Chapter13 Slides

7/31/2019 Chapter13 Slides

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Welcome to Powerpoint slidesfor

Chapter 13

Cluster Analysis

for

Market Segmentation

Marketing Research

Text and Cases

by

Rajendra Nargundkar


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1. A cluster, by definition, is a group of similar objects

2. There could be clusters of people, brands or other

objects

3. If clusters are formed of customers similar to one

another, then cluster analysis can help marketers

identify segments (clusters)

4. If clusters of brands are formed, this can be used to

gain insights into brands that are perceived as similar to

each other on a set of attributes

5. This chapter explains the use of cluster analysis for

customer segmentation

6. Cluster analysis is best performed when the variables

are interval or ratio-scaled

Slide 1


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1. There are two major classes of cluster analysis

techniques- hierarchical and non-hierarchical

2. In hierarchical clustering, some measure of

distance is used to identify distances between all pairs

of objects to be clustered. One of the popular distance

measures used is Euclidean Distance. Another is theSquared Euclidean Distance

3. We begin with all objects in separate clusters. Say,

we have ten objects in separate clusters. Two closest

objects are joined to form a cluster. The remaining 8

objects would remain separate. This is stage 1 of

hierarchical clustering.

Slide 2


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4. In stage 2, again the two closest objects form another

cluster. Now, we have two clusters, and 6 unclustered

objects. This means a total of eight clusters, two with

two objects each, and six with one object each.

5. This process continues, until points join existing

clusters (because they are closest to an existing cluster),

and clusters join other clusters, based on the shortestdistance criterion

6. In this way, a range of possible solutions is formed,

from a 10-cluster solution in the beginning, to a single

cluster solution at the end.

7. We have to decide how many clusters the data seems

to have, depending on either the agglomeration

schedule, or the dendrogram to help make the

decision. Both of these are computer outputs that

describe in numbers or visually, the sequence of cluster

formation. This decision is somewhat subjective, but

there are some guidelines one can follow, as illustrated

in the worked example

Slide 2 contd...


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Slide 3

1. In non-hierarchical clustering methods (also

known as k-means clustering methods), we need to

specify the number of clusters we want the objects to

be clustered into.

2. This can be done if we have a hypothesis that the

objects will group into a certain number of clusters.

Alternatively, we can first do a hierarchical clustering

on the data, find the approximate number of clusters,

and then perform a k-means clustering

3. In our illustration, we have used both hierarchical

and non-hierarchical methods in combination with one

another

4. Let us move on to our worked example


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Worked Out Example

Problem: A major Indian FMCG company wants to map

the profile of its target market in terms of lifestyle,attitudes and perceptions. The company's managers

prepare, with the help of their marketing research team, a

set of 15 statements, which they feel measure many of the

variables of interest. These 15 statements are given below.

The respondent had to agree or disagree (1 = Strongly

Agree, 2 = Agree, 3 = Neither Agree nor Disagree, 4 =Disagree, 5 = Strongly Disagree) with each statement.

1. I prefer to use e-mail rather than write a letter.2. I feel that quality products are always priced high.3. I think twice before I buy anything.

4. Television is a major source of entertainment.5. A car is a necessity rather than a luxury.6. I prefer fast food and ready to use products.7. People are more health conscious today.8. Entry of foreign companies has increased the efficiencyof Indian companies.

9. Women are active participants in purchase decisions.10. I believe politicians can play a positive role.11. I enjoy watching movies.12. If I get a chance, I would like to settle abroad.13. I always buy branded products.14. I frequently go out on weekends.15. I prefer to pay by credit card rather than in cash.

Slide 4


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Slide 5

For the purpose of this illustration, we will assume

that 20 respondents answered the questionnaire above

(In a real life situation, the sample size would be

higher). The input data matrix of 20 respondents x 15variables is shown in fig 1.

Fig. 1

var000

01

var0000

2

var0000

3

var0000

4

var0000

5

var0000

6

var0000

7

var00008

1.

