The difference between correlation and causation
When ice cream sales rise, so do drownings. Does ice cream drown people? Of course not. This classic example carries the single most important rule of data literacy: changing together is not causing.
Short answer
Correlation is the tendency of two things to change together; causation is one of them actually changing the other. Seeing a strong relationship between two variables does not show that one causes the other: the relationship may come from chance, from a shared third cause, or from an effect that runs the other way.
Two concepts, one great confusion
Correlation is an observation: when A rises, B rises (or falls) too. Causation is a claim about mechanism: if I change A, B will change. The difference is vital, because we base our decisions on assumptions about causes. A report headlined "people who do X are healthier" may be reporting correlation alone; it does not follow that taking up X will make you healthier. Perhaps the people who are able to do X are already healthier, wealthier or younger; the data alone cannot separate these possibilities. That is why the same correlation can be the source of headlines that flatly contradict each other.
Four possible explanations for a correlation
If A and B change together there are at least four possibilities. 1) A causes B. 2) B causes A: reading the direction backwards is an easy mistake; when low mood and little socialising are seen together, for instance, it is not obvious which came first. 3) A shared C affects both: the hidden third variable in the ice cream and drowning example is summer; hot weather sells ice cream and sends people swimming. 4) The relationship is chance: compare enough variables and even series with no connection whatsoever will show striking parallels. The last of these is especially misleading when it meets our minds' tendency to see patterns.
An example from the sky: the full moon night myth
Emergency departments and night shifts have a widespread belief: things get chaotic at full moon. The belief rests on sincere observation; but in many comparisons carried out on records, no consistent relationship has been found between emergency admissions, births or eventful nights and the phases of the Moon. So why is the feeling so strong? Because a busy full moon night stays in the memory and gets retold, while quiet full moons and busy nights without a full moon are not recalled. Selective recall can create in the mind a correlation that is not in the data, and this is confirmation bias at work in the field.
Spurious relationships in an age of abundant data
As data multiplies, finding a spurious correlation becomes easier; this is counter-intuitive but mathematically true. Anyone comparing thousands of variables with one another will catch pairs that run in parallel for years even though nothing connects them; collections that display such absurd matches (a country's cheese consumption rising hand in hand with some unrelated statistic) are famous online. The same trap exists in research: ask enough questions of one data set and results that look "significant" will appear by chance alone. Science has developed safeguards against this trap: declaring the hypothesis before looking at the data, retesting findings on independent data, and not treating a single study as conclusive. The practical lesson for the reader is that a report of a surprising relationship cannot be judged without knowing how many variables were scanned and whether the result has been repeated.
How do we test causation?
The gold standard for a causal claim is the controlled experiment: participants are allocated at random to groups, only the factor under study is changed, and the outcomes are compared. Random allocation balances all known and unknown common causes across the groups, and blind and double-blind designs are used to exclude expectancy effects. On questions where experiment is not possible, science reaches cautious conclusions by weighing clues together: large samples, long follow-up periods, a dose-dependent change in the relationship, and a plausible mechanism.
Practical questions for everyday use
When you meet a report that "X leads to Y", you can ask these questions. Is this an experiment or an observational study? Could the direction of the relationship be reversed? Does a third factor affecting both come to mind? How many people were studied, and for how long? Has the result been repeated in other research? None of these questions requires expertise, yet they make the exaggeration in most headlines visible.
Checklist
- Check whether the report rests on an experiment or on observation
- Reverse the direction of the relationship and see whether it still makes sense
- List third factors that could affect both
- Look at the sample size and at replication studies
- Treat confidently worded headlines based on a single study with caution
Frequently asked questions
Does correlation prove nothing at all?
Correlation is not worthless; it is a strong clue about where to look in research. What it does not prove is causation, and causation calls for additional design and evidence.
What does reverse causation mean?
It is where A is thought to cause B but in fact B causes A. When a habit and a health condition are seen together, for example, it must also be asked whether the condition gave rise to the habit.
Is the full moon's effect on sleep a myth too?
Sleep is the most contested heading in this area; some small studies have reported measurable small changes in sleep around the full moon, and others have failed to replicate them. Unlike the strong claims about behaviour and events, the evidence here is uncertain.
Can't we make decisions without establishing causation?
We can; most everyday decisions do not wait for certainty. What matters is matching the boldness of the decision to the strength of the evidence: making a major health or financial decision on a weak correlation is risky.
This guide draws on textbooks in statistics and research methods and on peer-reviewed review findings published on lunar phases and human behaviour.