elaboration and control
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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
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