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Chapter Eleven

Sampling:

Design and Procedures

2007 Prentice Hall 11-1


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Chapter Outline

1) Overview

2) Sample or Census

3) The Sampling Design Process

i. Define the Target Population

ii. Determine the Sampling Frame

iii. Select a Sampling Technique

iv. Determine the Sample Size

v. Execute the Sampling Process


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Chapter Outline

4) A Classification of Sampling Techniques

i. Nonprobability Sampling Techniques

a. Convenience Sampling

b. Judgmental Sampling

c. Quota Samplingd. Snowball Sampling

ii. Probability Sampling Techniques

a. Simple Random Sampling

b. Systematic Sampling

c. Stratified Sampling

d. Cluster Sampling

e. Other Probability Sampling Techniques


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Chapter Outline

5. Choosing Nonprobability Versus ProbabilitySampling

6. Uses of Nonprobability Versus ProbabilitySampling

7. Internet Sampling

8. International Marketing Research

9. Ethics in Marketing Research

10. Summary


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Sample Vs. CensusTable 11.1

Conditions Favoring the Use ofType of Study Sample Census

1. Budget Small Large

2. Time available Short Long

3. Population size Large Small

4. Variance in the characteristic Small Large

5. Cost of sampling errors Low High

6. Cost of nonsampling errors High Low

7. Nature of measurement Destructive Nondestructive

8. Attention to individual cases Yes No


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The Sampling Design Process

Fig. 11.1

Define the Population

Determine the Sampling Frame

Select Sampling Technique(s)

Determine the Sample Size

Execute the Sampling Process


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Define the Target Population

The target population is the collection of elements orobjects that possess the information sought by theresearcher and about which inferences are to be made.The target population should be defined in terms ofelements, sampling units, extent, and time.

An element is the object about which or from whichthe information is desired, e.g., the respondent.

Asampling unit is an element, or a unit containing

the element, that is available for selection at somestage of the sampling process.

Extent refers to the geographical boundaries.

Time is the time period under consideration.



Define the Target Population

Important qualitative factors in determining thesample size are:

the importance of the decision

the nature of the research

the number of variables

the nature of the analysis

sample sizes used in similar studies incidence rates

completion rates

resource constraints



Sample Sizes Used in MarketingResearch Studies

Table 11.2

Type of Study Minimum Size Typical Range

Problem identification research(e.g. market potential)

500 1,000-2,500

Problem-solving research (e.g.pricing)

200 300-500

Product tests 200 300-500

Test marketing studies 200 300-500

TV, radio, or print advertising (percommercial or ad tested)

150 200-300

Test-market audits 10 stores 10-20 stores

Focus groups 2 groups 6-15 groups



Classification of Sampling Techniques

Sampling Techniques

Nonprobability

Sampling Techniques

Probability

Sampling Techniques

ConvenienceSampling

JudgmentalSampling

QuotaSampling

SnowballSampling

SystematicSampling

StratifiedSampling

ClusterSampling

Other SamplingTechniques

Simple RandomSampling

Fig. 11.2



Convenience Sampling

Convenience samplingattempts to obtain asample of convenient elements. Often, respondentsare selected because they happen to be in the rightplace at the right time.

use of students, and members of socialorganizations

mall intercept interviews without qualifying therespondents

department stores using charge account lists

people on the street interviews



A Graphical Illustration ofConvenience SamplingFig. 11.3

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 a

convenient time and

place. So all theelements in this

Group are selected.

The resulting sample

consists of elements

16, 17, 18, 19 and 20.

Note, no elements are

selected from group

A, B, C and E.



Judgmental Sampling

Judgmental samplingis a form of conveniencesampling in which the population elements areselected based on the judgment of the researcher.

test markets

purchase engineers selected in industrialmarketing research

bellwether precincts selected in voting behaviorresearch

expert witnesses used in court



Graphical Illustration of JudgmentalSampling

Fig. 11.3

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 researcher considers

groups B, C and Eto betypical and convenient.

Within each of thesegroups one or two

elements are selectedbased on typicality and

convenience. The

resulting sampleconsists of elements 8,

10, 11,13, and 24. Note,no elements are selected

from groups A and D.



Quota Sampling

Quota samplingmay be viewed as two-stage restricted judgmentalsampling.

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



A Graphical Illustration ofQuota Sampling

Fig. 11.3

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 one

element from each

group, A to E, is

imposed. Within each

group, oneelement isselected based on

judgment or

convenience. The

resulting sample

consistsof elements3, 6, 13, 20 and 22.

