Part 3 | Univariate GLM
// understanding the population from a sample //Data is a sample drawn from an unobservable population. While we can summarize our data, our main questions are typically about the unobservable population our sample was drawn from. Part 3 develops the most basic tools of the General Linear Model (GLM), which allow us to make inferences about unknown populations from known samples. The core idea: the Central Limit Theorem tells us the distribution of the sample mean without needing to know the population distribution. This idea forms the backbone of modern empirical science. It's difficult to overstate how important this idea has been in our modern world.
Part 3.1 ~ Random Variables
Data is a sample drawn from an unobservable population. We can summarize the sample, but our questions are about the population.
Concept 3.1 // Random Variables
Data is the realization of repeated draws from the population random variable.
Part 3.2 ~ Sampling and Central Limit Theorem
The Central Limit Theorem tells us the distribution of the sample mean despite not knowing the population distribution.
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.
Exercise 3.3 // Interactive Confidence Intervals
Interactive examples with confidence interval calculations
Homework 3.3
Nothing due :)
Part 3.4 ~ Hypothesis Testing
Conduct one-sample t-tests. Calculate p-values and interpret statistical results.
Exercise 3.4 // Interactive Hypothesis Tests
Interactive examples with hypothesis testing procedures
Part 3.5 ~ Simplest GLM
Test the model coefficients.
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 the application of the concepts we've developed. Practice with Homework and Exercises to prepare effectively.