cluster analysis assignment 2013-2014(2)

MKT 3004 Analytical Techniques for Marketing

Assignment 2: Cluster Analysis

Name: Tiezheng Yuan

Student Number: 110562836

Degree Title: NN52 Marketing and Management

Word Count: 2618

Table of Contents

Section number and title Page

1. Introduction 1

2. Theory 2

3. Application to Marketing 5

4. Method 7

5. Results 8

6. Marketing Implications 13

7. Summary 16

List of References 18

Appendices

Appendix 1. Saved Factor Scores 19

Appendix 2. Preliminary Hierarchical Cluster Analysis 20

Appendix 3. Proportion of Each Cluster 21

Appendix 4. SPSS Output Chi-Square tests 21

List of Tables

Table 1. ANOVA Table for Three-Cluster Solution 8

Table 2. Average Factor Scores for Final Cluster Centres 9

Table 3. Cluster Profiles base on interpretation

of Final Cluster Centres 9

Table 4. Summary of Tests for Cluster Identity and Shopping

Behavioural Characteristics 10

Table 5. Summary of Cluster Profiles 11

1. Introduction

Name: Tiezheng Yuan

Student No: 110562836

The aim of this study concerns the application of cluster analysis to data in the form

of factor scores that measure the importance that students attach to supermarket

features representing dimensions of Economy, Payment system, Range and quality of

products, Friendly staff, and Accessibility.

Cluster analysis is a technique concerned with grouping objects on the basis of

numerical measures that reflect characteristics of interest of the objects. Cluster

analysis is commonly used to segment consumers. The application of cluster analysis

to the student data facilitates the segmentation of student shoppers on the basis of the

importance they attach to supermarket store features. Therefore, improving the

understanding of student food shoppers and allowing better marketing strategies to be

devised, targeting students.

This study is structured as follows, Section 2 explains the theoretical aspects of the

cluster analysis. Next, Section 3 will present a review of a research paper on the

application of cluster analysis. Following this, Section 4 will describe the method

used to conduct cluster analysis. Section 5 will present the result of the analysis.

Section 6 will mention the marketing implications of results. Lastly, Section 7 will

present the summary and conclusion of the study.

2. Theory

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This section aims to explain the theoretical aspect of cluster analysis by describing the

objectives of the technique, the data requirement, various techniques of distance

measurement and lastly explanation of main theoretical approaches which includes

both hierarchical and optimisation techniques.

The aim of cluster analysis is to group objects on the basis of numerical measures of

the objects.

Cluster analysis is concerned with deciding the number of clusters, identification of

the membership of each group and profiling the characteristic of each group in terms

of behaviour, attitudes and characteristics.

The criteria that are used to form the clusters are that objects within a group should be

as similar as possible, therefore, variance within group should be as small as possible.

Objects belonging to different groups should be as dissimilar as possible, therefore,

variance between groups should be as large as possible.

The basic data for cluster analysis are presented as a standard data matrix either as

original variables or factor scores. The data are then transformed into measures of the

closeness of the objects. The method of transformation depends on the measurement

properties, non-metric data uses similarity measures and metric data uses distance

measures.

In order to perform cluster analysis, object to object distance and group to group

distance needs to be considered. Typically, object to object distance is measured by

using Euclidean distance. However, other techniques such as City block metric and

Mahalanobis distance could also be used to measure object to object distance.

Group to group distance is most commonly measured using Between groups linkage.

However, other techniques such as Within groups linkage, Nearest neighbour,

Furthest neighbour, Centroid method, Median method and Ward’s method could also

be used to measure group to group distance.

The two broad types of clustering techniques are hierarchical clustering and

optimisation clustering.

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Hierarchical clustering is a sequential process that adopts a systematic approach to

establish a range of clusters. It proceeds as a series of stages where at each successive

stage there is one less cluster than at the previous stage. It begins with as many

clusters as there are objects and on completion, there is a single cluster of all objects.

The technique employs the information in a distance matrix and at any stage, merger

takes place between the objects that are nearest (similar) to each other so that at each

stage the number of clusters is reduced by one. The researcher has to decide the

appropriate number of clusters using information from the agglomeration schedule,

dendrogram and Gower diagram.

The optimisation approach groups objects into a pre-specified number of clusters

relative to an objective. It involves 2 stages, the first stage there is an initial grouping

of data and the second stage involves the application of a clustering criterion to reach

a final solution. From initial to final stages relocation of objects may occur.

