book

The Book of R

Name: The Book of R
Author: Tilman M. Davies
ISBN: 9781593276515

by Tilman M. Davies

July 2016

Beginner to intermediate

832 pages

21h 51m

English

No Starch Press

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Cover
Title
Copyright
Brief Contents
Contents in Detail
Preface
Acknowledgments
Introduction
A Brief History of RAbout This BookPart I: The LanguagePart II: ProgrammingPart III: Statistics and ProbabilityPart IV: Statistical Testing and ModelingPart V: Advanced GraphicsFor StudentsFor Instructors
Part I: The Language
Chapter 1: Getting Started
1.1 Obtaining and Installing R from CRAN1.2 Opening R for the First Time1.2.1 Console and Editor Panes1.2.2 Comments1.2.3 Working Directory1.2.4 Installing and Loading R Packages1.2.5 Help Files and Function Documentation1.2.6 Third-Party Editors1.3 Saving Work and Exiting R1.3.1 Workspaces1.3.2 Scripts1.4 Conventions1.4.1 Coding1.4.2 Math and Equation References1.4.3 ExercisesExercise 1.1

Chapter 2: Numerics, Arithmetic, Assignment, and Vectors
2.1 R for Basic Math2.1.1 Arithmetic2.1.2 Logarithms and Exponentials2.1.3 E-NotationExercise 2.12.2 Assigning ObjectsExercise 2.22.3 Vectors2.3.1 Creating a Vector2.3.2 Sequences, Repetition, Sorting, and LengthsExercise 2.32.3.3 Subsetting and Element ExtractionExercise 2.42.3.4 Vector-Oriented BehaviorExercise 2.5
Chapter 3: Matrices and Arrays
3.1 Defining a Matrix3.1.1 Filling Direction3.1.2 Row and Column Bindings3.1.3 Matrix Dimensions3.2 Subsetting3.2.1 Row, Column, and Diagonal Extractions3.2.2 Omitting and OverwritingExercise 3.13.3 Matrix Operations and Algebra3.3.1 Matrix Transpose3.3.2 Identity Matrix3.3.3 Scalar Multiple of a Matrix3.3.4 Matrix Addition and Subtraction3.3.5 Matrix Multiplication3.3.6 Matrix InversionExercise 3.23.4 Multidimensional Arrays3.4.1 Definition3.4.2 Subsets, Extractions, and ReplacementsExercise 3.3
Chapter 4: Non-numeric Values
4.1 Logical Values4.1.1 TRUE or FALSE?4.1.2 A Logical Outcome: Relational OperatorsExercise 4.14.1.3 Multiple Comparisons: Logical OperatorsExercise 4.24.1.4 Logicals Are Numbers!4.1.5 Logical Subsetting and ExtractionExercise 4.34.2 Characters4.2.1 Creating a String4.2.2 Concatenation4.2.3 Escape Sequences4.2.4 Substrings and MatchingExercise 4.44.3 Factors4.3.1 Identifying Categories4.3.2 Defining and Ordering Levels4.3.3 Combining and CuttingExercise 4.5
Chapter 5: Lists and Data Frames
5.1 Lists of Objects5.1.1 Definition and Component Access5.1.2 Naming5.1.3 NestingExercise 5.15.2 Data Frames5.2.1 Construction5.2.2 Adding Data Columns and Combining Data Frames5.2.3 Logical Record SubsetsExercise 5.2
Chapter 6: Special Values, Classes, and Coercion
6.1 Some Special Values6.1.1 Infinity6.1.2 NaNExercise 6.16.1.3 NA6.1.4 NULLExercise 6.26.2 Understanding Types, Classes, and Coercion6.2.1 Attributes6.2.2 Object Class6.2.3 Is-Dot Object-Checking Functions6.2.4 As-Dot Coercion FunctionsExercise 6.3
Chapter 7: Basic Plotting
7.1 Using plot with Coordinate Vectors7.2 Graphical Parameters7.2.1 Automatic Plot Types7.2.2 Title and Axis Labels7.2.3 Color7.2.4 Line and Point Appearances7.2.5 Plotting Region Limits7.3 Adding Points, Lines, and Text to an Existing PlotExercise 7.17.4 The ggplot2 Package7.4.1 A Quick Plot with qplot7.4.2 Setting Appearance Constants with Geoms7.4.3 Aesthetic Mapping with GeomsExercise 7.2
Chapter 8: Reading and Writing Files
8.1 R-Ready Data Sets8.1.1 Built-in Data Sets8.1.2 Contributed Data Sets8.2 Reading in External Data Files8.2.1 The Table Format8.2.2 Spreadsheet Workbooks8.2.3 Web-Based Files8.2.4 Other File Formats8.3 Writing Out Data Files and Plots8.3.1 Data Sets8.3.2 Plots and Graphics Files8.4 Ad Hoc Object Read/Write OperationsExercise 8.1
