The How Else Question: Making Controlled Comparisons

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The How Else Question Making Controlled
Comparisons

• Sharon Paynter
• Spring 2007

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Agenda

• 3 Scenarios for relationship between IV and DV,
  controlling for a rival cause
• Controlled comparisons using cross-tabs and mean
  comparison
• How to use 3 scenarios to interpret the results
  of controlled comparisons

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Terminology

• IV X
• DV Y
• Causal Connection
• X - Y
• X causes Y
• IV (alternative cause/control variable) Z

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Third Variable Problem

• For every explanation we describe, a plausible
  alternative explanation exists for the same
  phenomenon
• How else, besides the IV, are the subjects not
  the same?
• Is the DV being caused by the IV or some other
  IV?

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Gun Control Example

• Hypothesis
• In comparing individuals, Democrats will be more
  likely to favor a gun ban than Republicans

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Alternative Explanations

• How else, besides partisanship, are the subjects
  not the same?
• Sex
• Region of Country
• Race
• Income
• Zodiac Sign
• Voting Behavior
• Children

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Gun Control Example

• Hypothetical relationship between partisanship
  and gun control opinion, controlling for gender
• After controlling for sex, what can happen to the
  relationship between partisanship and gun control
  opinions?

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Scenarios One

• Spurious Relationship
• Falsedoes not survive when a rival cause is
  taken into consideration
• After controlling for gender, party
  identification no longer show causal link with
  gun control attitudes

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Scenario Two

• Additive Relationship
• IV and rival both help to explain the DV
• Each variable is an independent cause of DV
• Combination enhances our causal understanding of
  DV
• Regardless of party, women are more likely to
  favor a ban than are men
• Regardless of sex, Democrats are more likely to
  favor a ban than Republicans

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Scenario Three

• Interactive Relationship
• Relationship between the IV and DV depends on the
  value of the control variable
• Does partisanship cause gun control opinions?
• For women, no, but for men, yes
• Women partisanship has no effect on gun control
  attitudes
• Democratic and Republican women equally likely to
  favor a ban on handguns
• Men Democratic men are much more likely to
  favor a ban than are Republican men

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3 Scenarios

• Logical Possibilities
• Tell us what can happen to relationship between
  IV and DV, controlling for other variable
• Give us interpretive tools to describe what does
  happen during analysis
• Note Empirical data analysis rarely yields
  results that perfectly fit these three
  possibilities. However, most relationships
  closely approximate one of the three possible
  scenarios.

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Three ScenariosX-Y, Controlling for Z

• Hypothesis
• Testable statement about the relationship between
  and IV and DV
• Explanation
• How the IV is causally linked to the DV
• Proposed causal explanation between party
  identification and opinion on gun control.

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Alternative Cause / Rival Explanation

• Sex (Z) is main cause of opinions about gun
  control (Y)
• Z - Y
• Z causes Y
• Two IVs are related
• Z - X
• Women are more likely to be Democrats than men
• If women are more likely to favor a ban than men
• Then some part of relationship between X and Y
  is really the relationship between Z and Y

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X-Y, Controlling for Z

• Control for Z
• Isolate the effect of X on Y, controlling for Z
• Examine X - Y relationship within values of Z
• Comparing gun opinions of Democrats and
  Republicans only among women/men

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Spurious Relationships

• Mistakenly attributing differences in
  relationship between X and Y.
• Controlling for Z dissolves relationship between
  X Y
• Example
• Attributing differences in gun control to
  partisanship when gender is cause

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Importance of Spuriousness

• Smoking and Lung Cancer
• Critics argued spurious relationship
• Uncontrolled variables
• Now relationship is more firmly established
• Significantly strengthened by suggestion of it
  being spurious relationships

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Spurious Relationships

• Arrow Diagram
• Schematic representation that depicts causal
  relationship between variables.
• Z
• X Y

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Additive Relationships

• Z and X have no causal connection
• Changes in values of Z do not produce changes in
  values of X
• Both X and Z make independent contributions to
  the explanation of Y
• Knowing about both relationships adds to or
  strengthens the explanation of the DV

