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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 Measurement
- 2.5 Measurement (Continued)
- 2.6 Sampling from a Population
- 2.7 The Structure of Data
- 2.8 Manipulating Data
- 2.9 Summary
- 2.10 Chapter 2 Review Questions
- 2.11 Chapter 2 Review Questions 2
Chapter 3 - Examining Distributions
- 3.1 The Concept of Distribution
- 3.2 Visualizing Distributions with Histograms
- 3.3 Shape, Center, Spread, and Weird Things
- 3.4 The Data Generating Process
- 3.5 The Back and Forth Between Data and the DGP
- 3.6 The Back and Forth Between Data and the DGP (Continued)
- 3.7 The Five-Number Summary
- 3.8 Boxplots and the Five-Number Summary
- 3.9 Exploring Variation in Categorical Variables
- 3.10 Chapter 3 Review Questions
- 3.11 Chapter 3 Review Questions 2
Chapter 4 - Explaining Variation
- 4.1 Welcome to Explaining Variation
- 4.2 Explaining One Variable with Another
- 4.3 Outcome and Explanatory Variables
- 4.4 More Ways to Visualize Relationships: Point and Jitter Plots
- 4.5 Even More Ways: Putting these Plots Together
- 4.6 Representing Relationships Among Variables
- 4.7 Sources of Variation
- 4.8 Randomness
- 4.9 From Categorical to Quantitative Explanatory Variables
- 4.10 Quantitative Explanatory Variables
- 4.11 Research Design
- 4.12 Fooled by Chance: the Problem of Type I Error
- 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 The Mean as a Model
- 5.4 Fitting the Empty Model
- 5.5 Generating Predictions from the Empty Model
- 5.6 Venturing into the World of Mathematical Notation
- 5.7 DATA = MODEL + ERROR: Notation
- 5.8 Statistics and Parameters
- 5.9 The Power of Aggregation
- 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 Modeling the Shape of the Error Distribution
- 6.7 Modeling Error with the Normal Distribution
- 6.8 Using the Normal Model to Make Predictions
- 6.9 Getting Familiar with the Normal Distribution
- 6.10 Next Up: Reducing Error
- 6.11 Chapter 6 Review Questions
- 6.12 Chapter 6 Review Questions 2
Chapter 7 - Adding an Explanatory Variable to the Model
- 7.1 Explaining Variation
- 7.2 Specifying the Model
- 7.3 Fitting a Model with an Explanatory Variable
- 7.4 Generating Predictions from the Model
- 7.5 Examining Residuals from the Model
- 7.6 Quantifying Model Fit with Sums of Squares
- 7.7 Comparing Two Models: Proportional Reduction in Error
- 7.8 Measures of Effect Size
- 7.9 Modeling the DGP
- 7.10 Extending to a Three-Group Model
- 7.11 Improving Models by Adding Parameters
- 7.12 The F Ratio
- 7.13 Chapter 7 Review Questions
- 7.14 Chapter 7 Review Questions 2
Chapter 8 - Models with a Quantitative Explanatory Variable
- 8.1 Groups versus Quantitative Explanatory Variables
- 8.2 The Regression Line as a Model
- 8.3 Fitting a Regression Model
- 8.4 Using the Regression Model to Make Predictions
- 8.5 Examining Residuals from the Model
- 8.6 Assessing Model Fit with Sum of Squares
- 8.7 Assessing Model Fit with PRE and F
- 8.8 Correlation
- 8.9 The Correlation Coefficient: Pearson's R
- 8.10 Limitations to Keep in Mind
- 8.11 Chapter 8 Review Questions
- 8.12 Chapter 8 Review Questions 2
PART III: EVALUATING MODELS
Chapter 9 - The Logic of Inference
Chapter 10 - Model Comparison with F
- 10.1 Moving Beyond b1
- 10.2 Sampling Distributions of PRE and F
- 10.3 The Sampling Distribution of F
- 10.4 The F-Distribution: A Mathematical Model of the Sampling Distribution of F
- 10.5 Using F to Test a Regression Model
- 10.6 Type I and Type II Error
- 10.7 Using F to Compare Multiple Groups
- 10.8 Pairwise Comparisons
Chapter 11 - Parameter Estimation and Confidence Intervals
- 11.1 From Hypothesis Testing to Confidence Intervals
- 11.2 Using Bootstrapping to Calculate the 95% Confidence Interval
- 11.3 Shuffle, Resample, and Standard Error
- 11.4 Interpreting the Confidence Interval
- 11.5 Confidence Intervals for Other Parameters
- 11.6 What Affects the Width of the Confidence Interval