Correlation does not imply causation is a useful statement for a scientist to bear in mind. It is also good to remember it whenever a politician is claiming some statistic says their policy is a success, they are almost always using correlation to imply they their policy has caused the effect. The best way to see that correlation does not necessarily mean there is cause and effect, is to look at some examples of where two variables are correlated, i.e., where on a plot is one variable is changed so does the other, but where it would be very surprising if one causes the other. There are many examples of this, this paper goes for showing that as the USA imported more lemons from Mexico, fatalities on US highways dropped. Lemons are fine things, a slice of lemon is excellent in a G&T, but the only way they save lives if you have very bad scurvy.
Here the point is that both the number of lemons imported, and highway fatalities, are varying with time. The USA has been cutting road deaths and importing more lemons at the same time, which makes the two numbers correlated. But that is all there is to it.
There are many many other examples of this. One currently doing the rounds is the plot of Grayden Reece-Smith showing the correlation between the fraction of students who get a first class degree at a Cambridge college, and the college’s wine budget. Plot is in this article in a Cambridge student newspaper. The correlation is positive, the bigger the booze bill, the higher the fraction of firsts. But correlation does not imply causation, so sadly we cannot conclude that the way to a first is through the bottom of a glass.
Chance & Necessity 