Causation Math Example 2
Follow the full solution, then compare it with the other examples linked below.
Example 2
hardA study finds students who eat breakfast score higher on tests. Design an argument for why this might not be causal, and describe how you would establish causation.
Solution
- 1 Possible confounders: family income (wealthier families provide breakfast AND better educational resources), general health habits, parental involvement
- 2 The correlation might be spurious — both breakfast eating and test scores caused by the same underlying factors
- 3 To establish causation: conduct a randomized controlled experiment — randomly assign students to breakfast/no-breakfast groups, control all other variables, measure test scores
- 4 Only random assignment eliminates all confounders and allows causal conclusions
Answer
Causation requires eliminating confounders via randomized experiment; observational correlation could be spurious.
Establishing causation requires: (1) correlation, (2) temporal order (cause before effect), (3) elimination of alternative explanations (confounders). Only a randomized controlled experiment satisfies all three conditions definitively.
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 1 medium
Ice cream sales and drowning deaths are positively correlated. Explain why correlation does not impl
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