Thinking and Deciding

CORRELATION, CAUSE, AND CONTINGENCY 185
and then calculate the correlation by using the resulting numbers. (This yields a
“φ (phi) coefficient.”) Another reasonable way to measure the association between
two dichotomous variables is to subtract conditional probabilities. For example, we
can subtract the conditional probability of blue eyes given blond hair from the conditional
probability of blue eyes given nonblond hair. If the first conditional probability
is higher than the other, knowing that a person has blond hair makes it more probable
than otherwise that the person has blue eyes. If the two conditional probabilities are
equal, then whether a person has blond hair tells us nothing about whether the person
has blue eyes, and it makes sense to say that the two variables are unrelated. (We
shall discuss more examples of this measure later in this chapter.)
Correlations are sometimes confused, in scientific analysis and everyday reasoning,
with causal relationships. It is important to realize that they are not the same.
Establishing a correlation does not establish causation, though it often provides evidence
about causation, because causation is one reason that correlations can exist.
(To establish causation, other reasons must be ruled out.) For example, the use of
marijuana and the use of heroin may be correlated, but it is not necessarily true that
one causes the other. There may be some third factor, such as exposure to drug dealers
or rebellious attitudes, that is a more likely cause of both. If this third factor
explained the correlation, then stopping the use of marijuana would not necessarily
reduce the use of heroin. When we ask whether use of marijuana causes use
of heroin, we are asking what would happen to heroin use if marijuana use were
changed. A correlation between marijuana use and heroin use provides evidence for
some causal relationship, but it does not establish one with certainty. Often, a more
conclusive way to find out about causal relationships is to do an experiment. For
example, correlations between diets with high amounts of saturated fat and heart disease
provide evidence that the former causes the latter. Experiments in which some
people have been induced to eat less fat would show that the relationship is indeed a
causal one, if heart attacks become less frequent in these people (and not in others).
When we speak of correlations in a situation in which causal relationships are
assumed, we can use the term contingency. A contingent relationship exists if one
variable causally affects another. If smoking causes lung cancer, then lung cancer
is, to some extent, contingent upon smoking. Our perception of contingency is an
important determinant of our success at achieving our goals. Does Japan respond
favorably when the United States threatens it with trade restrictions? If I drink three
cups of coffee after dinner, will I be able to get to sleep tonight? If I try listening to
people more, will they like me better? Of course, getting the answers to these kinds
of questions does not always involve trial and error. There are ways of understanding
such things that allow us to make reasonable guesses without any experimenting at
all. We do not experiment, for example, in order to find out whether strong acids are
really dangerous to drink. (Those who do, at any rate, are probably not around to
argue with me.) Some of our learning, however, does involve observation.