Applied Statistics and Multivariate Data Analysis for Business and Economics: A Modern Approach Usin

Preface 2

List of Figures 11

List of Tables 18

1 Statistics and Empirical Research 19

1.1 Do Statistics Lie? 19

1.2 Different Types of Statistics 21

1.3 The Generation of Knowledge Through Statistics 24

1.4 The Phases of Empirical Research 26

1.4.1 From Exploration to Theory 26

1.4.2 From Theories to Models 27

1.4.3 From Models to Business Intelligence 31

References 33

2 From Disarray to Dataset 34

2.1 Data Collection 34

2.2 Level of Measurement 35

2.3 Scaling and Coding 39

2.4 Missing Values 41

2.5 Outliers and Obviously Incorrect Values 43

2.6 Chapter Exercises 43

2.7 Exercise Solutions 44

References 45

3 Univariate Data Analysis 46

3.1 First Steps in Data Analysis 46

3.2 Measures of Central Tendency 54

3.2.1 Mode or Modal Value 54

3.2.2 Mean 55

3.2.3 Geometric Mean 60

3.2.4 Harmonic Mean 61

3.2.5 The Median 64

3.2.6 Quartile and Percentile 67

3.3 The Boxplot: A First Look at Distributions 68

3.4 Dispersion Parameters 72

3.4.1 Standard Deviation and Variance 73

3.4.2 The Coefficient of Variation 75

3.5 Skewness and Kurtosis 76

3.6 Robustness of Parameters 79

3.7 Measures of Concentration 80

3.8 Using the Computer to Calculate Univariate Parameters 83

3.8.1 Calculating Univariate Parameters with SPSS 83

3.8.2 Calculating Univariate Parameters with Stata 84

3.8.3 Calculating Univariate Parameters with Excel 85

3.9 Chapter Exercises 86

3.10 Exercise Solutions 89

References 93

4 Bivariate Association 94

4.1 Bivariate Scale Combinations 94

4.2 Association Between Two Nominal Variables 95

4.2.1 Contingency Tables 95

4.2.2 Chi-Square Calculations 97

4.2.3 The Phi Coefficient 102

4.2.4 The Contingency Coefficient 105

4.2.5 Cramer's V 107

4.2.6 Nominal Associations with SPSS 107

4.2.7 Nominal Associations with Stata 112

4.2.8 Nominal Associations with Excel 112

4.3 Association Between Two Metric Variables 114

4.3.1 The Scatterplot 114

4.3.2 The Bravais-Pearson Correlation Coefficient 117

4.4 Relationships Between Ordinal Variables 121

4.4.1 Spearman's Rank Correlation Coefficient (Spearman's rho) 123

4.4.2 Kendall's Tau (t) 128

4.5 Measuring the Association Between Two Variables with Different Scales 135

4.5.1 Measuring the Association Between Nominal and Metric Variables 135

4.5.2 Measuring the Association Between Nominal and Ordinal Variables 138

4.5.3 Association between Ordinal and Metric variables 139

4.6 Calculating Correlation with a Computer 141

4.6.1 Calculating Correlation with SPSS 141

4.6.2 Calculating Correlation with Stata 142

4.6.3 Calculating Correlation with Excel 143

4.7 Spurious Correlations 146

4.7.1 Partial Correlation 148

4.7.2 Partial Correlations with SPSS 149

4.7.3 Partial Correlations with Stata 150

4.7.4 Partial Correlation with Excel 151

4.8 Chapter Exercises 152

4.9 Exercise Solutions 158

References 164

5 Classical Measurement Theory 165

5.1 Sources of Sampling Errors 166

5.2 Sources of Nonsampling Errors 169

References 172

6 Calculating Probability 173

6.1 Key Terms for Calculating Probability 173

6.2 Probability Definitions 176

6.3 Foundations of Probability Calculus 180

6.3.1 Probability Tree 180

6.3.2 Combinatorics 181

6.3.3 The Inclusion-Exclusion Principle for Disjoint Events 187

6.3.4 Inclusion-Exclusion Principle for Nondisjoint Events 188

6.3.5 Conditional Probability 189

6.3.6 Independent Events and Law of Multiplication 190

6.3.7 Law of Total Probability 191

6.3.8 Bayes' Theorem 192

6.3.9 Postscript: The Monty Hall Problem 193

6.4 Chapter Exercises 197

6.5 Exercise Solutions 200

References 209

7 Random Variables and Probability Distributions 210

7.1 Discrete Distributions 212

7.1.1 Binomial Distribution 212

7.1.1.1 Calculating Binomial Distributions using Excel 215

7.1.1.2 Calculating Binomial Distributions using Stata 216

7.1.2 Hypergeometric Distribution 217

7.1.2.1 Calculating Hypergeometric Distributions using Excel 220

7.1.2.2 Calculating the Hypergeometric Distribution using Stata 221

7.1.3 The Poisson Distribution 222

7.1.3.1 Calculating the Poisson Distribution using Excel 224

7.1.3.2 Calculating the Poisson Distribution using Stata 225

7.2 Continuous Distributions 226

7.2.1 The Continuous Uniform Distribution 228

7.2.2 The Normal Distribution 231

7.2.2.1 Calculating the Normal Distribution using Excel 241

7.2.2.2 Calculating the Normal Distribution using Stata 242

7.3 Important Distributions for Testing 243

7.3.1 The Chi-Squared Distribution 243

7.3.1.1 Calculating the Chi-Squared Distribution using Excel 245

7.3.1.2 Calculating the Chi-Squared Distribution using Stata 246

