Two things are correlated when they tend to move together: as one rises, the other tends to rise (a positive correlation) or fall (a negative correlation). Correlation is easy to find and often useful, but it does not by itself show that one thing causes the other. There are three common alternative explanations.
1. Confounders
A confounder is a third factor that affects both things being compared. Ice cream sales and drownings rise and fall together. Ice cream does not cause drowning; hot weather increases both, as more people buy ice cream and more people swim. Many health claims face this problem. People who take vitamins may be healthier, but they may also exercise more, smoke less and earn more.
2. Reverse causation
Sometimes the cause runs the other way. Neighborhoods with more police patrols may have more crime, not because patrols cause crime but because higher crime leads a city to send more patrols. That is reverse causation. Similarly, people who have recently given up driving may be in poorer health, because poor health led them to stop.
3. Coincidence
Search through enough pairs of numbers and some will line up by pure chance. Collections of such “spurious correlations” are entertaining: yearly figures for a snack food tracking a particular kind of accident, for example. With small samples or many comparisons, chance patterns are guaranteed.
Randomized controlled trials
The strongest way to test a cause is a randomized controlled trial (RCT). Participants are assigned at random to receive a treatment or not (the control group). Because chance alone decides who goes where, random assignment balances other factors, known and unknown, between the groups. If the groups then differ in outcome by more than chance would explain, the treatment is the likely cause. Where possible, trials are also blinded, so that participants and researchers do not know who received what.
A 1948 British trial of the antibiotic streptomycin for tuberculosis is often cited as the first modern randomized trial.
Trials can overturn confident beliefs. For years, observational studies found that women taking hormone therapy after menopause had less heart disease. But those women also tended to be healthier and better off. In 2002 a large randomized trial, the Women's Health Initiative, found no heart protection, despite what the earlier observational studies had suggested, and a small increase in some risks for the combined therapy it tested.
Natural experiments
Many questions cannot be tested by trials; we cannot randomly assign people to smoke or to live in poverty. Researchers then look for natural experiments, situations where something like random assignment happened by accident.
The most famous comes from London in 1854. Two water companies served many of the same streets, with pipes running side by side. One, Lambeth, had moved its intake upstream, above the city's sewage; the other, Southwark and Vauxhall, still drew water from a polluted stretch of the Thames. The physician John Snow realized that similar households received different water through no choice of their own, so comparing them could reveal whether water spread cholera. It did, dramatically.
Building a case without a trial
The link between smoking and lung cancer was established in the 1950s and 1960s without trials. Researchers such as Richard Doll and Austin Bradford Hill relied on many consistent observational studies showing a strong link that grew with the amount smoked, the right order in time, and a plausible biological mechanism. In 1965 Bradford Hill set out such considerations for judging causation, and they are still widely used.
Worked example: John Snow's numbers
In 1855 John Snow published figures comparing households supplied by the two water companies during the early weeks of the 1854 London cholera epidemic.
- Southwark and Vauxhall supplied about 40,046 houses, which suffered 1,263 cholera deaths.
- Lambeth supplied about 26,107 houses, which suffered 98 cholera deaths.
Why counts alone are not enough. Southwark and Vauxhall served more houses, so it would have more deaths even if its water were no worse. We need rates.
Calculate the rates. For Southwark and Vauxhall: 1,263 divided by 40,046 is about 0.0315, or about 315 deaths per 10,000 houses. For Lambeth: 98 divided by 26,107 is about 0.0038, or about 37 deaths per 10,000 houses.
Compare. 315 divided by 37 is about 8.5. Houses supplied by Southwark and Vauxhall suffered roughly eight to nine times the death rate of houses supplied by Lambeth.
Why the comparison is convincing. The two companies' pipes ran down the same streets. Rich and poor, large and small houses were served by both, and most residents did not even know which company supplied them. Water source was the main thing that differed systematically between the groups, so confounders were unlikely to explain such a large gap.
Snow's conclusion that cholera spread through contaminated water was not widely accepted at once; many experts still blamed bad air. It took years, and further evidence, for the waterborne theory to win. But his use of rates, a fair comparison and a natural experiment remains a model of reasoning about cause.