate the
average age of your study population (4
individuals)37
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PRINCIPLES OF SAMPLING
How many possible combinations of two
individuals?
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A and B
A and C
A and D
B and C
B and D
C and D
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PRINCIPLES OF SAMPLING
A+B = 18+20 = 38/2 = 19.0 years
A+C = 18+23 = 41/2 = 20.5 years
A+D = 18+25 = 43/2 = 21.5 years
B+C = 20+23 = 43/2 = 21.5 years
B+D = 20+25 = 45/2 = 22.5 years
C+D = 23+25 = 48/2 = 24.0 years
In two cases – no difference between sample
statistics and population parameters
Difference – Sampling error39
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PRINCIPLES OF SAMPLING
Sample Sample
Statistics
Population
Parameters
Difference
1 19.0 21.5 -2.5
2 20.5 21.5 -1.5
3 21.5 21.5 0.0
4 21.5 21.5 0.0
5 22.5 21.5 +1.0
6 24 21.5 +2.5
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PRINCIPLES OF SAMPLING
Principle I
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In majority of cases of sampling, there will
be a difference between sample statistics
and the true population parameters which
is attribuatable to the selection of the units
in the sample
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PRINCIPLES OF SAMPLING
Instead of samples of two – take a sample of
three
Four possible combinations
A+B+C = 18+20+23 = 61/3 = 20.33 years
A+B+D = 18+20+25 = 63/3 = 21.00 years
A+C+D = 18+23+25 = 66/3 = 22.00 years
B+C+D = 20+23+25 = 68/3 = 22.67 years
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PRINCIPLES OF SAMPLING
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Sample Sample
Statistics
Population
Parameters
Difference
1 20.33 21.5 -1.17
2 21.00 21.5 -0.5
3 22.00 21.5 +0.5
4 22.67 21.5 +1.17
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PRINCIPLES OF SAMPLING
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Sample Sample
Statistics
Population
Parameters
Difference
1 20.33 21.5 -1.17
2 21.00 21.5 -0.5
3 22.00 21.5 +0.5
4 22.67 21.5 +1.17
Sample Sample
Statistics
Population
Parameters
Difference
1 19.0 21.5 -2.5
2 20.5 21.5 -1.5
3 21.5 21.5 0.0
4 21.5 21.5 0.0
5 22.5 21.5 +1.0
6 24 21.5 +2.5
-2.5 to +2.5
-1.17 to +1.17
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PRINCIPLES OF SAMPLING
The gap between sample statistics and population parameters is reduced
Principle II
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The greater the sample size, the more
accurate will be the estimate of the true
population statistics
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PRINCIPLES OF SAMPLING
Same Example – Different Data
A =18 years
B = 26 years
C = 32 years
D = 40 years
Variable (age) – markedly different
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PRINCIPLES OF SAMPLING
Estimate average using
Samples of two
Samples of three
Difference in the average age:
Sample size of 2: -7.00 to +7.00 years
Sample size of 3: -3.67 to +3.67 years
Range of difference is greater than previously
calculated
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PRINCIPLES OF SAMPLING
Principle III
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The greater the difference in the variable
under study in a population for a given
sample size, the greater will be the
difference between the sample statistics
and the true population parameters
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FACTORS AFFECTING THE INFERENCE
Principles suggest that two factors may influence
the degree of certainity about the inferences
drawn from a sample
Size of sample
Larger the sample size, the more accurate will be the
findings
The extent of variation in the sampling population
Greater the variation in the study population w.r.t. the
chracteristics under study, the greater will be the
uncertainity for a given sample size
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AIMS IN SELECTING A SAMPLE
Achieve maximum precision in your estimate
Avoid bias in selection
Bias can occur if: Non-random sampling – consciously or unconsciously affected
by human choice
Sampling frame does not cover the sampling population
accurately or completely
A section of sampling population is impossible to find or
refuses to cooperate
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SAMPLING METHODS
Probability Sampling
Used to generate random/non-biased samples
required for conducting inferential analyses
Non-probability Sampling
Used mostly in qualitative analysis
Mixed Sampling
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SAMPLING METHODS
Probability Sampling
Non-probability Sampling
Mixed Sampling
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PROBABILITY SAMPLING
Each element in the population has an equal and independent chance of selection in the sample
Equal:
Probability of selection of each element is the same
Choice is not affected by other considerations –human preferences
Independent:
Choice of one element is not dependent upon the choice of another element
Selection or rejection of one element does not affect the inclusion or exclusion of another 53
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PROBABILITY SAMPLING
Example – Equal Chance
80 students in the class
20 refuse to participate in your study
Each of 80 students (population) does not have an
equal chance of selection
Sample is not representative of your class
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PROBABILITY SAMPLING
Example – Independence
Three close friends in the class
One is selected – Two are not
Refuses to participate without friends
Forced to chose all three or none
Not independent sampling
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Inferences drawn from random samples
can be generalized to the total sampling
population
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PROBABILITY SAMPLING
Simple Random Sampling
Fishbowl draw
Computer program
Table of random numbers
Stratified Sampling
Proportional
Disproportional
Cluster Sampling
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SIMPLE RANDOM SAMPLING
The Fishbowl Draw
Small population
Number each element on separate slips of paper for
each element
Put them in a box
Pick out one by one until you get desired sample size
Similar to lotteries
Computer Program
Write a program to select a random sample
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SIMPLE RANDOM SAMPLING
Table of random numbers
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Random
Number Table
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How to Use Random Number Tables
________________________________________________
1. Assign a unique number to each population element in the
sampling frame. Start with serial number 1, or 01, or 001,
etc. upwards depending on the number of digits required.