Note, one element is

selected from each

column or group.



Snowball Sampling

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

After being interviewed, these respondents areasked to identify others who belong to the targetpopulation of interest.

Subsequent respondents are selected based onthe referrals.



A Graphical 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 are

selected randomly

from groups A and B.

Element 2 referselements 12 and 13.

Element 9 refers

element 18. The

resulting sample

consistsof elements2, 9, 12, 13, and 18.

Note, there are no

element from group E.

Random

Selection Referrals



Simple Random Sampling

Each element in the population has a known andequal probability of selection.

Each possible sample of a given size (n) has aknown and equal probability of being the sampleactually selected.

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



A Graphical Illustration ofSimple Random Sampling

Fig. 11.4

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 to 25. Theresulting sample

consists of

population

elements 3, 7, 9,

16, and 24. Note,there is no

element from

Group C.



Systematic Sampling

The sample is chosen by selecting a random startingpoint and then picking every ith element insuccession from the sampling frame.

The sampling interval, i, is determined by dividing thepopulation size N by the sample size n and roundingto the nearest integer.

When the ordering of the elements is related to thecharacteristic of interest, systematic samplingincreases the representativeness of the sample.



Systematic Sampling

If the ordering of the elements produces a cyclicalpattern, systematic sampling may decrease therepresentativeness of the sample.

For example, there are 100,000 elements in thepopulation and a sample of 1,000 is desired. In thiscase the sampling interval, i, is 100. A randomnumber between 1 and 100 is selected. 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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A Graphical Illustration ofSystematic SamplingFig. 11.4

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 random

number between 1 to

5, say 2.The resulting sample

consists of

population 2,

(2+5=) 7, (2+5x2=) 12,

(2+5x3=)17, and

(2+5x4=) 22.Note, allthe elements are

selected from a

single row.


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Stratified Sampling

A two-step process in which the population ispartitioned into subpopulations, or strata.

The strata should be mutually exclusive and collectively

exhaustive in that every population element should beassigned to one and only one stratum and no populationelements should be omitted.

Next, elements are selected from each stratum by arandom procedure, usually SRS.

A major objective of stratified sampling is to increaseprecision without increasing cost.


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Stratified Sampling

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

The stratification variables should also be closelyrelated to the characteristic of interest.

Finally, the variables should decrease the cost ofthe stratification process by being easy to measureand apply.


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Stratified Sampling

In proportionate stratified sampling, the size ofthe sample drawn from each stratum is proportionateto the relative size of that stratum in the total

population.

In disproportionate stratified sampling, the sizeof the sample from each stratum is proportionate to

the relative size of that stratum and to the standarddeviation of the distribution of the characteristic ofinterest among all the elements in that stratum.


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A Graphical Illustration ofStratified SamplingFig. 11.4

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 a

number from 1 to 5

for each stratum, A toE. The resultingsample consists of

population elements4, 7, 13, 19 and 21.

Note, one elementis selected from each

column.


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Cluster Sampling

The target population is first divided into mutuallyexclusive and collectively exhaustive subpopulations,or clusters.

Then a random sample of clusters is selected, basedon a probability sampling technique such as SRS.

For each selected cluster, either all the elements areincluded in the sample (one-stage) or a sample ofelements is drawn probabilistically (two-stage).


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Cluster Sampling

Elements within a cluster should be asheterogeneous as possible, but clusters themselvesshould be as homogeneous as possible. Ideally,

each cluster should be a small-scale representationof the population.

In probability proportionate to sizesampling,the clusters are sampled with probability

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

G hi l ll i f


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A Graphical Illustration ofCluster Sampling (2-Stage)Fig. 11.4

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 3

clusters, B, D and E.

Within each cluster,

randomly select oneor two elements. The

resulting sample

consists of

population elements

7, 18, 20,21, and 23.Note, no elements

are selected from

clusters A and C.


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Types of Cluster Sampling

Fig 11.5

Cluster Sampling

One-StageSampling

MultistageSampling

Two-StageSampling

Simple ClusterSampling

ProbabilityProportionate

to Size Sampling

Strengths and Weaknesses of


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Technique Strengths WeaknessesNonprobability SamplingConvenience sampling

Least expensive, leasttime-consuming, mostconvenient

Selection bias, sample notrepresentative, not recommended fordescriptive or causal research

Judgmental sampling Low cost, convenient,not time-consuming

Does not allow generalization,subjective

Quota sampling Sample can be controlledfor certain characteristics

Selection bias, no assurance ofrepresentativeness

Snowball sampling Can estimate rarecharacteristics

Time-consuming

Probability samplingSimple random sampling(SRS)

Easily understood,results projectable

Difficult to construct samplingframe, expensive, lower precision,no assurance of representativeness.

