![\"\"](\"http:\/\/statweb.calpoly.edu\/arossman\/index_files\/image014.jpg\")
<\/p>\n<\/p>\n
Teachers of introductory statistics are increasingly using simulation-based methods to help students learn concepts and methods of statistical inference. Two quick anecdotes: Let me start by trying to clarify what I mean by the term \u201csimulation-based inference.\u201d I\u2019ll start with a relatively simple example involving a binomial process, for which you want to draw an inference about the underlying probability of success. I once spun my tennis racquet 100 times, wanting to test whether the spun racquet was equally likely to land with the label facing up or down. I found that my racquet landed with the label up on 46 of those 100 spins. How to proceed? I could use the binomial distribution to calculate the relevant p-value, or I could use a normal approximation to determine a z-score and approximate p-value. But the simulation-based approach would say to simulate a large number of repetitions of spinning a racquet 100 times, assuming a .5 probability of landing with the label up or down.<\/p>\n Examples of simulation-based inference in slightly more complicated settings include bootstrapping to illustrate sampling variability and determine confidence intervals, and simulating a randomization test to compare responses between two groups.<\/p>\n One thing I do NOT mean by this term is the use of simulation only to illustrate a statistical concept such as a sampling distribution. That\u2019s a great use of simulation as a teaching tool, but stopping there without proceeding to draw an inference based on the simulation results does not qualify as what I would consider to be simulation-based inference.<\/p>\n Where does this movement toward teaching introductory statistics with simulation-based inference come from? Many cite George Cobb as the driving force behind this initiative. George gave an inspiring after-dinner talk<\/a> at the first USCOTS in 2005 in which he challenged the audience of statistics educators to redesign introductory courses to focus on the logic of inference. George subsequently wrote an article, with the delightful and provocative title \u201cThe Introductory Statistics Course: A Ptolemaic Curriculum<\/a>,\u201d that appeared in the inaugural issue of Technology Innovations in Statistics Education.<\/p>\n Of course, the ideas behind these methods of statistical inference go back as least as far as Fisher, and they have been presented in classic textbooks such as Statistics for Experimenters by Box, Hunter, and Hunter. For the Stat 101 audience, Bob Wardrop wrote an entire textbook around simulation- and randomization-based inference in the early 1990s. But one big factor behind the current craze, of course, is high-speed computing: its ease, availability, and low cost allow for conducting simulations quickly and efficiently. Moreover, many people have developed highly visual, interactive, appealing software tools that students can use to explore and apply these methods.<\/p>\n
\n\u2022 The theme of the 2011 U.S. Conference on Teaching Statistics<\/a> was \u201cThe Next BIG Thing,\u201d and the consensus emerging from the conference was that the BIG thing is teaching introductory statistics with simulation-based methods.
\n\u2022 The recently conducted International Conference on Teaching Statistics <\/a>in Flagstaff (July 2014) included a large number of sessions on this topic, featuring presenters from around the world, often with standing-room-only crowds of attendees.<\/p>\n