Initial grouping forms cluster centres, which are specified by the researcher or,

generated from a random selection of centres from the data. The values of the

variables define coordinates which are the cluster centres.

Subsequently, in the second stage the clustering criterion is applied to find a better

solution than the initial stage. As a result, relocation may occur, merging clusters that

are close together, splitting up those which are very large. After initial grouping and

with subsequent relocation of objects, the cluster centres may change.

The relocation criterion is usually based on the relationship between total variances,

within group variance and between group variance. The group data variance is

defined by the identity:

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T = W + Bpxp pxp pxp

T = Total variance/covariance matrix for the pooled data

W = Within group variance and covariance

B = Between group variance and covariance

T is fixed for given data, whilst W and B vary according to location/relocation

decisions. Thus, relocation criteria either minimises W or Maximises B. Due to the

relationship between T, W and B, minimizing W automatically maximizes B.

3. Application to Marketing

This section aims to explain and evaluate the practical application of cluster analysis

through reviewing the study conducted by Sung and Jeon (2009). It will explain the

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aim of the study, provide description of data and measures, explain the result and

interpretation, mention the value of study and lastly critic the study.

The study conducted by Sung and Jeon (2009) aim to classify internet users by

fashion lifestyles, to profile the demographic and internet usage characteristics of each

segment, and to examine evaluation for fashion e-retailers’ attributes.

The measure consists of a 21-item scale designed to measure fashion lifestyle of

Korean online shoppers. A five-point Likert scale with anchors of 1 - strongly

disagree to 5 - strongly agree were used.

Factor analysis was applied to the original variables, resulting in five factors which

were defined respectively as ‘Fashion consciousness’, ‘Shopping enjoyment’, ‘Brand

consciousness’, ‘Personality pursuit’ and ‘Economical orientation’.

Factor scores from the five lifestyle factors were used to conduct cluster analysis to

identify market segments. Five clusters were identified through the study. The first

cluster comprising 19.6 percent showed the second highest level of personality and

economical perspectives, but did not care about fashion or brand names, and do not

enjoy shopping at all. It is therefore interpreted as Economical shopper.

Cluster 2 comprising 17.7 percent showed the highest levels of shopping enjoyment

and economical orientation. This group also enjoy shopping for fashion products,

considered values for money, but also considered well-known brands. It is therefore

interpreted as Recreational shopper.

Cluster 3 comprising 20.6 percent showed the highest level of fashion and brand

consciousness, but less cared about shopping enjoyment or economical orientation. It

is therefore interpreted as Fashion/Brand shoppers.

Cluster 4 comprising 23.6 percent showed the second highest levels of fashion, brand

consciousness and shopping enjoyment, but lowest in personality and economical

orientation. It is therefore interpreted as Fashion follower.

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Cluster 5 comprising 18.5 percent displayed the highest level of personality and brand

consciousness, but did not care about practicality or fashion. This cluster also had

neither desire for fashion leadership nor any interest in fashion, but cared about

personality and well-dressed appearance. It is therefore interpreted as Individualistic

shopper.

The result of the study contributes to the extant literature by improving the

understanding of Korean online fashion shoppers. Besides that, the study also offers

valuable recommendations to apparel e-retailers in Korea based on characteristics of

each segment. For example, the study characterise Economical shopper segment as

typical, practical online users. Therefore, e-retailers are recommended to sell basic

items at valued prices rather than trendy, well-known brands are also appropriate. The

study also recommends e-retailers to reinforce after service attributes and price-

related promotions to enhance purchase from Economical shopper segment. The

recommendations given by the study allows e-retailers to develop better marketing

strategies, targeting different segments.

There were some limitations of the study conducted by Sung and Jeon (2009). Firstly,

the quality of the data collected is questionable using web survey (Fricker and

Schonlau, 2002). There were about 30 percent of respondents in this study evaluates

e-retailers’ attributes without having past purchase experiences (Sung and Jeon,

2009). These respondents evaluate the web site performances based on indirect

experiences from other product categories. Therefore, the interpreting of findings may

not be accurate when respondents do not have the relevant experience (Forth et al.,

2010). Secondly, the instrument used in the study conducted by Sung and Jeon (2009)

was modified based on previous studies. Therefore, there is a possibility that some

elements of fashion lifestyles associated with apparel purchasing behaviours may not

have been captured.

