Module: Basic statistics
Quote of the page
Science is built up of facts, as a house is built of stones; but an accumulation of facts is no more a science than a heap of stones is a house.
- Henri Poincarè
Quite often, we don't want to know merely whether two quantities are correlated; we want to know whether they are causally connected. For example, we want to know not merely whether smoking is correlated with lung cancer, but whether it is causally connected with lung cancer.
By itself, the fact that two things are correlated doesn't entail that they are causally connected. For example, the rate of television ownership for a country is positively correlated with its average life expectancy, but this doesn't mean that countries should encourage their populations to buy TVs.
The mistake of confusing correlation with causation is a common one, and is often called the post hoc fallacy. The name comes from the Latin phrase post hoc ergo propter hoc, which (roughly!) translated means "after that, therefore because of that". If B usually occurs just after A, it is tempting to conclude that B occurred because of A, but this would be fallacious in the absence of other evidence. For example, the correlation may be the result of a common cause--a factor that causes both A and B. A common cause can explain the existence of the correlation, even if A does not cause B.
Could there be a common cause explanation for the fact that the rate of television ownership in a country is correlated with its average life expectancy?
Read the following excerpts from the South China Morning Post ("True believers' luckless stars", August 7, 2000):
No matter whether you are Pisces, Virgo or Cancer, the warning for this week is the same for every astrological sign--poring over your horoscope can damage your mental health.
If you take star signs too seriously or if you worry unduly about walking under a ladder, you are stunting your intelligence and making yourself depressed. Psychologists have discovered a strong link between belief in superstition and poor exam performance.
They also found that those students who took account of black cats and Friday the 13th were more likely to be neurotic, depressed and have a lower IQ than their more sceptical counterparts.
Is this an example of the post hoc fallacy? If so, what might explain the observed correlations?