Causation Math Example 1
Follow the full solution, then compare it with the other examples linked below.
Example 1
mediumIce cream sales and drowning deaths are positively correlated. Explain why correlation does not imply causation here, identifying the confounding variable.
Solution
- 1 Observed correlation: more ice cream sold → more drowning deaths
- 2 Confounding variable: hot weather (temperature) — hot days cause both more ice cream purchases AND more swimming
- 3 True relationship: temperature → ice cream sales AND temperature → swimming → drowning
- 4 Ice cream does not cause drowning; both are caused by the same third variable (heat)
Answer
Confounding variable is temperature. Ice cream and drowning are both caused by hot weather, not by each other.
Correlation means two variables move together, but a third variable (confounder) can cause both, creating spurious correlation. This is why observational studies cannot prove causation — only controlled experiments with random assignment can.
About Causation
Causation exists when one variable directly produces or influences a change in another variable — distinct from mere correlation or association.
Learn more about Causation →More Causation Examples
Example 2 hard
A study finds students who eat breakfast score higher on tests. Design an argument for why this migh
Example 3 easyCountries with more TV sets per capita have higher life expectancy. Does this mean buying TVs causes
Example 4 hardA pharmaceutical company's observational study finds Drug X correlates with recovery. Explain three