An Introduction to Nonparametric Statistics - An Introduction to Nonparametric Statistics -

Probability Background Probability Distributions for Observations Gaussian Distribution Uniform Distribution Laplace Distribution Cauchy Distribution Logistic Distribution Exponential Distribution Location and Scale Families Sampling Distributions Binomial Distribution ˜2-distribution T-distribution F-distribution Elementary Tasks in Frequentist Inference Hypothesis Testing One-Sided Hypothesis Tests Two-Sided Hypothesis Tests P-values Confidence Intervals P-value Inversion Test Inversion with Pivotal Statistics A Problematic Example Exercises One-Sample Nonparametric Inference Parametric Inference on Means Estimation Using Averages One-Sample Testing for Gaussian Observations The Need for Distribution-Free Tests One-Sample Median Methods Estimates of the Population Median Hypothesis Tests Concerning the Population Median Con dence Intervals for the Median Inference for Other Quantiles Comparing Tests Power, Sample Size, and Effect Size Power Sample and Effect Sizes Effciency Calculations Examples of Power Calculations Distribution Function Estimation Exercises Two-Sample Testing Two-Sample Approximately Gaussian Inference Two-Sample Approximately Gaussian Inference on Expectations Approximately Gaussian Dispersion Inference General Two-Sample Rank Tests Null Distributions of General Rank Statistics Moments of Rank Statistics A First Distribution-Free Test The Mann-Whitney-Wilcoxon Test Exact and Approximate Mann-Whitney Probabilities Moments and Approximate Normality Other Scoring Schemes Using Data as Scores: the Permutation Test Empirical Levels and Powers of Two-Sample Tests Adaptation to the Presence of Tied Observations Mann-Whitney-Wilcoxon Null Hypotheses E ciency and Power of Two-Sample Tests Efficacy of the Gaussian-Theory Test Efficacy of the Mann-Whitney-Wilcoxon Test Summarizing Asymptotic Relative Efficiency Power for Mann-Whitney-Wilcoxon Testing Testing Equality of Dispersion Two-Sample Estimation and Con dence Intervals Inversion of the Mann-Whitney-Wilcoxon Test Tests for Broad Alternatives Exercises Methods for Three or More Groups Gaussian-Theory Methods Contrasts Multiple Comparisons General Rank Tests Moments of General Rank Sums Construction of a Chi-Square-Distributed Statistic The Kruskal-Wallis Test Kruskal-Wallis Approximate Critical Values Other Scores for Multi-Sample Rank Based Tests Multiple Comparisons Ordered Alternatives Powers of Tests Power of Tests for Ordered Alternatives Power of Tests for Unordered Alternatives E ciency Calculations Ordered Alternatives Unordered Alternatives Exercises Group Differences with Blocking Gaussian Theory Approaches Paired Comparisons Multiple Group Comparisons Nonparametric Paired Comparisons Estimating the Population Median Di erence Con dence Intervals Signed-Rank Statistic Alternative Distribution Two-Way Non-Parametric Analysis of Variance Distribution of Rank Sums A Generalization of the Test of Friedman The Balanced Case The Unbalanced Case Multiple Comparisons and Scoring Tests for a Putative Ordering in Two-Way Layouts Exercises Bivariate Methods Parametric Approach Permutation Inference Nonparametric Correlation Rank Correlation Alternative Expectation of the Spearman Correlation Kendall's Bivariate Semi-Parametric Estimation via Correlation Inversion of the Test of Zero Correlation Inversion of the Pearson Correlation Inversion of Kendall's T Inversion of the Spearman Correlation Exercises Multivariate Analysis Standard Parametric Approaches Multivariate Estimation One-Sample Testing Two-Sample Testing Nonparametric Multivariate Estimation Equivariance Properties Nonparametric One-Sample Testing Approaches More General Permutation Solutions Con dence Regions for a Vector Shift Parameter Two-Sample Methods Hypothesis Testing Permutation Testing Permutation Distribution Approximations Exercises Density Estimation Histograms Kernel Density Estimates Exercises Regression Function Estimates Standard Regression Inference Kernel and Local Regression Smoothing Isotonic Regression Splines Quantile Regression Fitting the Quantile Regression Model Resistant Regression Exercises Resampling Techniques The Bootstrap Idea The Bootstrap Sampling Scheme Univariate Bootstrap Techniques The Normal Method Basic Interval The Percentile Method BCa Method Summary So Far, and More Examples Bootstrapping Multivariate Data Sets Regression Models and the Studentized Bootstrap Method Fixed X Bootstrap The Jackknife Examples of Biases of the Proper Order Bias Correction Correcting the Bias in Mean Estimators Correcting the Bias in Quantile Estimators Exercises Appendix A: Analysis Using the SAS System Appendix B: Construction of Heuristic Tables and Figures Using R Bibliography