Statistical Methods in Water Resources

Part 1 Summarizing data: characteristics of water resources data; measures of location; measures of spread; measures of skewness; other resistant measures; outliers; transformations. Part 2 Graphical data analysis: graphical analysis of single data sets; graphical comparisons of two or more data sets; scatterplots and enhancements; graphs for multivariate data. Part 3 Describing uncertainty: definition of interval estimates; interpretation of interval estimates; confidence intervals for the median; confidence intervals for the measn; nonparametric prediction intervals; parametric prediction intervals; confidence intervals for quantiles (percentiles); other uses for confidence intervals. Part 4 Hypothesis tests: classification of hypothesis tests; structure of hypothesis test; the rank-sum test as an example of hypothesis testing; tests for normality. Part 5 Differences between two independent groups: the rank-sum test; the t-test; graphical presentation of results; estimating the magnitude of differences between two groups. Part 6 Matched-pair tests: the sign test; the signed-rank test; the paired t-test; consequences of violating test assumptions; graphical presentation of results; estimating the magnitude of differences between two groups. Part 7 Comparing several independent groups: tests for differences due to one factor; test for the effects of more than one factor; blocking - the extension of matched-pair tests; multiple comparison tests; presentation of results. Part 8 Correlation: characteristics of correlation coefficients; Kendall's Tau; Spearman's Rho; pearson's r. Part 9 Simple linear regression: the linear regression model; computations; building a good regression model; hypothesis testing in regression; regression diagnostics; transformations of the response (y) variable; summary guide to a good SLR model. Part 10 Alternative methods to regression: Kendall-Theil robust line; alternative parametric linear equations; weighted least squares; iteratively weighted least squares; smoothing. Part 11 Multiple regression: why use MLR?; MLR model; hypothesis tests for multiple regression; confidence intervals; regression diagnostics; choosing the best MLR model; summary of the model selection criteria; analysis of covariance. Part 12 Trend analysis: general structure of trend tests; trend tests with no exogenous variable; accounting for exogenous variables; dealing with seasonality; use of transformations; use of transformations in trend studies; monotonic trend versus two sample (step) trend; applicability of trend tests with censored data. Part 13 Methods for data below the reporting limit: methods for estimating summary statistics; methods for hypothesis testing; methods for regression with censored data. Part 14 Discrete relationships: recording catagorical data; contingency tables (both variables nominal); Kruskal-Wallis test for ordered catagorical responses; Kendall's Tau for catagorical data (both variables ordinal). (Part contents)