1.00 3.00 5.00 4.00 3.00 5.00 3.00 2.00. 2.00 3.00 2.00 3.00 4.00 4.00 3.00 2.00. 3.00 2.00 3.00 4.00 3.00 5.00 3.00 3.00. 3.00 2.00 4.00 2.00 2.00 4.00 3.00 4.00. 2.00 2.00 4.00 2.00 2.00 5.00 3.00 3.00. 2.00 4.00 3.00 3.00 5.00 4.00 4.00 2.00. 1.00 1.00 2.00 4.00 4.00 1.00 2.00 4.00. 4.00 5.00 1.00 4.00 5.00 4.00 5.00 1.00. 2.00 1.00 5.00 3.00 4.00 4.00 2.00 1.000. 5.00 2.00 4.00 3.00 2.00 5.00 1.00 5.001. 4.00 3.00 3.00 2.00 1.00 2.00 1.00 5.002. 3.00 4.00 4.00 4.00 3.00 2.00 5.00 1.003. 4.00 3.00 2.00 2.00 3.00 3.00 4.00 2.004. 1.00 2.00 2.00 4.00 2.00 5.00 1.00 3.00

5. 2.00 3.00 4.00 1.00 5.00 4.00 2.00 4.006. 3.00 2.00 1.00 3.00 4.00 3.00 2.00 3.007. 5.00 1.00 1.00 5.00 1.00 2.00 4.00 2.008. 3.00 5.00 5.00 3.00 5.00 5.00 5.00 1.009. 3.00 2.00 4.00 2.00 4.00 4.00 1.00 4.00

0. 1.00 3.00 3.00 2.00 2.00 5.00 2.00 5.00


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var000

09

var0001

0

var00011 var00012 var00013 var00014 var00015

1. 3.00 2.00 4.00 1.00 1.00 1.00 5.00. 2.00 2.00 4.00 2.00 2.00 2.00 4.00. 4.00 2.00 4.00 3.00 4.00 4.00 3.00. 5.00 4.00 5.00 4.00 5.00 5.00 5.00.

4.00 4.00 5.00 5.00 3.00 3.00 4.00. 3.00 4.00 5.00 4.00 3.00 3.00 3.00. 2.00 5.00 4.00 3.00 3.00 3.00 1.00

8. 1.00 5.00 3.00 3.00 5.00 5.00 2.00. 2.00 1.00 2.00 2.00 4.00 4.00 3.00

10. 3.00 2.00 5.00 1.00 2.00 2.00 1.0011. 2.00 2.00 4.00 5.00 1.00 1.00 2.0012. 5.00 3.00 2.00 4.00 4.00 4.00 3.0013. 2.00 3.00 4.00 3.00 5.00 5.00 4.0014. 5.00 4.00 3.00 2.00 2.00 2.00 5.0015. 4.00 5.00 2.00 1.00 1.00 1.00 4.0016. 2.00 5.00 1.00 2.00 5.00 5.00 3.0017. 2.00 4.00 4.00 3.00 3.00 3.00 2.0018. 2.00 3.00 4.00 4.00 2.00 2.00 1.0019. 1.00 3.00 4.00 5.00 3.00 3.00 2.000. 1.00 3.00 4.00 4.00 3.00 3.00 3.00

Slide 5 contd...

Fig 1 contd...


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Slide 6

The computer output is obtained by first doing a

hierarchical cluster analysis to find the number of

clusters that exist in the data. These outputs are in

figs 2 to 4 (Agglomeration schedule, vertical Icicle

Plot and Dendrogram using Average Linkage,

respectively).

The second stage is a K-means (quick cluster)

output with a pre-determined number of clusters to

be specified. In this case, the output is for 4 clusters.We will look at both stage 1 and stage 2 outputs to

understand the interpretation of both stages.