Part II: Programming
Chapter 9: Calling Functions
9.1 Scoping9.1.1 Environments9.1.2 Search Path9.1.3 Reserved and Protected NamesExercise 9.19.2 Argument Matching9.2.1 Exact9.2.2 Partial9.2.3 Positional9.2.4 Mixed9.2.5 Dot-Dot-Dot: Use of EllipsesExercise 9.2
Chapter 10: Conditions and Loops
10.1 if Statements10.1.1 Stand-Alone Statement10.1.2 else Statements10.1.3 Using ifelse for Element-wise ChecksExercise 10.110.1.4 Nesting and Stacking Statements10.1.5 The switch FunctionExercise 10.210.2 Coding Loops10.2.1 for LoopsExercise 10.310.2.2 while LoopsExercise 10.410.2.3 Implicit Looping with applyExercise 10.510.3 Other Control Flow Mechanisms10.3.1 Declaring break or next10.3.2 The repeat StatementExercise 10.6
Chapter 11: Writing Functions
11.1 The function Command11.1.1 Function Creation11.1.2 Using returnExercise 11.111.2 Arguments11.2.1 Lazy Evaluation11.2.2 Setting Defaults11.2.3 Checking for Missing Arguments11.2.4 Dealing with EllipsesExercise 11.211.3 Specialized Functions11.3.1 Helper Functions11.3.2 Disposable Functions11.3.3 Recursive FunctionsExercise 11.3
Chapter 12: Exceptions, Timings, and Visibility
12.1 Exception Handling12.1.1 Formal Notifications: Errors and Warnings12.1.2 Catching Errors with try StatementsExercise 12.112.2 Progress and Timing12.2.1 Textual Progress Bars: Are We There Yet?12.2.2 Measuring Completion Time: How Long Did It Take?Exercise 12.212.3 Masking12.3.1 Function and Object Distinction12.3.2 Data Frame Variable Distinction
Part III: Statistics and Probability
Chapter 13: Elementary Statistics
13.1 Describing Raw Data13.1.1 Numeric Variables13.1.2 Categorical Variables13.1.3 Univariate and Multivariate Data13.1.4 Parameter or Statistic?Exercise 13.113.2 Summary Statistics13.2.1 Centrality: Mean, Median, Mode13.2.2 Counts, Percentages, and ProportionsExercise 13.213.2.3 Quantiles, Percentiles, and the Five-Number Summary13.2.4 Spread: Variance, Standard Deviation, and the Interquartile RangeExercise 13.313.2.5 Covariance and Correlation13.2.6 OutliersExercise 13.4
Chapter 14: Basic Data Visualization
14.1 Barplots and Pie Charts14.1.1 Building a Barplot14.1.2 A Quick Pie Chart14.2 Histograms14.3 Box-and-Whisker Plots14.3.1 Stand-Alone Boxplots14.3.2 Side-by-Side Boxplots14.4 Scatterplots14.4.1 Single Plot14.4.2 Matrix of PlotsExercise 14.1
Chapter 15: Probability
15.1 What Is a Probability?15.1.1 Events and Probability15.1.2 Conditional Probability15.1.3 Intersection15.1.4 Union15.1.5 ComplementExercise 15.115.2 Random Variables and Probability Distributions15.2.1 Realizations15.2.2 Discrete Random Variables15.2.3 Continuous Random Variables15.2.4 Shape, Skew, and ModalityExercise 15.2
Chapter 16: Common Probability Distributions
16.1 Common Probability Mass Functions16.1.1 Bernoulli Distribution16.1.2 Binomial DistributionExercise 16.116.1.3 Poisson DistributionExercise 16.216.1.4 Other Mass Functions16.2 Common Probability Density Functions16.2.1 UniformExercise 16.316.2.2 NormalExercise 16.416.2.3 Student’s t-distribution16.2.4 ExponentialExercise 16.516.2.5 Other Density Functions
Part IV: Statistical Testing and Modeling
Chapter 17: Sampling Distributions and Confidence
17.1 Sampling Distributions17.1.1 Distribution for a Sample Mean17.1.2 Distribution for a Sample ProportionExercise 17.117.1.3 Sampling Distributions for Other Statistics17.2 Confidence Intervals17.2.1 An Interval for a Mean17.2.2 An Interval for a Proportion17.2.3 Other Intervals17.2.4 Comments on Interpretation of a CIExercise 17.2
