Applied Statistics Using SPSS, STATISTICA, MATLAB and R

Contents
Preface to the Second Edition xv
Preface to the First Edition xvii
Symbols and Abbreviations xix
1 Introduction 1
1.1 Deterministic Data and Random Data.........................................................1
1.2 Population, Sample and Statistics ...............................................................5
1.3 Random Variables.......................................................................................8
1.4 Probabilities and Distributions..................................................................10
1.4.1 Discrete Variables .......................................................................10
1.4.2 Continuous Variables ..................................................................12
1.5 Beyond a Reasonable Doubt... ..................................................................13
1.6 Statistical Significance and Other Significances.......................................17
1.7 Datasets.....................................................................................................19
1.8 Software Tools ..........................................................................................19
1.8.1 SPSS and STATISTICA..............................................................20
1.8.2 MATLAB and R..........................................................................22
2 Presenting and Summarising the Data 29
2.1 Preliminaries .............................................................................................29
2.1.1 Reading in the Data .....................................................................29
2.1.2 Operating with the Data...............................................................34
2.2 Presenting the Data ...................................................................................39
2.2.1 Counts and Bar Graphs................................................................40
2.2.2 Frequencies and Histograms........................................................47
2.2.3 Multivariate Tables, Scatter Plots and 3D Plots ..........................52
2.2.4 Categorised Plots .........................................................................56
2.3 Summarising the Data...............................................................................58
2.3.1 Measures of Location ..................................................................58
2.3.2 Measures of Spread .....................................................................62
2.3.3 Measures of Shape.......................................................................64
2.3.4 Measures of Association for Continuous Variables.....................66
2.3.5 Measures of Association for Ordinal Variables...........................69
2.3.6 Measures of Association for Nominal Variables.........................73
Exercises.................................................................................................................77
3 Estimating Data Parameters 81
3.1 Point Estimation and Interval Estimation..................................................81
3.2 Estimating a Mean ....................................................................................85
3.3 Estimating a Proportion ............................................................................92
3.4 Estimating a Variance ...............................................................................95
3.5 Estimating a Variance Ratio......................................................................97
3.6 Bootstrap Estimation.................................................................................99
Exercises...............................................................................................................107
4 Parametric Tests of Hypotheses 111
4.1 Hypothesis Test Procedure......................................................................111
4.2 Test Errors and Test Power.....................................................................115
4.3 Inference on One Population...................................................................121
4.3.1 Testing a Mean ..........................................................................121
4.3.2 Testing a Variance.....................................................................125
4.4 Inference on Two Populations ................................................................126
4.4.1 Testing a Correlation .................................................................126
4.4.2 Comparing Two Variances........................................................129
4.4.3 Comparing Two Means .............................................................132
4.5 Inference on More than Two Populations..............................................141
4.5.1 Introduction to the Analysis of Variance...................................141
4.5.2 One-Way ANOVA ....................................................................143
4.5.3 Two-Way ANOVA ...................................................................156
Exercises...............................................................................................................166
5 Non-Parametric Tests of Hypotheses 171
5.1 Inference on One Population...................................................................172
5.1.1 The Runs Test............................................................................172
5.1.2 The Binomial Test .....................................................................174
5.1.3 The Chi-Square Goodness of Fit Test .......................................179
5.1.4 The Kolmogorov-Smirnov Goodness of Fit Test ......................183
5.1.5 The Lilliefors Test for Normality ..............................................187
5.1.6 The Shapiro-Wilk Test for Normality .......................................187
5.2 Contingency Tables.................................................................................189
5.2.1 The 2×2 Contingency Table ......................................................189
5.2.2 The rxc Contingency Table .......................................................193
5.2.3 The Chi-Square Test of Independence ......................................195
5.2.4 Measures of Association Revisited............................................197
5.3 Inference on Two Populations ................................................................200
5.3.1 Tests for Two Independent Samples..........................................201
5.3.2 Tests for Two Paired Samples ...................................................205
5.4 Inference on More Than Two Populations..............................................212
5.4.1 The Kruskal-Wallis Test for Independent Samples...................212
5.4.2 The Friedmann Test for Paired Samples ...................................215
5.4.3 The Cochran Q test....................................................................217
Exercises...............................................................................................................218
6 Statistical Classification 223
6.1 Decision Regions and Functions.............................................................223
6.2 Linear Discriminants...............................................................................225
6.2.1 Minimum Euclidian Distance Discriminant ..............................225
6.2.2 Minimum Mahalanobis Distance Discriminant.........................228
6.3 Bayesian Classification ...........................................................................234
6.3.1 Bayes Rule for Minimum Risk..................................................234
