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Getting Started (Don't Skip This Part)
Introduction to Statistics: A Modeling Approach
PART I: EXPLORING VARIATION
Chapter 1 - Welcome to Statistics: A Modeling Approach
Chapter 2 - Understanding Data
- 2.0 Starting with a Bunch of Numbers
- 2.1 From Numbers to Data
- 2.2 A Data Frame Example: MindsetMatters
- 2.3 Measurement
- 2.4 Measurement (Continued)
- 2.5 Sampling from a Population
- 2.6 The Structure of Data
- 2.7 Manipulating Data
- 2.8 Manipulating Data (Continued)
- 2.9 Summary
- 2.10 Chapter 2 Review Questions
- 2.11 Chapter 2 Review Questions 2
Chapter 3 - Examining Distributions
- 3.0 The Concept of Distribution
- 3.1 Visualizing Distributions with Histograms
- 3.2 Shape, Center, Spread, and Weird Things
- 3.3 The Data Generating Process
- 3.4 The Back and Forth Between Data and the DGP
- 3.5 The Back and Forth Between Data and the DGP (Continued)
- 3.6 The Five-Number Summary
- 3.7 Boxplots and the Five-Number Summary
- 3.8 Exploring Variation in Categorical Variables
- 3.9 Chapter 3 Review Questions
- 3.10 Chapter 3 Review Questions 2
Chapter 4 - Explaining Variation
- 4.0 Welcome to Explaining Variation
- 4.1 Explaining One Variable with Another
- 4.2 Outcome and Explanatory Variables
- 4.3 More Ways to Visualize Relationships: Point and Jitter Plots
- 4.4 Even More Ways: Putting these Plots Together
- 4.5 Representing Relationships Among Variables
- 4.6 Sources of Variation
- 4.7 Randomness
- 4.8 Quantitative Explanatory Variables
- 4.9 Research Design
- 4.10 Fooled by Chance: the Problem of Type I Error
- 4.11 Quantifying the Data Generating Process
- 4.12 Chapter 4 Review Questions
- 4.13 Chapter 4 Review Questions 2
PART II: MODELING VARIATION
Chapter 5 - A Simple Model
- 5.0 What is a Model, and Why Would We Want One?
- 5.1 Modeling a Distribution as a Single Number
- 5.2 The Mean as a Model
- 5.3 Fitting the Empty Model
- 5.4 Generating Predictions from the Empty Model
- 5.5 Venturing into the World of Mathematical Notation
- 5.6 DATA = MODEL + ERROR: Notation
- 5.7 Statistics and Parameters
- 5.8 The Power of Aggregation
- 5.9 Summarizing Where We Are
- 5.10 Chapter 5 Review Questions
- 5.11 Chapter 5 Review Questions 2
Chapter 6 - Quantifying Error
- 6.0 Quantifying Total Error Around a Model
- 6.1 The Beauty of Sum of Squares
- 6.2 Variance
- 6.3 Standard Deviation
- 6.4 Z Scores
- 6.5 Modeling the Shape of the Error Distribution
- 6.6 Modeling Error with the Normal Distribution
- 6.7 Using the Normal Model to Make Predictions
- 6.8 Getting Familiar with the Normal Distribution
- 6.9 Next Up: Reducing Error
- 6.10 Chapter 6 Review Questions
- 6.11 Chapter 6 Review Questions 2
Chapter 7 - Adding an Explanatory Variable to the Model
- 7.0 Explaining Variation
- 7.1 Specifying the Model
- 7.2 Fitting a Model with an Explanatory Variable
- 7.3 Generating Predictions from the Model
- 7.4 Examining Residuals from the Model
- 7.5 Quantifying Model Fit with Sums of Squares
- 7.6 Comparing Two Models: Proportional Reduction in Error
- 7.7 Measures of Effect Size
- 7.8 Extending to a Three-Group Model
- 7.9 Improving Models by Adding Parameters
- 7.10 The F Ratio
- 7.11 Chapter 7 Review Questions
- 7.12 Chapter 7 Review Questions 2
Chapter 8 - Models with a Quantitative Explanatory Variable
- 8.0 Groups versus Quantitative Explanatory Variables
- 8.1 The Regression Line as a Model
- 8.2 Fitting a Regression Model
- 8.3 Using the Regression Model to Make Predictions
- 8.4 Examining Residuals from the Model
- 8.5 Assessing Model Fit with Sum of Squares
- 8.6 Assessing Model Fit with PRE and F
- 8.7 Correlation
- 8.8 The Correlation Coefficient: Pearson's R
- 8.9 Limitations to Keep in Mind
- 8.10 Chapter 8 Review Questions
- 8.11 Chapter 2 Review Questions 2
PART III: EVALUATING MODELS
Chapter 9 - Distributions of Estimates
- 9.0 The Concept of Variation in Estimates
- 9.1 Exploring the Variation in an Estimate
- 9.2 Sampling Distributions: A Way to See the Variation in an Estimate
- 9.3 Simulations from a Different DGP, and Learning to Say 'If'
- 9.4 Simulating Samples to Create a Sampling Distribution
- 9.5 Notation and Terminology
- 9.6 Reasoning with Sampling Distributions
- 9.7 Reasoning with Sampling Distributions (Continued)
- 9.8 Exploring the Properties of Sampling Distributions
- 9.9 The Central Limit Theorem
- 9.10 Chapter 9 Review Questions
- 9.11 Chapter 9 Review Questions 2
Chapter 10 - Confidence Intervals and Their Uses
- 10.0 Confidence Intervals: Estimating the Error in an Estimate
- 10.1 Finding the 95% Confidence Interval with Simulation
- 10.2 Using Bootstrapping to Construct a Confidence Interval
- 10.3 Using the Normal Distribution to Construct a Confidence Interval
- 10.4 A Confession, and the T Distribution
- 10.5 Interpreting Confidence Intervals
- 10.6 Interpreting Confidence Intervals (Continued)
- 10.7 Using Confidence Intervals to Evaluate a Group Difference
- 10.8 Using Confidence Intervals to Evaluate a Regression Model
- 10.9 Chapter 10 Review Questions
- 10.10 Chapter 10 Review Questions 2
Chapter 11 - Model Comparison with the F Ratio
- 11.0 The Tipping Experiment Revisited
- 11.1 PRE and F Ratio Revisited
- 11.2 Sampling Distribution of PRE and F
- 11.3 The F Distribution
- 11.4 Comparing Models Using the F Ratio
- 11.5 Type I and II Error
- 11.6 Using the F Ratio to Compare Multiple Groups
- 11.7 The Problem of Simultaneous Comparisons
- 11.8 Model Comparison with a Quantitative Explanatory Variable
- 11.9 Chapter 11 Review Questions
- 11.10 Chapter 11 Review Questions 2