4. Method

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This section aims to explain and justify the method used by providing explanation of

data and measures, provide explanation of method used in particular hierarchical and

optimisation techniques and also provide justification for technique used.

The data consist of 14-item scale designed to measure the importance of supermarket

features (1 = Not at all important, 5 = Very important).


were defined respectively as ‘Economy’, ‘Payment systems’, ‘Range and quality of

products’, ‘Friendly staff’ and ‘Accessibility’. Factor scores were saved for cluster

analysis (See Appendix 1).

Cluster analysis was applied as a two-stage process to the five factor scores. In the

first stage, a hierarchical analysis was employed using the average linkage method to

provide an indication of the appropriate number of clusters. Information from the

agglomeration schedule in Appendix 2 suggested that the solution range from five-

cluster solution to two-cluster solution.

Consideration of relative cluster size, ANOVA and the desire for simplicity

(parsimony) led to the choice of a three-cluster solution. Subsequently, in the second

stage, the K-Means optimisation method was employed to derive a solution with the

specified number of clusters. A nominal cluster identity variable was saved for profile

analysis.

5. Results

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Name: Tiezheng Yuan


This section aims to present the results in a logical structure. Firstly, the cluster

analysis results will be presented. Secondly, the cluster profiles in terms of average

factor scores and behaviour shopping variables will be explained. Lastly, summary

table of profiles will be presented.

The cluster analysis results are presented as follows. Cluster analysis was applied to

the factor scores for the factors ‘Economy’, ‘Payment systems’, ‘Range and quality of

products’, ‘Friendly staff’ and ‘Accessibility’. The analysis established three clusters

comprising approximately 27 percent (Cluster 1), 44 percent (Cluster 2) and 29

percent (Cluster 3) of the student body (See Appendix 3). The nominal cluster identity

variable provides detail on individual student membership.

Table 1. ANOVA Table for Three-Cluster Solution

Factor Cluster Error F Sig.

Mean Square df Mean Square df

Economy 145.807 2 .589 705 247.467 .000

Payment systems 53.284 2 .852 705 62.564 .000

Range and quality of

products

63.507 2 .823 705 77.195 .000

Friendly staff 110.464 2 .689 705 160.217 .000

Accessibility 22.137 2 .940 705 23.549 .000

Table 1 presents the results of a descriptive ANOVA that tests the null hypothesis that

the average factor scores for the three clusters are equal against the alternative

hypothesis that they are not equal. Assuming a significance level of 5% (.050) the

significance statistic (Sig) indicates that the null hypothesis is rejected for ‘Economy’

(F(2, 705) = 247.467, Sig = .000), ‘Payment systems’ (F(2, 705) = 62.564, Sig

= .000), ‘Range and quality of products’ (F(2, 705) = 77.195, Sig = .000), ‘Friendly

staff’ (F(2, 705) = 160.217, Sig. = .000) and ‘Accessibility’ (F(2, 705) = 23.549, Sig.

= .000). Hence the results of the test confirm that the clusters are distinct. Next, the

cluster profiles will be explained using average factor scores for final cluster centres.

Table 2. Average Factor Scores for Final Cluster Centres

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FactorCluster

1 2 3

Economy -1.05774 .44846 .28904Payment systems .40466 .13830 -.58140Range and quality of products

.42505 .16458 -.64004

Friendly staff -.27364 .60530 -.66864Accessibility .17900 -.27888 .25951

The interpretation of results (Table 2) is presented in Table 3.

Table 3. Cluster Profiles base on interpretation of Final Cluster Centres

Lower than average importance within

cluster

Higher than average importance within

cluster

Least important within cluster

Most important within cluster

Least emphasis among clusters

Highest emphasis among clusters

Cluster 1 - economy- friendly staff

- payment system- range and quality of products- accessibility

economy range and quality of products

economy - payment system- range and quality of products

Cluster 2 - accessibility - friendly staff- economy- payment system- range and quality of products

accessibility friendly staff accessibility - economy- friendly staff

Cluster 3 - payment system- range and quality of products- friendly staff

- economy- accessibility

friendly staff economy - payment system- range and quality of products- friendly staff

accessibility

Factors

Cluster Profiles

Next, the cluster profiles will be explained using nominal measures of shopping

behaviour.

