Science and Critical Thinking · Lesson 1
Why two things happening together does not prove one caused the other
Outcome: In about 12 minutes, you will be able to explain the difference between correlation and causation in plain language and recognise one everyday trap where the two are mixed up.
The problem: “I saw them together, so one must have caused the other”
You notice that on days you sleep less, you feel more irritable. Or a news headline says people who drink coffee live longer. Or an advertisement claims “users of this app report better focus.” In each case two things appear together. The natural next thought is that one caused the other.
That leap is extremely common and often wrong. Seeing a relationship does not automatically tell you the direction of the relationship, or whether a third factor is driving both, or whether the link is just chance.
One picture: the rooster and the sunrise
A rooster crows every morning just before the sun appears. The two events are tightly correlated. Yet the crowing does not cause the sunrise. Both are driven by the rotation of the Earth and the time of day.
Many everyday “because” claims are like the rooster: the timing looks convincing, but the real driver is something else, or there is no driver at all beyond coincidence.
Three practical supporting ideas
- Correlation is a pattern of association. When one variable is higher, the other tends to be higher (or lower). You can observe it in data, personal experience, or news stories. It is real information, but limited.
- Causation requires a mechanism and evidence that rules out alternatives. To claim A causes B you need more than the association: a plausible way A could produce B, and preferably evidence from comparisons that hold other factors steady (or from well-designed experiments or natural experiments).
- Common alternative explanations. Reverse causation (B actually causes A), a common cause (C drives both A and B), selection or reporting bias, or pure chance. Any of these can produce a correlation without the causal story you first assumed.
Worked example: three everyday cases
See the same distinction in familiar situations:
- Ice cream and drowning. Sales of ice cream and the number of drowning incidents both rise in summer. They are correlated. The common cause is hot weather, which increases both swimming and ice-cream buying. Ice cream does not cause drowning.
- Shoe size and reading ability in children. Larger shoe size is correlated with better reading scores among young children. The common cause is age: older children have bigger feet and have had more time to learn to read.
- A productivity app and reported focus. Users who keep using the app later report better focus. Possible stories: the app helps; people who were already becoming more organised stay with the app; or people who feel better attribute the change to the app. Correlation alone does not decide which story is true.
In each case the association is real. The causal claim needs extra work.
Do not mix up these ideas
| Idea | What it means here | What it is not |
|---|---|---|
| Correlation | Two things tend to occur or change together | Proof that one produces the other |
| Causation | One factor produces a change in the other | Automatically true just because a correlation exists |
| Common cause | A third factor that drives both observed variables | Something that can be ignored once you see the correlation |
Try it in under three minutes
Pick one claim you have heard recently that links two things (a news headline, an advertisement, a personal observation, or a social-media post).
Write three short lines:
- What two things are said to go together?
- What causal story is being suggested (or implied)?
- Name one alternative explanation that could also produce the same association (common cause, reverse direction, selection, or chance).
Stop after three minutes. The goal is to practise the habit of asking “what else could explain this?”, not to settle the true cause.
Three-line recap
- Correlation means two things tend to move together; causation means one actually produces the change in the other.
- Many everyday “because” claims rest only on correlation and can be explained by a common cause, reverse causation, bias, or chance.
- When you see an association, the useful next question is: “What else could produce this pattern?”
Communication practice
Explain the idea to a non-technical friend in one short sentence:
A good answer mentions the possibility of a common cause, reverse direction, or coincidence and keeps the language plain.
Your review plan
These dates bring the central idea back with a different question. Check a box only after completing that review.
Sources and fact check
- Standard statistical distinction between association and causation, taught in introductory statistics and epidemiology. Classic illustrations (ice cream / drowning, shoe size / reading) appear in many university statistics teaching materials and textbooks (e.g., materials from OpenIntro Statistics and similar open educational resources).
- The logical fallacy “post hoc ergo propter hoc” (after this, therefore because of this) and the related error of inferring causation from correlation alone are documented in critical-thinking references and scientific method primers.
- Practical emphasis on alternative explanations (confounding, reverse causation, selection) follows the reasoning used in observational studies and the need for further design (randomisation, natural experiments, mechanistic evidence) before strong causal claims.
Sources checked 30 July 2026. The examples are classic teaching illustrations, not new empirical claims. The lesson teaches a reasoning habit, not a specific medical, financial or policy conclusion.
Q&A: answer before you reveal
Write whatever you remember. The attempt matters more than perfect wording, and your text stays saved in this browser.
Finished for today?
You only need the practical distinction between correlation and causation today. The review schedule will bring the idea back in new forms.