12. Sampling Design

8/7/2019 12. Sampling Design

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Sampling: Design and Procedures


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Lecture Plan

y Overview

y Sample Vs Census

y The Sampling Design Process

y A Classification of sampling Techniques


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The Sampling Design Process

Define thePopulation

Determine the SamplingFrame

Select Sampling Technique(s)

Determine the Sample Size

Execute the Sampling Process


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Sampling

y Sample size depends on the following:

Population size

Heterogeneity

Accuracy and reliability Allocation of resources


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Some terms and Definitions

y Unit is an element or a group of elements, living or nonliving, on

which observations can be made

y Population (or Universe) the collection of all the units of a specified

type at a particular point or period of time

y Sampling Frame The list of all the units with their identification is

known as sample frame.

y Sample one or more units, selected from a population according to

some specified procedure

y Sample size Thenumberofunits, selectedinthe sampleis called

sample size

y Sampling with or without replacement


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Classification of Sampling Techniques

Sampling Techniques

Nonprobability

Sampling Techniques

Probability

Sampling Techniques

Convenience

Sampling

Judgmental

Sampling

Quota

Sampling

Snowball

Sampling

Systematic

Sampling

Stratified

Sampling

Cluster

Sampling

Other Sampling

Techniques

Simple

Random

Sampling


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ProbabilitySampling

y Simple Random Sampling (With and withoutreplacement)

y Systematic Random Sampling

y

Stratified Sampling (Proportionate andDisproportionate)

y Cluster Sampling (Single and multi stage)


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Simple Random Sampling

y Each element in the population has aknown and equal probability of selection.

y Each possible sample of a given size (n) hasa known and equal probability of being the

sample actually selected.

y This implies that every element is selectedindependently of every other element.


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Procedures for DrawingSimple Random Sampling

1. Select a suitable sampling frame

2. Each element is assigned a number from 1 toN

(pop. size)

3. Generate n (sample size) different randomnumbers

between 1 and N

4. The numbers generated denote the elementsthat


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AGraphical Illustration ofSimple Random Sampling

A B C D E

1 6 11 16 21

2 7 12 17 22

3 8 13 18 23

4 9 14 19 24

5 10 15 20 25

Select five random

numbers from 1 to25. The resulting

sample consists ofpopulation

elements 3, 7, 9, 16,

and 24. Note, thereis no element from

Group C.


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Systematic Sampling

y If the ordering of the elements produces acyclical pattern, systematic sampling may

decrease the representativeness of the

sample.

For example, there are 100,000 elements inthe population and a sample of 1,000 is

desired. In this case the sampling interval, i,is 100. A random number between 1 and 100 isselected. If, for example, this number is 23,the sample consists of elements 23, 123, 223,

323, 423, 523, and so on.


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Procedures for DrawingSystematic Sampling

1. Select a suitable sampling frame

2. Each element is assigned a number from 1 to N (pop. 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 thesystematic random sample: r, r+i,r+2i,r+3i,r+4i,...,r+(n-1)i


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AGraphical Illustration ofSystematic Sampling

A B C D E

1 6 11 16 21

2 7 12 17 22

3 8 13 18 23

4 9 14 19 24

5 10 15 20 25

Select a randomnumber between 1

to 5, say 2.The resulting

sample consists ofpopulation 2,(2+5=) 7, (2+5x2=) 12,

(2+5x3=)17, and(2+5x4=) 22. Note, all

the elements areselected from a

single row.


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Stratified Sampling

y The elements within a stratum should be ashomogeneous as possible, but the elements indifferent strata should be as heterogeneous

as possible.

y The stratification variables should also beclosely related to the characteristic ofinterest.

y Finally, the variables should decrease thecost of the stratification process by beingeasy to measure and apply.


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Stratified Sampling

y In proportionate stratified sampling, the sizeof the sample drawn from each stratum is

proportionate to the relative size of thatstratum in the total population.

y In disproportionate stratified sampling, thesize of the sample from each stratum is

proportionate to the relative size of thatstratum and to the standard deviation of thedistribution of the characteristic of interestamong all the elements in that stratum.


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AGraphical Illustration ofStratified Sampling

A B C D E

1 6 11 16 21

2 7 12 17 22

3 8 13 18 23

4 9 14 19 24

5 10 15 20 25

Randomly select anumber from 1 to 5

for each stratum, Ato E. The resultingsample consists of

population elements4, 7, 13, 19 and 21.

Note, one elementis selected from

each column.


