Correlation vs Causation: What's the Difference?

Start hereIce-cream and sunscreen sales rise and fall together across a year. Neither one drives the other. So when two things move in step, how can you tell whether one is causing the other?

Correlation means two things move together. Causation means one of them makes the other happen. A correlation can come from a real cause. It can also come from a third factor driving both, from the cause running the other way, or from chance. This page sets the two side by side, then shows how researchers get from one to the other.

011. The two side by side

	Correlation	Causation
What it means	Two things change together, in the same or opposite direction	One event is the result of the other
What it tells you	The size and direction of a relationship	Whether changing one thing would change how often the other happens
How it is shown	A single number, r, from +1.0 to −1.0	A controlled study is the most effective way
Everyday example	Ice-cream and sunscreen sales rise and fall across a year	The season drives both: hotter weather brings more of each

The table draws on the Australian Bureau of Statistics and on the medical statistician Austin Bradford Hill. Both are introduced below.

022. What each word means

Correlation

The Australian Bureau of Statistics (ABS) describes correlation as a statistical measure, expressed as a number, of the size and direction of a relationship. Above 0, the two things move in tandem. Below 0, they move in opposite directions.

The word is older than the number. Francis Galton was the first, as far as he knew, to define it clearly and measure it, in a paper the Royal Society received on 5 December 1888. He wrote that two measurements are co-related when a change in one goes, on average, with more or less change in the other, in the same direction. His example: a person with a long arm usually has a long leg.

In his 1908 memoirs, Galton called his measure an “Index of Correlation”, a fraction “now commonly written r”. He added that Karl Pearson later extended it to variables that do not follow the Gaussian law, which a page earlier he calls the Gaussian “Law of Error”.

Causation

The ABS defines causation as one event being the result of the other, also called cause and effect.

Bradford Hill put the practical version in 1965. For him, the decisive question was whether changing A would change how often B happens. That is the question a correlation alone cannot answer.

033. Why moving together is not proof

Besides a real cause, this page looks at four other reasons two things can move together.

A third factor behind both

The ABS example is ice cream and sunscreen: their sales rise and fall together because of the season, not because one drives the other. Galton saw this from the start. He wrote that co-relation must come from the two measurements being “partly due to common causes”.

Statisticians call a hidden driver like this a lurking variable. An open statistics textbook defines lurking variables as additional variables that can cloud a study.

Here is a bigger example. For men born in the US in the 1930s, each extra year of education went with earnings about 7% higher, on average. But people who choose a long education differ in many ways from those who choose a short one. Some people may be talented at studying and at working, and would probably have earned well anyway.

The cause runs the other way

Hill called this the question of “which is the cart and which the horse?” His example: does a particular diet lead to a disease, or do the disease’s early stages lead to the diet?

Economists met the same puzzle. Many studies had pointed to a negative correlation between minimum wages and employment. Yet when unemployment rises, employers can set lower wages, which may lead to demands for a higher minimum wage. The arrow could point either way.

Chance

Tyler Vigen’s Spurious Correlations project compares 25,237 variables against each other to find pairs that randomly match up. He calls this data dredging, and warns that any sufficiently large dataset will yield strong correlations completely at random. Our guide to numbers that mislead has more traps of this kind.

Hill wrote that tests of significance remind us what the play of chance can do, and how large its effects are likely to be. Beyond that, he wrote, they add nothing to the proof of a cause.

A quirk in how the numbers were built

In 1897 Karl Pearson showed that ratios sharing the same denominator can be correlated even when the raw numbers were picked at random. He called this a spurious correlation. Our reading: when two rates share a bottom number, such as population, it is worth looking at the raw counts too.

044. How researchers get at cause

Randomised trials

In a randomised experiment, researchers use a random draw to decide who gets which treatment. The ABS calls a controlled study, with two groups comparable in almost every way, the most effective way of establishing causality.

Some trials cannot be run. As the prize committee notes, researchers cannot run a randomised experiment that decides who gets to attend upper-secondary school. And it would not be appropriate to make one group undergo something harmful. Our guide on how to read a study covers study types in more depth.

