Making Controlled Comparisons

Welcome

Topic: Making Controlled Comparisons

Goal: Understand how and why we control for rival explanations in political research

Why Controlled Comparisons?

• Suppose Democrats are more supportive of gun control than Republicans.
• But: Democrats are also more likely to be women.
• Women, on average, are more pro-gun control.
• Question: Is it party or gender causing the difference?

Controlling for a Rival Variable

To isolate the effect of X on Y:

1. Hold Z constant.
2. Compare the X–Y relationship within each level of Z.

This gives us the partial relationship.

Zero-Order vs. Partial Relationships

• Zero-order: The overall relationship between X and Y, ignoring Z.
• Partial relationship: X–Y relationship after controlling for Z.

Example:
- 58% of Democrats support gun control, vs 42% of Republicans
- But is this due to party, or gender differences?

Three Possible Outcomes

After controlling for Z:

1. Spurious Relationship
2. Additive Relationship
3. Interaction Relationship

Spurious Relationship

• The X–Y relationship disappears after controlling for Z.
• Example: Gender explains both party and gun attitudes.
• Party seems related to gun views, but it’s actually gender.

🧠 The original relationship was an illusion.

Additive Relationship (Example)

• X and Z independently affect Y.

Gun Control Support:

• Women: Dems 70%, Reps 50%
  
• Non-women: Dems 50%, Reps 30%

✅ Party and gender effects remain at each level — they add up.

Interaction Relationship (Example)

• The effect of X depends on Z.

Gun Control Support:

• Women: Dems 60%, Reps 60% → no party effect
• Non-women: Dems 70%, Reps 30% → strong party effect

🎯 Party only matters for men. That’s interaction.

Why This Matters

Controlled comparisons help us: - Rule out spurious relationships - Identify independent effects (additive) - Detect conditional effects (interaction)

🛠 A core tool for observational political research.

Another Example: Attitudes Toward LGBTQI+

Feeling thermometer (0–100) - Democrats score higher than Republicans

Control for age:

• Younger people are more supportive
• But the party gap still exists within age groups

✅ Additive relationship

What if the Gap Only Exists for Young People?

• Among older respondents: Dems and Reps = same scores
• Among younger respondents: Dems score much higher

🎯 That’s interaction. The party effect depends on age.

Summary

• Spurious: Relationship disappears after controlling
• Additive: Both X and Z affect Y independently
• Interaction: The effect of X depends on Z

🧪 Controlled comparisons bring us closer to causal inference.

Wrap-Up

• Always ask: “How else are these groups different?”