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.

摘要

理解随机性的概念是统计学入门课程学生的基础，但随机性的概念非常复杂，因此与概率和推理机制相比，它的重点往往较少。最常用的评估学生产生或感知随机性的课堂工具是二元选择，例如掷硬币和数字序列，例如掷骰子。心理学领域对随机选择的研究有着悠久的历史，我们复制了一些实验来支持在那里看到的关于空间几何中个体选择的集体分布的结果。这些实验的数据可以很容易地合并到本科课堂中，以直观地说明随机选择、完全空间随机性 (CSR) 和泊松过程的概念。此外，空间统计类可以使用此点模式数据来探索 CSR 的假设检验以及模拟。为了促进学生的参与，从学生那里收集额外的数据来评估与现有数据的一致性或开发相关的、独特的实验很简单。提供了所有用于复制结果的 R 代码和数据。