Correlation and Causation Visiting Associate Professor Giddings

1. Correlation and CausationVisiting Associate Professor Giddings Math/Econ 108

2. Outline • A Brief History of Correlation • What is Causation? • What is Correlation? • Spurious Correlations • Simpson’s Paradox • How scientists determine causation

4. What is Causation? • When changes in one variable (X) affect changes in another variable (Y), we say that X causes Y. • Examples: • The Sun Rises → Rooster Crows (unidirectional) • Education → Higher Wages (bidirectional?)

5. Important Questions • What causes poverty? • Will Obama’s tax cuts cause the economy to expand? • Does immigration cause lower wages? • Does Prozac cause suicide? • Does the burning of fossil fuel cause global warming?

6. The Importance of Causality • I would rather discover one causal law than be the King of Persia. • Democritus (460-370 B.C)

7. How do we determine Causation? • Correlation • Controlled Experiments • Theory

8. What is Correlation? • When two variables move together, we say they are correlated.

9. Sir Francis Galton

10. Sir Francis Galton

12. Karl Pearson1857-1936 • Protégé of Sir Francis Galton, he founded the world’s first statistics department at University College London. • Main contributions: • Linear regression an dcorrelation • Classification of distributions • Pearson’s chi-square test • Coefficient of correlation

21. Pearson’s r • Should be +1 if all points lie on line with a positive slope • Should be -1 if all points lie on line with a negative slope • Should be 0 if all points on horizontal or vertical line

22. Should be unchanged if the same constant is added to all x-values or all y-values. Put center of graph at

23. More Pearson’s

24. Here’s a different way of seeing it • If r = 1, every X should equal Y. • So, Pearson’s correlation coefficient essentially measures how far the Xs and Ys are from each other.

27. Examples

28. So, the Crucial Point is… • Correlation does not necessarily imply causality