Illustrating Randomness in Statistics Courses With Spatial Experiments

摘要

Understanding the concept of randomness is fundamental for students in introductory statistics courses, but the notion of randomness is deceivingly complex, so it is often emphasized less than the mechanics of probability and inference. The most commonly used classroom tools to assess students' production or perception of randomness are binary choices, such as coin tosses, and number sequences, such as dice rolls. The field of psychology has a long history of research on random choice, and we have replicated some experiments that support results seen there regarding the collective distribution of individual choices in spatial geometries. The data from these experiments can easily be incorporated into the undergraduate classroom to visually illustrate the concepts of random choice, complete spatial randomness (CSR), and Poisson processes. Furthermore, spatial statistics classes can use this point pattern data in exploring hypothesis tests for CSR along with simulation. To foster student engagement, it is simple to collect additional data from students to assess agreement with existing data or to develop related, unique experiments. All R code and data to duplicate results are provided.