Part 3 | Uncertainty in Data
// separate relationships from noise //Part 3 addresses the question that separates good analysis from great analysis: how do you know if what you're seeing is real? Every dataset contains random variation and measurement errors that can masquerade as a meaningful pattern. In this part you'll learn to quantify uncertainty and to distinguish genuine relationships from statistical noise using the Central Limit Theorem and the General Linear Model. Understanding the ideas with these tools will transform you from someone who can describe data into someone who can draw reliable conclusions from it.
Part 3.1 ~ Random Variables and Distributions
Refresh your understanding of random variables and other core ideas in statistics.

Concept 3.1 // Random Variables
Refresh of basic ideas in statistics
Exercise 3.1 // Random Variables
Interactive examples working with distributions
Homework 3.1
Due on Friday at 5PM on Gradescope
Part 3.2 ~ Sampling and Central Limit Theorem
Use the Central Limit Theorem to understand the distribution of a sample mean when you don't know the population distribution.

Concept 3.2 // Central Limmit Theorem
One of the most powerful ideas in science
Exercise 3.2 // CLT Demonstration
Interactive example showing Central Limit Theorem
Homework 3.2
Due on Friday at 5PM on Gradescope
Part 3.3 ~ Confidence Intervals
Calculate confidence intervals using the t-distribution. Interpret p-values and confidence intervals. Understand what "95% confident" actually means in practice.

Concept 3.3 // Confidence Intervals
How often the model is wrong
Exercise 3.3 // Interactive Confidence Intervals
Interactive examples with confidence interval calculations
Homework 3.3
Due on Friday at 5PM on Gradescope
Part 3.4 ~ Hypothesis Testing
Conduct one-sample t-tests. Calculate p-values and interpret statistical results.

Concept 3.4 // Hypothesis Testing
Inferring the truth from a sample
Exercise 3.4 // Interactive Hypothesis Tests
Interactive examples with hypothesis testing procedures
Homework 3.4
Continuation covering hypothesis testing
MiniExams
MiniExam 3 covers everything in Part 3, focussing on testing your understanding of statistical concepts including random variables, sampling theory, confidence intervals, and hypothesis testing.
MiniExams focuses on practical application of the concepts we've developed. Practice with Homework and Exercises to prepare effectively.
MiniExam 3 Demo
MiniExam 03 Demo covers all material from Parts 3.1 through 3.4.