What's in a Relationship?

Correlation is a tricky subject.  It is the measure of the mathematical relationship between two measurements.  These could be any measurements, and it becomes tricky when someone tries to attribute a physical relationship to this mathematical relationship, that is, they try to tell you that because two things change at the same time (increase or decrease) that one causes the other.

A common example is carbon dioxide (CO2) in the atmosphere and climate.  Over many thousands of years, when there was more CO2 in the atmosphere, global temperature has been higher.  It’s not possible to deduce immediately from that the one causes the other.  Scientists must find the mechanism by which the change in one leads to a change in the other – the greenhouse effect of reflecting the earth’s heat back toward the ground, for example.  But correlation alone is not good enough.  It only provides a clue, a reason for further investigation.

Unfortunately, we read about correlation, these relationships, frequently but the reporters are not careful to clarify this important point.  A recent example comes from the University of Texas.  “Fathers who worked in engineering were two times as likely to have a child with an autism spectrum disorder (ASD). Those who worked in finance were four times more likely and those who worked in health care occupations were six times more likely to have a child on the autism spectrum.”  This is correlation, a mathematical relationship.  Have they looked for a mechanism to explain their results?  Is it an inheritance issue?  Is it the way the father treats his children?  Is there any real-life relationship at all?  The article says nothing about it. Should someone opt not to become a doctor for fear of increasing his children’s odds of being autistic?  Does one cause the other; do they have a common cause; or are the findings of the study based on an odd coincidence?

Stranger coincidences are really quite common.  This link shows a few examples from “a law student at Harvard who, in his spare time, put together a website that finds very, very high correlations between things that are absolutely not related, like margarine consumption and the divorce rate in Maine.”  My favorite is a 96.97% correlation between deaths by getting tangled in bed sheets and the revenue of ski facilities.  This is extremely close to perfect correlation of 100%, and much better than scientists that present studies for publications usually achieve.

Readers of any scientific or medical reports beware.  A correlation is only the beginning of an investigation, not a conclusion.