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Slide 7

Fig. 2 : Agglomeration Schedule

ClustersCombined

Stage Cluster 1st

Appears Next

Sta

ge

Clus

ter1

Clus

ter2

Coefficient Clust

er1

Cluste

r2

Stage

1 4 5 14.000000 0 0 5

2 19 20 16.000000 0 0 73 6 18 17.000000 0 0 9

4 1 2 17.000000 0 0 8

5 3 4 20.000000 0 1 11

6 13 16 25.000000 0 0 13

7 11 19 28.000000 0 2 11

8 1 14 28.500000 0 0 10

9 6 8 32.500000 0 0 12

10 1 15 34.666668 0 0 14

11 3 11 36.444443 0 7 15

12 6 12 36.666668 0 0 19

13 7 13 39.500000 0 6 1714 1 9 41.000000 10 0 16

15 3 10 41.666668 11 0 16

16 1 3 46.342857 14 15 18

17 7 17 47.000000 13 0 18

18 1 7 51.791668 16 17 19

19 1 6 58.156250 18 12 0


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Slide 8

1. A look at fig 2, the agglomeration schedule,

can help us to identify large differences in thecoefficient (4th column). The agglomeration

schedule from top to bottom (stage 1 to 19)

indicates the sequence in which cases get

combined with others (or one cluster combines

with another), until all 20 cases are combined

together in one cluster at the last stage (stage19).

2. Therefore, stage 19 represents a 1 cluster

solution, stage 18 represents a 2 cluster solution,

stage 17 represents a 3 cluster solution, and so

on, going up from the last row to the first row.

We have to identify how many clusters are in the

data. We use the difference between rows in a

measure called coefficient (also known as fusion

coefficient) in column 4 to identify the number

of clusters in the data.


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3. We will look at this figure from the last row upwards,

because we would like to have lowest possible number of

clusters, for reasons of economy and ease of interpretation.

We see that there is a difference of (58.15 51.79) in thecoefficients between the 1 cluster solution (stage 19) and the 2

cluster solution (stage 18). This is a difference of 6.36. The

next difference is of (51.79 47.00) which is equal to 4.79

(between stage 18, the 2 cluster solution and stage 17, the 3

cluster solution). The next one after that is (47-46.34), only

0.66, between stage 17 and stage 16. After this, there is again

a large difference between the 4 cluster and 5 cluster

solutions, of (46.3441.660) or 4.68. Thereafter, the

differences are smaller between subsequent rows of

coefficients.

4. A large difference in the coefficient values between any two

rows indicates a solution pertaining to the number of clusters

which the lower row represents. Ignoring the first difference

of 6.36 which would indicate only 1 cluster in the data, we

look at the next largest differences. 4.79 is the difference

between row 2 from the bottom and row 3 from the bottom,indicating a 2 cluster solution. But almost the same is the

difference between stage 16 and 15, indicating a 4 cluster

solution. At this point, it is the judgement of the researcher,

which should decide whether to go for a 2 cluster or a 4

cluster solution. Just for illustration, we will choose the 4cluster solution.

Slide 8 Contd.


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Slide 9

Now, in stage 2, a k-means clustering is run with 4

cluster solution requested (as identified from the

hierarchical clustering done above). In the givenproblem, figs 5, 6, 7 and 8 indicate the outputs of K-

means clustering for a 4 cluster solution. These

outputs give us the initial cluster centres, the case

listing of cluster membership (i.e., which case

belongs to which of the clusters), the final cluster

centres (the solution) and an ANOVA table.

Fig. 7 : Final Cluster Centers

VAR00001 VAR00002 VAR00003 VAR00004

1 2.2000 2.2000 3.8000 3.2000

2 3.5000 3.6667 2.6667 3.5000

3 1.7500 2.0000 2.2500 3.0000

4 3.0000 2.4000 3.6000 2.2000

luster VAR00005 VAR00006 VAR00007 VAR000081 3.2000 4.4000 2.8000 2.4000

2 3.6667 3.3333 4.5000 1.5000

3 3.7500 3.2500 1.7500 3.5000

4 2.2000 4.2000 1.6000 4.4000

Cluster


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luster VAR00009 VAR00010 VAR00011 VAR00012

1 3.2000 2.2000 3.8000 2.4000

2 2.5000 3.6667 3.6667 3.5000

3 3.2500 4.7500 2.5000 2.0000

4 2.2000 2.8000 4.4000 4.0000

Cluster VAR00013 VAR00014 VAR00015

1 2.4000 3.2000 4.0000

2 4.1667 3.6667 2.5000

3 1.2500 2.7500 3.2500

4 3.0000 2.4000 2.4000

Slide 9 Contd.

Fig 7 contd...


