Reasoning and Decisions

Correlation and Causation Explained

Why two things rising and falling together do not prove one causes the other, with everyday examples of confounders, reverse causation and coincidence.

On this page
  1. The basic distinction
  2. A classic example
  3. Four reasons a pattern may not be causal
  4. A hypothetical illustration
  5. What helps show causation
  6. Careful reading of headlines
  7. Sorting it out in daily life
  8. The takeaway

The basic distinction

Two things are correlated when they tend to change together: when one is higher, the other is usually higher too (or lower, for a negative correlation). Causation means that a change in one thing actually produces a change in the other.

The two are easily confused because causes often do produce correlations. If a cause is real, we would expect to see the pattern. The trouble is that the reverse does not hold. Seeing a pattern is not enough to show that one thing is making the other happen.

A classic example

On warm days, ice cream sales tend to rise, and so do visits to swimming pools and, unfortunately, sunburn. Ice cream sales and sunburn are correlated, but eating ice cream does not burn skin. Both are driven by a third factor, hot sunny weather. That hidden driver is called a confounder (or lurking variable).

This example is silly on purpose. The real danger comes when the confounder is less obvious and the story is attractive.

Four reasons a pattern may not be causal

1. A third factor drives both. As above. People who carry lighters are more likely to have lung problems, but the lighter is not the cause; smoking is the common factor.

2. The arrow runs the other way (reverse causation). Suppose people who exercise more report better moods. Perhaps exercise lifts mood, but perhaps people who already feel good are more likely to exercise. Both directions can be true at once. The correlation alone cannot tell you which.

3. Coincidence. If you compare enough unrelated things over a short period, some will line up by chance. Two lines on a chart that rise together for a few years may mean nothing. With many possible comparisons, striking-looking matches are almost guaranteed to turn up somewhere.

4. Selection effects. The group you are looking at may not be typical. If a program only records people who finished it, its results can look better than they would for everyone who started. Whatever made them finish may be the real reason for their success.

A hypothetical illustration

Imagine a (made-up) survey in which students who use a study app score higher on tests than students who do not. It is tempting to say the app works. But consider other explanations:

  • Motivated students may be more likely to try an app, and they might have scored higher anyway.
  • Students with more free time or support may be more able to use it.
  • Students who are already doing well may be the ones who keep using it.

The survey fits the claim “the app helps,” but it fits those alternatives equally well. To say more, you would need a better design, such as comparing similar students who were or were not given access, ideally by random assignment.

What helps show causation

No single test is perfect, but some kinds of evidence are stronger than others.

  • Experiments with random assignment. If people are randomly placed into two groups and only one gets the change, other differences between the groups tend to even out. This is why randomized trials carry weight.
  • Timing. A cause should come before its effect. This rules out some reverse-causation stories, though not all.
  • A plausible mechanism. It helps if there is a believable way for one thing to produce the other, though a plausible story alone is cheap, and plausible stories can be wrong.
  • Consistency. The pattern appears across different groups, places and methods, not only in one study.
  • Dose and response. More of the supposed cause leads to more of the effect, in a regular way. This is supportive but not conclusive.
  • Ruling out alternatives. Researchers try to account for confounders, and the more carefully they do, the more confidence the result deserves.

Even then, conclusions are usually described in terms of how strong the evidence is, not as absolute proof.

Careful reading of headlines

News reports and social posts often turn “linked to” into “causes.” Words like “associated with,” “linked to,” “tied to” and “may increase the risk of” describe correlations, even when the surrounding text suggests more. When you see such a claim, you can ask:

  1. What was actually measured, and in whom?
  2. Was it an experiment, or only an observation of what people already did?
  3. Could something else explain both things?
  4. Could the effect run the other way?
  5. How big is the difference, and is it large enough to matter?

Asking these questions is part of source evaluation. A claim can come from a perfectly honest study and still be reported in a way that overstates what the study found.

Sorting it out in daily life

The same confusion appears outside research. If you notice that you sleep badly on days you drink coffee late, it is easy to blame the coffee. That may be right, but you might also drink more coffee on days when you are already tired and stressed, which are the days you sleep badly. A simple personal experiment, such as skipping late coffee for a couple of weeks while otherwise keeping routines steady, will tell you more than the pattern you first noticed, though even that is imperfect. Our tendency to see patterns that confirm what we already suspect, as described in discussions of confirmation bias, makes casual observations especially unreliable.

Likewise, this is one of the standard logical fallacies to watch for: concluding that because B followed A, A caused B.

The takeaway

Correlation is a clue, often a valuable one, that tells you where to look. It is not a conclusion. When you meet a claim that one thing causes another, ask what else could produce the same pattern, and treat the answer as more important than the pattern itself.

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