In Christchurch we have a weather phenomenon known as the “Nor-wester”, which is a warm dry wind, preceding a cold southerly change. When the wind is from this direction, aeroplanes make their approach to the airport over the city. Our university is close to the airport in the direct flightpath, so we are very aware of the planes. A new colleague from South Africa drew the amusing conclusion that the unusual heat of the day was caused by all the planes flying overhead.
Statistics experts and educators spend a lot of time refuting claims of causation. “Correlation does not imply causation” has become a catch cry of people trying to avoid the common trap. This is a great advance in understanding that even journalists (notoriously math-phobic) seem to have caught onto. My own video on important statistical concepts ends with the causation issue. (You can jump to it at 3:51)
So we are aware that it is not easy to prove causation.
In order to prove causation we need a randomised experiment. We need to make random any possible factor that could be associated, and thus cause or contribute to the effect.
There is also the related problem of generalizability. If we do have a randomised experiment, we can prove causation. But unless the sample is also a random representative sample of the population in question, we cannot infer that the results will also transfer to the population in question. This is nicely illustrated in this matrix from The Statistical Sleuth by Fred L. Ramsey and Daniel W Schafer.
A student posed this question: Is it possible to prove a causal link based on an observational study alone?
It would be very useful if we could. It is not always possible to use a randomised trial, particularly when people are involved. Before we became more aware of human rights, experiments were performed on unsuspecting human lab rats. A classic example is the Vipeholm experiments where patients at a mental hospital were the unknowing subjects. They were given large quantities of sweets in order to determine whether sugar caused cavities in teeth. This happened into the early 1950s. These days it would not be acceptable to randomly assign people to groups who are made to smoke or drink alcohol or consume large quantities of fat-laden pastries. We have to let people make those lifestyle choices for themselves. And observe. Hence observational studies!
There is a call for “evidence-based practice” in education to follow the philosophy in medicine. But getting educational experiments through ethics committee approval is very challenging, and it is difficult to use rats or fruit-flies to impersonate the higher learning processes of humans. The changing landscape of the human environment makes it even more difficult to perform educational experiments.
To find out the criteria for justifying causal claims in an observational study I turned to one of my favourite statistics text-books, Chance Encounters by Wild and Seber (page 27). They cite the Surgeon General of the United States. The criteria for the establishment of a cause and effect relationship in an epidemiological study are the following:
In high school, and entry-level statistics courses, the focus is often on statistical literacy. This concept of causation is pivotal to correct understanding of what statistics can and cannot claim. It is worth spending some time in the classroom discussing what would constitute reasonable proof and what would not. In particular it is worthwhile to come up with alternative explanations for common fallacies, or even truths in causation. Some examples for discussion might be drink-driving and accidents, smoking and cancer, gender and success in all number of areas, home game advantage in sport, the use of lucky charms, socks and undies. This also ties nicely with probability theory, helping to tie the year’s curriculum together.