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An Interesting Example
During World War II, Abraham Wald worked for the New York company Statistical Research Group. The American military approached him with a problem. War planes were coming back from air battles covered in bullet holes, and the military was interested in protecting future planes by using minimal armour placement. The question was where to best place this armour so as to protect the planes and pilots. The bullet holes were roughly distributed as such:
Where would you choose to place the minimal armour?
If you said any section other than the engine section, then you would be absolutely… wrong. Wald’s explanation is as follows: the statistics that were presented were gathered from planes that had survived battle – the planes that didn’t survive battle were not included in the numbers. Thus, the planes that returned were not a random sample and conclusions could not be made by only reflecting on the surviving planes. Wald recommended adding armour to the sections of the plane that returned home relatively unscathed (here, the engine section) would be wise, as the surviving planes tell us the regions of the plane that can take damage and still return home safely.
Suggesting to give armour to regions of the plane that are damaged the most reflects a statistical bias known as survivorship bias.
Assurbanipal: "Passant, mange, bois, divertis-toi ; tout le reste n’est rien".
Franck Ramus : "Les sciences de l'éducation à la française se font fort de produire un discours savant sur l'éducation, mais ce serait visiblement trop leur demander que de mettre leur discours à l'épreuve des faits".
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