Science is often perceived as precise, deterministic, and systematic. However, modern statistics embraces an unexpected ally: randomness. Far from being a source of error, randomness is crucial for ensuring the generalizability of our results, making our samples representative of larger populations, and allows us to estimate causal effects. Consequently, randomness and uncertainty paradoxically lead to more reliable and generalizable scientific conclusions!

This lecture covers two main themes:

1. The importance of randomness in statistical methods.
2. A review of statistical inference (\(\hat{\sigma}\), \(t\), \(p\), and \(95\%\text{-CI}\)),
   to demonstrate how randomness allows us to extrapolate from our specific dataset to broader populations and contexts.

Lecture 3 slides

Reading: Veaux, Velleman, and Bock (2021, Ch. 17.1-17.3, Ch. 18.1-18.3, & Ch. 19.2).