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Slide 10

1. The final cluster centres (above) describe the mean valueof each variable for each of the 4 clusters. For example,cluster 1 is described by the mean values of variable 1 = 2.2,

variable 2 = 2.2, variable 3 = 3.8, variable 4 = 3.2 and so on.Similarly, cluster 3 is described by variable 1 = 1.75,variable 2 = 2.0, variable 3 = 2.25, and variable 4 = 3.0, andso on.

2. We now go back to the original variables (in this case the15 statements in our questinnaire), and interpret the clustersin terms of the 15 variables. For example, cluster 3 consistsof people who are on the e-mail rather than writingconventional letters (variable 1 value = 1.75 which isequivalent to agree on the scale of 1 to 5). Similarly, theyare also people who tend to think twice before buyinganything (variable 3 value 2.25) in other words, careful

spenders. They also agree (variable 2 value = 2.00) thatquality products are always priced high that is, they have apositive correlation in their minds about a products qualityand price.

3. On these same variables, cluster 2 shows people who

prefer conventional mail to e-mail (variable 1 value = 3.5 orclose to disagree), people who do not necessarily associatehigh price with good quality (variable 2 value = 3.67), andtend to be neutral about care in spending (variable 3 value =2.67). In this way, when we compare final cluster centrevalues on each of the 15 variables, for 1 cluster at a time, a

complete picture of the clusters emerges.


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Slide 11

In this case, we will briefly describe each of the 4 clusters

as follows:

Cluster 1

E-mail users, feel quality comes at a price, not carefulspenders, do not like television much, do not think a car is

a necessity, do not like fast food and ready to use products,

are not sure whether people are more health-conscious

today, think foreign companies have increased somewhat

the efficiency of Indian companies, disagree that women

are active purchasing decision makers, feel that politicians

can play an active role, do not enjoy watching movies,

might consider settling abroad, tend to buy branded

products, do not go out much on weekends and like to pay

cash, rather than charging to their credit cards (if they have

one).

It is thus a cluster exhibiting many traditional values,

except that they have adapted to email use. They are also

beginning to loosen their purse strings, and are probably in

transition in some other factors like acceptance of women

as decision makers and the advent of credit cards.


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Cluster 2

Regular mail writers, bargain hunters or aggressive buyers,

not too particular about thinking before spending, not great

valuers of TV, believe the car is a luxury not too fond of fastfood and convenience products, do not think people are very

health conscious, feel foreign companies have done us good,

think women are active purchasing decision makers, do not

believe in politicians, do not like movies, do not want to

settle abroad, do not stress on branded products, do not go out

on weekends, but do prefer credit cards for payments.

It is a group which likes to use credit, spends more freely,

believes in woman power, believe in economics rather than

politics, and feel quality products can be cheap. Also, they

seem to have a patriotic streak, as they do not want to settleabroad.

Slide 11 contd...


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Cluster 3

E-mail users, quality measured by price, think twice before

buying, indifferent to TV, car is a luxury to them, not too

fond of fast food, agree that people are health conscious, do

not think foreign companies have made us efficient, do not

believe in woman power, detest politicians, enjoy watchingmovies, willing to settle abroad, always buy branded

products, go out on weekends, slightly prefer cash to credit

cards.

This group is not a free spending one, but health conscious,

more patriarchical, more brand loyal to branded products,but outgoing compared to other groups, even willing to go

abroad to settle.

Slide 12


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Cluster 4

Not too particular about e-mail, measure quality by

price, free spending, enjoy watching TV, think a car is

necessary, not fond of fast food, think people are health

conscious, do not think foreign companies have made

us efficient, believe in woman power, somewhatpositive about politicians, not movie watchers, do not

want to settle abroad, indifferent to branding,

moderately outgoing and moderately in favour of credit

cards rather than cash.

This group is optimistic, free spending and a good

target for TV advertising, particularly consumer

durables and entertainment. But they are not necessarily

influenced by brands. They may want value for money,

but if they see value, they may spend a lot.

In summary, the cluster analysis of this sample of

respondents tells us a lot about the possible segments

which exist in the target population.

Slide 12 contd...


