Explain why a correlation between two variables does not necessarily imply that one variable causes the other to vary as it does. Give an example.
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1$\begingroup$ Welcome to the site Nick. If this is a standard textbook question or homework then please add the self-study tag. $\endgroup$ – Andy Sep 24 '14 at 16:32
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$\begingroup$ Another great duplicate of this question is at stats.stackexchange.com/questions/36/…. Many more threads add relevant commentary. $\endgroup$ – whuber♦ Sep 24 '14 at 17:28
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Example from Wikipedia: http://en.wikipedia.org/wiki/Correlation_does_not_imply_causation
Suppose during a summer, ice cream sales increases. Also, the rate of drowning deaths increases sharply as well. Can we conclude that therefore ice cream consumption causes drowning? Obviously not, and it is easy to see a "third variable" involved here: the proportion of the population going for a swim or water-related activities.
This "third variable" is otherwise known as a confounder, and confounding is one of many mechanisms why correlation between two variables does not necessarily imply that one variable causes the other to vary as it does.
