By Julie Deeke (University of Illinois, Urbana-Champaign)
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To help students in developing useful models to conceptualize hypothesis testing, I implement a set of three motivating examples that explore properties of hypothesis tests, including the concept that parameters have true but unobserved values and the proof by contradiction approach for p-value calculations in my large (100+ student), undergraduate, second semester data science course at a large, public university.
The first activity provides students with candy in a paper sack. Students are asked to evaluate whether they have a certain type of candy in their bag without looking, assessing theories based on available data. Then, students reveal their true candy and determine whether they made an error. In the second demonstration, I develop a persuasive argument for leaving dirty dishes in the sink until the end of the day. I build my argument using proof by contradiction, starting with the claim that dishes should be cleaned immediately before logically exploring the consequences of this decision. Students experience how effective and convincing this strategy is before later seeing it applied to the p-value calculation. Finally, I use the changemyview subreddit to show how data and reasonable arguments can convince a skeptic to abandon their original claim (the null hypothesis) in favor of a new position (the alternative hypothesis) if presented with enough evidence.
These three engaging demonstrations were designed to provide tangible examples and helpful, concrete references before hypothesis test procedures were formally introduced in the next class, building students' foundational models and intuition for hypothesis testing.