Part 3 | Univariate GLM
> studying the population using a sampleData 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 | Quantifying Uncertainty
Build confidence intervals, test hypotheses, and interpret p-values using the t-distribution.
Concept 3.3 // Quantifying Uncertainty
Confidence intervals, hypothesis testing, and p-values
Exercise 3.3 // Interactive Confidence Intervals
Interactive examples with confidence interval calculations
Part 3.4 | The Simplest Linear Model
Express the sample mean as a model parameter. Connect the t-test to the general linear model framework.
Concept 3.4 // The Simplest Linear Model
The intercept-only model and the general linear model framework
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.