Introduction to Robust Estimating and Hypothesis Testing, 4th Editon, is a ‘how-to’ on the application of robust methods using available software. Modern robust methods provide improved techniques for dealing with outliers, skewed distribution curvature and heteroscedasticity that can provide substantial gains in power as well as a deeper, more accurate and more nuanced understanding of data. Since the last edition, there have been numerous advances and improvements. They include new techniques for comparing groups and measuring effect size as well as new methods for comparing quantiles. Many new regression methods have been added that include both parametric and nonparametric techniques. The methods related to ANCOVA have been expanded considerably. New perspectives related to discrete distributions with a relatively small sample space are described as well as new results relevant to the shift function. The practical importance of these methods is illustrated using data from real world studies. The R package written for this book now contains over 1200 functions. New to this edition *35% revised content *Covers many new and improved R functions *New techniques that deal with a wide range of situations Table Of Contents Preface Chapter 1: Introduction Abstract 1.1. Problems with Assuming Normality 1.2. Transformations 1.3. The Influence Curve 1.4. The Central Limit Theorem 1.5. Is the ANOVA F Robust? 1.6. Regression 1.7. More Remarks 1.8. R Software 1.9. Some Data Management Issues 1.10. Data Sets References Chapter 2: A Foundation for Robust Methods Abstract 2.1. Basic Tools for Judging Robustness 2.2. Some Measures of Location and Their Influence Function 2.3. Measures of Scale 2.4. Scale Equivariant M-Measures of Location 2.5. Winsorized Expected Values References Chapter 3: Estimating Measures of Location and Scale Abstract 3.1. A Bootstrap Estimate of a Standard Error 3.2. Density Estimators 3.3. The Sample Trimmed Mean 3.4. The Finite Sample Breakdown Point 3.5. Estimating Quantiles 3.6. An M-Estimator of Location 3.7. One-Step M-Estimator 3.8. W-Estimators 3.9. The Hodges-Lehmann Estimator 3.10. Skipped Estimators 3.11. Some Comparisons of the Location Estimators 3.12. More Measures of Scale 3.13. Some Outlier Detection Methods 3.14. Exercises References Chapter 4: Confidence Intervals in the One-Sample Case Abstract 4.1. Problems when Working with Means 4.2. The g-and-h Distribution 4.3. Inferences About the Trimmed and Winsorized Means 4.4. Basic Bootstrap Methods 4.5. Inferences About M-Estimators 4.6. Confidence Intervals for Quantiles 4.7. Empirical Likelihood 4.8. Concluding Remarks 4.9. Exercises References Chapter 5: Comparing Two Groups Abstract 5.1. The Shift Function 5.2. Student's t Test 5.3. Comparing Medians and Other Trimmed Means 5.4. Inferences Based on a Percentile Bootstrap Method 5.5. Comparing Measures of Scale 5.6. Permutation Tests 5.7. Rank-Based Methods and a Probabilistic Measure of Effect Size 5.8. Comparing Two Independent Binomial and Multinomial Distributions 5.9. Comparing Dependent Groups 5.10. Exercises References Chapter 6: Some Multivariate Methods Abstract 6.1. Generalized Variance 6.2. Depth 6.3. Some Affine Equivariant Estimators 6.4. Multivariate Outlier Detection Methods 6.5. A Skipped Estimator of Location and Scatter 6.6. Robust Generalized Variance 6.7. Multivariate Location: Inference in the One-Sample Case 6.8. Comparing OP Measures of Location 6.9. Multivariate Density Estimators 6.10. A Two-Sample, Projection-Type Extension of the Wilcoxon-Mann-Whitney Test 6.11. A Relative Depth Analog of the Wilcoxon-Mann-Whitney Test 6.12. Comparisons Based on Depth 6.13. Comparing Dependent Groups Based on All Pairwise Differences 6.14. Robust Principal Components Analysis 6.15. Cluster Analysis 6.16. Multivariate Discriminate Analysis 6.17. Exercises References Chapter 7: One-Way and Higher Designs for Independent Groups Abstract 7.1. Trimmed Means and a One-Way Design 7.2. Two-Way Designs and Trimmed Means 7.3. Three-Way Designs and Trimmed Means Including Medians 7.4. Multiple Comparisons Based on Medians and Other Trimmed Means 7.5. A Random Effects Model for Trimmed Means 7.6. Global Tests Based on M-Measures of Location 7.7. M-Measures of Location and a Two-Way Design 7.8. Ranked-Based Methods for a One-Way Design 7.9. A Rank-Based Method for a Two-Way Design 7.10. MANOVA Based on Trimmed Means 7.11. Nested Designs 7.12. Exercises References Chapter 8: Comparing Multiple Dependent Groups Abstract 8.1. Comparing Trimmed Means 8.2. Bootstrap Methods Based on Marginal Distributions 8.3. Bootstrap Methods Based on Difference Scores 8.4. Comments on Which Method to Use 8.5. Some Rank-Based Methods 8.6. Between-by-Within and Within-by-Within Designs 8.7. Some Rank-Based Multivariate Methods 8.8. Three-Way Designs 8.9. Exercises References Chapter 9: Correlation and Tests of Independence Abstract 9.1. Problems with Pearson's Correlation 9.2. Two Types of Robust Correlations 9.3. Some Type M Measures of Correlation 9.4. Some Type O Correlations 9.5. A Test of Independence Sensitive to Curvature 9.6. Comparing Correlations: Independent Case 9.7. Exercises References Chapter 10: Robust Regression Abstract 10.1. Problems with Ordinary Least Squares 10.2. Theil-Sen Estimator 10.3. Least Median of Squares 10.4. Least Trimmed Squares Estimator 10.5. Least Trimmed Absolute Value Estimator 10.6. M-Estimators 10.7. The Hat Matrix 10.8. Generalized M-Estimators 10.9. The Coakley-Hettmansperger and Yohai Estimators 10.10. Skipped Estimators 10.11. Deepest Regression Line 10.12. A Criticism of Methods with a High Breakdown Point 10.13. Some Additional Estimators 10.14. Comments About Various Estimators 10.15. Outlier Detection Based on a Robust Fit 10.16. Logistic Regression and the General Linear Model 10.17. Multivariate Regression 10.18. Exercises References Chapter 11: More Regression Methods Abstract 11.1. Inferences About Robust Regression Parameters 11.2. Comparing the Regression Parameters of J=2 Groups 11.3. Detecting Heteroscedasticity 11.4. Curvature and Half-Slope Ratios 11.5. Curvature and Nonparametric Regression 11.6. Checking the Specification of a Regression Model 11.7. Regression Interactions and Moderator Analysis 11.8. Comparing Parametric, Additive and Nonparametric Fits 11.9. Measuring the Strength of an Association Given a Fit to the Data 11.10. Comparing Predictors 11.11. Marginal Longitudinal Data Analysis: Comments on Comparing Groups 11.12. Exercises References Chapter 12: ANCOVA Abstract 12.1. Methods Based on Specific Design Points and a Linear Model 12.2. Methods when There Is Curvature and a Single Covariate 12.3. Dealing with Two Covariates when There Is Curvature 12.4. Some Global Tests 12.5. Methods for Dependent Groups 12.6. Exercises References References Index