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This lecture covers the application of two-way ANOVA to assess the impact of two categorical variables on a quantitative outcome, focusing on potential interaction effects. It also includes a demonstration using a dataset about cars. Additionally, the lecture introduces the chi-square test for analyzing the relationship between two categorical variables in contingency tables, serving as an alternative when ANOVA assumptions are not met. The instructor explains how to run these analyses, interpret the results, and check the assumptions, emphasizing the importance of model comparison and transformation when necessary.