Chapter XX

Cluster Analysis

Chapter OutlineChapter Outline

1) Overview1) Overview

2) Basic Concept2) Basic Concept

3) Statistics Associated with Cluster Analysis3) Statistics Associated with Cluster Analysis

4) Conducting Cluster Analysis4) Conducting Cluster Analysis

i. Formulating the Problemi. Formulating the Problem

ii. Selecting a Distance or Similarity Measure ii. Selecting a Distance or Similarity Measure

iii. Selecting a Clustering Procedureiii. Selecting a Clustering Procedure

iv. Deciding on the Number of Clustersiv. Deciding on the Number of Clusters

v. Interpreting and Profiling the Clustersv. Interpreting and Profiling the Clusters

vi. Assessing Reliability and Validityvi. Assessing Reliability and Validity

5) Applications of Nonhierarchical Clustering 5) Applications of Nonhierarchical Clustering

6) Clustering Variables6) Clustering Variables

7) Internet & Computer Applications7) Internet & Computer Applications

8) Focus on Burke8) Focus on Burke

9) Summary9) Summary

10) Key Terms and Concepts10) Key Terms and Concepts

11) Acronyms11) Acronyms

An Ideal Clustering SituationAn Ideal Clustering SituationFigure 20.1Figure 20.1

Variable 2

Var

iab

le 1

XX

A Practical Clustering SituationA Practical Clustering SituationFigure 20.2Figure 20.2

Variable 2

Var

iab

le 1

Conducting Cluster AnalysisConducting Cluster AnalysisFig. 20.3Fig. 20.3

Select a Distance Measure

Formulate the Problem

Select a Clustering Procedure

Decide on the Number of Clusters

Interpret and Profile Clusters

Assess the Validity of Clustering

Case No. V1 V2 V3 V4 V5 V6

1 6 4 7 3 2 32 2 3 1 4 5 43 7 2 6 4 1 34 4 6 4 5 3 65 1 3 2 2 6 46 6 4 6 3 3 47 5 3 6 3 3 48 7 3 7 4 1 49 2 4 3 3 6 310 3 5 3 6 4 611 1 3 2 3 5 312 5 4 5 4 2 413 2 2 1 5 4 414 4 6 4 6 4 715 6 5 4 2 1 416 3 5 4 6 4 717 4 4 7 2 2 518 3 7 2 6 4 319 4 6 3 7 2 720 2 3 2 4 7 2

Attitudinal Data For ClusteringAttitudinal Data For ClusteringTable 20.1Table 20.1

Fig. 20.4Fig. 20.4

Clustering Procedures

A Classification of Clustering ProceduresA Classification of Clustering Procedures

Hierarchical Nonhierarchical

Agglomerative Divisive

SequentialThreshold

ParallelThreshold

OptimizingPartitioning

LinkageMethods

VarianceMethods

CentroidMethods

Ward’s Method

Single Complete Average

Linkage Methods of ClusteringLinkage Methods of ClusteringFigure 20.5Figure 20.5

Single Linkage

Minimum Distance

Complete Linkage

Maximum Distance

Average Linkage

Average Distance

Cluster 1 Cluster 2

Cluster 1 Cluster 2

Cluster 1 Cluster 2

Other Agglomerative Clustering MethodsOther Agglomerative Clustering MethodsFig. 20.6Fig. 20.6

Ward’s Procedure

Centroid Method

Vertical Icicle Plot Using Ward’s MethodVertical Icicle Plot Using Ward’s MethodFig. 20.7Fig. 20.7

1 1 1 21 1 11 11 1

8+

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2+

3+

11+

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98 4 0 4 09 6 3 2 8 31 5 7 62 75 1

Case Label and NumberCase Label and Number

Num

ber

of C

lust

ers

Num

ber

of C

lust

ers

Results of Hierarchical ClusteringResults of Hierarchical ClusteringTable 20.2Table 20.2

Stage cluster Stage cluster Clusters combined Clusters combined first appears first appears

