Causality vs Correlation Quiz

Study Notes

Correlation shows a relationship between variables, but not a specific type of causality (cause and effect)
Formal education level (X) and crime rate (Y) show a negative correlation. A possible causal structure is:
- Higher education leads to better job opportunities, decreasing the need for crime.
- A safer area attracts more educated individuals, leading to higher education levels in that area.
- A third factor (Z), such as good infrastructure, might cause both higher education and lower crime rates.

Granger causality is a concept used in time series analysis, a weaker form of causality than other models.
It determines if one time series can help predict another.
If variable X occurs before variable Y in time and they are linked (correlated), X predicting Y is considered more reasonable than Y predicting X.
Granger causality ignores any third variable that might be influencing both.

If an event (X) happens before another event (Y), then X potentially Granger-causes Y.
P(Y│I(t-1)) ≠ P(Y│Ix(t-1)): The probability of Y observed at time t, given all information available up to time t–1, is not equal to the probability of Y at time t given all information up to time t–1 without information from X. This demonstrates causality.
The concept is related to conditional independence.
This means the information from X is useful in predicting Y.

Granger causality test: The null hypothesis (Ho) is that variable X is not helpful in forecasting variable Y (ignoring previous lags of Y itself).
The alternative hypothesis (HA) states that lags of X are informative to predict Y.
Useful in forecasting, as it determines whether prior values of one time series are informative, when forecasting future values of another.

It can oversimplify real-world scenarios, leading to inaccurate or nonsensical conclusions regarding the direction of causality, or overlooking common causes of events.
- For instance, rooster crowing and sunrise are correlated, but not causative. A common cause (like the passage of time) would be more realistic.
- Similarly, carrying umbrellas and car accidents are correlated, yet not causally linked, as both are effects of a common cause (e.g., rainfall.)