I’ve spend part of this school year tutoring a student in AP Statistics. The course seems to be designed to help reinforce the classic paper “Why Most Published Research Findings Are False”. If the goal of high school is to prepare young people for citizenship and making decisions at work, AP Statistics seems like a spectacular failure. If the goal were to help people make decisions, wouldn’t the core of the class be hypothesis testing? People who take high school stats aren’t necessarily going to become professional statisticians but at least if hypothesis testing were the core they could be appropriately skeptical with regard to claims regarding, e.g., the efficacy of a new drug that taxpayers were being asked to pay for.
Hypothesis testing, however, is relegated to the end of the class/textbook/prep books. Thus for most of the class students have little context for why they are learning most of the material. Is it critically important to know what percentage of people think X based on a survey? Maybe for political pollsters who can then tell candidates how to pander to voters, but the most interesting uses of statistics seem generally to involve answering a question about whether an intervention was effective or not.
What do readers who are stats experts say? Would it make sense to weave hypothesis testing into the entire course?
Related:
- “Supplementary materials for teaching AP statistics?”
- “The Wrong Way to Teach Math” (New York Times article from February 27 using AP stats as the poster child for U.S. incompetence at designing math syllabi)
- “Everybody’s getting paid, but Raheem still can’t read.” (from “Schooled” in New Yorker)
Yes, I have tutored this, and AP Stat is a badly designed course for the reasons you say. Unfortunately, that is because it is faithfully mirroring college statistics courses, which also suck.
The first statistics course a student takes should be MUCH more conceptual and less “cookbook”. The first third of the course should be entirely about elementary probability, permutations and combinations, Bayes’s theorem (easily the most important concept for practical rationality), and the concept of randomness. The statistics part should stick to a handful of simple but important distributions (binomial, exponential, Poisson, Gaussian, power law, that’s all) and emphasize the MEANING of the central limit theorem, type 1 and 2 errors, p-values, confidence intervals, and statistical significance.
Only in the last third of the course should hypothesis testing be given a technical treatment, and only for a handful of simple tests, each of which should, by virtue of the previous lessons, be intuitively sensible — the question should ALWAYS be of the form “if we summarize the data by a single number in this specific way, how likely would we be to see something like this number by chance, and how likely would we be to see something like it if our hypothesis were true?”
All the way along, common cognitive biases and errors and fallacies should be explained very clearly (students should be able to identify these errors in news stories, selected published articles, etc.).
The problem with the AP racket is that even though I could write a great textbook for such a course, no schools would offer it instead of an exam-focused course.
Why not just focus on the problem of small data sets, that’s what we’re talking about here, really. Can you just give a plain explanation to this student about why small samples are problematic and see if it sinks in? Seems like you’ll be doing this person a world of good.
You have a valid point, but it is such a small point.
https://youtu.be/8xe6nLVXEC0?list=RDWkGkv7NWyl4
When I was in medical school, one of the classes was actually about “buying” test results and trying to come to a conclusion about whether the drug worked or not, as the simulated researcher in the lab. Perhaps that sort of exercise (with appropriate prizes) would be useful in a class?
(Create a database of fake results that students can have access to make queries against, and then run stats on, but they have to draw conclusions on those stats.)