Correlation and Causality
In 1994, executives of the seven largest US tobacco companies gave sworn testimony before a congressional inquiry. Despite decades of research, they testified (under oath) that there is no scientific evidence whatsoever that smoking causes lung cancer in humans. This event was widely regarded as a low point in business ethics—CEOs of major corporations willing to make bald-face lies under oath in order to preserve their businesses.
It may be that the tobacco executives behaved extremely badly. But what was missed was the opportunity for the public to better understand how empirical research works. Let’s go into some detail.
The Third Variable Problem.
There is a strong positive correlation between death by drowning and consumption of ice cream: whenever ice cream consumption increases, more people die by drowning and vice versa. It’s hard to imagine how one might cause the other. So what is responsible for this correlation?
The likely origin of this relationship is warm summer days. When the weather is nice, people tend to go to the beach. Lots of people go swimming, and regretably, some of those people are likely to drown. At the same time, warm summer days are also likely to encourage people to eat ice cream. So it is not that news of a drowning causes mourners to drown their sorrows by eating ice cream, or that eating large amounts of ice cream before swimming causes cramps and so leads to drowning. Instead, both ice cream consumption and swimming are caused by a third variable—warm summer days.
Now consider the case of cigarette smoking and lung cancer. There is, in fact, a strong positive correlation between the two. The question is: Is this relationship causal, or just correlational?
Suppose that there exists a gene: some people have this gene, and others don’t. The gene predisposes people who carry it to get lung cancer. At the same time, this gene also predisposes people to enjoy the experience of smoking. In short, there exists a third variable that is responsible both for smoking and for lung cancer. Notice that, in this scenario, smoking is not the cause of lung cancer, in the same way that consumption of ice cream is not the cause of drowning.
Whenever we have a correlation between two phenomena, we cannot claim that one causes the other. There could always be some third variable (also called a hidden variable) that is responsible for both.
There is, of course, a method for testing whether a relationship is causal—namely, the true experiment. In the experiment, we manipulate one of the variables and observe the result. Let’s apply this to the case of tobacco. What kind of experiment would we need to perform in order to test the hypothesis that smoking causes lung cancer?
Let us assemble a large sample of people for the experiment. We randomly divide our volunteers into two groups. One group we force to engage in smoking (whether they like it or not). The second group we force to never smoke (whether they like it or not). If there is a third variable (like a gene), this should be randomly distributed between the two groups, and so the group forced to smoke should be no more likely to get lung cancer.
Of course, the problem with this experiment is that it would be impractical and immoral. We would never be able to enforce human behavior like this for a prolonged period of time. As you might expect, the proper controlled experiment needed to test the idea that smoking causes lung cancer in humans has never been carried out. The relationship is correlational, and so we cannot discount the possibility of causation through a third variable—unrelated to smoking. It is for this reason, that the tobacco company executive were able (under oath) to claim that “there is no evidence whatsoever that cigarette smoking causes lung cancer in humans.”
Now here’s what they left out. Although the appropriate experiment has never been carried out with humans, these experiments have been carried out with mice, rats, and monkeys. Researchers have randomly divided animals into treatment and control groups, forcing some animals to regularly breath cigarette smoke. Sure enough, there is an association consistent with the hypothesis that smoking causes lung cancer. In addition, histological tests (tests with tissue samples) have shown that when tobacco chemicals are added to colonies of human lung tissue, the cells are more likely to become abnormal, and some cells become cancerous much beyond the normal rate of mutation. All of this was known at the time the tobacco company CEOs made their testimonies.
The third variable problem reminds us of the importance of true experiments in order to test causality.
Slogan: No causation without manipulation.