I teach at a math-science magnet program for high school students. All of our juniors and seniors conduct research projects of their own design. The majority of these projects are biological, but some of them are chemical, environmental, or engineering projects, and a few are physics projects. Most of these projects have limited replication sample sizes (3 ≤ N ≤ 10) due to time constraints. Currently, we use frequentist statistics to analyze data. I'm interested in learning more about Bayesian statistics to see if it would make sense for our students to use Bayesian analysis on their data. I'm looking for recommendations for a good book, or possibly other material, that would help me better understand Bayesian statistics, including a comparison between the virtues of using Bayesian and frequentist statistics to analyze data. If we decide that Bayesian analysis would be useful, we'd be interested in finding materials to help our students understand Bayesian analysis, but that's not my main focus right now. All of our juniors and seniors study calculus: either AP Calculus AB followed by AP Calculus BC or AP Calculus BC followed by multivariable calculus.
Thank you in advance for your recommendations.
Daniel Crowe
Loudoun County Public Schools
Academy of Science
dan.crowe@lcps.org