Elaboration and Control

1
Elaboration and Control

• POL 242
• Renan Levine
• January 24/26, 2006

2
Did an advertisement make a difference?

• In 2004, Harper was portrayed as too
  conservative, too pro-American for Canada.
• In 2006, Conservatives used a hard hitting ad
  blasting the Grits for corruption.
• And Harper did his best to appear centrist.
• We observe two very different electoral results.
• Question Did the ad make a difference?

3
Experiments One way to find out

• 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.
• You can ask questions (or make observations) of
  the people beforehand enabling one to compare
  before/after opinions.

4
Relevant aside

• FRIENDS of Canadian Broadcasting is pleased to
  announce the 2006 Dalton Camp Award, a 5,000
  prize to each of up to three winners of an essay
  competition on how the media influence Canadian
  democracy. The deadline for entries is March 31,
  2006.
• http//www.daltoncampaward.ca

5
Other examples

• Split-samples on surveys with different question
  wording.
• Key is random assignment.
• If there is no random assignment, then we have a
  quasi-experimental design
• Ex. Effect of a program or intervention on
  people.
• E.g. People who seek treatment program for
  alcohol, drivers who attend extra driving
  classes, effect of cutting the sales tax in
  Alberta.
• Warning there may be self-selection effects or
  unique history, or normal maturation and
  regression to the mean.

6
Moving Beyond Experiments

• Social and political observations rarely have
  luxury of random control.
• What was the effect of the advertisement?
• Some people have seen advertisement, some not.
• I can ask people if they have in a survey.
• Some people already agree with the advertisement,
  so I will need to control for prior beliefs.
• How?
• Some people may have changed their mind as a
  result of some other factor around the same time
  (crime?).

7
Use of Statistics

• 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 (like an experiment) one effect.
• Up until now, you have learned how to evaluate
  the relationship between two variables.
• This is the start of learning how to understand
  how three or more variables relate.

8
From Two to Three (or more!)

• Contingency table crosstabulation
• Two variables
• Introduce a third, test variable, often known
  as the control variable.
• Question is what happens to the relationship
  between the first two variables when controlling
  for or holding constant the test variable.

9
When controlling

• When controlling for a test variable, you look at
  the relationship between the two original
  variables at each level or category of the test
  variable.
• Partial relationship
• When the partial relationships are essentially
  the same as the original relationship, we call
  the result replication.
• Ex. Relationship between gender and income is
  similar across different education levels
  (StatCanada)

10
Its 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.
• Ex. Do storks deliver babies?

11
TTC
12
Age, Income and Voting in the US

• Turnout is higher among people with high incomes.
• Turnout is higher among whites people.
• What is the relationship among these three
  variables?
• Is one relationship spurious?

13
Intervening

• Independent variable -gt Test variable -gt
  Dependent variable
• Race -gt Income -gt Vote
• Alternatively, the test variable race may be
  antecedent if there is no (or little) connection
  between income and vote.

14
Antecedent
15
Do Storks Deliver Babies

• Thats the way it was in the Dumbo.
• Thats how my parents told me babies were made.
• Why this story?
• Observe many babies in areas with storks.
• High, positive relationship between storks and
  birthrates.
• The relationship is spurious
• At least two variables are antecedent.
  Urban/rural and (country level) Catholicism.

16
Specification

• What if partial relationships differ from each
  other?
• How can you tell from cross tabs?
• Differences in s
• Association
• Chi-squared
• Specification we have specified the conditions
  in which the original relationship occurs.

17
When you add a 3rd Variable

• You have two variables, the DV and the IV.
• Lets assume you look at the cross-tab and find a
  relationship between these two variables.
• You want to see what happens when you introduce a
  third test variable as a control.
• What is the relationship between DV and IV when
  controlling for test variable?

18
Possible Outcomes I

• When you add a third variable
• Relationship between independent and dependent
  variables remains unchanged.
• Control variable is not related to dependent
  variable.
• Eliminate control variable from further analysis.

19
Possible Outcomes II

• When you add a third variable
• Relationship between independent and dependent
  variables virtually disappears.
• independent variable is not related to dependent
  variable OR
• There is a sequence independent variable affects
  third variable which affects DV.
• Third variable becomes new IV.

20
Possible Outcomes III

• When you add a third variable
• Relationship between independent and dependent
  variables changes markedly relationship
  between IV and DV is not consistent across
  categories of control variable.
• The relationship is interactive the control
  variable specifies the relationship between DV
  and IV.
• Include control variable in all future analyses.

21
Possible Outcomes IV

• Relationship between independent variable and
  dependent variable is slightly changed
  relationship between IV and DV is consistent
  across categories of control.
• Both IV and the 3rd variable are related to DV.
• Include both IV and DV in future analyses.

22
When partial relationships are different

• Suppressor variable
• Distorter variable

23
Conclusion

• Three steps
• Partition sample by categories of control
  variable
• Cross-tab for each sub-sample to view partial
  relationships
• Interpret and compare the cross-tabs.
• Limits Pain in the posterior for more than three
  variables or when the test variable have many
  categories.