6.3.2 Normal Bayesian Classification ................................................240
6.3.3 Dimensionality Ratio and Error Estimation...............................243
6.4 The ROC Curve ......................................................................................246
6.5 Feature Selection.....................................................................................253
6.6 Classifier Evaluation...............................................................................256
6.7 Tree Classifiers .......................................................................................259
Exercises...............................................................................................................268
7 Data Regression 271
7.1 Simple Linear Regression .......................................................................272
7.1.1 Simple Linear Regression Model ..............................................272
7.1.2 Estimating the Regression Function ..........................................273
7.1.3 Inferences in Regression Analysis.............................................279
7.1.4 ANOVA Tests ...........................................................................285
7.2 Multiple Regression ................................................................................289
7.2.1 General Linear Regression Model.............................................289
7.2.2 General Linear Regression in Matrix Terms .............................289
7.2.3 Multiple Correlation ..................................................................292
7.2.4 Inferences on Regression Parameters ........................................294
7.2.5 ANOVA and Extra Sums of Squares.........................................296
7.2.6 Polynomial Regression and Other Models ................................300
7.3 Building and Evaluating the Regression Model......................................303
7.3.1 Building the Model....................................................................303
7.3.2 Evaluating the Model ................................................................306
7.3.3 Case Study.................................................................................308
7.4 Regression Through the Origin...............................................................314
7.5 Ridge Regression ....................................................................................316
7.6 Logit and Probit Models .........................................................................322
Exercises...............................................................................................................327
8 Data Structure Analysis 329
8.1 Principal Components .............................................................................329
8.2 Dimensional Reduction...........................................................................337
8.3 Principal Components of Correlation Matrices.......................................339
8.4 Factor Analysis .......................................................................................347
Exercises...............................................................................................................350
9 Survival Analysis 353
9.1 Survivor Function and Hazard Function .................................................353
9.2 Non-Parametric Analysis of Survival Data.............................................354
9.2.1 The Life Table Analysis ............................................................354
9.2.2 The Kaplan-Meier Analysis.......................................................359
9.2.3 Statistics for Non-Parametric Analysis......................................362
9.3 Comparing Two Groups of Survival Data ..............................................364
9.4 Models for Survival Data........................................................................367
9.4.1 The Exponential Model .............................................................367
9.4.2 The Weibull Model....................................................................369
9.4.3 The Cox Regression Model .......................................................371
Exercises...............................................................................................................373
10 Directional Data 375
10.1 Representing Directional Data ................................................................375
10.2 Descriptive Statistics...............................................................................380
10.3 The von Mises Distributions ...................................................................383
10.4 Assessing the Distribution of Directional Data.......................................387
10.4.1 Graphical Assessment of Uniformity ........................................387
10.4.2 The Rayleigh Test of Uniformity ..............................................389
10.4.3 The Watson Goodness of Fit Test .............................................392
10.4.4 Assessing the von Misesness of Spherical Distributions...........393
10.5 Tests on von Mises Distributions............................................................395
10.5.1 One-Sample Mean Test .............................................................395
10.5.2 Mean Test for Two Independent Samples .................................396
10.6 Non-Parametric Tests..............................................................................397
10.6.1 The Uniform Scores Test for Circular Data...............................397
10.6.2 The Watson Test for Spherical Data..........................................398
10.6.3 Testing Two Paired Samples .....................................................399
Exercises...............................................................................................................400
Appendix A - Short Survey on Probability Theory 403
A.1 Basic Notions ..........................................................................................403
A.1.1 Events and Frequencies .............................................................403
A.1.2 Probability Axioms....................................................................404
A.2 Conditional Probability and Independence .............................................406
A.2.1 Conditional Probability and Intersection Rule...........................406
A.2.2 Independent Events ...................................................................406
A.3 Compound Experiments..........................................................................408
A.4 Bayes’ Theorem ......................................................................................409
A.5 Random Variables and Distributions ......................................................410
A.5.1 Definition of Random Variable .................................................410
A.5.2 Distribution and Density Functions ...........................................411
A.5.3 Transformation of a Random Variable ......................................413
A.6 Expectation, Variance and Moments ......................................................414
A.6.1 Definitions and Properties .........................................................414
A.6.2 Moment-Generating Function ...................................................417
A.6.3 Chebyshev Theorem..................................................................418
A.7 The Binomial and Normal Distributions.................................................418
A.7.1 The Binomial Distribution.........................................................418
