As we saw in the previous section, the fact that two things
are correlated does not by itself show that one causes the
other. To establish causal claims, statisticians use a method
called the controlled trial. For example, suppose you
wish to know whether a particular medicine is effective at
curing baldness. What you wish to know is whether taking the
medicine causes hair to grow. To establish this, you divide
your test subjects into two groups, chosen at random (to avoid
bias). Half the subjects (the treatment group) are given the
medicine. The other half (the control group) are given a
placebo, which looks just like the medicine but contains no
active ingredients. You can then measure the hair growth in
the two groups and compare the results. If the medicine is
effective, then the difference between the two groups should
be large enough that you can reject the null hypothesis that
the medicine works no better than the placebo, at your chosen
significance level.
The important point here is the random assignment of
patients to the two groups. The only factor that differs
between the groups in a systematic (as opposed to
random) way is the treatment, so if there is a difference in
hair growth, then either the medicine caused it, or it was the
result of pure chance (sampling error). As long as the
probability that the result was due to chance is small enough
(smaller than the chosen significance level), we can conclude
that the medicine was the cause.
Controlled trials are difficult to perform in many areas. For
example, one cannot perform a controlled trial to test whether
smoking causes cancer in humans, because one cannot take two
groups at random and force one group to smoke for twenty
years! Instead, the groups that are studied are
self-selected--some people choose to smoke and some choose
not to. There is always the possibility that those people who
choose to smoke have some other factor in common that causes
cancer. This makes it much more difficult to establish
causation in this area. However, controlled trials on animals
can be used, and these strongly support a causal link.
The trial for the baldness treatment described above is
a blind trial. This means that the patients do not
know whether they are in the treatment group or the control
group--this is why the patients in the control group are
given a placebo. Blind trials are used wherever possible. Why
might this be important?
The importance of blind trials is to make sure that no
factor varies systematically between the treatment group and
the control group other than the treatment itself. If the
patients know which group they are in, then this knowledge
itself constitutes a systematic difference between the two
groups. This might not seem like an important difference, but
in fact simply believing that you are being treated can have a
measurable effect for a wide range of medical conditions.
Patients who are given a placebo to take often show a
measurable improvement compared to patients who are given
nothing at all. This is called the placebo effect.
A double blind trial is one in which neither the
patient nor the doctor knows whether the patient is in the
treatment group or the control group. The doctor doesn't know
whether the tablets they give to the patient are genuine or
placebos. Why might this be important?
Again, the importance here is to rule out any factors
which might vary systematically between the treatment group
and the control group. It has been shown that if the doctor
knows whether the patient is in the treatment group or the
control group, this knowledge can unconsciously alter their
behaviour towards the patient and their perception of the
patient's condition. In this case, if the doctor knows which
group the patient is in, this might unconsciously influence
their perception of slight changes in hair growth or of the
severity of side effects. This makes the data provided by the
doctor less reliable.
Reread the excerpt from the South China Morning
Post in the previous question set. Would it be possible to
conduct a controlled trial to determine whether superstitious
beliefs cause neurosis, depression and low IQ?
No, a controlled trial is unlikely to be possible in
this case. We can't assign people randomly to two groups and
make one group believe in superstitions. Hence the two groups
(superstitious and non-superstitious) are self-selecting, and
this introduces the possibility of bias. It may be that
people with a predisposition to neurosis, depression or low IQ
are more likely to end up in the superstitious group than in
the non-superstitious group. This is why the correlation
reported in the newspaper article does not establish a causal
link.