Linked is not the same as caused
Two things that rise and fall together may share a hidden cause, run the other way round, or be pure chance. Learn the three questions to ask before believing "X causes Y".
PsychologyRead claims about the mindAbout 6 min: 3 reading, 3 practiceUpdated
Educational, not medical or mental-health advice.
- Explain what a correlation is and what it can't show
- Name the three other explanations for a link (a third factor, reverse direction, chance)
- Rewrite a causal headline so it says only what the evidence shows
Builds toward: Read claims about the mind. Judge a headline or a study about psychology before believing it or passing it on.
Read claims about the mind: lesson 1 of 5
- Read claims about the mind
- Linked is not the same as caused 6 min
- How experiments show cause 5 min
- Samples, effect sizes and "significant" 5 min
- What holds up: the replication crisis 7 min
- Popular psychology myths, checked 7 min
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Pairs with OpenStax, Psychology 2e, section 2.2 "Approaches to Research"
What it is
A correlation is a link between two things: when one is higher, the other tends to be higher too (a positive correlation), or lower (a negative correlation). Researchers measure its strength with a number, r, from −1 to +1. Zero means no link.
A correlation tells you two things go together. It does not tell you that one causes the other. Before accepting "X causes Y", rule out three other explanations:
- A third factor (a confounding variable) causes both.
- Reverse direction: Y causes X.
- Chance: with enough comparisons, some links appear by luck.
Quick check
Tap an answer to check it.
Ice-cream sales and drownings rise and fall together. What is the most likely explanation?
- The link is real, but a third factor explains it
Show answer
A third factor: hot weather brings both more ice cream and more swimming. Warm weather raises both, so they move together without one causing the other.
Why it matters
Headlines turn links into causes every day: "Coffee drinkers live longer", "Screen time linked to unhappiness", "People who read are kinder". Each may be true as a link and still mislead as a cause.
A tongue-in-cheek paper with a serious point. In 2012 the doctor Franz Messerli showed that countries that eat more chocolate win more Nobel prizes per person, with a strong correlation. Few people think chocolate makes Nobel laureates. Richer countries can afford both more chocolate and more science: a third factor.
Reverse direction. People who exercise more report better moods. Exercise may lift mood, but people in a good mood may also find it easier to exercise. A correlation alone can't tell which way it runs; often both do.
Links we "see" that aren't there. Many people believe the full moon brings more madness, crime and hospital visits. A review of 37 studies (Rotton and Kelly, 1985) found no reliable link. One likely reason the belief persists: we notice and remember the busy full-moon nights. A link people believe in that the evidence doesn't show is called an illusory correlation, a cousin of confirmation bias.
To show cause, researchers usually need an experiment, the subject of the next lesson.
Worked example
Headline: "Teens who use social media more are more anxious, study finds."
Ask the three questions:
- Third factor? Teens with less sleep, or more stress at home, might both use social media more and feel more anxious.
- Reverse direction? Anxious teens might turn to their phones more.
- Chance? One survey, one link. Was it repeated in other samples?
A fair rewrite: "Teens who use social media more also tend to report more anxiety; this study can't show which causes which." Less exciting, and accurate.
Common mistake
Treating "linked to", "associated with" and "tied to" as if they meant "causes". They are the words researchers use precisely because the study can't show cause. When you see them, read them literally.
Key terms
- correlation
- a link where two things tend to change together
- positive correlation
- both tend to be high together, or low together
- negative correlation
- when one is higher, the other tends to be lower
- r (correlation coefficient)
- a number from −1 to +1 showing how strong a correlation is
- confounding variable
- a third factor that affects both things and creates a link between them
- reverse causation
- the effect actually causing the supposed cause
- illusory correlation
- a link people believe in that the evidence doesn't show
Practise the key terms
Tap a card to turn it over. 7 cards.
| Front | Back |
|---|---|
| correlation | a link where two things tend to change together |
| positive correlation | both tend to be high together, or low together |
| negative correlation | when one is higher, the other tends to be lower |
| r (correlation coefficient) | a number from −1 to +1 showing how strong a correlation is |
| confounding variable | a third factor that affects both things and creates a link between them |
| reverse causation | the effect actually causing the supposed cause |
| illusory correlation | a link people believe in that the evidence doesn't show |
Practice
Sort it
Which group does this belong to?
Children with bigger shoe sizes read better, because older children have bigger feet and read better
Age drives bothShow answer
Third factor. Age drives both
People with bad backs take more painkillers, so painkillers seem to "cause" back pain
The pain leads to the pillsShow answer
Reverse direction. The pain leads to the pills
Out of 200 foods tested, one is linked to better test scores, and no later study finds it again
Test enough things and some links appear by luckShow answer
Chance. Test enough things and some links appear by luck
Towns with more fire engines have more fires, because bigger towns have more of both
Town size drives bothShow answer
Third factor. Town size drives both
Quick quiz
Tap an answer to check it.
Which headline wording claims more than a correlation can show?
- This states a link, which is what the study found
Show answer
"Reading novels makes you more empathetic". "Makes you" claims cause; a correlation only shows the two go together.
What does r = −0.6 mean?
- That would be r close to 0
- r measures a link, not a cause
Show answer
A moderately strong link where one tends to be lower when the other is higher. The sign gives the direction of the link; the size gives its strength.
Why do countries that eat more chocolate win more Nobel prizes?
- There's no evidence for that, and a third factor explains it simply
Show answer
Probably a third factor, such as national wealth, that raises both. Richer countries can afford more chocolate and more research.
Many people believe the full moon brings more madness and crime. What did a review of 37 studies find?
- The review found no reliable link
Show answer
No reliable link. It is an illusory correlation; memorable full-moon cases probably keep the belief alive.
In short
- A correlation shows two things change together; it doesn't show one causes the other.
- Check three other explanations: a third factor, reverse direction, chance.
- Chocolate and Nobel prizes: a strong link, most likely explained by a third factor such as national wealth.
- "Linked to" and "associated with" mean what they say: a link, not a cause.
- Showing cause usually needs an experiment.
Mastery check
Answer without looking back. Score 80% or more and the lesson is marked done. Your result is kept only in this browser.
Check yourself
Answer in your head first, then open the answer. Nothing is saved.
Name the three alternatives to "X causes Y" for a correlation.
Show answer
A third factor causing both, reverse direction (Y causes X), and chance.
What is a confounding variable?
Show answer
A third factor that affects both things and makes them appear linked.
Rewrite "Breakfast eaters are slimmer, so breakfast helps you lose weight" so it says only what the link shows.
Show answer
For example: "People who eat breakfast tend to be slimmer; this doesn't show breakfast causes weight loss, since other habits or health could explain both."
Further reading
- OpenStax, Psychology 2e, section 2.2, free online.
- Messerli, F. H. (2012). Chocolate consumption, cognitive function, and Nobel laureates. New England Journal of Medicine, 367(16), 1562–1564.
- Rotton, J., & Kelly, I. W. (1985). Much ado about the full moon: A meta-analysis of lunar-lunacy research. Psychological Bulletin, 97(2), 286–306.
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