A.7.2 The Laws of Large Numbers .....................................................419
A.7.3 The Normal Distribution ...........................................................420
A.8 Multivariate Distributions .......................................................................422
A.8.1 Definitions .................................................................................422
A.8.2 Moments....................................................................................425
A.8.3 Conditional Densities and Independence...................................425
A.8.4 Sums of Random Variables .......................................................427
A.8.5 Central Limit Theorem ..............................................................428
Appendix B - Distributions 431
B.1 Discrete Distributions .............................................................................431
B.1.1 Bernoulli Distribution................................................................431
B.1.2 Uniform Distribution .................................................................432
B.1.3 Geometric Distribution..............................................................433
B.1.4 Hypergeometric Distribution.....................................................434
B.1.5 Binomial Distribution................................................................435
B.1.6 Multinomial Distribution...........................................................436
B.1.7 Poisson Distribution ..................................................................438
B.2 Continuous Distributions ........................................................................439
B.2.1 Uniform Distribution .................................................................439
B.2.2 Normal Distribution...................................................................441
B.2.3 Exponential Distribution............................................................442
B.2.4 Weibull Distribution..................................................................444
B.2.5 Gamma Distribution ..................................................................445
B.2.6 Beta Distribution .......................................................................446
B.2.7 Chi-Square Distribution.............................................................448
B.2.8 Student’s t Distribution..............................................................449
B.2.9 F Distribution ...........................................................................451
B.2.10 Von Mises Distributions............................................................452
Appendix C - Point Estimation 455
C.1 Definitions...............................................................................................455
C.2 Estimation of Mean and Variance...........................................................457
Appendix D - Tables 459
D.1 Binomial Distribution .............................................................................459
D.2 Normal Distribution ................................................................................465
D.3 Student´s t Distribution ...........................................................................466
D.4 Chi-Square Distribution ..........................................................................467
D.5 Critical Values for the F Distribution .....................................................468
Appendix E - Datasets 469
E.1 Breast Tissue...........................................................................................469
E.2 Car Sale...................................................................................................469
E.3 Cells ........................................................................................................470
E.4 Clays .......................................................................................................470
E.5 Cork Stoppers..........................................................................................471
E.6 CTG ........................................................................................................472
E.7 Culture ....................................................................................................473
E.8 Fatigue ....................................................................................................473
E.9 FHR.........................................................................................................474
E.10 FHR-Apgar .............................................................................................474
E.11 Firms .......................................................................................................475
E.12 Flow Rate................................................................................................475
E.13 Foetal Weight..........................................................................................475
E.14 Forest Fires..............................................................................................476
E.15 Freshmen.................................................................................................476
E.16 Heart Valve .............................................................................................477
E.17 Infarct......................................................................................................478
E.18 Joints .......................................................................................................478
E.19 Metal Firms.............................................................................................479
E.20 Meteo ......................................................................................................479
E.21 Moulds ....................................................................................................479
E.22 Neonatal ..................................................................................................480
E.23 Programming...........................................................................................480
E.24 Rocks ......................................................................................................481
E.25 Signal & Noise........................................................................................481
E.26 Soil Pollution ..........................................................................................482
E.27 Stars ........................................................................................................482
E.28 Stock Exchange.......................................................................................483
E.29 VCG ........................................................................................................484
E.30 Wave .......................................................................................................484
E.31 Weather...................................................................................................484
E.32 Wines ......................................................................................................485
Appendix F - Tools 487
F.1 MATLAB Functions...............................................................................487
F.2 R Functions .............................................................................................488
F.3 Tools EXCEL File ..................................................................................489
F.4 SCSize Program ......................................................................................489
References 491
Index 499

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