Illustrating Randomness in Statistics Courses With Spatial Experiments

Abstract

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.

Keywords:

• Complete spatial randomness
• Hypothesis testing
• Point patterns
• Randomness

Supplementary Materials

We provide the data and the code to reproduce the results of this study, which can be accessed by emailing the corresponding author or at the following link: https://baylor.box.com/s/fjqr43a0b1kflre0t9ssszan7h2kdc4k.

Acknowledgments

We would like to thank the students and faculty at Colorado School of Mines who participated in collecting these data, especially Terry Bridgman, Debra Carney, Scott Strong, and Jennifer Strong. We also thank A. Alexander Beaujean of Baylor University’s Department of Psychology and Neuroscience for suggesting useful references in the psychology literature. We also thank the editor, associate editor, and three referees whose anonymous comments have helped improved the content and presentation of this work.