A more philosophical answer to your question might be to think about how you present the
two approaches, e.g., side by side or start with simulation to get across the concepts and
then focus more on the theoretical approach. We (though this is response is just my own,
non-AP-stat-teacher opinion) like to show them the simulation results and the theoretical
results together to reinforce each other and to emphasize both are just approximations of
the same thing (tail area). So we often have them looking at a “simulation-based” p-value
and a “theory-based” p-value together and thinking about what it means if they don’t match
so well. I also want them to see the simulation results with the theoretical model
overlaid on the same graph as much as possible. This allows me to focus a bit less on the
computation of the theory-based p-value but I do think it’s important to emphasize the
idea of “standardization” and why the idea of a test statistic is important with inference
as well. But I’m able to try to convince them also that this is one general idea vs. a
separate unrelated formula for each situation. I think if students can use their
calculator to get a p-value but also be comfortable with the test statistics, as well as
really be able to interpret a p-value and confidence interval, then they will be well
prepared for the AP Exam?
Beth
From: sbi-bounces(a)causeweb.org [mailto:sbi-bounces@causeweb.org] On Behalf Of Robert
Peterson
Sent: Thursday, January 01, 2015 7:55 PM
To: Simulation-Based Inference
Subject: Re: [SBI] Simulation methods in an AP course
HI Josh,
Thanks. I piloted the ISI material 2 years ago after Alan asked if I was interested. My
only concern was the lack of probability and some of the other AP stuff. Last year I did
infuse some of the simulation activities. I don't know of many AP teachers that are
doing this, so I really appreciate the response.
I am still using The Practice of Statistics 2e, so I am sure you cam imagine how I must
supplement. I do plan on starting each simulation chapter with a simulation and then move
into the traditional approach.
I am also an AP reader, so maybe I can spend a little time in KC and "compare
notes".
Thanks for your response!
Bob Peterson
@apstatspeterson
On Thu, Jan 1, 2015 at 10:43 PM, Josh Tabor <joshtabor(a)hotmail.com> wrote:
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.
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