Causal Inference

Describing Causal Inference

  • Correlation is defined as the association (or dependence) between two variables (typically referring to a linear relationship)
  • Causation is defined as the cause of one variable results in an effect in the other variable
  • Correlation is not causation
  • Not even statistical dependence is causation
  • At best, both of these statements tell us that there's an association between two variable, but not necessarily causation

Examples of Correlation but not Causation

  • Confounding variables

    • This happens when a third variable causes our response and predictor variable
    • For example, ice cream sales and homicide rates are correlated, but the relationship is not causal (i.e. ice cream sales and homicides are most likely caused by weather)
  • Reversed causality

    • This happens when our predictor variable actually causes our response variable
    • An example of this is saying my bad mood causes it to rain, rather than rain causes me to be in a bad mood
  • Bidirectional causality

    • Causality is not necessarily one-way
    • An example of this is preserving grasslands causes there to be more elephants
    • Also, having more elephants causes better preservation of grasslands

      • This is because elephants feed the grass with manure and play a role in the ecosystem such that more elephants create more grass and vice versa
  • Coincidental causality

    • This happens when our predictor variable and response variable aren't related at all, but correlate by chance
    • An example of this relates to alternating bald-hairy Russian leaders
    • Specifically, a bald state leader of Russia has succeeded a non-bald (i.e. hairy) leader, and vice versa, for nearly 200 years

Testing Correlation and Causation

  • Determining correlation between two variable involves simpler statistical testing, such as hypothesis testing
  • Determining causation between two variables involves complicated statistical testing in a completely controlled environment using AB testing

References

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Hypothesis Testing

Multicollinearity