Lesson 4: 3.4 More About Correlation
Duration of Days: 2
Lesson Objective
Students will understand the limitations of correlation, including its lack of resistance to outliers and the critical distinction between correlation and causation.
If ice cream sales and shark attacks are highly correlated, does eating ice cream cause shark attacks?
How much power does a single "outlier" have to change the correlation of an entire study?
Non-resistance
Causation
Lurking variable (or confounding variable)
HSS-ID.C.9: Distinguish between correlation and causation.
A classic SAT "trap" presents a study with a high correlation and asks for a conclusion. The answer "X causes Y" is almost always wrong; students must choose "There is an association between X and Y."
This is the "critical thinking" section. It warns students that $r$ is a sensitive tool that can be easily manipulated by outliers or misinterpreted by assuming a cause-and-effect relationship.
The Problem: There is a strong positive correlation between the number of fire trucks sent to a fire and the amount of damage done.
Task: Does this mean fire trucks cause damage? Identify a lurking variable that explains this relationship.
Students struggle to identify what the third variable might be. They need practice brainstormed environmental factors.
Support: Provide "Spurious Correlation" examples (like the famous correlation between Nicholas Cage movies and pool drownings) to highlight the absurdity of assuming causation.
Extension: Discuss "Standardizing" and have students prove algebraically why the correlation of (x, y) is the same as the correlation of (y, x).
Teacher assigns examples from the textbook and other resources.
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