2. Choose a random starting position.
3. Select serial numbers systematically across rows or down
columns.
4. Discard numbers that are not assigned to any population
element and ignore numbers that have already been
selected.
5. Repeat the selection process until the required number of
sample elements is selected.
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How to Use a Table of Random Numbers to Select a Sample
Your supervisor wants to randomly select 20 students from your class of 100
students. Here is how he can do it using a random number table.
Step 1: Assign all the 100 members of the population a unique number.You may
identify each element by assigning a two-digit number. Assign 01 to the first name
on the list, and 00 to the last name. If this is done, then the task of selecting the
sample will be easier as you would be able to use a 2-digit random number table.
NAME NUMBER NAME NUMBER
Adam, Tan 01 Tan Teck Wah
…………..
42
………………
…………………… … Carrol, Chan 08 Tay Thiam Soon
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………………. … ……………….. … Jerry Lewis 18 Teo Tai Meng 87
………………. … …………………. … Lim Chin Nam 26 …………………… …
………………. … Yeo Teck Lan 99
Singh, Arun
……………….
30 Zailani bt Samat 00
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Step 2: Select any starting point in the Random Number Table and find the first number that
corresponds to a number on the list of your population. In the example below, # 08 has been
chosen as the starting point and the first student chosen is Carol Chan.
10 09 73 25 33 76
37 54 20 48 05 64
08 42 26 89 53 19
90 01 90 25 29 09
12 80 79 99 70 80
66 06 57 47 17 34
31 06 01 08 05 45
Step 3: Move to the next number, 42 and select the person corresponding to that number into
the sample. #42 – Tan Teck Wah
Step 4: Continue to the next number that qualifies and select that person into the sample.
# 26 -- Jerry Lewis, followed by #89, #53 and #19
Step 5: After you have selected the student # 19, go to the next line and choose #90. Continue
in the same manner until the full sample is selected. If you encounter a number selected
earlier (e.g., 90, 06 in this example) simply skip over it and choose the next number.
Starting point: move right to the end of the row, then down to the next row row; move left to the end, then down to the next row, and so on.
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TABLE OF RANDOM NUMBERS
Suppose you are using a table like this:
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TABLE OF RANDOM NUMBERS
Sampling population – 256 individuals
Numbered from 1 to 256
You chose to select 10% - 25 individuals
Randomly select any starting point
Pick last three digits of the number
Select the valid ones (001-256) and skip the
invalid numbers (257-999)
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DRAWING A RANDOM SAMPLE
Two ways of selecting a random sample
Sampling without replacement
Sampling with replacement
Example
20 students to be selected out of 80
First student is selected – Probability 1/80
For second student – 79 left, Probability 1/79
By the time you select the 20th – Probability 1/61
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DRAWING A RANDOM SAMPLE
Sampling without replacement
Contrary to randomization – Each element should
have equal probability of selection
Sampling with replacement
Selected element is replaced in the population
If it is selected again – it is discarded
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PROBABILITY SAMPLING
Simple Random Sampling
Fishbowl draw
Computer program
Table of random numbers
Stratified Sampling
Proportional
Disproportional
Cluster Sampling
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STRATIFIED SAMPLING
Step 1- Divide the population into homogeneous,
mutually exclusive and collectively exhaustive
subgroups or strata using some stratification variable.
Step 2- Select an independent simple random sample
from each stratum.
Step 3- Form the final sample by consolidating all
sample elements chosen in step 2.
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STRATIFIED SAMPLING
Example
Stratify on the basis of gender
Two groups – male and female
Select random samples from each group
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STRATIFIED SAMPLING
Stratified samples can be:
Proportionate: involving the selection of sample
elements from each stratum, such that the ratio of sample
elements from each stratum to the sample size equals that
of the population elements within each stratum to the
total number of population elements.
