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 Conference @ 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.

XYX

12

Start with a relationship

X YQuestion: Will this relationship be the same at all levels of Z???

Focus on the relationship

X Y

X Y

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

X Y

X YStrong

Strong

When Z = α:

When Z = β:

Positive

Positive

But if it is not…

X Y

X YCould 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

X YObserve: 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

X Y

X Y

Positive

When Z = No Clearasil

When Z = Twice Daily Clearasil

Teens Pimples

Teens PimplesPositive*

*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.

NL

PE

NS

NB

QC

ON

MB

SK

AB

YT

NT

NU

5060

7080

90%

turn

out f

or 2

000

fede

ral e

lect

ion

20 25 30 35 40median age 2001

NL

PE

NS

NB

QC

ON

MB

SK

AB

5060

7080

90%

turn

out f

or 2

000

fede

ral e

lect

ion

35 36 37 38 39median age 2001

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 X1 on Y holding X2 & X3 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.

NL

PE

NS

NB

QC

ON

MB

SK

AB

YT

NT

NU

5060

7080

90%

turn

out f

or 2

000

fede

ral e

lect

ion

20 25 30 35 40median age 2001

NL

PE

NS

NB

QC

ON

MB

SK

AB

5060

7080

90%

turn

out f

or 2

000

fede

ral e

lect

ion

35 36 37 38 39median age 2001

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

X YQuestion: Will this relationship be the same at different levels of education???

Men Income

Men (on average) make more money than women.

Strong

Positive

What do you think?

When Z = No/Low Education:

When Z = University Education:

X YGender

(Men)Income

X YMen Income

Positive or negative?

Strong or weak?

Men make more money

X Y

X YStrong

Strong

When Z = Low levels of education

When Z = High levels of education

Positive

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 = -0.09.

Cells contain:Who will win the election?

-Column percent

-N of cases 1 3 ROW

 John Kerry

George W. Bush

TOTAL

What will happen to

the economy

in the next 12

months?

1: Much better9.2 8.6 8.7

28 59 87

2: Somewhat better

23.6 31.3 28.9

72 216 288

3: Same (3 in F2)

44.6 45.9 45.5

136 317 453

4: Somewhat worse

16.1 11.0 12.6

49 76 125

5: Much worse6.6 3.2 4.2

20 22 42

COL TOTAL 100.0 100.0 100.0

305 690 995

I wonder, if you are voting for Kerry…

X Y

X YStrong

Moderate

When Z = Vote Kerry:

When Z = Vote Bush:

Negative

Positive

Bush will winEconomy will improve

Bush will winEconomy will improve

1 3 ROW

Kerry Voters Only 

John Kerry

George W. Bush

TOTAL

Econ

1: Much better

9.1 1.9 6.1

26 4 30

Somewhat better

22.1 12.5 18.1

63 26 89

3: Same

44.9 55.3 49.3

128 115 243

Somewhat worse

16.8 21.6 18.9

48 45 93

5: Much worse

7.0 8.7 7.7

20 18 38

COL TOTAL100.0 100.0 100.0

285 208 493

Means 2.91 3.23 3.04

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 3rd 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

Income Vote

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