Chapter 18: Hypothesis Testing
18.1 Components of a Hypothesis Test18.1.1 Hypotheses18.1.2 Test Statistic18.1.3 p-value18.1.4 Significance Level18.1.5 Criticisms of Hypothesis Testing18.2 Testing Means18.2.1 Single MeanExercise 18.118.2.2 Two MeansExercise 18.218.3 Testing Proportions18.3.1 Single Proportion18.3.2 Two ProportionsExercise 18.318.4 Testing Categorical Variables18.4.1 Single Categorical Variable18.4.2 Two Categorical VariablesExercise 18.418.5 Errors and Power18.5.1 Hypothesis Test Errors18.5.2 Type I Errors18.5.3 Type II ErrorsExercise 18.518.5.4 Statistical PowerExercise 18.6
Chapter 19: Analysis of Variance
19.1 One-Way ANOVA19.1.1 Hypotheses and Diagnostic Checking19.1.2 One-Way ANOVA Table Construction19.1.3 Building ANOVA Tables with the aov FunctionExercise 19.119.2 Two-Way ANOVA19.2.1 A Suite of Hypotheses19.2.2 Main Effects and Interactions19.3 Kruskal-Wallis TestExercise 19.2
Chapter 20: Simple Linear Regression
20.1 An Example of a Linear Relationship20.2 General Concepts20.2.1 Definition of the Model20.2.2 Estimating the Intercept and Slope Parameters20.2.3 Fitting Linear Models with lm20.2.4 Illustrating Residuals20.3 Statistical Inference20.3.1 Summarizing the Fitted Model20.3.2 Regression Coefficient Significance Tests20.3.3 Coefficient of Determination20.3.4 Other summary Output20.4 Prediction20.4.1 Confidence Interval or Prediction Interval?20.4.2 Interpreting Intervals20.4.3 Plotting Intervals20.4.4 Interpolation vs. ExtrapolationExercise 20.120.5 Understanding Categorical Predictors20.5.1 Binary Variables: k = 220.5.2 Multilevel Variables: k > 220.5.3 Changing the Reference Level20.5.4 Treating Categorical Variables as Numeric20.5.5 Equivalence with One-Way ANOVAExercise 20.2
Chapter 21: Multiple Linear Regression
21.1 Terminology21.2 Theory21.2.1 Extending the Simple Model to a Multiple Model21.2.2 Estimating in Matrix Form21.2.3 A Basic Example21.3 Implementing in R and Interpreting21.3.1 Additional Predictors21.3.2 Interpreting Marginal Effects21.3.3 Visualizing the Multiple Linear Model21.3.4 Finding Confidence Intervals21.3.5 Omnibus F-Test21.3.6 Predicting from a Multiple Linear ModelExercise 21.121.4 Transforming Numeric Variables21.4.1 Polynomial21.4.2 Logarithmic21.4.3 Other TransformationsExercise 21.221.5 Interactive Terms21.5.1 Concept and Motivation21.5.2 One Categorical, One Continuous21.5.3 Two Categorical21.5.4 Two Continuous21.5.5 Higher-Order InteractionsExercise 21.3
Chapter 22: Linear Model Selection and Diagnostics
22.1 Goodness-of-Fit vs. Complexity22.1.1 Principle of Parsimony22.1.2 General Guidelines22.2 Model Selection Algorithms22.2.1 Nested Comparisons: The Partial F-Test22.2.2 Forward Selection22.2.3 Backward Selection22.2.4 Stepwise AIC SelectionExercise 22.122.2.5 Other Selection Algorithms22.3 Residual Diagnostics22.3.1 Inspecting and Interpreting Residuals22.3.2 Assessing Normality22.3.3 Illustrating Outliers, Leverage, and Influence22.3.4 Calculating Leverage22.3.5 Cook’s Distance22.3.6 Graphically Combining Residuals, Leverage, and Cook’s DistanceExercise 22.222.4 Collinearity22.4.1 Potential Warning Signs22.4.2 Correlated Predictors: A Quick Example
Part V: Advanced Graphics
Chapter 23: Advanced Plot Customization
23.1 Handling the Graphics Device23.1.1 Manually Opening a New Device23.1.2 Switching Between Devices23.1.3 Closing a Device23.1.4 Multiple Plots in One Device23.2 Plotting Regions and Margins23.2.1 Default Spacing23.2.2 Custom Spacing23.2.3 Clipping23.3 Point-and-Click Coordinate Interaction23.3.1 Retrieving Coordinates Silently23.3.2 Visualizing Selected Coordinates23.3.3 Ad Hoc AnnotationExercise 23.123.4 Customizing Traditional R Plots23.4.1 Graphical Parameters for Style and Suppression23.4.2 Customizing Boxes23.4.3 Customizing Axes23.5 Specialized Text and Label Notation23.5.1 Font23.5.2 Greek Symbols23.5.3 Mathematical Expressions23.6 A Fully Annotated ScatterplotExercise 23.2
