At the University of Auckland, our first year statistics course is large. By large we mean about 4500 students per year, with approximately 300 in our summer school semester (lasting 6 weeks, starting early January), 2500 in our first semester (lasting 12 weeks, starting early March) and 1800 in our second semester (starting 12 weeks, starting mid-July). Apart from summer school, we teach in multiple streams with class sizes ranging from 100 students to 400 students per class. Most of our students will not major in statistics and are taking the course because it is a requirement. Over one-half of our students will have taken a statistics course in their last year at school. These students will most likely have taken the Use statistical methods to make a formal inference standard which includes bootstrap confidence intervals. A smaller percentage, say about 20%, may have taken the Conduct an experiment to investigate a situation using experimental design principles standard which includes randomization tests.[pullquote] From a teaching perspective, we believe that the concept of the tail proportion in the randomization test enhances student understanding of p-values.[/pullquote]
Mine Cetinkaya-Rundel, Duke University
Just a couple years ago I would have answered the question “Why simulation based?” with the following:
- opportunity to introduce inference before (or without) discussing details of probability distributions
- conceptual understanding of p-values – both the “assume the null hypothesis is true” part and the “observed or more extreme” part
[pullquote]Being able to introduce computation as an essential tool for conducting statistical inference is a huge benefit of simulation based inference. [/pullquote]These are the reasons why in the first chapter of OpenIntro Statistics (link), a textbook I co-authored, we decided to include a section on randomization tests. The Introductory Statistics with Randomization and Simulation (link) textbook takes these ideas a step further and provides an introduction to statistical inference completely from a simulation based perspective. I believe these are important reasons for teaching simulation based inference, and many have already discussed them at length. However, for this post I’d like to focus on a lesser-discussed reason for teaching simulation based inference: it provides an opportunity to teach computation.
Andrew Walter, Shawnee Mission East High School
I am in my second year of implementing simulation-based methods, and I’m thrilled with how it has enhanced my AP Statistics course. My struggles teaching the course are probably familiar to others, and include: difficultly teaching vocabulary, difficulty spiraling review topics, and difficulty helping students grasp some of the key topics in ways that indicate true understanding. Using the simulation-based inference methods throughout the school year has helped me address all of these concerns and more. I will briefly explain how I use this method in my class, and then comment specifically about how it has helped.[pullquote]Simulation activities are a perfect way to blend “hands-on” learning with using technology.[/pullquote]