Elaboration and Control

1. Elaboration and Control POL 242 Renan Levine January 16/18, 2006

2. Announcements • Weds 2- 4 pm tutorial, 4-6 pm? • Honors thesis • Midwest Political Science Association Mtg in Chicago • Crossing Borders Conference @ Brock

3. X Y 1 X 2 Earlier • Discussed addition of additional variables. • Many independent variables influencing the dependent variable - How X1, X2 affect Y. • Described antecedent and intervening variables. • Now: How an additional variable can affect the relationship between X and Y.

4. X Y Start with a relationship Question: Will this relationship be the same at all levels of Z???

5. X X Y Y Focus on the relationship When Z = α Can be positive or negative. Can be strong, weak or have no effect. ? When Z = β NOT what is the effect of Z on Y.

6. If relationship is the same When Z = α: X Y Positive Strong When Z = β: X Y Positive Strong

7. But if it is not… When Z = α: X Y Strong Positive When Z = β: X Y Could be weak Could be negative See Pollock, p. 82 for a set of diagrams of all of the possible interactions

8. Focus is on X & Y • Focus on the relationship between X & Y • Not on how Z affects Y • The question is: • Did the relationship between X and Y change at different levels of Z? • Did the relationship get weaker? stronger? • Did the sign change or stay the same?

9. X Y Sample relationship - I Teens [Age] Pimples Observe: Teenagers/younger people get pimples. Question: Will this relationship be the same if the teen is using Clearasil?

10. When Z = Clearasil Zit Medication When Z = No Clearasil X Y Strong Teens Pimples Positive When Z = Twice Daily Clearasil X Y Weak Teens Pimples Positive* *I’m guessing.

11. Example: Age and Turnout • Median age of province/territory -> % turnout. • When z = province, there is a strong, positive relationship. • When z = territory, there is a weak relationship.

12. Experiments Achieving full control

13. Experiments • Like other drugs, Clearasil had to be tested to make sure it worked and didn’t cause leprosy. • Test by giving medication to some randomly selected teens (and rats) while giving nothing more than an alcohol pad (“placebo”) to the others. • Look to see whether there is specification.

14. Some applications to politics • Campaigns & scholars will test advertisements. • Randomly assign people to one of two groups: • People who watch the ad • A control group: people who do not watch the ad • Afterwards, you ask both groups their opinion about the topic. • Same as split-samples on surveys with different question wording.

15. Quasi-Experiment • Political observations rarely have luxury of random control. • If there is no random assignment, then we have a quasi-experimental design • Effect of a program or intervention on people. • People in treatment program for alcohol • Some court ordered, some voluntary. Who’s sober? • Effect of cutting the PST in Ontario. • Income drives consumption – even more so in the GTA? • Warning: there may be self-selection effects or unique history, or normal maturation and regression to the mean.

16. No experiment is possible • Statistics can be used to estimate if there was an effect when controlling for other factors. • Way of estimating what might be the case if one could isolate one effect – like in an experiment. • Tells us effect of X1 on Y holding X2 & X3 constant • Elaboration is the start of learning how to understand how three or more variables relate.

17. Example: Age and Turnout • Median age of province/territory -> % turnout. • When z = province, there is a strong, positive relationship. • When z = territory, there is a weak relationship.

18. When controlling • When controlling for a third “test” variable, you look at the relationship between the two original variables at each level or category of the test variable. • Age and Turnout example: compare correlations between age and turnout for provinces and for territory. • Next: an example where you need a control, because you cannot experiment with different levels of the test variable (Z).

19. X Y Sample relationship - II Men (on average) make more money than women. Strong Men Income Positive Question: Will this relationship be the same at different levels of education???

20. X X Y Y What do you think? When Z = No/Low Education: Positive or negative? Strong or weak? Gender (Men) Income When Z = University Education: Men Income

21. Men make more money When Z = Low levels of education X Y Positive Gender (Men) More Income Strong When Z = High levels of education X Y Positive Gender (Men) More Income Strong

22. “Partial relationship” • Relationship between gender and income is similar across different education levels (StatsCanada) • When controlling for education level, men make more money than women. • You can test this using Canadian Election Study (and others) using income as DV. • Run cross-tab for gender and income, with different table for low level of education, college and post-graduate. • When the partial relationships are essentially the same as the original relationship, we call the result “replication.”

23. Example II: What will happen to the economy after the election? • 2004 Bush vs. Kerry. • Hypothesis: People who think Bush will win will think that the economy will get better. • Rationale: Republicans are generally thought to be pro-business, Bush cut taxes, the markets may not approve of a change in leadership… • Relationship (see next slide) is weak • Tau-c = -0.09.

25. I wonder, if you are voting for Kerry… When Z = Vote Kerry: X Y Negative Economy will improve Bush will win Moderate When Z = Vote Bush: X Y Positive Economy will improve Bush will win Strong

27. And if you are voting for Bush • Most Bush voters thought that Bush would win and the economy would improve. • Compared to Kerry voters who thought Kerry would win, Kerry voters who thought Bush would win were • more likely to think the economy would worsen and • less likely to think the economy would improve or stay the same.

28. Intervening • What happens if the test variable also has an effect on Y? • In this case, X -> Y, Z->Y, AND relationship between X and Y changes at different levels of Z. • Z is an intervening variable. • Independent variable -> Test variable -> Dependent variable. • If, after introducing Z, X no longer influences Y, the relationship is spurious.

29. Do Storks Deliver Babies? • That’s the way it was in the “Dumbo.” • That’s where my parents told me babies came from.

30. It’s a FAKE!! • Spurious relationship= when there appears to be a relationship between two variables, but the relationship is not real; it is produced because each variable is itself related to a 3rd variable. • Contingency tables can provide evidence of non-spurious relationships.

31. Why this story? • Observe many babies in areas with storks. • High, positive relationship between countries that have storks and birthrates. • The relationship is spurious • At least two variables are antecedent. Urban/rural and (country level) Catholicism.

32. Does income influence the US Vote? • Blacks (on average) are poorer than Whites in the US. • Vast majority of blacks vote Democrat regardless of income. • Income is not a good predictor of vote among whites either! • Since there is little (or no) connection between income and vote, race is antecedent to both income and vote.

33. Take-Aways • New variable (Z) can affect original relationship between the independent variable (X) and the dependent variable (Y). • In some circumstances, we can do an experiment to observe what happens to X and Y at different levels of Z. • In politics, often one cannot and must use statistics to control for Z. • Controlling for third variable may reveal specification, or that original relationship was spurious