Statistical Methods in Water Resources (eBook)

Front Cover 1
Statistical Methods in Water Resources 4
Copyright Page 5
Contents 8
Preface 16
Chapter 1. Summarizing Data 18
1.1. Characteristics of Water Resources Data 19
1.2. Measures of Location 20
1.3. Measures of Spread 24
1.4. Measures of Skewness 26
1.5. Other Resistant Measures 27
1.6. Outliers 28
1.7. Transformations 29
Chapter 2. Graphical Data Analysis 34
2.1. Graphical Analysis of Single Data Sets 36
2.2. Graphical Comparisons of Two or More Data Sets 52
2.3. Scatterplots and Enhancements 62
2.4. Graphs for Multivariate Data 68
Chapter 3. Describing Uncertainty 82
3.1. Definition of Interval Estimates 83
3.2. Interpretation of Interval Estimates 84
3.3. Confidence Intervals For The Median 87
3.4. Confidence Intervals For The Mean 91
3.5. Nonparametric Prediction Intervals 93
3.6. Parametric Prediction Intervals 96
3.7. Confidence Intervals For Quantiles (Percentiles) 98
3.8. Other Uses For Confidence Intervals 107
Chapter 4. Hypothesis Tests 114
4.1. Classification of Hypothesis Tests 116
4.2. Structure of Hypothesis Tests 118
4.3. The Rank-Sum Test as an Example of Hypothesis Testing 126
4.4. Tests for Normality 130
Chapter 5. Differences Between Two Independent Groups 134
5.1. The Rank-Sum Test 135
5.2. The t-Test 141
5.3. Graphical Presentation of Results 145
5.4. Estimating the Magnitude of Differences Between Two Groups 148
Chapter 6. Matched-Pair Tests 154
6.1. The Sign Test 155
6.2. The Signed-Rank Test 159
6.3. The Paired t-Test 164
6.4. Consequences of Violating Test Assumptions 166
6.5. Graphical Presentation of Results 168
6.6. Estimating the Magnitude of Differences Between Two Groups 170
Chapter 7. Comparing Several Independent Groups 174
7.1. Tests for Differences Due to One Factor 176
7.2. Tests For The Effects of More Than One Factor 186
7.3. Blocking – The Extension of Matched-Pair Tests 198
7.4. Multiple Comparison Tests 212
7.5. Presentation of Results 219
Chapter 8. Correlation 226
8.1. Characteristics of Correlation Coefficients 227
8.2. Kendall's Tau 229
8.3. Spearman's Rho 234
8.4. Pearson's r 235
Chapter 9. Simple Linear Regression 238
9.1. The Linear Regression Model 239
9.2. Computations 243
9.3. Building a Good Regression Model 245
9.4. Hypothesis Testing in Regression 255
9.5. Regression Diagnostics 262
9.6. Transformations of the Response (y) Variable 270
9.7. Summary Guide to a Good SLR Model 278
Chapter 10. Alternative Methods to Regression 282
10.1. Kendall-Theil Robust Line 283
10.2. Alternative Parametric Linear Equations 291
10.3. Weighted Least Squares 297
10.4. Iteratively Weighted Least Squares 300
10.5. Smoothing 302
Chapter 11. Multiple Regression 312
11.1. Why Use MLR? 313
11.2. MLR Model 313
11.3. Hypothesis Tests for Multiple Regression 314
1I.4. Confidence Intervals 316
11.5. Regression Diagnostics 317
11.6. Choosing the Best MLR Model 326
11.7. Summary of Model Selection Criteria 332
11.8. Analysis of Covariance 332
Chapter 12. Trend Analysis 340
12.1. General Structure of Trend Tests 341
12.2. Trend Tests With No Exogenous Variable 343
12.3. Accounting for Exogenous Variables 346
12.4. Dealing With Seasonality 354
12.5. Use of Transformations in Trend Studies 363
12.6. Monotonic Trend versus Two Sample (Step) Trend 365
12.7. Applicability of Trend Tests With Censored Data 369
Chapter 13. Methods for Data Below the Reporting Limit 374
13.1. Methods for Estimating Summary Statistics 375
13.2. Methods for Hypothesis Testing 383
13.3. Methods For Regression With Censored Data 388
Chapter 14. Discrete Relationships 394
14.1. Recording Categorical Data 395
14.2. Contingency Tables (Both Variables Nominal) 395
14.4. Kendall's Tau for Categorical Data (Both Variables Ordinal) 402
14.5. Other Methods for Analysis of Categorical Data 407
Chapter 15. Regression for Discrete Responses 410
15.1. Regression For Binary Response Variables 411
15.2. Logistic Regression 412
15.3. Alternatives to Logistic Regression 419
15.4. Logistic Regression for More Than Two Response Categories 420
Chapter 16. Presentation Graphics 426
16.1. The Value of Presentation Graphics 427
16.2. Precision of Graphs 428
16.3. Misleading Graphics To Be Avoided 440
References 450
Appendix A. Construction of Boxplots 468
Appendix B. Tables 473
Appendix C. Data Sets 487
Appendix D. Answers to Exercises 508