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J.P. Verma

Data Analysis

in Management

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J.P. Verma

Research and Advanced Studies Lakshmibai National University

of Physical Education Gwalior, MP, India

ISBN 978-81-322-0785-6 ISBN 978-81-322-0786-3 (eBook) DOI 10.1007/978-81-322-0786-3

Springer New Delhi Heidelberg New York Dordrecht London Library of Congress Control Number: 2012954479

The IBM SPSS Statistics has been used in solving various applications in different chapters of the book with the permission of the International Business Machines Corporation,# SPSS, Inc., an IBM Company. The various screen images of the software are Reprinted Courtesy of International Business Machines Corporation,#SPSS. “SPSS was acquired by IBM in October, 2009.”

IBM, the IBM logo, ibm.com, and SPSS are trademarks of International Business Machines Corp., registered in many jurisdictions worldwide. Other product and service names might be trademarks of IBM or other companies. A current list of IBM trademarks is available on the Web at “IBM Copyright and trademark information” at www.ibm.com/legal/copytrade.shtml.

#Springer India 2013

This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law.

The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.

Printed on acid-free paper

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To my elder sister Sandhya Mohan for

having me introduced in statistics

Brother-in-law Rohit Mohan for his

helping gesture

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Preface

While serving as a faculty of statistics for the last 30 years, I have experienced that the non-statistics faculty and research scholars in different disciplines find it difficult to use statistical techniques in their research problems. Even if their theoretical concepts are sound its troublesome for them to use statistical software. This book provides readers with a greater understanding of a variety of statistical techniques along with the procedure to use the most popular statistical software package SPSS.

The book strengthens the intuitive understanding of the material, thereby increasing the ability to successfully analyze data in the future. It enhances readers capability in using data analysis techniques to a broader spectrum of research problems.

The book is intended for the undergraduate and postgraduate courses along with pre-doctoral and doctoral course work on data analysis, statistics, and/or quantita-tive methods taught in management and other allied disciplines like psychology, economics, education, nursing, medical, or other behavioral and social sciences. This book is equally useful to the advanced researchers in the area of humanities and behavioural and social sciences in solving their research problems.

The book has been written to provide solutions to the researchers in different disciplines for using one of the powerful statistical software SPSS. The book will serve the students as a self-learning text of using SPSS for applying statistical techniques in their research problems.

In most of the research studies, data are analyzed using multivariate statistics which poses an additional problem for the beginners. These techniques cannot be understood without in-depth knowledge of statistical concepts. Further, several fields in science, engineering, and humanities have developed their own nomencla-ture assigning different names to the same concepts. Thus, one has to gather sufficient knowledge and experience in order to analyze their data efficiently. This book covers most of the statistical techniques including some of the most powerful multivariate techniques along with their detailed analysis and interpreta-tion of the SPSS output that are required by the research scholars in different discipline to achieve their research objectives.

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The USP of this book is that even without having the indepth knowledge of statistics, one can learn various statistical techniques and their applications on their own.

Each chapter is self-contained and starts with the topics like Introductory concepts, application areas, statistical techniques used in the chapter and step-by-step solved example with SPSS. In each chapter in depth interpretation of SPSS output has been made to help the readers in understanding the application of statistical techniques in different situations. Since the SPSS output generated in different statistical applications are raw and cannot be directly used for reporting hence model way of writing the results has been shown wherever it is required.

This book focuses on providing readers with the knowledge and skills needed to carry out research in management, humanities, and social and behavioral sciences by using SPSS. Looking at the contents and prospects of learning computing skills using SPSS, this book is a must for every researcher from graduate-level studies onward. Towards the end of each chapter, short answer questions, multiple-choice questions, and assignments have been provided as a practice exercise for the readers. The common mistakes like using two-tailed test for testing one-tailed hypothe-sis, using the term “level of confidence” for defining level of significance or using the statement like “accepting the null hypothesis” instead of “not able to reject the null hypothesis” have been explained extensively in the text so that the readers may avoid such mistakes during organizing and conducting their research work.

The faculty who uses this book will find it very useful as it presents many illustrations with either real or simulated data to discuss analytical techniques in different chapters. Some of the examples cited in the text are from my own and my colleagues’ research studies.

This book consists of 14 chapters. Chapter1 deals with the data types, data cleaning, and procedure to start SPSS on the system. Notations used throughout the book in using SPSS commands have been explained in this chapter. Chapter2deals with descriptive study. Different situations have been discussed under which such studies can be undertaken. The procedure of computing various descriptive statis-tics has been discussed in this chapter. Besides computing procedure through SPSS, a new approach has been shown towards the end of the second chapter to develop the profile graph which can be used for comparing different domains of the populations.

