During WWII, statistician Abraham Wald was asked to help the British decide where to add armor to their bombers. After analyzing the records, he recommended adding more armor to the places where there was no damage!
Why did he do this? Think about it a minute. If you are looking over the records of damaged bombers, where they got hit and what the effects were, why would you want to add armor to places where there was no recorded damage?
The answer is here. (linked from Marginal Revolution)
This is a good lesson in how to think about the big picture. The technical term is 'selection bias' which means that the things you are looking at are not the whole picture; there was some process that made you look at only a small fraction of reality. Without considering that process, all of the best statistics in the world will not help you find the truth.
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