The Illusion of Randomness: Evaluating Student Sampling Performance

Randomness is a critical concept in the study of statistics, both for everyday consumers of statistical information and producers of statistical analyses. However, students at all levels do not always hold concept images that translate to non-uniform or complex sampling contexts. In this article, we explore the way statistics students relate the idea of “drawing at random” to visual sampling tasks. We collected data from approximately 1,000 college students where students attempted to click 50 points at random from shapes that included optical illusions and distractions. One task included a disc, while another included a rectangle with highlighted sectors of unequal size. The survey we administered also included a number of questions and statements to determine which events that the participants identified as random or not. We used a Kolmogorov-Smirnov test to identify how students' samples may or may not diverge from a truly random sample. Findings reveal challenges in perceiving and replicating randomness, particularly in the presence of optical illusions or constraints that interfere with a uniform or equiprobability assumption. The study highlights the complexity and difficulty in understanding randomness and correctly applying it in real-world scenarios, both among students in an introductory statistics course and among upper-level students enrolled in a statistics major.