Chapter 24: Going Further with the Grammar of Graphics
24.1 ggplot or qplot?24.2 Smoothing and Shading24.2.1 Adding LOESS Trends24.2.2 Constructing Smooth Density Estimates24.3 Multiple Plots and Variable-Mapped Facets24.3.1 Independent Plots24.3.2 Facets Mapped to a Categorical VariableExercise 24.124.4 Interactive Tools in ggvisExercise 24.2
Chapter 25: Defining Colors and Plotting in Higher Dimensions
25.1 Representing and Using Color25.1.1 Red-Green-Blue Hexadecimal Color Codes25.1.2 Built-in Palettes25.1.3 Custom Palettes25.1.4 Using Color Palettes to Index a Continuum25.1.5 Including a Color Legend25.1.6 Opacity25.1.7 RGB Alternatives and Further FunctionalityExercise 25.125.2 3D Scatterplots25.2.1 Basic Syntax25.2.2 Visual EnhancementsExercise 25.225.3 Preparing a Surface for Plotting25.3.1 Constructing an Evaluation Grid25.3.2 Constructing the z-Matrix25.3.3 Conceptualizing the z-Matrix25.4 Contour Plots25.4.1 Drawing Contour Lines25.4.2 Color-Filled ContoursExercise 25.325.5 Pixel Images25.5.1 One Grid Point = One Pixel25.5.2 Surface Truncation and Empty PixelsExercise 25.425.6 Perspective Plots25.6.1 Basic Plots and Angle Adjustment25.6.2 Coloring Facets25.6.3 Rotating with LoopsExercise 25.5
Chapter 26: Interactive 3D Plots
26.1 Point Clouds26.1.1 Basic 3D Cloud26.1.2 Visual Enhancements and Legends26.1.3 Adding Further 3D ComponentsExercise 26.126.2 Bivariate Surfaces26.2.1 Basic Perspective Surface26.2.2 Additional Components26.2.3 Coloring by z Value26.2.4 Dealing with the Aspect RatioExercise 26.226.3 Trivariate Surfaces26.3.1 Evaluation Coordinates in 3D26.3.2 Isosurfaces26.3.3 Example: Nonparametric Trivariate Density26.4 Handling Parametric Equations26.4.1 Simple Loci26.4.2 Mathematical AbstractionsExercise 26.3
Appendix A: Installing R and Contributed Packages
A.1 Downloading and Installing RA.2 Using PackagesA.2.1 Base PackagesA.2.2 Recommended PackagesA.2.3 Contributed PackagesA.3 Updating R and Installed PackagesA.4 Using Other Mirrors and RepositoriesA.4.1 Switching CRAN MirrorA.4.2 Other Package RepositoriesA.5 Citing and Writing PackagesA.5.1 Citing R and Contributed PackagesA.5.2 Writing Your Own Packages
Appendix B: Working with RStudio
B.1 Basic Layout and UsageB.1.1 Editor Features and Appearance OptionsB.1.2 Customizing PanesB.2 Auxiliary ToolsB.2.1 ProjectsB.2.2 Package Installer and UpdaterB.2.3 Support for DebuggingB.2.4 Markup, Document, and Graphics Tools
Reference List
Index

Content preview from The Book of R

17SAMPLING DISTRIBUTIONS AND CONFIDENCE

In Chapters 15 and 16, you applied the idea of a probability distribution to examples where a random variable is defined as some measurement or observation of interest. In this chapter, you’ll consider sample statistics themselves as random variables to introduce the concept of a sampling distribution—a probability distribution that is used to account for the variability naturally present when you estimate population parameters using sample statistics. I’ll then introduce the idea of a confidence interval, which is a direct reflection of the variability in a sampling distribution, used in a way that results ...

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The Book of R

by Tilman M. Davies

17SAMPLING DISTRIBUTIONS AND CONFIDENCE

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