Data Analysis in Management with SPSS Software
J.P. Verma Data Analysis in Management with SPSS Software
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 Springer is part of Springer Science+Business Media (www.springer.com)
To my elder sister Sandhya Mohan for having me introduced in statistics Brother-in-law Rohit Mohan for his helping gesture And their angel daughter Saumya
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 quantitative 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 nomenclature 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 interpretation of the SPSS output that are required by the research scholars in different discipline to achieve their research objectives. vii
viii Preface 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-bystep 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 hypothesis, 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. Chapter 1 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. Chapter 2 deals with descriptive study. Different situations have been discussed under which such studies can be undertaken. The procedure of computing various descriptive statistics 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. Chapter 3 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. Chapter 4 explains the procedure of computing correlation matrix and partial correlations using SPSS. The emphasis has been given on how to interpret the relationships. In Chapter 5, 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.
Preface ix 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 the p-value concept. In Chapter 8, 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 Chapter 10, 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. Chapter 11 deals with the factor analysis, one of the most widely used multivariate 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 procedure 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 classificatory 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 popularity 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
x Preface 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 vermajp@sancharnet.in, to which timely reply will be sent. Professor (Statistics) J.P. Verma
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 xi
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 Table 1.1... 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 xiii
xiv Contents 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
Contents xv 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
xvi Contents 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 Is p Value?... 177 Degrees of Freedom..................................... 177 One-Sample t-test... 178 Application of One-Sample Test.......................... 179 Two-Sample t-test for Unrelated Groups... 181 Assumptions in Using Two-Sample t-test................... 181 Application of Two-Sampled t-test........................ 182 Assumptions in Using Paired t-test........................ 192 Testing Protocol in Using Paired t-test..................... 192 Solved Example of Testing Single Group Mean................. 196 Computation of t-statistic and Related Outputs................ 196 Interpretation of the Outputs.... 201 Solved Example of Two-Sample t-test for Unrelated Groups with SPSS 201 Computation of Two-Sample t-test for Unrelated Groups....... 202 Interpretation of the Outputs.... 207 Solved Example of Paired t-test with SPSS......... 208 Computation of Paired t-test for Related Groups.............. 209 Interpretation of the Outputs.... 213 Summary of SPSS Commands for t-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 Several t-tests Instead of ANOVA.... 228
Contents xvii 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
xviii Contents 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 for K-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
Contents xix 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
xx Contents 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
Contents xxi 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