Chapter3 explains the chi-square and its different applications by means of solved examples. The step-by-step procedure of computing chi-square using SPSS has been discussed. Chi-square is the test of significance for association between the attributes, but it provides comparison of the two groups as well, in case of the responses being measured on the nominal scale. This fact has been discussed for the benefit of the readers.

Chapter4 explains the procedure of computing correlation matrix and partial correlations using SPSS. The emphasis has been given on how to interpret the relationships.

In Chapter5, computing multiple correlations and regression analysis have been discussed. Both the approaches of regression analysis in SPSS i.e. Stepwise and Enter methods have been discussed for estimating any measurable phenomenon.

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In Chapter 6, application of t-test in testing the significance of difference between groups in all the three situations, that is, in one sample, two independent samples, and two dependent samples, has been discussed in detail. Procedures of using one-tailed and two-tailed tests have been thoroughly detailed.

Chapter 7 explains the procedure of applying one-way analysis of variance (ANOVA) with equal and unequal groups for testing the significance of variability among group means. The graphical approach has been discussed for post hoc comparisons of means besides using thep-value concept.

In Chapter8, two-way ANOVA for understanding the causes of variation has been discussed in detail by means of solved examples using SPSS. The model way of writing the results has been shown, which the students should note. Procedure for doing interaction analysis has been discussed in detail by using the SPSS output.

In Chapter 9, the application of ANCOVA to study the role of covariate in experimental research has been discussed by means of a research example. Students can find the procedure of analyzing their data much easier after going through this chapter.

In Chapter10, cluster analysis technique has been discussed in detail for market segmentation. The readers will come to know about the situations where cluster analysis can be used in their research studies. Discussions of all its basic concepts have been elaborated so that even a non-statistician can also appreciate and use it for their research data.

Chapter11deals with the factor analysis, one of the most widely used multivari-ate statistical techniques in management research. By going through this chapter, the readers can understand to study the characteristics of a group of data by means of few underlying structures instead of a large number of parameters. The proce-dure of developing the test battery using the factor analysis technique has also been discussed in detail.

In Chapter 12, we have discussed discriminant analysis and its application in various research situations. By learning this technique, one can develop classifica-tory model in classifying a customer into any of the two categories based on their relevant profile parameters. The technique is very useful in classifying a customer as good or bad for offering various services in the area of banking and insurance.

Chapter 13 explains the application of logistic regression for probabilistic classification of cases into one of the two groups. Basics of this technique have been discussed before explaining the procedure in solving logistic regression with SPSS. Interpretations of each and every output have been very carefully explained for easy understanding of the readers.

In Chapter 14, multidimensional scaling has been discussed to find the brand positioning of different products. This technique is especially useful if the popular-ity of products is to be compared on different parameters.

At each and every step, care has been taken so that the readers can learn to apply SPSS and understand minutest possible detail of analysis discussed in this book. The purpose of this book is to give a brief and clear description of how to apply variety of statistical analysis using any version of SPSS. We hope that this book will

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provide students and researchers with a self-learning material of using SPSS to analyze their data.

Students and other readers are welcome to e-mail me their query related to any portion of the book at [email protected], to which timely reply will be sent. Professor (Statistics) J.P. Verma

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Acknowledgements

I would like to extend my sincere thanks to my professional colleagues Prof. Y.P. Gupta, Prof. S. Sekhar, Dr. V.B. Singh, Prof. Jagdish Prasad and Dr. J.P. Bhukar for their valuable inputs in completing this text. I must thank to my research scholars who always motivated me to solve varieties of complex research problems which has contributed a lot in preparing this text. Finally I must appreciate the effort of my wife Hari Priya who not only provided me the peaceful environment in preparing this text but also helped me in correcting the manuscript language and format to a great extent. Finally I owe my loving gesture to my children Prachi and Priyam who have provided me the creative inputs in the preparation this manuscript.