Disproportionate: the sample is disproportionate when
the above mentioned ratio is unequal.
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To select a stratified sample of 20 members of the Island Video Club which has 100 members
belonging to three language based groups of viewers i.e., English (E), Mandarin (M) and Others
(X).
Step 1: Identify each member from the membership l ist by his or her respective language groups
00 (E ) 20 (M) 40 (E ) 60 ( X ) 80 (M)
01 (E ) 21 ( X ) 41 ( X ) 61 (M) 81 (E )
02 ( X ) 22 (E ) 42 ( X ) 62 (M) 82 (E )
03 (E ) 23 ( X ) 43 (E ) 63 (E ) 83 (M)
04 (E ) 24 (E ) 44 (M) 64 (E ) 84 ( X )
05 (E ) 25 (M) 45 (E ) 65 ( X ) 85 (E )
06 (M) 26 (E ) 46 ( X ) 66 (M) 86 (E )
07 (M) 27 (M) 47 (M) 67 (E ) 87 (M)
08 (E ) 28 ( X ) 48 (E ) 68 (M) 88 ( X )
09 (E ) 29 (E ) 49 (E ) 69 (E ) 89 (E )
10 (M) 30 (E ) 50 (E ) 70 (E ) 90 ( X )
11 (E ) 31 (E ) 51 (M) 71 (E ) 91 (E )
12 ( X ) 32 (E ) 52 ( X ) 72 (M) 92 (M)
13 (M) 33 (M) 53 (M) 73 (E ) 93 (E )
14 (E ) 34 (E ) 54 (E ) 74 ( X ) 94 (E )
15 (M) 35 (M) 55 (E ) 75 (E ) 95 ( X )
16 (E ) 36 (E ) 56 (M) 76 (E ) 96 (E )
17 ( X ) 37 (E ) 57 (E ) 77 (M) 97 (E )
18 ( X ) 38 ( X ) 58 (M) 78 (M) 98 (M)
19 (M) 39 ( X ) 59 (M) 79 (E ) 99 (E )
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Step 2: Sub-divide the club members into three homogeneous sub-groups or strata by the
language groups: English, Mandarin and others .
EnglishLanguage Mandarin Language Other Language
Stratum Stratum Stratum .
00 22 40 64 82 06 35 66 02 42
01 24 43 67 85 07 44 68 12 46
03 26 45 69 86 10 47 72 17 52
04 29 48 70 89 13 51 77 18 60
05 30 49 71 91 15 53 78 21 65
08 31 50 73 93 19 56 80 23 74
09 32 54 75 94 20 58 83 28 84
11 34 55 76 96 25 59 87 38 88
14 36 57 79 97 27 61 92 39 90
16 37 63 81 99 33 62 98 41 95
1. Calculate the overall sampling fraction, f, in the following manner:
f = n = 20 = 1 = N 100 5
where n = sample size and N = population size
0.2
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Determine the number of sample elements (n1) to be selected from the English
language stratum. In this example, n1 = 50 x f = 50 x 0.2 =10. By using a simple
random sampling method [using a random number table] members whose numbers
are 01, 03, 16, 30, 43, 48, 50, 54, 55, 75, are selected.
Next, determine the number of sample elements (n2) from the Mandarin language
stratum. In this example, n2 = 30 x f = 30 X 0.2 = 6. By using a simple random
sampling method as before, members having numbers 10,15, 27, 51, 59, 87 are
selected from the Mandarin language stratum.
In the same manner, the number of sample elements (n3) from the „Other language‟
stratum is calculated. In this example, n3 = 20 x f = 20 X 0.2 = 4. For this stratum,
members whose numbers are 17, 18, 28, 38 are selected‟
These three different sets of numbers are now aggregated to obtain the ultimate
stratified sample as shown below.
S = (01, 03, 10, 15, 16, 17, 18, 27, 28, 30, 38, 43, 48, 50, 51, 54, 55, 59, 75, 87)
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PROBABILITY SAMPLING
Simple Random Sampling
Fishbowl draw
Computer program
Table of random numbers
Stratified Sampling
Proportional
Disproportional
Cluster Sampling
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CLUSTER SAMPLING
Simple Random, Symmetric and Stratified
sampling – based on researcher’s ability to
identify each element in population
Small population size – easy
Large population – country
Cluster sampling
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CLUSTER SAMPLING
Divide population into clusters
Select elements wihtin each cluster
Cluster formation
Geographical proximity
Common characteristic – similar to stratified
sampling
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STRATIFIED VS CLUSTER SAMPLING
In startified sampling the target population is
sub-divided into a few subgroups or strata, each
containing a large number of elements.
In cluster sampling, the target population is sub-
divided into a large number of sub-population or
clusters, each containing a few elements.
