Statistical Methods in Water Resources

1. Summarizing Data. 1.1. Characteristics of Water Resources Data. 1.2.Measures of Location. 1.3. Measures of Spread. 1.4. Measures of Skewness. 1.5.Other Resistant Measures. 1.6. Outliers. 1.7. Transformations. 2. GraphicalData Analysis. 2.1. Graphical Analysis of Single Data Sets. 2.2. GraphicalComparisons of Two or More Data Sets. 2.3. Scatterplots and Enhancements. 2.4.Graphs for Multivariate Data. 3. Describing Uncertainty. 3.1. Definitionof Interval Estimates. 3.2. Interpretation of Interval Estimates. 3.3.Confidence Intervals For The Median. 3.4. Confidence Intervals For The Mean.3.5. Nonparametric Prediction Intervals. 3.6. Parametric Prediction Intervals.3.7. Confidence Intervals For Quantiles (Percentiles). 3.8. Other Uses ForConfidence Intervals. 4. Hypothesis Tests. 4.1. Classification ofHypothesis Tests. 4.2. Structure of Hypothesis Tests. 4.3. The Rank-Sum Testas an Example of Hypothesis Testing. 4.4. Tests for Normality. 5.Differences Between Two Independent Groups. 5.1. The Rank-Sum Test. 5.2.The t-Test. 5.3. Graphical Presentation of Results. 5.4. Estimating theMagnitude of Differences Between Two Groups. 6. Matched-Pair Tests.6.1. The Sign Test. 6.2. The Signed-Rank Test. 6.3. The Paired t-Test. 6.4.Consequences of Violating Test Assumptions. 6.5. Graphical Presentation ofResults. 6.6. Estimating the Magnitude of Differences Between Two Groups.7. Comparing Several Independent Groups. 7.1. Tests for Differences Dueto One Factor. 7.2. Tests For The Effects of More Than One Factor. 7.3.Blocking - The Extension of Matched-Pair Tests. 7.4. Multiple ComparisonTests. 7.5. Presentation of Results. 8. Correlation. 8.1.Characteristics of Correlation Coefficients. 8.2. Kendall's Tau. 8.3.Spearman's Rho. 8.4. Pearson's r. 9. Simple Linear Regression. 9.1. TheLinear Regression Model. 9.2. Computations. 9.3. Building a Good RegressionModel. 9.4. Hypothesis Testing in Regression. 9.5. Regression Diagnostics.9.6. Transformations of the Response (y) Variable. 9.7. Summary Guide to aGood SLR Model. 10. Alternative Methods to Regression. 10.1. Kendall-Theil Robust Line. 10.2. Alternative Parametric Linear Equations. 10.3.Weighted Least Squares. 10.4 Iteratively Weighted Least Squares. 10.5.Smoothing. 11. Multiple Regression. 11.1. Why Use MLR? 11.2. MLR Model.11.3. Hypothesis Tests for Multiple Regression. 11.4. Confidence Intervals.11.5. Regression Diagnostics. 11.6. Choosing the Best MLR Model. 11.7. Summaryof Model Selection Criteria. 11.8. Analysis of Covariance. 12. TrendAnalysis. 12.1. General Structure of Trend Tests. 12.2. Trend Tests With NoExogenous Variable. 12.3. Accounting for Exogenous Variables. 12.4. DealingWith Seasonality. 12.5. Use of Transformations in Trend Studies. 12.6.Monotonic Trend versus Two Sample (Step) Trend. 12.7. Applicability of TrendTests With Censored Data. 13. Methods for Data Below the ReportingLimit. 13.1. Methods for Estimating Summary Statistics. 13.2. Methods forHypothesis Testing. 13.3. Methods for Regression With Censored Data. 14.Discrete Relationships. 14.1. Recording Categorical Data. 14.2.Contingency Tables (Both Variables Nominal). 14.3. Kruskal-Wallis Test forOrdered Categorical Responses. 14.4. Kendall's Tau for Categorical Data (BothVariables Ordinal). 14.5. Other Methods for Analysis of Categorical Data.15. Regression for Discrete Responses. 15.1. Regression For BinaryResponse Variables. 15.2. Logistic Regression. 15.3. Alternatives to LogisticRegression. 15.4. Logistic Regression for More Than Two Response Categories.16. Presentation Graphics. 16.1. The Value of Presentation Graphics.16.2. Precision of Graphs. 16.3. Misleading Graphics To Be Avoided.References. Appendix A: Construction of Boxplots. Appendix B: Tables.Appendix C: Data Sets. Appendix D: Answers to Exercises.