The behavioural is based upon nominal shopping behaviour measures. The statistical

analysis is based upon a chi-square contingency test. The hypotheses are:

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H0: The nominal cluster identity variable and the profile variable are

independent

H1: The nominal cluster identity variable and the profile variable are not

independent (are associated).

A summary of the results of the tests (See Appendix 4) is provided in Table 4. From

the table it is evident that at the five percent significance level, there are significant

differences between clusters with respect to storecard ownership, use of budget and

weekly expenditure. Therefore, the null hypothesis is rejected.

Table 4. Summary of Tests for Cluster Identity and Shopping Behavioural

Characteristics

Behavioural

Characteristic

Chi-square Statistic and Significance

Null Hypothesis

Storecard Ownership 2 (2)= 12.387, Sig = 0.002 Reject

Use of Budget 2 (2)= 34.602, Sig = 0.000 Reject

Weekly Expenditure 2 (4)= 28.595, Sig = 0.000 Reject

Storecard Ownership

Cluster 1 typically owns a storecard but with a more even storecard ownership

balance (Yes = 50.8%, No = 49.2%) and it is the least amongst the 3 clusters. Cluster

2 also indicates that a majority owns a storecard but it is the highest amongst the 3

clusters with 66.2% owning one. Cluster 3 indicates that a majority (59.0%) owns a

storecard. However, Cluster 3 has fewer members owning a storecard compared to

cluster 2 but has more compared to Cluster 1.

Use of Food Budget

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Cluster 1 indicates that majority (77.1%) do not use food budget and it has the highest

percentage of not using food budget amongst the 3 clusters. Cluster 2 indicates that

majority (58.5%) do not use food budget however it has fewer not using food budget

compared to Cluster 1. Cluster 3 indicates a marginal majority (51.5%) use food

budget and it has the lowest percentage (48.5%) that do not use food budget amongst

the 3 clusters.

Weekly Expenditure on Food

Cluster 1 typically spend £16-30 but 80.9% spend at least £16 (£16-30 = 59.6%, >£31

= 21.3%). Cluster 2 typically spend £16-30 but 85.3% spend no more than £30 (£0-15

= 37.6%, £16-30 = 47.7%). Similarly Cluster 3 typically spend £16-30 but 91.2%

spend no more than £30 (£0-15 = 39.0%, £16-30 = 52.2%).

Next, the summary table of cluster profile will be presented.

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Table 5. Summary of Cluster Profiles

Profile Cluster 1 (27%) Cluster 2 (44%) Cluster 3 (29%)

Descriptive label Rich, quality seeking Price and value, experience seeking

Budget conscious, convenient seeking

Importance of store features factors

Economy Least important Most importance Some importance

Payment systems Most important Some importance Least importance

Range and Quality of Products Most important Some importance Least importance

Friendly Staff Less important Most important Least importance

Accessibility Some importance Least important Most important

Shopping behaviour measures:

Storecard Ownership Least ownership Most ownership Some ownership

Use of Budget Least use Some use Most use

Weekly Expenditure Medium to high spenders Low to medium spenders Low to medium spenders

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6. Marketing Implications of Results

This section aims to apply strategic and tactical marketing theory to the results

through the use of Segmentation, Targeting and Positioning (STP) framework.

Implications will be made based on the characteristics of the clusters using marketing

mix 7ps. The 7ps are Product, Price, Place, Promotion, People, Process and Physical

evidence.

Cluster 1

Cluster 1 comprising 27 percent of student body is interpreted as rich and quality

seeking.

Product

Supermarkets could focus on ensuring a wide range of high quality products as range

and quality is most valued in this segment. Supermarkets could also engage more in

purchasing well-known brands from suppliers which have good reputation in product

quality. Besides that, retailers could communicate clearly with its suppliers regarding

quality standards. Furthermore, customer feedback on quality could be conducted by

supermarkets as a way to monitor quality and satisfaction. In addition, internal

(employee) feedback on quality could also be encouraged. Maintaining high quality

standard could be integrated into the organisation culture.

Process

Retailers could introduce convenient transaction methods to improve customer

shopping process as Cluster 1 place most importance on payment system. It could

introduce cash-back service at the tiles. Besides that, retailers could provide variety of

payment methods. For example customers could pay by credit card, direct debit or

cash.

