Course Preview
This is only a preview of the course. Although it includes all course content, it will not grade responses or provide feedback to students.
To use the course with your students,
click here to request an instructor account.
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