Stat Training Presentation - Day 1 - Sampling

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

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Stat Training Presentation - Day 1 - Sampling