By Dylan Glotzer (Meredith College)
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Statistics is full of apparent paradoxes, and students regularly bristle at the rarity of simple concrete conclusions. Twice during the semester of a general education introductory Statistics course for primarily first-year students at a small liberal arts women’s college, I conduct a class-wide discussion activity to encourage deeper thinking on several counterintuitive topics. For a corresponding short-answer written assignment, I assess students on their thoughtful engagement in the exercise, rather than correctness. In the first discussion, students encounter Simpson’s paradox in a Bureau of Labor Statistics report and explore Berkson’s paradox as a possible explanation for early pandemic data showing a negative correlation between smoking and COVID-19 in hospitals. The second discussion has students facing the reevaluation of p-values among statisticians, scientists, and educators by reading discussion in the literature. Additionally, we consider two concerns of the p-value: p-hacking through multiple comparisons illustrated by a 2015 hoax study which concluded that chocolate helps weight loss, and the high variability of p-values demonstrated in Geoff Cumming’s “Dance of the p-values”. According to anonymous survey results, students valued the activities for requiring ways of critical thinking that they didn't expect on interesting applications relevant to the world around them.