Module: Basic statistics
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We all have a tendency to think that the world must conform to our prejudices. The opposite view involves some effort of thought, and most people would die sooner than think – in fact they do so.
- Bertrand Russell
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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.