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Additive Relationships

• Arrow
• Z
• X Y

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Interaction Relationships

• Also called Specification Relationships
• Combination of Spurious Additive Relationships
• Relationship between X Y depends on the value
  of Z
• For one value of Z, the effect of X on Y is zero
• For another value of X, the effect of X on Y is
  large

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Interaction Relationships

• Z
• X Y

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Interaction Relationships

• Controlling Variable
• Women No difference in support of gun control
  between Democrats and Republicans
• Men Democratic men much more supportive of gun
  ban than Republican men
• For women partisanship has no effect on gun
  control attitudes, but for men partisanship has a
  big effect

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Making Controlled Comparisons

• Cross-tabs
• Zero-order relationship
• Overall relationship between 2 variables. Does
  not take into account other possible differences
  between subjects.
• Invites How Else? Questions

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Representing RelationshipsSpurious Relationships

• Line Graph
• Horizontal IV (Partisanship)
• Vertical DV (Opinion on Gun Control)
• Lines in Graph Controlling Variable (Sex)
• See Pg 81
• No difference in IV
• Difference in CV

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Representing RelationshipAdditive Relationship

• Line Graph (see pg 83)
• Difference in IV
• Difference in CV

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Representing RelationshipsAdditive Relationships

• Line Graph (pg 84)
• Small gender gap between Democrats
• Large gender gap between Republicans
• Wedge Issue (Figure 4.7 1996 NES)
• Issue capable of attracting the votes of a large
  loc of supporters from the opposing party
• Democrat advocating strict gun laws
• May loose support from Democratic Males (14)
• May attract large numbers of Republican Females
  (35)

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Representing RelationshipsInteractive
Relationships

• Different Possibilities
• For one value of Z, the X-Y relationship is 0
• X-Y has same tendency, but tendency is stronger
  for some values of Z
• Relationship between X Y have different
  tendency for each value of Z
• Crossover Interaction
• Disordinal interaction

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Mean Comparison Analysis

• Same rules apply
• Same graphic representations apply

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Rule of Direction for Nominal Variables

• Normally dont talk about direction
• Rule
• Take left-most value of IV as base category
• Subtract comparison category from base
• Positive if higher than the comparison category
• Negative if lower than the comparison category
• Repeat for each value of Control Variable

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Go to SPSS

• GSS2002

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Example Hypothesis

• In comparing individuals, whites will be more
  likely to vote than will blacks.
• 1996 National Election Study

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Example Hypothesis Control

• What other explanations are there for differences
  in vote turnout?
• What is the relationship between race (X) and
  turnout (Y), controlling for education (Z)?

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Controlled Comparison Table

• Also called Control Table
• Cross Tab between IV (X) and DV (Y) for each
  value of a control variable (Z)
• Partial Relationship
• Difference obtained from Controlled Comparison
• Separating subject on Z
• Comparing Y for different values of X
• Can also isolate effect of Control Variable on
  DV, controlling for IV

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Controlled Comparison Table

• After controlling for Education do racial
  differences still exist?
• Yes Controlling for education whites are still
  more likely to vote than blacks
• about 7 for each value of control variable
• What is relationship between education and
  turnout among whites?
• What is relationship between education and
  turnout among blacks?
• Partial effect of education on turnout (effect of
  Z on Y controlling for X) 19

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How do we explain this Relationship?

• Spurious
• Falsedoes not survive when a rival is considered
• Additive
• IV and rival both help to explain the DV
• Each variable is an independent cause of DV
• Combination enhances our causal understanding of
  DV
• Interactive
• Relationship between the IV and DV depends on the
  value of the control variable

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Spurious

• Controlling for Education would remove
  explanatory power of race
• Little difference in the turnouts of
  less/more-educated whites and blacks
• However
• Racial differences persist, controlling for
  education

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Interaction

• Strength or tendency of the race turnout
  relationship would be different for different
  levels of control variable
• Less-educated
• More-educated
• However
• The effect of race on turnout is about the same
  for both values of the control

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Additive

• Both variable would explain differences in voter
  turnout
• Race (X) explains 7 difference in DV
• Education (Z) explains 19 difference in DV
• Combined effect depends on comparison
• LT HS Black vs MT HS White 26
• LT HS White vs MT HS Black 12