Frank Di Traglia writes,

I’m going to be teaching a three-week, introductory statistics course for local high school students next summer, and wanted to ask for your advice. I have two questions in particular.

First, I doubt that three weeks will be enough time to teach the usual Statistics 101 course. If you had only three weeks, what would you skip and what would you emphasize?

Second, since next year is an election year, I thought it might be fun to build the course around substantive examples from political science. Although I’ve enjoyed many of your poly-sci papers, my own background is not in this area (I did my masters in Statistics, and am currently pursuing a PhD in Economics). What would you consider to be the ten most interesting and accessible quantitative papers in this field?

My reply:

1. It’s gotta depend on how many hours per week you have! To consider the larger question, I’m unsatisfied with the usual intro stat course (including what I’ve taught) because it comes across as a disconnected set of topics. As I wrote here about the “sampling distribution of the sample mean”:

The hardest thing to teach in any introductory statistics course is the sampling distribution of the sample mean, a topic that is at the center of the typical intro-stat-class-for-nonmajors. All of probability theory builds up to it, and then this sample mean is used over and over again for inferences for averages, paired and unparied differences, and regression. This is the standard sequence, as in the books by Moore and McCabe, and De Veaux et al.

The trouble is, most students don’t understand it. I’m not talking about proving the law of large numbers or central limit theorem–these classes barely use algebra and certainly don’t attempt rigorous proofs. No, I’m talking about tha dervations that lead to the sample mean of an average of independent, identical measurments having a distribution with mean equal to the population mean, and sd equal to the sd of an individual measurement, divided by the square root of n.

This is key, but students typically don’t understand the derivation, don’t see the point of the result, and can’t understand it when it gets applied to examples.

What to do about this? I’ve tried teaching it really carefully, devoting more time to it, etc.–nothing works. So here’s my proposed solution: de-emphasize it. I’ll still teach the samling distribution of the sample mean, but now just as one of many topics, rather than the central topic of the course. In particular, I will not treat statistical inference for averages, differences, etc., as special cases or applications of the general idea of the sampling distribution of the sample mean. Instead, I’ll teach each inferential topic on its own, with its own formula and derivation. Of course, they mostly won’t follow the derivations, but then at least if they’re stuck on one of them, it won’t muck up their understanding of everything else.

Given these thoughts, my first suggestion would be for you to indeed focus on one particular thing, for example public opinion, and focus your course on that. Have the students download raw data from polls and do some analyses (maybe using JMP-in). This is what Bob Shapiro does when he teaches intro stats here.

2. If you’d rather do something closer to standard statistics, I’d recommend focusing on sampling, experimentation, and observational studies. You can do one week of each–in each week, they first do an in-class demo (a survey in week 1, an experiment in week 2, an obs study in week 3), then they together do something larger. I have some examples in my book with Deb, but I can’t say I’ve worked out all the details of such a course. It’s easier to talk about it than to do it.

3. The ten most interesting and accessible quantitative papers in political science? That’s a good question. Of my own papers, these are the most accessible, I think: Why are American Presidential election campaign polls so variable when votes are so predictable?, Voting, fairness, and political representation, Voting as a rational choice: why and how people vote to improve the well-being of others, A catch-22 in assigning primary delegates, Rich state, poor state, red state, blue state: What’s the matter with Connecticut? I also like the paper, Methodology as ideology: mathematical modeling of trench warfare, even though it’s not really statistical.

I wouldn’t include all of these in a top-ten list, but I’d include at least one! Beyond this, perhaps the blog readers have some suggestions?