List of Figures. List of Tables. Preface to the Second Edition. Preface to the First Edition

Transcription

1 List of Figures List of Tables Preface to the Second Edition Preface to the First Edition xv xxv xxix xxxi 1 What Is R? Introduction to R Downloading and Installing R Installing R under Windows Launching R A First Look at R (Interactive Mode) Vectors Naming Cautions Vector Indexing Generating Vector Sequences and Repeating Vector Constants Filtering Vectors Mode and Class of an Object Getting Help External Editors RStudio Packages R Data Structures Arrays and Matrices Vector and Matrix Operations Factors Lists Data Frames Creating Data Frames Accessing Data Frames Accessing Data from Packages Reading and Saving Data in R Using read.table() Using download.file() Reading Data from Secure Websites Using scan() Reading Excel (.xlsx) Files Saving Data Frames to External Files Working with Data Dealing with NA Values Creating New Variables in a Data Frame v

2 vi Sorting a Data Frame by One or More of Its Columns Merging Data Frames Using Logical Operators with Data Frames Tables Summarizing Functions Probability Functions Flow Control Creating Functions Simple Imputation Using plot() Coordinate Systems and Traditional Graphic s States Problems Exploring Data What Is Statistics? Data Displaying Qualitative Data Tables Barplots Dot Charts Pie Charts Displaying Quantitative Data Stem-and-Leaf Plots Strip Charts Density Curves for Exploring Univariate Data Histograms Kernel Density Estimators Summary Measures of Location The Mean The Median Mode Quantiles Hinges and the Five-Number Summary Boxplots Summary Measures of Spread Range Interquartile Range Variance Sample Coe cient of Variation The Median Absolute Deviation (MAD) Bivariate Data Two-Way Contingency Tables Graphical Representations of Two-Way Contingency Tables Comparing Samples Relationships between Two Numeric Variables Correlation Fitting Lines to Bivariate Data Complex Plot Arrangements Multivariate Data Graphs for Categorical Data Lattice Graphs

3 vii Arranging Several Lattice Graphs on a Single Page Panel Functions Graphics with ggplot Shading a Region of a Density Curve Violin Plots Adding a Smoothed Line Choropleth Maps Arranging Several ggplot Graphs on a Single Page Problems General Probability and Random Variables Introduction Counting Techniques Sampling with Replacement Sampling without Replacement Combinations Axiomatic Probability Sample Space and Events Set Theory Interpreting Probability Relative Frequency Approach to Probability Axiomatic Approach to Probability Conditional Probability The Law of Total Probability and Bayes Rule Independent Events Random Variables Discrete Random Variables Mode, Median, and Percentiles Expected Values Moments Continuous Random Variables Numerical Integration with R Mode, Median, and Percentiles Expected Values Markov s Theorem and Chebyshev s Inequality Weak Law of Large Numbers Skewness Moment Generating Functions Problems Univariate Probability Distributions Introduction Discrete Univariate Distributions Discrete Uniform Distribution Bernoulli and Binomial Distributions Poisson Distribution Geometric Distribution Negative Binomial Distribution Hypergeometric Distribution Continuous Univariate Distributions Uniform Distribution (Continuous)

4 viii Exponential Distribution Gamma Distribution Hazard Function, Reliability Function, and Failure Rate Weibull Distribution Beta Distribution Normal (Gaussian) Distribution Problems Multivariate Probability Distributions Joint Distribution of Two Random Variables Joint pdf for Two Discrete Random Variables Joint pdf for Two Continuous Random Variables Independent Random Variables Several Random Variables Conditional Distributions Expected Values, Covariance, and Correlation Expected Values Covariance Correlation Multinomial Distribution Bivariate Normal Distribution Problems Sampling and Sampling Distributions Sampling Simple Random Sampling Stratified Sampling Systematic Sampling Cluster Sampling Parameters Infinite Populations Parameters Finite Populations Parameters Estimators Plug-In Principle Sampling Distribution of the Sample Mean Sampling Distribution for a Statistic from an Infinite Population Sampling Distribution for the Sample Mean First Case: Sampling Distribution of X When Sampling from a Normal Distribution Second Case: Sampling Distribution of X When X Is Not a Normal Random Variable Sampling Distribution for X Ȳ When Sampling from Two Independent Normal Populations Sampling Distribution for the Sample Proportion Expected Value and Variance of the Uncorrected Sample Variance and the Sample Variance Sampling Distributions Associated with the Normal Distribution Chi-Square Distribution ( 2 ) The Relationship between the 2 Distribution and the Normal Distribution

5 ix Sampling Distribution for S 2 u and S 2 When Sampling from Normal Populations t-distribution The F Distribution Problems Point Estimation Introduction Properties of Point Estimators Mean Square Error Unbiased Estimators E ciency Relative E ciency Consistent Estimators Robust Estimators Point Estimation Techniques Method of Moments Estimators Likelihood and Maximum Likelihood Estimators Fisher Information Fisher Information for Several Parameters Properties of Maximum Likelihood Estimators Finding Maximum Likelihood Estimators for Multiple Parameters Multi-Parameter Properties of MLEs Problems Confidence Intervals Introduction Confidence Intervals for Population Means Confidence Interval for the Population Mean When Sampling from a Normal Distribution with Known Population Variance Determining Required Sample Size Confidence Interval for the Population Mean When Sampling from a Normal Distribution with Unknown Population Variance Confidence Interval for the Di erence in Population Means When Sampling from Independent Normal Distributions with Known Equal Variances Confidence Interval for the Di erence in Population Means When Sampling from Independent Normal Distributions with Known but Unequal Variances Confidence Interval for the Di erence in Means When Sampling from Independent Normal Distributions with Variances That Are Unknown but Assumed Equal Confidence Interval for a Di erence in Means When Sampling from Independent Normal Distributions with Variances That Are Unknown and Unequal Confidence Interval for the Mean Di erence When the Di erences Have a Normal Distribution Confidence Intervals for Population Variances Confidence Interval for the Population Variance When Sampling from a Normal Population

