TEACHING RESAMPLING IN AN INTRODUCTORY STATISTICS COURSE

There is a movement underway among statistical educators to use resampling techniques in introductory statistics courses. For these techniques to be effective, students must have access to appropriate computer software. To help in this process, a number of resampling applets are now available within the StatCrunch package, which can be customized using specific data sets. These applets are discussed in detail in the context of classroom activities with an emphasis on how they may be used to enhance the learning process. Some practical issues related to introducing resampling methods into an introductory course are also discussed. INTRODUCTION At the inaugural United States Conference on Teaching Statistics (USCOTS) in 2005, George Cobb created a firestorm among statistical educators with a very convincing argument for replacing much of the standard introductory statistics curriculum based on normal distribution theory with a resampling approach. In his address and subsequent paper (Cobb, 2007), his argument compared the rather convoluted path through basic inference found in the standard curriculum with the overly complicated model of the universe put forward by Ptolemy. As Ptolemy added an ever-increasing number of orbital paths to explain the observed movements of planets, Cobb noted the standard curriculum is full of complicated bifurcation points inserted in order to overcome issues related to the necessary assumptions required for standard inferential methods. Cobb pointed out that technology had advanced to the point that alternative computationally intensive approaches were now plausible for use at the introductory level. These methods, he argued, require far less in the way of assumptions and might allow students to focus on the big picture concepts rather than on the gritty details with the standard approach. As was the case with many in attendance, I left Cobb's address energized to explore these ideas for teaching introductory statistics. My interest was spurred not only because of my role as a statistics educator but also because of my role as developer of the StatCrunch software package, which has a strong presence in statistical education. I began focusing on ways to present resampling ideas in my own classes and on developing the corresponding software to support this implementation. On the content side, I collaborated with Roger Woodard on the INCIST (Improving National acceptance of Computationally Intensive Statistical Techniques) project funded by the National Science Foundation (DUE #0817262). This project developed a number of teaching techniques for incorporating resampling into introductory statistics courses using several activities where students were asked to initially collect resamples by hand before being introduced to software. These ideas were presented at a number of teacher training workshops offered around the United States. On the software side, I began by adding the capability within StatCrunch to easily collect multiple samples from columns of data and to compute and store basic statistics based on these samples. This preliminary work allowed for a very manual method of implementing basic resampling methods using the software. One drawback to this approach is that it required the storage of large amounts of data in the data table which could be quite memory intensive. As a follow up, I developed a general resampling tool for the package that allowed users to implement very sophisticated resampling ideas provided they understood how to specify rather complicated mathematical expressions. Realizing some of the potential issues with using either of these approaches with students in the introductory classroom, I then focused on building interactive applets into StatCrunch that not only allowed for doing the necessary resampling calculations but also provided a visualization of how the methods worked. The applets were designed to be complimentary to the INCIST activities so that teacher's could first build the intuitive ideas behind resampling methods using the activities. These activities were then well connected to the applets for repeating the calculations a much larger number of times. I have used this merger between the