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Slide 13

ANOVA:

Fig. 8 : Analysis of Variance

Variable Cluster MS DF Error MS DF F Prob

VAR00001 3.0500 3 1.315 16.0 2.3183 .114

VAR00002 3.0722 3 1.083 16.0 2.8359 .071

VAR00003 2.5722 3 1.630 16.0 1.5778 .234

VAR00004 1.6333 3 .943 16.0 1.7307 .201

VAR00005 2.5056 3 1.605 16.0 1.5609 .238

VAR00006 1.7056 3 1.505 16.0 1.1331 .365

VAR00007 9.6500 3 .390 16.0 24.7040 .000VAR00008 8.5500 3 .681 16.0 12.5505 .000

VAR00009 1.3000 3 1.865 16.0 .6968 .567

VAR00010 5.5.56 3 .730 16.0 7.5397 .002

VAR00011 2.7389 3 1.020 16.0 2.6830 .082

VAR00012 4.0833 3 1.293 16.0 3.1562 .054

VAR00013 7.2556 3 .799 16.0 9.0813 .001VAR00014 1.6222 3 1.880 16.0 .8628 .480

VAR00015 2.8500 3 1.465 16.0 1.9446 .163


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The ANOVA table (fig. 8) tells us which of the 15

variables is significantly different across the 4

clusters. The last column indicates that variables 2, 7,

8, 10, 11, 12, 13 are significant at the 0.10 level

(equivalent to 90% confidence level) as they have

prob. Values less than 0.10. The other variables arenot statistically significant, as they all have prob.

Values greater then 0.10. But there is divided opinion

about the utility of statistical testing for cluster

analysis. Most established writers seen to feel that

these tests (ANOVA or other tests) are not valid.

Therefore, it is left to the researchers judgementwhether he would like to use these in determining

which variables are significant. If the tests were used,

then the interpretation of clusters and differences

across clusters should be only on the basis of those

variables which are (statistically) significantly

different across clusters at 0.10 or 0.05 or some otherlevel.

Slide 13 contd...


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Slide 14Additional Comments on Cluster Analysis

Objects

We have looked at an example of classifying people,with interval-scaled data. It is possible to classify objectssuch as brands, products, cities, etc. with clusteranalysis. For example, which brands are clusteredtogether in terms of consumer perceptions for apositioning exercise, or which cities are clusteredtogether in terms of income, education and age profile ofits residents.

Number of Clusters

One of the main decisions of a researcher is to decidehow many clusters are present in the data. In certain

cases, if for example we have a prior hypothesis abouthow many clusters ought to be present, this decisionmay already be made. But otherwise, it tends to be asubjective decision. One of the criteria that can be usedin addition to ones we have described in the chapter isthat every cluster must have a reasonable or minimum

number of objects. Which means, if a cluster comes outwith only one or two objects in it, look for anothersolution.It may be useful to experiment with two or threepossible solutions before deciding on the number ofclusters.


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Slide 15

Variables

Once the reader is aware of the basics of clusteranalysis, he can begin to use it creatively. For example,

a cluster analysis can be done on some of the measured

variables, and then other variables can be checked to

see if they also exhibit differences across clusters. In

the worked out example discussed earlier, only

Psychographics or behavioural variables were used toget the 4 clusters. We could then see if they belonged to

different places, had different education levels, or

whether one gender figured predominantly in any one

of the clusters.

Scale

Cluster analysis is ideally suited to interval scaled

variables, because Euclidean distance is a commonly

used distance measure used in the clustering process.

But nominal and ordinal level data can be used afterstandardisation if appropriate. This may also necessitate

the use of other measures of distance, more appropriate

with the scales of variables being used. But this should

be done with care. In general, it is a good idea to

standardise the variables before clustering, if the units

of measurement are radically different.


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Statistical Tests

As mentioned briefly earlier, some statistical tests

for cluster analysis are available. But their validity

being questionable, caution is recommended in

using either ANOVA or any other tests.

A general caution about cluster analysis itself is

that it tends to produce different results with

different methods and some methods are quite

vulnerable to errors in data. So, the stability of the

clusters can be checked through splitting the

sample and repeating the cluster analysis.

Slide 15 Contd...

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