Home Preview Teach About Log in

Home Preview Teach About Log in

Statistics and Data Science: A Modeling Approach

Expand All Collapse All

Getting Started (Don't Skip This Part)

First Things First! (Don’t Skip This Page)
Student Survey (REQUIRED)

Statistics and Data Science: A Modeling Approach

Statistics and Data Science (Title Page)
About CourseKata and Your Data

PART I: EXPLORING VARIATION

Part I: Exploring Variation

Chapter 1 - Welcome to Statistics: A Modeling Approach

1.0 Welcome to Statistics
1.1 What is Understanding?
1.2 Doing Statistics with R
1.3 Introduction to R Functions
1.4 Save Your Work in R Objects
1.5 Goals of this Course
1.6 Chapter 1 Review Questions

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 Summary
2.9 Chapter 2 Review Questions
2.10 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 From Quantitative to Categorical Explanatory Variables
4.9 Quantitative Explanatory Variables
4.10 Research Design
4.11 Fooled by Chance: the Problem of Type I Error
4.12 Quantifying the Data Generating Process
4.13 Chapter 4 Review Questions
4.14 Chapter 4 Review Questions 2

PART II: MODELING VARIATION

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

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

Chapter 12 - What You Have Learned

12.0 What You Have Learned About Exploring Variation
12.1 What You Have Learned About Modeling Variation
12.2 What You Have Learned About Evaluating Models

Finishing Up (Don't Skip This Part!)

End of Course Survey (Required)

Resources

References
R Sandbox
R Cheatsheet
R in the Real World

Statistics and Data Science: A Modeling Approach

Version:

Responses

Chapter 3 Review Questions

3.8 Exploring Variation in Categorical Variables 3.10 Chapter 3 Review Questions 2

CourseKata.org is a project of the UCLA Psychology Department’s Teaching and Learning Lab. It is supported in part by a grant from the Chan Zuckerberg Initiative DAF, an advised fund of Silicon Valley Community Foundation.