Confounding, and Matching Design to Conclusion

Lesson 2 of 2: Why Observation Can't Prove Cause

In this lesson:

• See why an observational study can't establish causation
• Build a routine that reads any study's licensed conclusion

The Students Who Chose Tutoring Scored Higher

In an observational study, students who chose tutoring scored higher.

• The gap is real and clean
• The obvious conclusion: tutoring raised the scores

Your instinct says "tutoring works." Hold that thought — it's about to be tested.

Does This Gap Prove Tutoring Works?

The tutoring-choosers scored higher. Does that prove tutoring caused it?

• A. Yes, the gap proves it
• B. No, something else could explain it

Commit to A or B. Remember: nobody was assigned here.

A Confounder: Linked to Both Variables

• Motivation points to both tutoring and score
• A variable linked to both is a confounder

Motivation Could Be Driving Both

The score gap could be caused by:

• the tutoring, or
• motivation (motivated kids chose tutoring and score higher), or
• both, mixed together

The study can't separate these. The gap is real; its cause is ambiguous.

Why the Observed Gap Is Ambiguous

Whenever a confounder exists, the association has a rival explanation.

• Ice cream sales and drownings rise together
• Hot weather drives both — ice cream doesn't cause drowning

Name the lurking variable, and the slogan becomes an argument.

Random Assignment Breaks the Confounder

• Chance spreads motivated and unmotivated evenly
• Both groups start with the same mix — motivation is balanced

It Balances Even Unmeasured Variables

Random assignment balances every variable — even ones we never measured.

• Sleep, home support, prior grades — all spread evenly
• Observation can only adjust for what you measured

Assignment handles the variables you didn't even think of. That's its power.

Name a Confounder for This Claim

Claim: people who eat breakfast regularly get better grades.

• Name a plausible confounder
• Explain how it links to both breakfast and grades

Think: what produces both habits? Write your confounder and its two links.

Assignment Defeats Confounders — Now the Routine

You've seen the mechanism. Now the practical tool.

• Two randomizations → two independent powers
• Check each separately, then combine

Was there selection? Was there assignment? Ask both, then combine.

The Two-Question Routine for Any Study

Ask the two questions separately, then combine. Never collapse them into one.

Scenario: Random Sample, No Assignment

A firm randomly selects 1,000 adults and asks their policy support.

• Random selection? Yes → generalizes to all adults
• Random assignment? No → association only

Conclusion: a population estimate, but no cause

Scenario: An Experiment on Volunteers

200 volunteers are randomly assigned to a drug or placebo.

• Random selection? No → limited generalization
• Random assignment? Yes → causal within these subjects

Conclusion: cause for these volunteers, not the whole population

Scenario: Both, and the Big-Survey Trap

A study randomly selects and randomly assigns → causal and generalizable.

• The trap: "a survey of 50,000 proves cause"
• No — a survey never assigns, so never causal

Size affects precision, never the kind of conclusion.

Routing to the Next Two Lessons

Your classification picks your tool:

• Random selection → survey branch → margin of error (next)
• Random assignment → experiment branch → significance test (after)

Classifying the study is the first step of every later analysis.

Name the Confounder, Then Conclude

Claim: cities with more police have more crime.

1. Name a plausible confounder
2. Classify the study; answer selection? assignment?
3. State the licensed conclusion

Do all three steps before advancing.

Four Errors About Randomization and Cause

Observational association → not proof of cause (name a confounder)
Experiment → does not auto-generalize (needs selection)
Big survey → never causal (no manipulation, any size)
Control group → the baseline, not pointless

Four overclaims, four fixes — all from the two-job distinction.

Key Takeaways From Lesson Two

✓ A confounder makes observational association ambiguous
✓ Random assignment balances even unmeasured variables → cause
✓ Two questions: selection (generalize?) and assignment (cause?)

Never read observational association as proof of cause
Generalization needs selection; cause needs assignment

Coming Up Next: From Classifying to Measuring

You can now classify any study. Next, you'll measure.

The survey branch becomes a margin of error; the experiment branch becomes a significance test.