Preface xi
1 The R-Package, Sampling Procedures, and Random Variables 1
1.1 Introduction 1
1.2 The Statistical Software Package R 1
1.3 Sampling Procedures and Random Variables 4
2 Point Estimation 11
2.1 Introduction 11
2.2 Estimating Location Parameters 12
2.3 Estimating Scale Parameters 24
2.4 Estimating Higher Moments 27
2.5 Contingency Tables 29
3 Testing Hypotheses - One- and Two-Sample Problems 39
3.1 Introduction 39
3.2 The One-Sample Problem 41
3.3 The Two-Sample Problem 63
4 Confidence Estimations - One- and Two-Sample Problems 83
4.1 Introduction 83
4.2 The One-Sample Case 84
4.3 The Two-Sample Case 96
5 Analysis of Variance (ANOVA) - Fixed Effects Models 105
5.1 Introduction 105
5.2 Planning the Size of an Experiment 106
5.3 One-Way Analysis of Variance 108
5.4 Two-Way Analysis of Variance 115
5.5 Three-Way Classification 134
6 Analysis of Variance -Models with Random Effects 159
6.1 Introduction 159
6.2 One-Way Classification 159
6.3 Two-Way Classification 176
6.4 Three-Way Classification 186
7 Analysis of Variance -Mixed Models 201
7.1 Introduction 201
7.2 Two-Way Classification 201
7.3 Three-Way Layout 223
8 Regression Analysis 257
8.1 Introduction 257
8.2 Regression with Non-Random Regressors - Model I of Regression 262
8.3 Models with Random Regressors 322
9 Analysis of Covariance (ANCOVA) 339
9.1 Introduction 339
9.2 Completely Randomised Design with Covariate 340
9.3 Randomised Complete Block Design with Covariate 358
9.4 Concluding Remarks 365
10 Multiple Decision Problems 367
10.1 Introduction 367
10.2 Selection Procedures 367
10.3 The Subset Selection Procedure for Expectations 371
10.4 Optimal Combination of the Indifference Zone and the Subset Selection Procedure 372
10.5 Selection of the Normal Distribution with the Smallest Variance 375
10.6 Multiple Comparisons 375
11 Generalised Linear Models 393
11.1 Introduction 393
11.2 Exponential Families of Distributions 394
11.3 Generalised Linear Models - An Overview 396
11.4 Analysis - Fitting a GLM - The Linear Case 398
11.5 Binary Logistic Regression 399
11.6 Poisson Regression 411
11.7 The Gamma Regression 417
11.8 GLM for Gamma Regression 418
11.9 GLM for the Multinomial Distribution 425
12 Spatial Statistics 429
12.1 Introduction 429
12.2 Geostatistics 431
12.3 Special Problems and Outlook 450
References 451
Appendix A List of Problems 455
Appendix B Symbolism 483
Appendix C Abbreviations 485
Appendix D Probability and Density Functions 487
Index 489
