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

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

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. X Y X 1 2

Start with a relationship XY Question: Will this relationship be the same at all levels of Z???

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

If relationship is the same XY XY Strong When Z = α: When Z = β: Positive

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

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?

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

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

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.

Experiments Achieving full control

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.

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.

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.

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 X 1 on Y holding X 2 & X 3 constant Elaboration is the start of learning how to understand how three or more variables relate.

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.

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).

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

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

Men make more money XY XY Strong When Z = Low levels of education When Z = High levels of education Positive Gender (Men) More Income Gender (Men) More Income

“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.”

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 =

Cells contain: Who will win the election? -Column percent -N of cases 13 ROW John Kerry George W. Bush TOTAL What will happen to the economy in the next 12 months? 1: Much better : Somewhat better : Same (3 in F2) : Somewhat worse : Much worse COL TOTAL

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

13 ROW Kerry Voters Only John Kerry George W. Bush TOTAL Econ 1: Much better Somewhat better : Same Somewhat worse : Much worse COL TOTAL Means

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.

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.

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

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 3 rd variable. Contingency tables can provide evidence of non-spurious relationships.

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.

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. Race IncomeVote

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