Spurious Relationship

1. Spurious Relationship A correlation between two variables that have no causal relationship; both variables are caused by another variable

2. Examples of spurious relationships • Amount of ice cream sold and death by drowning (units are months) • Number of doctors and number of people dying of disease (units are cities) • Number of libraries and number of people on drugs (units are years)

3. What causes the price of rum? • There is a positive relationship between the salaries of Presbyterian ministers in Massachusetts and the price of rum in Havana. • What is the causal mechanism?

4. Causal Mechanism? International business conditions: prices and salaries increasing everywhere Ministers’ salaries Price of rum

5. Popular Study: Smoking causes bad grades • True or spurious? • What could be the variable (or variables) that drive both?

6. News reports • Bottled water causes healthier babies • Drinking tea makes you less likely to contract lung cancer

7. Research question: Does education cause political tolerance? • Many scholars have found a positive relationship between political tolerance (support for liberty for political enemies) and education. • Causal mechanism? • As people are educated, they are introduced to different kinds of people and perceived danger of political enemies decreases. • As people are educated, they are socialized to the correctness of constitutional rights.

8. Alternative Explanation • Political tolerance is actually caused by cognitive sophistication, as measured by IQ. • Causal mechanism? • It is difficult to reconcile the emotional reaction to named political enemies (i.e. Nazis) with constitutional rights and it takes a high IQ to understand that democracy benefits from giving liberties to “bad people.”

9. Relationship between Education and Political Tolerance High Political Tolerance Medium Low Low Medium High Education

10. Relationship between Education and Political Tolerance High Political Tolerance Medium Low Low Medium High Education

11. Controlling for IQ • X = high IQ • Y = low IQ

12. Education and Political Tolerance High Political Tolerance Medium Low Low Medium High Education

13. Education and Political Tolerance - High IQ High Political Tolerance Medium Low Low Medium High Education

14. Education and Political Tolerance - High IQ High Political Tolerance Medium Low Low Medium High Education

15. Education and Political Tolerance - Low IQ High Political Tolerance Medium Low Low Medium High Education

16. Education and Political Tolerance - Low IQ High Political Tolerance Medium Low Low Medium High Education

17. Conclusion? • What was the hypothesis? • What was the alternative explanation? • What do we conclude about the likely cause of political tolerance?

18. Review • A spurious effect is a specific case when correlation is not causation. • The specific case is related to whether the two things correlated are caused by a third variable. • Correlation does not always equal causation.

19. An illustration with a causal model A and B are spuriously correlated if: Z B A

20. A test of whether A and B are spurious • Look at the relationship between A and B, controlling for Z • This means, that for all values of Z, you should look at the relationship between A and B.

21. Crosstab analysis testing for spurious relationships, part I (z = 1 or 2)

22. Crosstab analysis testing for spurious relationships, part 2 (z = 1)

23. Crosstab analysis testing for spurious relationships, part 3 (z = 2)

24. Scatterplot illustration of a spurious relationship Z = 1 or 2 A Z = 1 B Z = 2 A A B B