7.3.2 The t-Distribution 247

7.3.2.1 Calculating the t-Distribution using Excel 249

7.3.2.2 Calculating the t-Distribution using Stata 250

7.3.3 The F -distribution 251

7.3.3.1 Calculating the F-Distribution using Excel 252

7.3.3.2 Calculating the F -Distribution using Stata 253

7.4 Chapter Exercises 254

7.5 Exercise Solutions 258

References 268

8 Parameter Estimation 269

8.1 Point estimation 269

8.2 Interval estimation 277

8.2.1 The confidence interval for the mean of a population (m) 277

8.2.2 Planning the sample size for mean estimation 284

8.2.3 Confidence intervals for proportions 287

8.2.4 Planning sample sizes for proportions 290

8.2.5 The confidence interval for variances 291

8.2.6 Calculating confidence intervals with the computer 292

8.2.6.1 Calculating confidence intervals with Excel 292

8.2.6.2 Calculating confidence intervals with SPSS 296

8.2.6.3 Calculating confidence intervals with Stata 297

8.3 Chapter Exercises 301

8.4 Exercise Solutions 303

References 306

9 Hypothesis Testing 307

9.1 Fundamentals of Hypothesis Testing 307

9.2 One-Sample Tests 312

9.2.1 One-sample Z-test (when s is known) 312

9.2.2 One-sample t-test (when s is not known) 316

9.2.3 Probability value (p-value) 319

9.2.4 One-sample t-test with SPSS, Stata, and Excel 319

9.3 Tests for two dependent samples 323

9.3.1 The t-test for dependent samples 323

9.3.1.1 The paired t-test with SPSS 328

9.3.1.2 The paired t-test with Stata 329

9.3.1.3 The paired t-test with Excel 331

9.3.2 The Wilcoxon signed-rank test 332

9.3.2.1 The Wilcoxon signed-rank test with SPSS 337

9.3.2.2 The Wilcoxon signed-rank test with Stata 338

9.3.2.3 The Wilcoxon signed-rank test with Excel 339

9.4 Tests for two independent samples 340

9.4.1 The t-test of two independent samples 340

9.4.1.1 The t-test for two independent samples with SPSS 343

9.4.1.2 The t-test for two independent samples with Stata 345

9.4.1.3 The t-test for two independent samples with Excel 346

9.4.2 The Mann-Whitney U test (Wilcoxon rank-sum test) 348

9.4.2.1 The Mann-Whitney U test with SPSS 352

9.4.2.2 The Mann-Whitney U test with Stata 353

9.5 Tests for k independent samples 354

9.5.1 Analysis of Variance (ANOVA) 354

9.5.1.1 One-way Analysis of Variance (ANOVA) 355

9.5.1.2 Two-way Analysis of Variance (ANOVA) 360

9.5.1.4 ANOVA/ANCOVA with SPSS 367

9.5.1.5 ANOVA/ANCOVA with Stata 368

9.5.1.6 ANOVA with Excel 369

9.5.2 Kruskal-Wallis test (H test) 371

9.5.2.1 Kruskal-Wallis H Test with SPSS 376

9.5.2.2 Kruskal-Wallis H Test with Stata 378

9.6 Other Tests 379

9.6.1 Chi-square test of independence 379

9.6.1.1 Chi-square test of independence with SPSS 381

9.6.1.2 Chi-Square Test of Independence with Stata 384

9.6.1.3 Chi-Square Test of Independence with Excel 384

9.6.2 Tests for normal distribution 386

9.6.2.1 Testing for normal distribution with SPSS 388

9.6.2.2 Testing for normal distribution with Stata 389

9.7 Chapter Exercises 389

9.8 Exercise Solutions 400

References 415

10 Regression Analysis 418

10.1 First Steps in Regression Analysis 418

10.2 Coefficients of Bivariate Regression 420

10.3 Multivariate Regression Coefficients 425

10.4 The Goodness of Fit of Regression Lines 426

10.5 Regression Calculations with the Computer 429

10.5.1 Regression Calculations with Excel 429

10.5.2 Regression Calculations with SPSS and Stata 430

10.6 Goodness of Fit of Multivariate Regressions 432

10.7 Regression with an Independent Dummy Variable 433

10.8 Leverage Effects of Data Points 435

10.9 Nonlinear Regressions 437

10.10 Approaches to Regression Diagnostics 441

10.11 Chapter Exercises 447

10.12 Exercise Solutions 454

References 457

11 Time Series and Indices 458

11.1 Price Indices 459

11.2 Quantity Indices 466

11.3 Value Indices (Sales Indices) 468

11.4 Deflating Time Series by Price Indices 469

11.5 Shifting Bases and Chaining Indices 470

11.6 Chapter Exercises 472

11.7 Exercise Solutions 473

References 475

12 Cluster Analysis 476

12.1 Hierarchical Cluster Analysis 477

12.2 K-Means Cluster Analysis 493

12.3 Cluster Analysis with SPSS and Stata 495

12.4 Chapter Exercises 499

12.5 Exercise Solutions 502

References 503

13 Factor Analysis 505

13.1 Factor Analysis: Foundations, Methods, Interpretations 505

13.2 Factor Analysis with SPSS and Stata 514

13.3 Chapter Exercises 517

13.4 Exercise Solutions 518

References 519

List of Formulas 520

Appendix 532

Appendix 1: The Standard Normal Distribution 533

Appendix 2: The Chi-Squared Distribution 534

Appendix 3: The Student's t-Distribution 536

Appendix 4: Critical Values for the Wilcoxon Signed-Rank Test 537

Index 538