Systematic sampling Can increaserepresentativeness,easier to implement thanSRS, sampling frame notnecessary

Can decrease representativeness

Stratified sampling Include all importantsubpopulations,

precision

Difficult to select relevantstratification variables, not feasible tostratify on many variables, expensive

Cluster sampling Easy to implement, costeffective

Imprecise, difficult to compute andinterpret results

Table 11.3

Strengths and Weaknesses ofBasic Sampling Techniques


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A Classification of Internet Sampling

Fig. 11.6

Internet Sampling

Online InterceptSampling Recruited OnlineSampling Other Techniques

Nonrandom Random Panel Nonpanel

RecruitedPanels

Opt-inPanels

Opt-in ListRentals


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Procedures for DrawingProbability Samples

Exhibit 11.1

Simple Random

Sampling

1. Select a suitable sampling frame

2. Each element is assigned a number from 1 to N(pop. size)

3. Generate n (sample size) different random numbersbetween 1 and N

4. The numbers generated denote the elements thatshould be included in the sample


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Exhibit 11.1, cont.Systematic

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

Procedures for Drawing


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1. Select a suitable frame

2. Select the stratification variable(s) and the number of strata, H

3. Divide the entire population into H strata. Based on theclassification variable, each element of the population is assignedto one of the H strata

4. In each stratum, number the elements from 1 to Nh (the pop.size of stratum h)

5. Determine the sample size of each stratum, nh, based onproportionate or disproportionate stratified sampling, where

6. In each stratum, select a simple random sample of size nh

Exhibit 11.1, cont.

nh = nh=1

H

Stratified

Sampling

P oced es fo D a ing


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Exhibit 11.1, cont.

Cluster

Sampling

1. Assign a number from 1 to N to each element in the population

2. Divide the population into C clusters of which c will be included inthe sample

3. Calculate the sampling interval i, i=N/c (round to nearest integer)

4. Select a random number r between 1 and i, as explained in simplerandom sampling

5. Identify elements with the following numbers:r,r+i,r+2i,... r+(c-1)i

6. Select the clusters that contain the identified elements7. Select sampling units within each selected cluster based on SRS

or systematic sampling

8. Remove clusters exceeding sampling interval i. Calculate newpopulation size N*, number of clusters to be selected C*= C-1,and new sampling interval i*.

Procedures for Drawing


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Repeat the process until each of the remaining

clusters has a population less than the sampling

interval. If b clusters have been selected withcertainty, select the remaining c-b clusters

according to steps 1 through 7. The fraction of units

to be sampled with certainty is the overall sampling

fraction = n/N. Thus, for clusters selected with

certainty, we would select ns=(n/N)(N1+N2+...+Nb)

units. The units selected from clusters selected

under two-stage sampling will therefore be n*=n- ns.

Cluster

SamplingExhibit 11.1,cont.

Choosing Nonprobability Vs


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Choosing Nonprobability Vs.Probability Sampling

Conditions Favoring the Use ofFactors Nonprobability

samplingProbabilitysampling

Nature of research Exploratory Conclusive

Relative magnitude of samplingand nonsampling errors

Nonsamplingerrors arelarger

Samplingerrors arelarger

Variability in the population Homogeneous(low)

Heterogeneous (high)

Statistical considerations Unfavorable Favorable

Operational considerations Favorable Unfavorable

Table 11.4

Tennis' Systematic Sampling


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Tennis Systematic SamplingReturns a Smash

Tennis magazine conducted a mail survey of its subscribers togain a better understanding of its market. Systematic samplingwas employed to select a sample of 1,472 subscribers from thepublication's domestic circulation list. If we assume that thesubscriber list had 1,472,000 names, the sampling intervalwould be 1,000 (1,472,000/1,472). A number from 1 to 1,000

was drawn at random. Beginning with that number, every1,000th subscriber was selected.

A brand-new dollar bill was included with the questionnaire asan incentive to respondents. An alert postcard was mailed oneweek before the survey. A second, follow-up, questionnaire

was sent to the whole sample ten days after the initialquestionnaire. There were 76 post office returns, so the neteffective mailing was 1,396. Six weeks after the first mailing,778 completed questionnaires were returned, yielding aresponse rate of 56%.

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