Professor (Statistics) J.P. Verma

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Contents

1 Data Management. . . 1 Introduction . . . 1 Types of Data . . . 3 Metric Data . . . 3 Nonmetric Data . . . 4 Important Definitions . . . 5 Variable . . . 5 Attribute . . . 6

Mutually Exclusive Attributes . . . 6

Independent Variable . . . 6

Dependent Variable . . . 6

Extraneous Variable . . . 6

The Sources of Research Data . . . 7

Primary Data . . . 7

Secondary Data . . . 9

Data Cleaning . . . 9

Detection of Errors . . . 10

Typographical Conventions Used in This Book . . . 11

How to Start SPSS . . . 11

Preparing Data File . . . 13

Defining Variables and Their Properties Under Different Columns . . 13

Defining Variables for the Data in Table1.1. . . 16

Entering the Data . . . 16

Importing Data in SPSS . . . 17

Importing Data from an ASCII File . . . 18

Importing Data File from Excel Format . . . 22

Exercise . . . 25

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2 Descriptive Analysis. . . 29

Introduction . . . 29

Measures of Central Tendency . . . 31

Mean . . . 31

Median . . . 36

Mode . . . 38

Summary of When to Use the Mean, Median, and Mode . . . 40

Measures of Variability . . . 41

The Range . . . 41

The Interquartile Range . . . 41

The Standard Deviation . . . 42

Variance . . . 45

The Index of Qualitative Variation . . . 46

Standard Error . . . 47 Coefficient of Variation (CV) . . . 48 Moments . . . 49 Skewness . . . 50 Kurtosis . . . 51 Percentiles . . . 52 Percentile Rank . . . 53

Situation for Using Descriptive Study . . . 53

Solved Example of Descriptive Statistics using SPSS . . . 54

Computation of Descriptive Statistics Using SPSS . . . 54

Interpretation of the Outputs . . . 58

Developing Profile Chart . . . 62

Summary of the SPSS Commands . . . 63

Exercise . . . 64

3 Chi-Square Test and Its Application. . . 69

Introduction . . . 69

Advantages of Using Crosstabs . . . 70

Statistics Used in Cross Tabulations . . . 70

Chi-Square Statistic . . . 70

Chi-Square Test . . . 72

Application of Chi-Square Test . . . 73

Contingency Coefficient . . . 79 Lambda Coefficient . . . 79 Phi Coefficient . . . 79 Gamma . . . 80 Cramer’s V . . . 80 Kendall Tau . . . 80

Situation for Using Chi-Square . . . 80

Solved Examples of Chi-square for Testing an Equal Occurrence Hypothesis . . . 81

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Computation of Chi-Square Using SPSS . . . 82

Interpretation of the Outputs . . . 84

Solved Examples of Chi-square for Testing the Significance of Association Between Two Attributes . . . 87

Computation of Chi-Square for Two Variables Using SPSS . . . 88

Interpretation of the Outputs . . . 96

Summary of the SPSS Commands . . . 96

Exercise . . . 98

4 Correlation Matrix and Partial Correlation: Explaining Relationships. . . 103

Introduction . . . 103

Details of Correlation Matrix and Partial Correlation . . . 105

Product Moment Correlation Coefficient . . . 106

Partial Correlation . . . 112

Situation for Using Correlation Matrix and Partial Correlation . . . 115

Research Hypotheses to Be Tested . . . 116

Statistical Test . . . 117

Solved Example of Correlation Matrix and Partial Correlations by SPSS 117 Computation of Correlation Matrix Using SPSS . . . 118

Interpretation of the Outputs . . . 120

Computation of Partial Correlations Using SPSS . . . 123

Interpretation of Partial Correlation . . . 125

Summary of the SPSS Commands . . . 126

Exercise . . . 128

5 Regression Analysis and Multiple Correlations: For Estimating a Measurable Phenomenon. . . 133

Introduction . . . 133

Terminologies Used in Regression Analysis . . . 134

Multiple Correlation . . . 135

Coefficient of Determination . . . 137

The Regression Equation . . . 138

Multiple Regression . . . 145

Application of Regression Analysis . . . 149

Solved Example of Multiple Regression Analysis Including Multiple Correlation . . . 149

Computation of Regression Coefficients, Multiple Correlation, and Other Related Output in the Regression Analysis . . . 150

Interpretation of the Outputs . . . 155

Summary of the SPSS Commands For Regression Analysis . . . 159

Exercise . . . 161

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6 Hypothesis Testing for Decision-Making. . . 167 Introduction . . . 167 Hypothesis Construction . . . 168 Null Hypothesis . . . 170 Alternative Hypothesis . . . 170 Test Statistic . . . 170 Rejection Region . . . 171

Steps in Hypothesis Testing . . . 171

Type I and Type II Errors . . . 172

One-Tailed and Two-Tailed Tests . . . 174

Criteria for Using One-Tailed and Two-Tailed Tests . . . 175

Strategy in Testing One-Tailed and Two-Tailed Tests . . . 176

What IspValue? . . . 177

Degrees of Freedom . . . 177

One-Samplet-Test . . . 178

Application of One-Sample Test . . . 179

Two-Samplet-Test for Unrelated Groups . . . 181

Assumptions in Using Two-Samplet-Test . . . 181

Application of Two-Sampledt-Test . . . 182

Assumptions in Using Pairedt-Test . . . 192

Testing Protocol in Using Pairedt-Test . . . 192

Solved Example of Testing Single Group Mean . . . 196

Computation oft-Statistic and Related Outputs . . . 196

Interpretation of the Outputs . . . 201

Solved Example of Two-Samplet-Test for Unrelated Groups with SPSS 201 Computation of Two-Samplet-Test for Unrelated Groups . . . 202

