Joachim Andersen

Accelerated Learning

Correlation vs. Causation: Why Moving Together Is Not Proof

Two small antique brass and wood metronomes side by side on a dark walnut desk at night with their pendulum arms tilted at the same angle, lit by a single candle in a brass holder behind them
Two things can keep perfect time, without one setting the beat for the other.


Correlation vs. Causation is the reminder that two things moving together does not mean that one causes the other. A correlation tells us that two things tend to rise and fall together. A cause tells us that changing one will change the other. The first is much easier to find than the second, and our minds constantly confuses them.

I notice it whenever I read a headline that says people who do one thing are fitter, more capable or happier than those who don’t. The tempting conclusion is that doing the thing will make me fitter, more capable or happier too. But the people who do it may differ in many other ways, the arrow may point the other way, or the link may be pure coincidence.

The essence of Correlation vs. Causation is to ask: “What else could explain why these two things move together, and what would happen if I changed one of them?”


Origin: Spurious Correlation

The mathematics of correlation was developed in the late 19th century by Francis Galton and Karl Pearson. Almost immediately, Pearson saw the danger. In 1897, he described what he called a “spurious correlation”, a relationship that appears in the numbers because of the way they are calculated, rather than because of any real connection between the things measured.

The idea itself is much older. Philosophers have long named the error cum hoc ergo propter hoc, Latin for “with this, therefore because of this”. It’s a close relative of post hoc ergo propter hoc, “after this, therefore because of this”, where we assume that because one thing happened after another, it was caused by it.


Key Concepts

  • Confounding Variables
    A hidden third factor can cause both things, so that they move together without affecting each other at all.

  • Reverse Causation
    The arrow may point the other way, so that what we think is the effect is actually the cause.

  • Coincidence
    When we look at enough pairs of numbers, some will move together by chance alone.

  • Simpson’s Paradox
    A pattern that appears in combined data can disappear or even reverse when the data is split into groups.

  • Experiments
    The most reliable way to show cause is to change one thing deliberately, ideally at random, and see what happens, as I describe in Evaluating the Quality of a Scientific Study.


Some Examples

  • Chocolate and Nobel Prizes
    In 2012, the cardiologist Franz Messerli published a short, tongue-in-cheek note in the New England Journal of Medicine showing that countries that eat more chocolate per person have won more Nobel Prizes per person, a strikingly strong correlation across 23 countries. Nobody seriously believes that chocolate wins Nobel Prizes. Wealthier countries can afford both more chocolate and more research, which is a far more plausible explanation.

  • The Night Light and the Glasses
    In 1999, a study in Nature reported that young children who slept with a light on were much more likely to become nearsighted, and the finding received wide press coverage. The next year, a study at Ohio State University found no such effect from night lighting, but a strong link between nearsighted parents and nearsighted children. Nearsighted parents were also more likely to leave a light on in their children’s room, so the parents explained both.

  • The Admissions That Seemed Biased
    In 1973, the University of California, Berkeley admitted about 44% of the men who applied to its graduate programs, but only about 35% of the women. In 1975, Peter Bickel, Eugene Hammel and J. W. O’Connell examined the numbers department by department and found no pattern of bias against women. Women had applied more often to departments that admitted fewer applicants of either sex, and the overall difference came from where people applied, not from how they were treated.

  • The Weeks I Exercised
    Looking back at my calendar, I found that my most productive weeks were also the weeks I exercised most. It would be nice to conclude that exercise made me productive, and it may well help. But calm weeks with fewer emergencies also left more time to exercise, so the calm may explain both. The only way to find out is to keep exercising during a hectic week and see whether it still helps.


Applying Correlation vs. Causation

Correlations are not useless. They are often the first clue to a real cause. In 1950, Richard Doll and Austin Bradford Hill found that lung cancer patients were far more likely to be heavy smokers, and in 1965, Hill set out a list of questions for judging whether an association is likely to be causal. This is the simple process I follow, inspired by them:

  1. Look for a Third Factor
    I ask what could cause both things at once, such as wealth, age, health, season or the type of people involved.

  2. Check the Direction
    I ask whether the effect could actually be causing the supposed cause, and which one came first.

  3. Look at the Strength and Consistency
    A strong link that appears again and again in different places and groups is more likely to be real than a weak one found once.

  4. Look for a Dose Response
    If more of the cause leads to more of the effect, as more cigarettes led to more lung cancer, a causal link becomes more plausible.

  5. Prefer Experiments
    When I can, I test the cause directly by changing one thing and watching what happens, even in small personal experiments.


Pitfalls and Limitations

  • Correlation is still a form of evidence. Dismissing every finding with “correlation is not causation” is as lazy as accepting every correlation as proof.

  • Experiments are not always possible. Many important questions, such as the effects of smoking, cannot be tested by randomly assigning people, so careful reasoning about observational data is often the best I have.

  • No correlation does not mean no cause. Two opposing effects can cancel each other out, hiding a real cause in the data.

  • Testing many links produces false alarms. When I look for patterns among many variables, some will appear by chance alone, which is why a single surprising correlation deserves to be replicated before I act on it.

  • Splitting data can also mislead. Simpson’s paradox shows that the right level of analysis depends on understanding how the data was produced, not on simply slicing it until a pattern appears.


Related Mental Models

Correlation vs. Causation reminds me that two things moving together is the beginning of a question, not the end of one. By looking for hidden third factors, checking the direction of the arrow and testing causes directly when I can, I can learn from patterns in the world without being fooled by them.



To learn more about mental models and philosophy,
check out: Wise: How to Attain a Deep Understanding of the World, History, Our Place in It, and How to Live Well



📚 Sources and References