George Cobb, Mount Holyoke College
I’m writing to respond to a pair of questions we often hear from teachers who are considering a simulation-based alternative to the traditional normal-centric course: (1) “If the simulation-based approach is so great, why even bother to teach the normal-based stuff at all?” (2) If I’m going to include the normal-based stuff, do you have any suggestions about how to make the transition? ”
The “theory” in what some of us call the “theory-based approach” is the Central Limit Theorem, actually a cluster of theorems about convergence of sampling distributions to normal (Gaussian).
Tisha Hooks, Winona State University
As an undergraduate student, I learned a lot in my intro stat course about what formulas/tables to use and when to use them; unfortunately, I learned very little about why these methods worked. As a young professor, I set out to give my students an experience that was very different from mine. Fortunately for me I landed at Winona State University where I was able to work with Chris Malone, who had recently revamped his intro course. One of the first papers Chris encouraged me to read was written by George Cobb (referenced below), and the following quote hit home: “Our curriculum is needlessly complicated because we put the normal distribution, as an approximate sampling distribution for the mean, at the center of our curriculum, instead of putting the core logic of inference at the center.” Early on in my career, I’m pretty sure that Chris and I talked at least once a day about how to center our curriculum on core inferential concepts, and I started using a simulation-based curriculum which has allowed me to get to these core concepts early and often.
… my transition to normal-based methods involves using simulations/randomizations to introduce the logic of inference, connecting the empirical probabilities obtained from simulation studies to theoretical probabilities used in traditional tests…