StageStage Cluster 1Cluster 1 Cluster 2Cluster 2 Coefficient Cluster 1 Cluster 2 Next stage Coefficient Cluster 1 Cluster 2 Next stage11 1414 1616 1.000000 1.000000 0 0 0 0 7 722 2 2 1313 2.500000 2.500000 0 0 0 0 15 1533 7 7 1212 4.000000 4.000000 0 0 0 0 10 1044 5 5 1111 5.500000 5.500000 0 0 0 0 11 1155 3 3 8 8 7.000000 7.000000 0 0 0 0 16 1666 1 1 6 6 8.500000 8.500000 0 0 0 0 10 1077 1010 1414 10.166667 10.166667 0 0 1 1 9 988 9 9 2020 12.666667 12.666667 0 0 0 0 11 1199 4 4 1010 15.250000 15.250000 0 0 7 7 12 121010 1 1 7 7 18.250000 18.250000 6 6 3 3 13 131111 5 5 9 9 22.750000 22.750000 4 4 8 8 15 151212 4 4 1919 27.500000 27.500000 9 9 0 0 17 171313 1 1 1717 32.700001 32.700001 1010 0 0 14 141414 1 1 1515 40.500000 40.500000 1313 0 0 16 161515 2 2 5 5 51.000000 51.000000 2 2 1111 18 181616 1 1 3 3 63.125000 63.125000 1414 5 5 19 191717 4 4 1818 78.291664 78.291664 1212 0 0 18 181818 2 2 4 4 171.291656171.291656 1515 1717 19 191919 1 1 2 2 330.450012330.450012 1616 1818 0 0

Agglomeration Schedule Using Ward’s ProcedureAgglomeration Schedule Using Ward’s Procedure

Number of ClustersNumber of Clusters

Label caseLabel case 44 33 22

11 11 11 1122 22 22 2233 11 11 1144 33 33 2255 22 22 2266 11 11 1177 11 11 1188 11 11 1199 22 22 221010 33 33 221111 22 22 221212 11 11 111313 22 22 221414 33 33 221515 11 11 111616 33 33 221717 11 11 111818 44 33 221919 33 33 222020 22 22 22

Cluster Membership of Cases Using Ward’s ProcedureCluster Membership of Cases Using Ward’s Procedure Table 20.2 Contd.Table 20.2 Contd.

Dandogram Using Ward’s MethodDandogram Using Ward’s MethodFig. 20.8Fig. 20.8

3

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0 15 20 255 10Case Label Seq

Rescaled Distance Cluster Combine

Means of Variables

Cluster No. V1 V2 V3 V4 V5 V6

1 5.750 3.625 6.000 3.125 1.750 3.875

2 1.667 3.000 1.833 3.500 5.500 3.333

3 3.500 5.833 3.333 6.000 3.500 6.000

ClusterCluster CentroidsCentroidsTable 20.3Table 20.3

ClusterCluster V1V1 V2V2 V3V3 V4V4 V5V5 V6V611 4.00004.0000 6.00006.0000 3.00003.0000 7.00007.0000 2.00002.0000 7.00007.000022 2.00002.0000 3.00003.0000 2.00002.0000 4.00004.0000 7.00007.0000 2.00002.000033 7.00007.0000 2.00002.0000 6.00006.0000 4.00004.0000 1.00001.0000 3.00003.0000

Initial Cluster CentersInitial Cluster Centers

Results of Nonhierarchical ClusteringResults of Nonhierarchical ClusteringTable 20.4Table 20.4

Classification Cluster CentersClassification Cluster CentersClusterCluster V1V1 V2V2 V3V3 V4V4 V5V5 V6V611 3.81353.8135 5.89925.8992 3.25223.2522 6.48916.4891 2.51492.5149 6.69576.695722 1.85071.8507 3.02343.0234 1.83271.8327 3.78643.7864 6.44366.4436 2.50562.505633 6.35586.3558 2.83562.8356 6.15766.1576 3.67363.6736 1.30471.3047 3.20103.2010

Case Listing of Cluster MembershipCase Listing of Cluster MembershipCase IDCase ID ClusterCluster DistanceDistance Case IDCase ID ClusterCluster DistanceDistance11 33 1.7801.780 22 22 2.2542.25433 33 1.1741.174 44 11 1.8821.88255 22 2.5252.525 66 33 2.3402.34077 33 1.8621.862 88 33 1.4101.41099 22 1.8431.843 1010 11 2.1122.1121111 22 1.9231.923 1212 33 2.4002.4001313 22 3.3823.382 1414 11 1.7721.7721515 33 3.6053.605 1616 11 2.1372.1371717 33 3.7603.760 1818 11 4.4214.4211919 11 0.8530.853 2020 22 0.8130.813

Final Cluster CentersFinal Cluster CentersTable 20.4 contd.Table 20.4 contd.

