Hi Robert-

I am an AP teacher and love to incorporate simulation-based inference into my AP course.  I do this in several ways.

1.  When we cover experimental design at the beginning of the year, we always do an actual experiment in class.  Typically we do a completely randomized experiment to see if caffeine affects pulse rates (using Coke and caffeine-free Coke).  Then, we analyze the results using simulation.  We start the simulation by hand using notecards and finish using an applet.  If you are interested in the applets, there are several good sites that are set up for various randomization tests (see below).

2.  In the middle of the year, we spend a few days on simulations as part of the probability chapters.  Whenever possible, I try to incorporate the logic of inference in these questions.  For example, instead of saying that “If 25% of all boxes of cereal have a prize, how likely is it to get at most 1 prize in 10 boxes?” I say “Johnny bought 10 boxes and only got 1 prize.  He is suspicious that the cereal company actually puts prizes in fewer than 25% of the boxes.  Find the probability that he gets at most 1 prize in 10 boxes, assuming that 25% of the boxes have a prize.  Is Johnny’s suspicion justified? Explain.”

3.  At the beginning of most major inference test (one proportion, difference of two means, difference of two proportions, chi square goodness-of-fit, slope), I start with a simulation based approach to introduce the big ideas. It definitely helps students understand the logic of inference and the meaning of p-values.  My textbook (The Practice of Statistics 5e) has some of these built in to the student edition and others in the teacher’s edition.  Or, you can design your own based on examples or exercises from the chapter. 

Another benefit of using the simulation-based approach in AP is that there have also been several simulation-based inference questions on recent AP exams, including 2009 #6, 2009B #5, 2010 #6, and 2013 #5.  These items can be found at the following website: http://apcentral.collegeboard.com/apc/members/exam/exam_information/8357.html (scroll down) for those interested in seeing them.

Regarding applets, there are several good sites with applets designed for the most common randomization tests.  Check out www.lock5stat.com/statkey, www.whfreeman.com/SRIS, or http://www.rossmanchance.com/ISIapplets.html. 

I hope this helps!

Josh

From: sbi-bounces@causeweb.org [mailto:sbi-bounces@causeweb.org] On Behalf Of Robert Peterson
Sent: Thursday, January 01, 2015 6:25 AM
To: sbi@causeweb.org
Subject: [SBI] Simulation methods in an AP course

Does anyone have some insight on how to blend simulation methods concepts with the AP curriculum. Also I will be starting inference soon, so I would love to hear ideas and experiences. My problem is I really love the ISI material, but at the same time my students must know the formulas and conditions from the theory based methods.