Interpretation of the Outputs . . . 207

Solved Example of Pairedt-Test with SPSS . . . 208

Computation of Pairedt-Test for Related Groups . . . 209

Interpretation of the Outputs . . . 213

Summary of SPSS Commands fort-Tests . . . 214

Exercise . . . 215

7 One-Way ANOVA: Comparing Means of More than Two Samples. . . 221

Introduction . . . 221

Principles of ANOVA Experiment . . . 222

One-Way ANOVA . . . 222

Factorial ANOVA . . . 223

Repeated Measure ANOVA . . . 223

Multivariate ANOVA . . . 224

One-Way ANOVA Model and Hypotheses Testing . . . 224

Assumptions in Using One-Way ANOVA . . . 228

Effect of Using Severalt-tests Instead of ANOVA . . . 228

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Application of One-Way ANOVA . . . 229

Solved Example of One-Way ANOVA with Equal Sample Size Using SPSS . . . 233

Computations in One-Way ANOVA with Equal Sample Size . . . 234

Interpretations of the Outputs . . . 238

Solved Example of One-Way ANOVA with Unequal Sample . . . 241

Computations in One-Way ANOVA with Unequal Sample Size . . . 242

Interpretation of the Outputs . . . 246

Summary of the SPSS Commands for One-Way ANOVA (Example 7.2) . . . 248

Exercise . . . 249

8 Two-Way Analysis of Variance: Examining Influence of Two Factors on Criterion Variable. . . 255

Introduction . . . 255

Principles of ANOVA Experiment . . . 256

Classification of ANOVA . . . 257

Factorial Analysis of Variance . . . 257

Repeated Measure Analysis of Variance . . . 258

Multivariate Analysis of Variance (MANOVA) . . . 258

Advantages of Two-Way ANOVA over One-Way ANOVA . . . 259

Important Terminologies Used in Two-Way ANOVA . . . 259

Factors . . . 259

Treatment Groups . . . 260

Main Effect . . . 260

Interaction Effect . . . 260

Within-Group Variation . . . 260

Two-Way ANOVA Model and Hypotheses Testing . . . 261

Assumptions in Two-Way Analysis of Variance . . . 265

Situation Where Two-Way ANOVA Can Be Used . . . 266

Solved Example of Two-Way ANOVA Using SPSS . . . 272

Computation in Two-Way ANOVA Using SPSS . . . 273

Model Way of Writing the Results of Two-Way ANOVA and Its Interpretations . . . 279

Summary of the SPSS Commands for Two-Way ANOVA . . . 285

Exercise . . . 286

9 Analysis of Covariance: Increasing Precision in Comparison by Controlling Covariate. . . 291

Introduction . . . 291

Introductory Concepts of ANCOVA . . . 292

Graphical Explanation of Analysis of Covariance . . . 293

Analysis of Covariance Model . . . 294

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What We Do in Analysis of Covariance? . . . 296