ClusterCluster V1V1 V2V2 V3V3 V4V4 V5V5 V6V611 3.50003.5000 5.83335.8333 3.33333.3333 6.00006.0000 3.50003.5000 6.00006.000022 1.66671.6667 3.00003.0000 1.83331.8333 3.50003.5000 5.50005.5000 3.33333.333333 5.75005.7500 3.62503.6250 6.00006.0000 3.12503.1250 1.75001.7500 3.87503.8750

Distances between Final Cluster CentersDistances between Final Cluster CentersClusterCluster 1 1 2 2 3 311 0.00000.000022 5.56785.5678 0.00000.000033 5.73535.7353 6.99446.9944 0.00000.0000

Analysis of VarianceAnalysis of VarianceVariableVariable Cluster MS df Error MS df F p Cluster MS df Error MS df F pV1V1 29.1083 29.1083 22 0.60780.6078 17 47.8879 .000 17 47.8879 .000V2V2 13.5458 13.5458 22 0.62990.6299 17 21.5047 .000 17 21.5047 .000V3V3 31.3917 31.3917 22 0.83330.8333 17 37.6700 .000 17 37.6700 .000V4V4 15.7125 15.7125 22 0.72790.7279 17 21.5848 .000 17 21.5848 .000V5V5 24.1500 24.1500 22 0.73530.7353 17 32.8440 .000 17 32.8440 .000V6V6 12.1708 12.1708 22 1.07111.0711 17 11.3632 .001 17 11.3632 .001

Number of Cases in each ClusterNumber of Cases in each ClusterClusterCluster Unweighted Cases Unweighted Cases Weighted Cases Weighted Cases 11 6 6 6622 6 6 6633 8 8 88Missing Missing 0 0TotalTotal 2020 20 20

How do consumers in different countries perceive brands in different product categories? Surprisingly, the answer is that the product perception parity rate is quite high. Perceived product parity means that consumers perceive all/most of the brands in a product category as similar to each other or at par. A new study by BBDO Worldwide shows that two-thirds of consumers surveyed in 28 countries considered brands in 13 product categories to be at parity. The product categories ranged from airlines to credit cards to coffee.

Perceived Product Parity - Once Rarity - Now Reality

RIP 20.1RIP 20.1

Perceived parity averaged 63% for all categories in all countries. The Japanese

have the highest perception of parity across all product categories at 99% and Colombians the lowest at 28%. Viewed by product category, credit cards have

the highest parity perception at 76% and cigarettes the lowest at 52%.

BBDO clustered the countries based on product parity perceptions to arrive at

clusters that exhibited similar levels and patterns of parity perceptions.

The highest perception parity figure came from Asia/Pacific region (83%) which included countries of Australia, Japan, Malaysia, and South Korea, and also France. It is no surprise that France was in this list since for most products they use highly emotional, visual advertising that is feelings oriented. The next cluster was U.S.-influenced markets (65%) which included Argentina, Canada, Hong Kong, Kuwait, Mexico, Singapore, and the U.S. The third cluster, primarily European countries (60%) included Austria, Belgium, Denmark, Italy, the Netherlands, South Africa, Spain, the U.K., and Germany.

RIP 20.1 Contd.RIP 20.1 Contd.

What all this means is that in order to differentiate the product/brand,

advertising can not just focus on product performance, but also must relate the

product to the person's life in an important way. Also, much greater

marketing effort will be required in the Asia/Pacific region and in France in

order to differentiate the brand from competition and establish a unique

image. A big factor in this growing parity is of course the emergence of the global

market.

Cluster analysis can be used to explain differences in ethical perceptions by using a large multi-item, multi-dimensional scale developed to measure how ethical different situations are. One such scale was developed by Reidenbach and Robin. This scale has 29 items which compose five dimensions that measure how a respondent judges a certain action. For example, a given respondent will read about a marketing researcher that has provided proprietary information of one of his clients to a second client. The respondent is then asked complete the 29 item ethics scale. For example, to indicate if this action is:

Just :___:___:___:___:___:___:___: UnjustTraditionally :___:___:___:___:___:___:___: Unacceptable acceptable Violates :___:___:___:___:___:___:___: Does not violate an

unwritten contract

Clustering Marketing Professionals Based on Ethical Evaluations

RIP 20.2RIP 20.2

This scale could be administered to a sample of marketing professionals. By clustering respondents based on these 29 items, two important questions should be investigated. First, how do the clusters differ with respect to the five ethical dimensions; in this case, Justice, Relativist, Egoism, Utilitarianism, Deontology (see Chapter 24). Second, what types of firms compose each cluster? The clusters could be described in terms of industry classification (SIC), firm size, and firm profitability. Answers to these two questions should provide insight into what type of firms use what dimensions to evaluate ethical situations. For instance, do large firms fall in to a different cluster than small firms? Do more profitable firms perceive questionable situations more acceptable than less-profitable firms?

RIP 20.2 Contd.RIP 20.2 Contd.