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. _______________________________________________ SBI mailing list SBI(a)causeweb.org https://www.causeweb.org/mailman/listinfo/sbi

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. _______________________________________________ SBI mailing list SBI(a)causeweb.org https://www.causeweb.org/mailman/listinfo/sbi _______________________________________________ SBI mailing list SBI(a)causeweb.org https://www.causeweb.org/mailman/listinfo/sbi