Natural experiments

Natural experiments are real-life situations that resemble randomised experiments. They can come from natural random variation, institutional rules or policy changes. In 2021 half of the economics prize in memory of Alfred Nobel went to Joshua Angrist and Guido Imbens for their methodological contributions to the analysis of causal relationships.

The education example shows how one works. In the US, children can leave school at 16 or 17, depending on the state, and those born early in the year can leave sooner. Because chance decides when a person is born, Angrist and Alan Krueger could use this to study schooling and pay.

In the prize committee’s account, an extra year of education raised earnings by 9%. The committee calls this surprising, because it was stronger than the 7% association. If able, ambitious people both study longer and earn more regardless of schooling, the committee notes, the correlation should have been the stronger number. The committee adds that this raised new questions about how to interpret natural experiments, questions that Angrist and Imbens later answered.

Bradford Hill’s nine viewpoints

In a 1965 address, Hill listed aspects of an association to weigh before deciding that cause is the most likely reading. He called them “nine different viewpoints from all of which we should study association before we cry causation”. He wrote with occupational medicine in mind. Our reading: the questions travel well beyond medicine.

1. Strength. How big is the link? In the opening weeks of the 1854 cholera epidemic, John Snow recorded 71 deaths per 10,000 houses supplied with the grossly polluted water of the Southwark and Vauxhall Company. That was 14 times the 5 per 10,000 houses supplied with the rival Lambeth Company’s sewage-free water.
2. Consistency. Has it been seen repeatedly, by different people, in different places and times?
3. Specificity. Is the link limited to particular workers and particular kinds of disease? Hill warned not to over-emphasise it: diseases may have more than one cause.
4. Temporality. Which came first, the cart or the horse?
5. Biological gradient. Does more of the exposure go with more of the effect, a dose-response curve?
6. Plausibility. Does it make sense? Hill warned this cannot be demanded, because it depends on the knowledge of the day.
7. Coherence. It should not seriously conflict with what is known about the disease.
8. Experiment. When action is taken because of the link, such as reducing dust in a workshop, does the outcome change?
9. Analogy. In some circumstances, it is fair to judge by similar cases.

Hill wrote that none of the nine can bring indisputable evidence for or against cause and effect, and none is an essential condition. His question was whether there is “any other answer equally, or more, likely than cause and effect”.

A 2005 commentary says the “Bradford Hill criteria” have long been a background framework, in one close colleague’s words an “aid to thought”. The same commentary treats one as necessary: temporality, meaning the exposure must come before the outcome. The commentary also says Hill did not prescribe his criteria as rules that must be fulfilled. Our reading: Hill made no exception in his list, so on temporality the two differ.

055. Common mix-ups

• “No correlation means no link.” Correlation coefficients usually measure a straight-line relationship, and a curved one may give a value closer to 0.
• “A strong correlation must mean cause.” The ABS says the correlation coefficient should not be used to say anything about cause and effect.
• “So a correlation tells you nothing.” The Internet Encyclopedia of Philosophy notes that correlations are often good evidence of causal connection; the mistake is leaping to the cause hastily. The ABS adds that a correlation may guide further research into whether one thing causes the other. Our logical fallacies cheat sheet covers the related “after this, therefore because of this” mistake.
• “A small link cannot be real.” Hill warned against dismissing a cause-and-effect idea just because the association looks slight.

066. How to tell them apart

Our reading: when you see “X is linked to Y”, these six questions do most of the work. Each comes from the sources above.

1. Which came first?
2. What could be driving both?
3. Could the arrow point the other way?
4. How many pairs were searched to find this one?
5. Did chance decide who got what, in a trial or a natural experiment?
6. Has the link shown up in different places, studied in different ways?

07Quick answers

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How we checked this · Last checked October 2026

• We read the Australian Bureau of Statistics page, the 2021 prize committee's background and press release, an open statistics textbook, Tyler Vigen's site and the Internet Encyclopedia of Philosophy directly.
• We read Bradford Hill's 1965 paper from its scanned PubMed Central copy and its 2015 reprint, and a 2005 commentary on it from the Bulletin of the World Health Organization.
• We read Galton's 1888 paper, his 1908 memoirs and Pearson's 1897 paper in scans of the originals.
• We use the minimum-wage studies only for the reverse-causation point and do not report their results.

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