When to Use ANCOVA . . . 297

Assumptions in ANCOVA . . . 298

Efficiency in Using ANCOVA over ANOVA . . . 298

Solved Example of ANCOVA Using SPSS . . . 298

Computations in ANCOVA Using SPSS . . . 300

Model Way of Writing the Results of ANCOVA and Their Interpretations . . . 307

Summary of the SPSS Commands . . . 310

Exercise . . . 311

10 Cluster Analysis: For Segmenting the Population. . . 317

Introduction . . . 317

What Is Cluster Analysis? . . . 318

Terminologies Used in Cluster Analysis . . . 318

Distance Measure . . . 318

Clustering Procedure . . . 321

Standardizing the Variables . . . 328

Icicle Plots . . . 328

The Dendrogram . . . 329

The Proximity Matrix . . . 329

What We Do in Cluster Analysis . . . 330

Assumptions in Cluster Analysis . . . 331

Research Situations for Cluster Analysis Application . . . 332

Steps in Cluster Analysis . . . 332

Solved Example of Cluster Analysis Using SPSS . . . 333

Stage 1 . . . 335

Stage 2 . . . 335

Stage 1: SPSS Commands for Hierarchal Cluster Analysis . . . 335

Stage 2: SPSS Commands forK-Means Cluster Analysis . . . 340

Interpretations of Findings . . . 344

Exercise . . . 354

11 Application of Factor Analysis: To Study the Factor Structure Among Variables. . . 359

Introduction . . . 359

What Is Factor Analysis? . . . 361

Terminologies Used in Factor Analysis . . . 361

Principal Component Analysis . . . 362

Factor Loading . . . 362

Communality . . . 362

Eigenvalues . . . 363

Kaiser Criteria . . . 363

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The Scree Plot . . . 363

Varimax Rotation . . . 364

What Do We Do in Factor Analysis? . . . 365

Assumptions in Factor Analysis . . . 366

Characteristics of Factor Analysis . . . 367

Limitations of Factor Analysis . . . 367

Research Situations for Factor Analysis . . . 367

Solved Example of Factor Analysis Using SPSS . . . 368

SPSS Commands for the Factor Analysis . . . 370

Interpretation of Various Outputs Generated in Factor Analysis . . . 374

Summary of the SPSS Commands for Factor Analysis . . . 381

Exercise . . . 382

12 Application of Discriminant Analysis: For Developing a Classification Model. . . 389

Introduction . . . 389

What Is Discriminant Analysis? . . . 390

Terminologies Used in Discriminant Analysis . . . 391

Variables in the Analysis . . . 391

Discriminant Function . . . 392

Classification Matrix . . . 392

Stepwise Method of Discriminant Analysis . . . 392

Power of Discriminating Variables . . . 393

Box’s M Test . . . 393

Eigenvalues . . . 393

The Canonical Correlation . . . 394

Wilks’ Lambda . . . 394

What We Do in Discriminant Analysis . . . 394

Assumptions in Using Discriminant Analysis . . . 396

Research Situations for Discriminant Analysis . . . 396

Solved Example of Discriminant Analysis Using SPSS . . . 397

SPSS Commands for Discriminant Analysis . . . 399

Interpretation of Various Outputs Generated in Discriminant Analysis 403 Summary of the SPSS Commands for Discriminant Analysis . . . 407

Exercise . . . 407

13 Logistic Regression: Developing a Model for Risk Analysis. . . 413

Introduction . . . 413

What Is Logistic Regression? . . . 414

Important Terminologies in Logistic Regression . . . 415

Outcome Variable . . . 415

Natural Logarithms and the Exponent Function . . . 415

Odds Ratio . . . 416

Maximum Likelihood . . . 416

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Logit . . . 417

Logistic Function . . . 417

Logistic Regression Equation . . . 417

Judging the Efficiency of the Logistic Model . . . 418

Understanding Logistic Regression . . . 419

Graphical Explanation of Logistic Model . . . 419

Logistic Model with Mathematical Equation . . . 421

Interpreting the Logistic Function . . . 422

Assumptions in Logistic Regression . . . 423

Important Features of Logistic Regression . . . 423

Research Situations for Logistic Regression . . . 424

Steps in Logistic Regression . . . 425

Solved Example of Logistics Analysis Using SPSS . . . 426

First Step . . . 427

Second Step . . . 428

SPSS Commands for the Logistic Regression . . . 428

Interpretation of Various Outputs Generated in Logistic Regression . . . 431

Explanation of Odds Ratios . . . 437

Conclusion . . . 437

Summary of the SPSS Commands for Logistic Regression . . . 437

Exercise . . . 438

14 Multidimensional Scaling for Product Positioning. . . 443

Introduction . . . 443

What Is Multidimensional Scaling . . . 444

Terminologies Used in Multidimensional Scaling . . . 444

Objects and Subjects . . . 444

Distances . . . 445

Similarity vs. Dissimilarity Matrices . . . 445

Stress . . . 445

Perceptual Mapping . . . 445

Dimensions . . . 446

What We Do in Multidimensional Scaling? . . . 446

Procedure of Dissimilarity-Based Approach of Multidimensional Scaling . . . 446

Procedure of Attribute-Based Approach of Multidimensional Scaling 447 Assumptions in Multidimensional Scaling . . . 448

Limitations of Multidimensional Scaling . . . 449

Solved Example of Multidimensional Scaling (Dissimilarity-Based Approach of Multidimensional Scaling) Using SPSS . . . 449

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SPSS Commands for Multidimensional Scaling . . . 450

Interpretation of Various Outputs Generated in Multidimensional Scaling . . . 452

Summary of the SPSS Commands for Multidimensional Scaling . . . 457

Exercise . . . 457

Appendix: Tables. . . 461

References and Further Readings. . . 469

Index. . . 475

References

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