Notes on Correlation, Causation, and the Third Variable Problem

Correlation vs Causation

• Headlines with bold terms imply causation, but they actually reflect correlation only.
• Correlation means two variables change together; it does not prove one causes the other.
• Predicting one event from another does not establish causality.
• Causality requires ruling out alternative explanations; simple correlation provides no such proof.

Third Variable Problem (Confounds)

• A third, unmeasured variable may account for the observed correlation.
• These variables are called confounds or the third-variable problem.
• When a confound exists, the relation between the two observed variables may be spurious.

Example: Ice Cream vs Violent Crimes

• Observed correlation: $r = +0.50$ (positive correlation)
• Interpreting as causation (e.g., "Ice Cream Consumption Leads to Violence") is not justified.
• Possible third variable: factors like weather/season that increase both ice cream sales and crime.
• Key point: correlation does not equal causation; causality requires controlled methods or experimental evidence.

Key Takeaways

• Correlation does not imply causation.
• Always consider potential confounds/third variables.
• Use experiments or statistical controls to infer causal relationships.