One of my Facebook friends made a post this morning asking for general advice on teaching a statistics course for graduate students in a program that is unlikely to lead them into research-based careers. (I’m fuzzing the details a bit for his privacy.)

One of the nice things about creating an all-new course from scratch is that you get to use the Veronica Mars/Woodshop principle when creating the course. Have you seen the first season of Veronica Mars? There was an overarching mystery for the whole season, solving the murder of her friend Lily Kane. Each episode also had its own small mystery to solve. And did you take woodshop in middle school? When I took woodshop, we spent the entire quarter working on a project. We learned how to use the band saw so that we could do the first rough cut of the base for our project. Our pieces wouldn’t fit together until we learned how to square a board. We had to learn how to use the jigsaw to make detailed cuts. Likewise, the belt sander and the drill press were all necessary for completing our projects. In both these cases, each part (episode or tool) has its own intrinsic worth, but it is an essential part of the whole. When you’re not building off of an existing curriculum, you have so much more freedom to apply the Veronica Mars/Woodshop principle.

Part of the discussion on the Facebook post led to the idea of finding examples of graduate theses in this field that used data and statistics nicely and using those (with permission) as key examples in the class. Making the content relevent to the students is also a great curricular design principle.

So far my ideas haven’t had that much to do with statistics.

In other design principles, I would rather the students have a deep understanding of a few things than know the names of a lot of statistical tests. I want them to be confident enough in what they do know that they can recognize how it feels different to know something than it does to not know something and to feel comfortable asking questions when they don’t know something. Also how to ask a good question.

I’d want them to be comfortable with the idea of quantity and uncertainty. I’d have them answer some questions without numbers about “which group did better” or “which is more likely” or “would you call these collections of numbers roughly the same” before they used formulas to answer the more specific versions.

Anscombe’s quartet. The datasaurus. Simpson’s paradox.

They really need to understand the concept of slope if they are going to do anything at all with linear regression. Lots of students pass algebra without understanding slope. I’ve met some math teachers who don’t understand slope. If you ask me what the most important concept is in algebra class, I will tell you that it is slope.

I’m sure my friend can figure out which statistical tests to teach. I have a hunch about what the top three would be, but that would just be a guess. I’ll wait for him to check the actual literature in their field and make a data-driven decision.