Distinguishing Correlation from Causation

Lesson 1 of 1: When Does Together Mean Caused?

In this lesson:

• Tell a correlation claim from a causation claim
• Find what really explains a correlation

Learning Objectives for This Lesson

By the end of this lesson, you should be able to:

1. Define correlation and causation as distinct claims
2. Explain why correlation doesn't imply causation
3. Name the four explanations for a correlation
4. Recognize that an experiment supports causation

Headlines Turn Correlation Into Cause

Everyday claims quietly turn correlation into causation:

• "Coffee drinkers live longer" → coffee causes long life?
• "More police, more crime" → police cause crime?

Most such leaps are unjustified. Let's build the habit to spot them.

Shoe Size and Reading: Correlation, Not Cause

In children, shoe size and reading ability correlate strongly.

• Do bigger feet cause better reading? Obviously not
• The correlation is real — but there's no causal link

"Move together" and "one causes the other" are different claims.

Correlation Moves Together; Causation Produces

Two precise, different claims:

• Correlation: two variables tend to move together (measured by r)
• Causation: changing one produces a change in the other

Exercise causes fitness (real mechanism); shoe size doesn't cause reading.

Two Different Claims, Each a Sentence

Force any statement into one of two molds:

• Correlation: "X and Y tend to occur together"
• Causation: "X makes Y happen"

One is an observed pattern; the other an asserted mechanism.

Classify: Correlation or Causation Claim?

Label each statement:

1. "Students who sleep more tend to get higher grades"
2. "This vitamin lowers your risk of sickness"
3. "Taller people generally weigh more"

Classify each, then advance.

Answer: 1. Correlation. 2. Causation. 3. Correlation.

If Not Cause, What Else Explains It?

A correlation is real — so something explains it.

• Direct causation is only one possibility
• There's a short menu of explanations

Knowing the menu replaces the reflex "correlate, so cause."

The Four Explanations for Any Correlation

Direct, reverse, lurking common cause, or coincidence — which fits?

Direct and Reverse Causation Explained

The arrow's direction isn't given by the correlation:

• Direct: A causes B (exercise → fitness)
• Reverse: B causes A — does stress cause poor sleep, or the reverse?

Correlation is symmetric — it carries no direction.

The Lurking Variable: A Hidden Common Cause

Summer drives both — the ice-cream–drowning link is real but not causal.

Coincidence: A Spurious, Meaningless Correlation

Sometimes two variables move together by pure chance.

• No mechanism, no lurking variable — just accident
• With enough data, random matches appear

Not every correlation means anything — some are coincidence.

A Lurking Variable Doesn't Make It Fake

Finding the lurking variable doesn't erase the correlation:

• Ice cream really does predict drowning risk (both track summer)
• Only the direct-cause reading is false

The relationship is real; the cause story is what's wrong.

Explain Each Correlation; Name the Lurking Variable

Pick the explanation; name any lurking variable:

1. More firefighters at a fire more damage
2. More sunscreen use more sunburns
3. Chocolate consumption Nobel prizes (by country)

Explain each, then advance.

Answer: 1. Lurking: fire size. 2. Lurking: sun exposure. 3. Lurking: national wealth.

So What Evidence Proves Cause?

A lurking variable can always hide behind a correlation.

• Observed correlation can't rule out hidden factors
• We need evidence that controls for them

That evidence is the randomized experiment.

Observation Alone Can't Prove Cause

An observational study just watches what already happens.

• The groups differ in countless other ways
• Any lurking variable could explain the difference

Observation reveals correlation, not a single cause.

A Randomized Experiment Balances Lurking Variables

• Random assignment balances the groups on everything else
• A difference in outcome can be attributed to the treatment

Correlation Is Still a Useful Tool

Don't dismiss correlation just because it isn't cause:

• It predicts one variable from another
• It flags relationships worth an experiment

A useful tool with a limit — not a trap to discard.

Evaluate a Headline: Experiment or Observation?

"Coffee drinkers live longer." Walk the questions:

• Observational — no one was randomly assigned to drink coffee
• A lurking variable (wealth, exercise?) could explain it

The causal claim isn't justified — only an association.

Does This Headline Justify Its Causal Claim?

"Students who eat breakfast score higher on tests."

• Experiment or observation? What lurking variable?
• Is the causal claim justified?

Decide, then advance.

Answer: Observational; lurking variable like home stability or income; cause not justified.

Full Task: Explain, Find the Lurking Variable, Judge

A correlation: neighborhoods with more bookstores have higher incomes.

1. Best explanation? Name any lurking variable
2. Does the correlation justify a causal claim?
3. What study would establish cause?

Do all three, then advance.

Answer: Lurking (wealth draws bookstores); no, it's observational; only an experiment could.

Key Takeaways and What's Next

✓ Correlation and causation are different claims

✓ Ask "what else explains this?" — reverse, lurking, coincidence

✓ Only a randomized experiment establishes cause

A lurking variable makes the correlation real, the cause false

Correlation is still useful — it predicts and flags

Next: study design (HSS.IC).