This blog post is written by Russell Mayhew, who taught our math seminar at the 2024 Oxford Academia at Yale program.
The Math: Probability and Statistics seminar capped off our first week with a trip to a minor league baseball game in nearby Hartford. It was a beautiful night for a ball game. For many of our students, visiting a ballpark was a new experience. The home team could not pull out the win, but with pencil, paper, and our phones we gathered data on hits, foul balls, the pitch clock, and even the prevalence of team jerseys among the other game attendees. During our next class, we parsed the data to look for anything noteworthy and discussed the challenges of gathering data in real-time.
In the second week of our seminar, we gathered data for an observational study on Yale’s campus. We were interested in whether people tend to walk clockwise or counterclockwise around an object on the ground, and whether other variables may predict the direction a person may choose. We ventured out onto campus in three groups, inviting passersby to participate in our study. Some said no, but most said yes! It was important to emphasize that being a statistician is much more than crunching numbers. The class experienced the challenges of gathering “clean” data in the field and avoiding biased or non-representative sampling strategies.
The evidence suggested a preference for walking counterclockwise, but our bootstrapping simulation revealed that our result was still within the margin of error, but only by the slightest bit. Our evidence of a preference for counterclockwise walking was strong, but not technically statistically significant.
This field study was an opportunity to introduce and discuss many statistical concepts and terms to students: null hypothesis, alternative hypothesis, confidence interval, margin of error, p-value, significance level, and more.
Our emphasis has been on running simulations to approximate probabilities. Still, on our final day, by special request, we derived and discussed permutations, combinations, the binomial theorem, and Pascal’s triangle, and showed how these mathematical tools provide exact probabilities for one of the dice games we learned last week.
This was an amazing group to work with! Their willingness to dive into activities and concepts propelled us through two weeks of impressive progress with the material. Most importantly, we had a blast doing it!