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Cluster Sampling

y The target population is first divided intomutually exclusive and collectivelyexhaustive subpopulations, or clusters.

y Then a random sample of clusters is selected,based on a probability sampling techniquesuch as SRS.

y For each selected cluster, either all the

elements are included in the sample (onestage) or a sample of elements is drawnprobabilistically (twostage).


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Cluster Sampling

y Elements within a cluster should be asheterogeneous as possible, but clusters

themselves should be as homogeneous as

possible. Ideally, each cluster should be a smallscale representation of the population.

y In probability proportionate to size sampling,

the clusters are sampled with probability

proportional to size. In the second stage, theprobability of selecting a sampling unit in aselected cluster varies inversely with the sizeof the cluster.


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Types of Cluster Sampling

Cluster Sampling

One-Stage

Sampling

Multistage

Sampling

Two-Stage

Sampling

Simple Cluster

SamplingProbability

Proportionate

to Size Sampling


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Non-ProbabilitySampling

y Quota Sampling

y Convenience Sampling

y Judgment Sampling

y

Snowball Sampling


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Convenience Sampling

Convenience sampling attempts to obtain asample of convenient elements. Often,

respondents are selected because they happento be in the right place at the right time.

use of students, and members of socialorganizations

mall intercept interviews without qualifyingthe respondents

department stores using charge accountlists

people on the street interviews


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AGraphical Illustration ofConvenience Sampling

A B C D E

1 6 11 16 21

2 7 12 17 22

3 8 13 18 23

4 9 14 19 24

5 10 15 20 25

Group D happens to

assemble at aconvenient time and

place. So all the

elements in thisGroup are selected.

The resulting

sample consists ofelements 16, 17, 18,

19 and 20. Note, noelements are

selected from groupA, B, C and E.


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Judgmental Sampling

Judgmental sampling is a form ofconvenience sampling in which thepopulation elements are selected based on

the judgment of the researcher.

test markets

purchase engineers selected in industrial

marketing research

bellwether precincts selected in votingbehavior research

expert witnesses used in court


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Graphical Illustration ofJudgmental Sampling

A B C D E

1 6 11 16 21

2 7 12 17 22

3 8 13 18 23

4 9 14 19 24

5 10 15 20 25

The researcherconsiders groups B, C

and E to be typical andconvenient. Within

each of these groupsone or two elementsare selected based on

typicality andconvenience. Theresulting sample

consists of elements 8,10, 11, 13, and 24. Note,

no elements areselected

from groups A and D.


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Quota Sampling

Quota sampling may be viewed as twostage restrictedjudgmental sampling.

The first stage consists of developing control categories,or quotas, of population elements.

In the second stage, sample elements are selected based onconvenience or judgment.

Population Samplecomposition composition

Control

Characteristic Percentage Percentage NumberSexMale 48 48 480Female 52 52 520

____ ____ ____100 100 1000


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AGraphical Illustration ofQuota Sampling

A B C D E

1 6 11 16 21

2 7 12 17 22

3 8 13 18 23

4 9 14 19 24

5 10 15 20 25

A quota of oneelement from eachgroup, A to E, isimposed. Withineach group, one

element is selectedbased on judgment

or convenience. Theresulting sample

consists of elements

3, 6, 13, 20 and 22.Note, one element isselected from eachcolumn or group.


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Snowball Sampling

In snowball sampling, an initial group ofrespondents is selected, usually at random.

After being interviewed, these respondentsare asked to identify others who belong tothe target population of interest.

Subsequent respondents are selected basedon the referrals.


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AGraphical Illustration ofSnowball Sampling

A B C D E

1 6 11 16 21

2 7 12 17 22

3 8 13 18 23

4 9 14 19 24

5 10 15 20 25

Elements 2 and 9 areselected randomly from

groups A and B. Element 2refers elements 12 and 13.

Element 9 refers

element 18. The resultingsample consists of elements2, 9, 12, 13, and 18. Note,

there are no element fromgroup E.

Random Selection

Referrals


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Choosing Nonprobability Vs.Probability Sampling

Conditions Favoring the Use of

Factors Nonprobability

sampling

Probability

sampling

Nature of research Exploratory Conclusive

Relative magnitude of sampling and

nonsampling errors

Nonsampling

errors are larger

Sampling errors

are larger

Variability in the population Homogeneous(low)

Heterogeneous(high)

Statistical considerations Unfavorable Favorable

Operational considerations Favorable Unfavorable

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12. Sampling Design