6 x Confidence Interval for the Ratio of Population Variances When Sampling from Independent Normal Distributions Confidence Intervals Based on Large Samples Confidence Interval for the Population Proportion Score Confidence Interval Agresti-Coull Confidence Interval for the Population Proportion Clopper-Pearson Interval for the Population Proportion So Which Confidence Interval Do I Use? Confidence Interval for a Di erence in Population Proportions Confidence Interval for the Mean of a Poisson Random Variable Problems Hypothesis Testing Introduction Type I and Type II Errors Power Function Uniformly Most Powerful Test }-Value or Critical Level Tests of Significance Hypothesis Tests for Population Means Test for the Population Mean When Sampling from a Normal Distribution with Known Population Variance Test for the Population Mean When Sampling from a Normal Distribution with Unknown Population Variance Test for the Di erence in Population Means When Sampling from Independent Normal Distributions with Known Variances Test for the Di erence in Means When Sampling from Independent Normal Distributions with Variances That Are Unknown but Assumed Equal Test for a Di erence in Means When Sampling from Independent Normal Distributions with Variances That Are Unknown and Not Assumed Equal Test for the Mean Di erence When the Di erences Have a Normal Distribution Hypothesis Tests for Population Variances Test for the Population Variance When Sampling from a Normal Distribution Test for Equality of Variances When Sampling from Independent Normal Distributions Hypothesis Tests for Population Proportions Testing the Proportion of Successes in a Binomial Experiment (Exact Test) Testing the Proportion of Successes in a Binomial Experiment (Normal Approximation) Testing Equality of Proportions with Fisher s Exact Test Large Sample Approximation for Testing the Di erence of Two Proportions Problems

7 xi 10 Nonparametric Methods Introduction Sign Test Confidence Interval Based on the Sign Test Normal Approximation to the Sign Test Wilcoxon Signed-Rank Test Confidence Interval for Based on the Wilcoxon Signed-Rank Test Normal Approximation to the Wilcoxon Signed-Rank Test The Wilcoxon Rank-Sum or the Mann-Whitney U-Test Confidence Interval Based on the Mann-Whitney U-Test Normal Approximation to the Wilcoxon Rank-Sum and Mann- Whitney U-Tests The Kruskal-Wallis Test Friedman Test for Randomized Block Designs Goodness-of-Fit Tests The Chi-Square Goodness-of-Fit Test Kolmogorov-Smirnov Goodness-of-Fit Test Shapiro-Wilk Normality Test Categorical Data Analysis Test of Independence Test of Homogeneity Nonparametric Bootstrapping Bootstrap Paradigm Confidence Intervals Bootstrapping and Regression Permutation Tests Problems Experimental Design Introduction Fixed E ects Model Analysis of Variance (ANOVA) for the One-Way Fixed E ects Model Power and the Non-Central F Distribution Checking Assumptions Checking for Independence of Errors Checking for Normality of Errors Checking for Constant Variance Fixing Problems Non-Normality Non-Constant Variance Multiple Comparisons of Means Fisher s Least Significant Di erence The Tukey s Honestly Significant Di erence Displaying Pairwise Comparisons Other Comparisons among the Means Orthogonal Contrasts The Sche é Method for All Contrasts Summary of Comparisons of Means Random E ects Model (Variance Components Model) Randomized Complete Block Design Two-Factor Factorial Design

8 xii Problems Regression Introduction Simple Linear Regression Multiple Linear Regression Ordinary Least Squares Properties of the Fitted Regression Line Using Matrix Notation with Ordinary Least Squares The Method of Maximum Likelihood The Sampling Distribution of ˆ ANOVA Approach to Regression ANOVA with Simple Linear Regression ANOVA with Multiple Linear Regression Coe cient of Determination Extra Sum of Squares Tests on a Single Parameter Tests on Subsets of the Regression Parameters General Linear Hypothesis Model Building Testing-Based Procedures Backward Elimination Forward Selection Stepwise Regression Criterion-Based Procedures Summary Diagnostics Checking Error Assumptions Assessing Normality and Constant Variance Testing Autocorrelation Identifying Unusual Observations High Leverage Observations Transformations Collinearity Transformations for Non-Normality and Unequal Error Variances Model Validation The Validation Set Approach Leave-One-Out Cross-Validation k-fold Cross-Validation Interpreting a Logarithmically Transformed Model Qualitative Predictors Estimation of the Mean Response for New Values X h Prediction and Sampling Distribution of New Observations Y h(new) Simultaneous Confidence Intervals Simultaneous Confidence Intervals for Several Mean Responses Confidence Band Predictions of g New Observations Distinguishing Pointwise Confidence Envelopes from Confidence Bands Problems

9 xiii A R Commands 903 B Quadratic Forms and Random Vectors and Matrices 917 B.1 Quadratic Forms B.2 Random Vectors and Matrices B.3 Variance of Random Vectors Bibliography 921 Index 931