By Zhaolin Li, Wenqi Zeng, Kelly Findley, Stephen Portnoy
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Understanding randomness is fundamental to comprehending statistical inference (GAISE, 2016) and for making sense of complex scientific ideas in areas such as climate change and water quality monitoring (Gougis et al., 2016). However, it is difficult to recognize and apply randomness to real-world situations. When asked to “draw at random,” people usually think of discrete uniform distributions (e.g., drawing a ticket from a bowl) and struggle to replicate randomness in continuous or non-uniform contexts (Gougis et al., 2016). We designed an online survey to explore how students relate the idea of “drawing at random” to visual sampling tasks. We collected data from approximately 1,000 undergraduate students at a large public university. Participating students were enrolled in either an introductory statistics course (n=361), a mathematical statistics course (n=354), or a senior-level elective statistics course (n=45). Students attempted to click 50 points at random from shapes that included optical illusions and distractions. We used a Kolmogorov-Smirnov test to determine how likely each student’s sample was to follow the true underlying distribution. Our findings highlight the complexity and difficulty in applying notions of randomness to real-world scenarios for both novice and advanced students in statistics.