Lecture 10: Confidence Intervals (part 2)
October 4th, 2024 (5th week of classes)Read and watch everything
Key statistical details to understand confidence intervals and other critical statistical methods
The goal of this lecture is to explain the statistical foundations of confidence intervals, which are crucial for developing intuition and understanding the majority of statistical methods in biology and beyond. Building on concepts from Lecture 9 and Tutorial 5, we will use simulations to demonstrate how sampling distributions relate to confidence intervals and how these intervals should be interpreted - demonstrating that they are effective! Simulations play a key role in strengthening intuition around these concepts.
Recorded lectures (videos + slides)
To help integrate the simulations from Tutorial 5 with the lecture concepts, I’ve created videos that will guide you through this material. These videos combine R programming with the key ideas from Lecture 10. I recommend watching the videos carefully and taking notes as you go. This is the most effective way to engage with the content. You can also pause the videos to take screenshots of important frames and annotate them for further reference.
Slides:
Download lecture: 3 slides per page and outline
Download lecture: 1 slide per page
Videos:
part 1
General theory: transitioning from a computational approach, where sampling distributions are developed based on a limited number of sample means, to a broader statistical theory that applies to an ‘infinite’ (or a very large number) of sample means.
part 2
Statistical populations can vary in shape (e.g., symmetric, asymmetric, uniform, etc.) as well as in their mean and standard deviation. So, how can a single distribution fit all the infinite possible types of distributions? Part 2 delves into the mathematical details, extending the theory from Part 1 to work with any statistical population—under a key assumption.
Introduction to the t-Distribution (non-technical) by JBstatistics: This video offers an overview of the widely-used t-distribution, which we will revisit multiple times throughout BIOL322.