Physical Evidence

The layout and design of the supermarket could be aesthetically appealing to indicate

quality and class. Besides that, posters showing commitment towards quality

assurance could be displayed.

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Cluster 2

Cluster 2 comprising 44 percent of student body is interpreted as price and value, and

experience seeking.

Price

Price and value is most important for Cluster 2. Supermarkets could adopt a cost-plus

pricing strategy when targeting Cluster 2. Besides that, supermarkets could adopt lean

production techniques such as Just-in-time (JIT) stock management approach.

Retailers only hold stocks that it need and therefore reducing storage cost. The cost

saved could be passed on to customers thus lowering product price to attract more

Cluster 2 consumers.

Promotion

Promotional efforts could focus on price and value. Retailers could step up

promotional efforts when there are special discounts. Rewards for frequent usage of

storecards (highest storecard ownership amongst 3 clusters) could also be adopted.

Retailers could use both above and below the line promotion methods. For example

advertise through internet, radio and magazines.

People

Friendly staff is most important for Cluster 2. Organisations could place more

importance in its human resource management. It needs to recruit people with the

right values and attitudes. Adequate training could be provided to equip employees

with the necessary skills to provide quality service. Employees could also be rewarded

for showing consistent good attitude. Customer feedback could be encouraged to

reflect on staff attitude.

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Cluster 3

Cluster 3 comprising 29 percent of student body is interpreted as budget conscious

and convenient seeking.

Price

Setting price within the budget of consumers is important targeting Cluster 3. Package

deals at reasonable price could be one strategy targeting Cluster 3. Retailers have to

find out the budget range of Cluster 3 and set reasonable prices within the range.

Place

Accessibility is most important for Cluster 3. There could be parking facilities nearby

supermarkets. If the supermarket is located at an inconvenient location, the

availability of parking facilities gives students the opportunities to use their cars.

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7. Summary

This section will provide a brief summary of research aim, research method, key

results and value of results. It will also evaluate the study and provide suggestions for

future research.

The aim of this study concerns the application of cluster analysis to data in the form

of factor scores that measure the importance that students attach to supermarket

features representing dimensions of Economy, Payment system, Range and quality of

products, Friendly staff, and Accessibility.

The data consist of 14-item scale designed to measure the importance of supermarket

features (1 = Not at all important, 5 = Very important).


were defined respectively as ‘Economy’, ‘Payment systems’, ‘Range and quality of

products’, ‘Friendly staff’ and ‘Accessibility’. Factor scores were saved for cluster

analysis.

Cluster analysis was applied as a two-stage process to the five factor scores. In the

first stage, a hierarchical analysis was employed. Subsequently, in the second stage,

the K-Means optimisation method was employed. Three-cluster solutions was derived

and are interpreted as Rich and quality seeking comprising 27% (Cluster 1), Price and

value, and experience seeking comprising 44% (Cluster 2) and Budget conscious and

convenient seeking comprising 29% (Cluster 3). The application of cluster analysis to

the student data facilitates the segmentation of student shoppers. Therefore, improving

the understanding of student food shoppers and allowing better marketing strategies to

be devised, targeting students.

The study can be further improved by using probability sampling technique such as

stratified sampling to provide a better representation of the population. The use of

quota sampling (non-probability) technique in the study may not provide an unbiased

representation of population (Peterson and O’Dell, 1950). As a result, objective

statistical inferences are difficult to make when non-probability sampling is used

(Ngulube, 2005).

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In future research, the study could be conducted using mixed method approach. For

example, focus group could be conducted before factor and cluster analysis. Such a

way, the data gathered is triangulated and therefore improve the credibility and

validity of result (Homburg et al., 2012). In addition, more information could be

gathered using mixed method approach. Participants might be willing to provide more

information in a focus group compared to face-to-face survey as they feel more secure

answering questions in a group (Powell and Single, 1996). Therefore enable the

researcher to gather more information.

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List of References

Forth, J., Bewley, H., Bryson, A., Dix, G. and Oxenbridge, S. (2010) 'Survey errors and survey costs: a response to Timming’s critique of the survey of employees questionnaire in WERS 2004', Work Employment and Society, 24(3), pp. 578-590.

Fricker, R.D. and Schonlau, M. (2002) 'Advantages and disadvantages of internet research surveys: Evidence from the literature', Field Methods, 14(4), pp. 347-367.

