Title: A Golden Rule: correlation is not causation
Course: UGQuants (SSPS) > Section: Correlation and Regression

A Golden Rule: correlation is not causation

Just because we find correlation between two variables, we do not necessarily have any evidence about causation, let alone the direction of cause and effect (i.e. whether variable A causes variable B or the other way around).

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Consider the relationship between age and height of boys in Toronto. The data are equally compatible with the theory that changes in height cause boys to get older as it is with the theory that ageing causes growth. Our preference for the second theory cannot come from anything the data tell us.  Rather it comes from other sources, such as our ideas about the nature of time or our understandings of the physiological development of the human body.  Marsh and Elliott (2008, p. 244) give a good example of the kind of logic we need to be careful to avoid.

Supposing we collected data on the number of fire engines sent to a fire and the amount of economic losses sustained as a result of the fire.  We would almost certainly find the two variables to be closely correlated. But were we to assume that such a correlation also implied causation, we would reach the conclusion that a good way to reduce the cost of fire damage would be to stop sending fire engines to deal with fires! This nonsensical conclusion follows from our failure to take account of another variable that has more to do with the probable causal path: the size of fire in the first place!