Statistics for Earth and Environmental Scientists - John H Schuenemeyer

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Preface ix

1 Role of Statistics and Data Analysis 1

1.1 Introduction 1

1.2 Case Studies 1

1.3 Data 2

1.4 Samples Versus the Population: Some Notation 3

1.5 Vector and Matrix Notation 4

1.6 Frequency Distributions and Histograms 5

1.7 Distribution as a Model 6

1.8 Sample Moments 9

1.9 Normal (Gaussian) Distribution 12

1.10 Exploratory Data Analysis 13

1.11 Estimation 17

1.12 Bias 18

1.13 Causes of Variance 21

1.14 About Data 21

1.15 Reasons to Conduct Statistically Based Studies 24

1.16 Data Mining 25

1.17 Modeling 25

1.18 Transformations 27

1.19 Statistical Concepts 28

1.20 Statistics Paradigms 30

1.21 Summary 33

Exercises 34

2 Modeling Concepts 37

2.1 Introduction 37

2.2 Why Construct a Model? 37

2.3 What Does a Statistical Model Do? 38

2.4 Steps in Modeling 39

2.5 Is a Model a Unique Solution to a Problem? 44

2.6 Model Assumptions 45

2.7 Designed Experiments 47

2.8 Replication 49

2.9 Summary 49

Exercises 49

3 Estimation and Hypothesis Testing on Means and Other Statistics 51

3.1 Introduction 51

3.2 Independence of Observations 51

3.3 Central Limit Theorem 52

3.4 Sampling Distributions 53

3.5 Confidence Interval Estimate on a Mean 59

3.6 Confidence Interval on the Difference Between Means 64

3.7 Hypothesis Testing on Means 70

3.8 Bayesian Hypothesis Testing 79

3.9 Nonparametric Hypothesis Testing 82

3.10 Bootstrap Hypothesis Testing on Means 83

3.11 Testing Multiple Means via Analysis of Variance 85

3.12 Multiple Comparisons of Means 87

3.13 Nonparametric ANOVA 90

3.14 Paired Data 91

3.15 Kolmogorov-Smirnov Goodness-of-Fit Test 92

3.16 Comments on Hypothesis Testing 94

3.17 Summary 95

Exercises 97

4 Regression 99

4.1 Introduction 99

4.2 Pittsburgh Coal Quality Case Study 99

4.3 Correlation and Covariance 100

4.4 Simple Linear Regression 105

4.5 Multiple Regression 125

4.6 Other Regression Procedures 139

4.7 Nonlinear Models 143

4.8 Summary 146

Exercises 147

5 Time Series 151

5.1 Introduction 151

5.2 Time Domain 152

5.3 Frequency Domain 181

5.4 Wavelets 189

Contents vii

5.5 Summary 189

Exercises 190

6 Spatial Statistics 193

6.1 Introduction 193

6.2 Data 193

6.3 Three-Dimensional Data Visualization 196

6.4 Spatial Association 199

6.5 Effect of Trend 208

6.6 Semivariogram Models 210

6.7 Kriging 218

6.8 Space-Time Models 237

6.9 Summary 239

Exercises 240

7 Multivariate Analysis 243

7.1 Introduction 243

7.2 Multivariate Graphics 244

7.3 Principal Components Analysis 246

7.4 Factor Analysis 257

7.5 Cluster Analysis 263

7.6 Multidimensional Scaling 276

7.7 Discriminant Analysis 276

7.8 Tree-Based Modeling 286

7.9 Summary 289

Exercises 290

8 Discrete Data Analysis and Point Processes 293

8.1 Introduction 293

8.2 Discrete Process and Distributions 293

8.3 Point Processes 301

8.4 Lattice Data and Models 308

8.5 Proportions 309

8.6 Contingency Tables 312

8.7 Generalized Linear Models 318

8.8 Summary 329

Exercises 330

9 Design of Experiments 335

9.1 Introduction 335

9.2 Sampling Designs 335

9.3 Design of Experiments 347

9.4 Comments on...