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AREA SAMPLING
A common form of cluster sampling where clusters consist of geographic areas, such as
districts, housing blocks or townships. Area sampling could be one-stage, two-stage, or
multi-stage.
How to Take an Area Sample Using Subdivisions
Your company wants to conduct a survey on the expected patronage of its new outlet in a new
housing estate. The company wants to use area sampling to select the sample households to be
interviewed. The sample may be drawn in the manner outlined below.
___________________________________________________________________________________
Step 1: Determine the geographic area to be surveyed, and identify its subdivisions. Each
subdivision cluster should be highly similar to all others. For example, choose ten housing
blocks within 2 kilometers of the proposed site [say, Model Town ] for your new retail outlet;
assign each a number.
Step 2: Decide on the use of one-step or two-step cluster sampling. Assume that you decide to
use a two-stage cluster sampling.
Step 3: Using random numbers, select the housing blocks to be sampled. Here, you select 4
blocks randomly, say numbers #102, #104, #106, and #108.
Step 4: Using some probability method of sample selection, select the households in each of the
chosen housing block to be included in the sample. Identify a random starting point (say,
apartment no. 103), instruct field workers to drop off the survey at every fifth house
(systematic sampling).
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SAMPLING METHODS
Probability Sampling
Non-probability Sampling
Mixed Sampling
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NON-PROBABILITY SAMPLING
Do not follow probability theory
Useful when the number of elements in
population is unknown or cannot be individually
identified
Four common designs
Quota Sampling
Accidental Sampling
Judgemental Sampling
Snowball Sampling
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QUOTA SAMPLING
Main consideration – ease of access to sample
population
Guided by some visible chracteristic of study
population – age, gender etc.
Sample selection – location convenient to the
researcher
Whenever a person with required characteristic
is seen – asked to participate in the study
Process continues until the required number of
respondents (quota) is reached
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QUOTA SAMPLING - EXAMPLE
Average age of male students in the university
Select a sample of 20 male students
You decide to stand at the entrance of the
university - convenient
Whenever a male student arrives – ask his age
When you get 20 – Target is achieved
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QUOTA SAMPLING
Advantages
Convenient
Less expensive
Disadvantages
Not probability based
May not be generalized to the population
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ACCIDENTAL SAMPLING
Also based on convenience
Quota sampling – include people with some
obvious characteristic
Accidental sampling – no such attempt
Common in market research and newspaper
reporters
Since you just pick up the people – may not get
the required information
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JUDGEMENTAL SAMPLING
Judgement of the researcher as to who can
provide the best information to achieve the
objectives of the study
Sampling based on some judgment, gut-feelings
or experience of the researcher.
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SNOWBALL SAMPLING
Sample selection using network
Start with few individuals or organizations and
collect the information
They are then asked to identify other
participants – people selected by them become a
part of sample
The process continues……
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SAMPLING METHODS
Probability Sampling
Non-probability Sampling
Mixed Sampling
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MIXED SAMPLING
Systematic sampling
Divide the frame into segments or intervals
Select one element from first interval using SRS
Select elements from subsequent intervals
depending upon the element selected from the
first interval
Example
5th element selected from first element
Select the 5th from each interval
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SYSTEMATIC SAMPLING
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To use systematic sampling, a researcher needs:
[i] A sampling frame of the population; .
[ii] A skip interval calculated as follows:
Skip interval = population list size
Sample size
Names are selected using the skip interval.
If a researcher were to select a sample of 1000 people using the local telephone
directory containing 215,000 listings as the sampling frame, skip interval is
[215,000/1000], or 215. The researcher can select every 215th
name of the entire
directory [sampling frame], and select his sample.
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Example: How to Take a Systematic Sample
Step 1: Select a listing of the population, say the City Telephone Directory, from which to
sample. Step 2: Compute the skip interval by dividing the number of entries in the directory by the
desired sample size.
Example: 250,000 names in the phone book, desired a sample size of 2500,
So skip interval = every 100th name
Step 3: Using random number(s), determine a starting position for sampling the list.
Example: Select: Random number for page number. (page 01)
Select: Random number of column on that page. (col. 03)
Select: Random number for name position in that column (#38, say, A..Mahadeva)
Step 4: Apply the skip interval to determine which names on the list will be in the sample.
Example: A. Mahadeva (Skip 100 names), new name chosen is A Rahman b Ahmad.
Step 5: Consider the list as “circular”; that is, the first name on the list is now the init ial name
you selected, and the last name is now the name just prior to the initially selected one.
Example: When you come to the end of the phone book names (Zs), just continue on
through the beginning (As).
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CREDITS
Chapter 12, Research Methodology, Ranjit
Kumar
Sampling in Market Research - APMF
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