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.ht… (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(a)causeweb.org [mailto:sbi-bounces@causeweb.org] On Behalf Of Robert
Peterson
Sent: Thursday, January 01, 2015 6:25 AM
To: sbi(a)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.