Surveys and Sampling
This lesson is a bit on the thick side. It is reasonable to break it up into smaller parts and move them around as you see fit. Some items are interesting, but not always productive (like the discourse on randomness).
Something I like to do is find more of the bad sampling practices (or bad conclusions) and present them to students and ask them to figure out what probably went wrong. Some classic examples are the Dewey v. Truman presidential election (complete with incorrect newspaper headline!), why Yao Ming has made the NBA all-star game nearly every year, even when he is hurt and not playing, and others. Frequently these are not so cut and dry that one factor can singled out, but often many things combined to make a bad survey or poll. This is partially where students begin to understand the cliché “You can make statistics say anything you want...” which is frequently used by the undereducated to discredit well done surveys. The educated student realizes that there is plenty of opportunity for errors, and because of that, and other factors, absolute certainty is impossible, but a well done survey is a very solid source of information. Students need not memorize each type of bias by name. This is only useful for cocktail parties to stress that you know what you are talking about in terms of studies and surveys.
The randomness idea is lots of fun, but maybe beyond the scope of this class. Since we have not yet looked at the Uniform Distribution, which is how most computers generate random numbers (hence the TI calculators always returning a number between and ), we really don’t have the impetus to work with computer generated randomness. An easy way to show the book’s point about seeded generators is to reset the calculator. Don’t do this if you have lots of programs in memory. A reset all, will set each calculators seed to the same number, and therefore every TI calculator will return the same “random” number after a reset. Even better, because the seed is incremented the same way for each calculator, the entire sequence of random numbers will all be identical until the seed is changed.
It may not be critical to the AP examination, but one of the mantras in my classroom, whether it be a stats class or not, appears at the bottom of p235. “Correlation is not causation.” For my students who are not going to pursue a future in math or science this is a critical idea. While any student at the end of a year of probability and stats can understand why, the more people who understand, and can communicate the idea, the more intelligent and informed decisions can be made as a community. It’s one of the few chances we have as math instructors to teach for social justice.
Experiment design is one of the hardest things to “master” as a professional. Teachers are very familiar with this and I encourage you to share your experiences with educational research. It’s tough for any study to give clear results due to the impossibility of true control, many, many confounding variables and the reality that a classroom will never be a lab, nor a lab a classroom. A task that is usually taken on by most AP stats classes after the exam is to design and carry out a large scale study involving their school or peers. I’ve had some amazing work done by students, including some really salient studies about drug use by students that was in direct conflict with the findings for our site from the CA Healthy Kids survey. The discussions about why the two findings were different were some of the best moments in any of my classes ever. It’s maybe good to have the students start thinking about their projects now, if you plan to conduct one after the exam. It will help reinforce the ideas here, as well as set students up for success later on. With the way things go, the month and a half after the exam always seems like a ton of time, until you get there and it runs out in a hurry. Preparations must be made so that surveying can begin shortly after the test.