Post on 09-Apr-2018
8/8/2019 Stat Training Presentation - Day 1 - Sampling
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TWO TYPES OF SAMPLES:
1. Non-Probability Samples
Samples are obtained haphazardly, selectedpurposively or are taken as volunteers
Probabilities of selection are unknown
May not be used for statistical inference
Results from the use of judgement sampling,
accidental sampling, purposively sampling, etc.
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TWO TYPES OF SAMPLES:
2. Probability Samples Samples are obtained using some objective
chance mechanism, thus involving randomization Requires the use of a complete listing of the
universe called the sampling frame Probabilities of selection are known
Generally referred to as random samples Allows one to make valid generalizations about
the universe/population
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TYPES OF PROBABILITY SAMPLING METHODS:
1. Simple Random Sampling
2. Stratified Random Sampling
3. Systematic Random Sampling
4. Cluster Sampling5. Simple TwoStage Sampling
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SIMPLE RANDOM SAMPLING
Most basic method of drawing a probability sample
Assigns equal probabilities of selection to each
possible sample
Results to obtaining a simple random sample
Types of SRS:
1. SRS Without Replacement does not allow repeats inthe selection of the sample
2. SRS With Replacement allows repeats in the
selection of the sample
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STRATIFIED RANDOM SAMPLING
The universe is divided into L mutually exclusive sub-universes
called strata
Independent simple random samples are obtained from each stratum
Illustration:
III
IIIIV V
Stratified
Sample
Note:
1
1
L
h
h
L
h
h
N N
n n
!
!
!
!
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ADVANTAGES OF STRATIFICATION:
1. Gives a better cross-section of the population
2. Simplifies the administration of the survey/datagathering
3. The nature of the population dictates some inherent
stratification
4. Allows one to draw inferences for varioussubdivisions of the population
5. Generally increases the precision of estimates
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SYSTEMATIC SAMPLING
Adopts a skipping pattern in the selection of
sample units
Gives a better cross-section if the listing is
linear in trend but has high risk of bias if there
is periodicity in the listing of units in the
sampling frame
Allows the simultaneous listing and selection
of samples in one operation
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CLUSTER SAMPLING
Considers a universe divided into N mutually exclusive sub-
groups called clusters
A random sample of n clusters is selected and are completelyenumerated
Administratively convenient and has simpler frame
requirements
Illustration:
From the ten clusters
(enumeration areas) delineated
within the barangay, four are
completely enumerated.
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SAMPLE SIZE
DETERMINATION
Considerations:
1. Budget Constraint2. Size of the population
3. Variability of the population
4. Complexity of the analysis to be performed
Approaches:1. Subjective Approach
2. Sampling Fraction Approach
3. Via Precision Point of View
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Requirements forSample Size Determination
Via Precision Point of View:
1. Level of confidence (1-E) measures the degree
of confidence on the estimate
2. Maximum tolerable error (B) the margin of error
one is willing to tolerate
3. Variance of the population (S2) measures the
variation of the target population
4. Perceived value of P needed when the objective
of the survey is to estimate a population proportion
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Some Formulas for Sample Size
Determination Using SRS
1. When estimating for the population mean:
where
If N is not known,
2
21
NSn
N D S!
2
2
2
BD
ZE
!
2
2
2Z
n SB
E !
-
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Some Formulas for Sample Size
Determination Using SRS
2. When estimating for the population proportion:
where:
If N is not known,
1Npqn
N D pq!
2
2
2
BD
ZE
!
2
2
Zn pq
B
E !
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EXAMPLE:
A survey of faculty member of the CAS is being proposed
to assess the proportion of faculty members who needs
some intervention in their teaching skills. How large asample should be taken if there are 300 faculty members
in the CAS?B Confidence Z D N P Q PQ n
0.01 0.99 2.575 1.51E-05 300 0.5 0.5 0.25 295
0.01 0.95 1.960 2.60E-05 300 0.5 0.5 0.25 291
0.01 0.90 1.665 3.70E-05 300 0.5 0.5 0.25 287
0.05 0.99 2.575 3.77E-04 300 0.5 0.5 0.25 207
0.05 0.95 1.960 6.51E-04 300 0.5 0.5 0.25 169
0.05 0.90 1.665 9.24E-04 300 0.5 0.5 0.25 143
0.10 0.99 2.575 1.51E-03 300 0.5 0.5 0.25 107
0.10 0.95 1.960 2.60E-03 300 0.5 0.5 0.25 73
0.10 0.90 1.665 3.70E-03 300 0.5 0.5 0.25 55
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WORKSHOP 3c