Fire-fighters cause damage?!

This is an example of what is called Simpson's Paradox. The apparent association is due to the omission of some important information. In the example of house fires, the size of the fire needs to be taken into account—more fire-fighters are sent to larger fires and the larger the fires, the worse the damage.

In many situations, the explanation for some apparent association cannot be identified easily. One example is the association between smoking and lung cancer. It has been argued that the apparent association between the two may be due to some genetic factor that predisposes people both to nicotine addiction and lung cancer. If this is true, then smoking cannot be blamed for causing cancer. It was only after considerable research, with the aid of statistical methods, that it is now generally accepted that smoking is a contributory cause of lung cancer.