Homburg, C., Klarmann, M., Reimann, M. and Schilke, O. (2012) 'What drives key informant accuracy?', Journal of Marketing Research (JMR), 49(4), pp. 594-608.

IBM SPSS (2012), SPSS for Windows (Version 21.0), Chicago, IL, USA: SPSS Inc.

Ngulube, P. (2005) 'Research procedures used by Master of Information Studies students at the University of Natal in the period 1982–2002 with special reference to their sampling techniques and survey response rates: A methodological discourse', The International Information & Library Review, 37(2), pp. 127–143.

Peterson, P.G. and O'Dell, W.F. (1950) 'Selecting sampling methods in commercial research', Journal of Marketing, 15(2), pp. 182-189.

Powell, R.A. and Single, H.M. (1996) 'Focus Groups', International Journal for Quality in Health Care, 8(55), pp. 499-504.

Sung, H. and Jeon, Y. (2009) 'A profile of Koreans: who purchases fashion goods online?', Journal of Fashion Marketing and Management, 13(1), pp. 79-97.

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Appendix 1. Saved Factor Scores

Factors, Associated Variables and Interpretation

Factor Number

Associated Variables Coefficient Interpretation

Factor 1 Low pricesValue for moneySpecial Offers

.833

.767

.757

Economy

Factor 2 Cash back facilitiesMethod of payment

.846

.824Payment systems

Factor 3 Wide Range of well known brandsHigh quality products .769

.734

Range and quality of products

Factor 4 Friendly, helpful staff .805 Friendly staff

Factor 5 Car parking facilitiesConvenient location

.781-.769

Accessibility

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Appendix 2. Preliminary Hierarchical Cluster Analysis

Gower Diagram from Preliminary Hierarchical Analysis

Final Ten Stages of Hierarchical Cluster Analysis

Stage

Cluster Combined

Coefficients

Stage Cluster First Appears

Next Stage

Number of

clustersCluster 1 Cluster 2 Cluster 1 Cluster 2

698 10 85 12.062 683 691 702 10

699 1 18 12.432 697 680 700 9

700 1 62 13.819 699 690 702 8

701 79 226 14.297 533 687 706 7

702 1 10 15.814 700 698 703 6

703 1 38 15.965 702 651 704 5

704 1 48 25.527 703 0 706 4

705 511 518 26.156 639 0 707 3

706 1 79 27.646 704 701 707 2

707 1 511 38.909 706 705 0 1

20

-1 1 3 5 7 9 11

0

5

10

15

20

25

30

35

40

Number of Clusters

Dis

tanc

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Appendix 3. Proportion of Each Cluster

Number of Cases in Each Cluster

Cluster

number

Number Per cent

1 189.000 27

2 313.000 44

3 206.000 29

Valid 708.000 100

Missing 23.000

Appendix 4. SPSS Output Chi-Square tests

Crosstab for Cluster Identity and Storecard Ownership

Cluster numberStorecard Total

Yes No

Cluster identity

Cluster 1Count 91 88 179

% within Cluster identity 50.8% 49.2% 100.0%





TotalCount 400 278 678


Chi-square Test for Cluster Identity and Storecard Ownership

TestValue df Asymp. Sig. (2-

sided)

Pearson Chi-Square 12.387a 2 .002

Likelihood Ratio 12.447 2 .002

Linear-by-Linear Association .632 1 .427

N of Valid Cases 678

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Crosstab for Cluster Identity and Use of Food Budget

Cluster numberBudget Total

Yes No

Cluster identity







TotalCount 278 427 705


Chi-square Test for Cluster Identity and Use of a Food Budget


sided)



Linear-by-Linear Association 33.201 1 .000


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Crosstab for Cluster Identity and Weekly Expenditure on Food

Cluster numberWeekly Expenditure Total

£0-15 £16-30 £31+

Cluster identity

Cluster 1Count 36 112 40 188

% within Cluster identity 19.1% 59.6% 21.3% 100.0%





TotalCount 228 361 102 691


Chi-square Test for Crosstab for Cluster Identity and Weekly Expenditure on Food


sided)



Linear-by-Linear Association 22.649 1 .000


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cluster analysis assignment 2013-2014(2)

Documents

aim of cluster analysis

cluster identity

cluster solution

summary of cluster profiles

cluster profiles base

student data

anova table

tiezheng yuan student