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Getting Started (Don't Skip This Part)
Statistics and Data Science: A Modeling Approach
PART I: EXPLORING VARIATION
Chapter 1 - Welcome to Statistics: A Modeling Approach
Chapter 2 - Understanding Data
- 2.1 Starting with a Bunch of Numbers
- 2.2 From Numbers to Data
- 2.3 A Data Frame Example: MindsetMatters
- 2.4 Frequency Tables and Sorting Data Frames
- 2.5 Measurement
- 2.6 Quantitative and Categorical Variables
- 2.7 Values and Variables
- 2.8 Sampling from a Population
- 2.9 The Structure of Data
- 2.10 Missing Data
- 2.11 Creating and Recoding Variables
- 2.12 Chapter 2 Review Questions
- 2.13 Chapter 2 Review Questions 2
Chapter 3 - Examining Distributions
- 3.1 The Concept of Distribution
- 3.2 Histograms
- 3.3 Visualizing Data With Histograms
- 3.4 Shape, Center, Spread, and Weird Things
- 3.5 The Five-Number Summary
- 3.6 Quartiles and the Five-Number Summary
- 3.7 Box Plots and the Five-Number Summary
- 3.8 Outliers on a Box Plot
- 3.9 Exploring Variation in Categorical Variables
- 3.10 The Data Generating Process
- 3.11 The Back and Forth Between Data and the DGP
- 3.12 From DGP to Population to Samples
- 3.13 Weird DGPs and Their Samples
- 3.14 Chapter 3 Review Questions
- 3.15 Chapter 3 Review Questions 2
Chapter 4 - Explaining Variation
- 4.1 Outcome and Explanatory Variables
- 4.2 Visualizing Relationships with Scatter Plots
- 4.3 Categorical Explanatory Variables
- 4.4 Using Box Plots to Explore Relationships
- 4.5 Faceted Histograms
- 4.6 Categorical Outcomes
- 4.7 Contingency Tables
- 4.8 Adding More Explanatory Variables to a Plot
- 4.9 Sources of Variation
- 4.10 Research Design
- 4.11 Considering Randomness as a Possible DGP
- 4.12 Shuffling Can Help Us Understand Real Data Better
- 4.13 Quantifying the Data Generating Process
- 4.14 Chapter 4 Review Questions
- 4.15 Chapter 4 Review Questions 2
PART II: MODELING VARIATION
Chapter 5 - A Simple Model
- 5.1 What is a Model, and Why Would We Want One?
- 5.2 Modeling a Distribution as a Single Number
- 5.3 Median vs. Mean as a Model
- 5.4 Exploring the Mean
- 5.5 Fitting the Empty Model
- 5.6 Generating Predictions from the Empty Model
- 5.7 Thinking About Error
- 5.8 The World of Mathematical Notation
- 5.9 DATA = MODEL + ERROR: Notation
- 5.10 Summarizing Where We Are
- 5.11 Chapter 5 Review Questions
- 5.12 Chapter 5 Review Questions 2
Chapter 6 - Quantifying Error
- 6.1 Quantifying Total Error Around a Model
- 6.2 The Beauty of Sum of Squares
- 6.3 Variance
- 6.4 Standard Deviation
- 6.5 Z-Scores
- 6.6 Interpreting and Using Z-Scores
- 6.7 Modeling the Shape of the Error Distribution
- 6.8 Modeling Error with the Normal Distribution
- 6.9 Using the Normal Model to Make Predictions
- 6.10 Getting Familiar with the Normal Distribution
- 6.11 The Empirical Rule
- 6.12 Next Up: Explaining Error
- 6.13 Chapter 6 Review Questions
- 6.14 Chapter 6 Review Questions 2
Chapter 7 - Adding an Explanatory Variable to the Model
- 7.1 Explaining Variation
- 7.2 Using R to Fit the Group Model
- 7.3 GLM Notation for the Group Model
- 7.4 How the Model Makes Predictions
- 7.5 Error Leftover From the Group Model
- 7.6 Graphing Residuals From the Model
- 7.7 Error Reduced by the Group Model
- 7.8 Using SS Error to Compare Group to Empty Model
- 7.9 Partitioning Sums of Squares into Model and Error
- 7.10 Using Proportional Reduction in Error (PRE) to Compare Two Models
- 7.11 Chapter 7 Review Questions
Chapter 8 - Digging Deeper into Group Models
Chapter 9 - Models with a Quantitative Explanatory Variable
- 9.1 Using a Quantitative Explanatory Variable in a Model
- 9.2 Specifying the Height Model with GLM Notation
- 9.3 Interpreting the Parameter Estimates for a Regression Model
- 9.4 Comparing Regression Models to Group Models
- 9.5 Error from the Height Model
- 9.6 Sums of Squares in the ANOVA Table
- 9.7 Assessing Model Fit with PRE and F
- 9.8 Correlation
- 9.9 More on Pearson's R
- 9.10 Using Shuffle to Interpret the Slope of a Regression Line
- 9.11 Limitations to Keep in Mind
- 9.12 Chapter 9 Review Questions
- 9.13 Chapter 9 Review Questions 2
PART III: EVALUATING MODELS
Chapter 10 - The Logic of Inference
- 10.1 The Problem of Inference
- 10.2 Constructing a Sampling Distribution
- 10.3 Exploring the Sampling Distribution of b1
- 10.4 What Counts as Unlikely
- 10.5 The p-Value
- 10.6 Calculating the p-Value for a Sample
- 10.7 A Mathematical Model of the Sampling Distribution of b1
- 10.8 Things That Affect p-Value
- 10.9 Hypothesis Testing for Regression Models
- 10.10 Chapter 10 Review Questions
- 10.11 Chapter 10 Review Questions 2
Chapter 11 - Model Comparison with F
- 11.1 Moving Beyond b1
- 11.2 Sampling Distribution of PRE
- 11.3 Sampling Distribution of F
- 11.4 Using the Sampling Distribution of F
- 11.5 Calculating P-Value from the Sampling Distribution of F
- 11.6 The F-Distribution: A Mathematical Model of the Sampling Distribution of F
- 11.7 F-Distribution and t-Distribution
- 11.8 Using F to Test a Regression Model
- 11.9 Type I and Type II Error
- 11.10 Using F to Compare Multiple Groups
- 11.11 Pairwise Comparisons
- 11.12 The Problem of Simultaneous Comparisons
- 11.13 The Chi-Square Test of Independence
- 11.14 Chapter 11 Review Questions
- 11.15 Chapter 11 Review Questions 2
Chapter 12 - Parameter Estimation and Confidence Intervals
- 12.1 From Hypothesis Testing to Confidence Intervals
- 12.2 Thinking With Sampling Distributions
- 12.3 The Basic Idea Behind Confidence Intervals
- 12.4 Using Bootstrapping to Calculate the 95% Confidence Interval
- 12.5 Using the Bootstrapped Sampling Distribution to Find the Confidence Interval
- 12.6 Shuffle, Resample, and Standard Error
- 12.7 Using the t-Distribution to Construct a Confidence Interval
- 12.8 Interpreting the Confidence Interval
- 12.9 Confidence Intervals and Model Comparison
- 12.10 Confidence Interval for Beta0
- 12.11 Confidence Interval for the Slope of a Regression Line
- 12.12 Confidence Intervals for Pairwise Comparisons
- 12.13 What Affects the Width of the Confidence Interval
- 12.14 Chapter 12 Review Questions
- 12.15 Chapter 12 Review Questions 2