Observation selection bias

From the Titelbaum book on Bayesian epistemology I have mentioned here before. There is a nice explanation in a footnote near the end about "observation selection bias" as a ubiquitous problem in statistics and, really, in the understanding of probability. The explanation is illustrated with a World War II throwback.

US War Department statisticians observed in 1943 that bombers returning to London from their flights over occupied Europe generally had more bullet holes in their fuselage than in their engine. Somebody drew the conclusion that the German fire tended to hit the fuselage, and that there should be extra plating there.

Such a reinforcement of the fuselage was not a decision to be taken lightly. Reinforcement adds weight. Heavier aircraft are less maneuverable, have a lesser range, etc.

So Abraham Wald, a Hungarian Jew known before the war for econometrics research, who at this point was working at Columbia with the Statistical Research Group, consulting with the military, was shown the data on the frequency of fuselage holes. And he argued successfully against any such reinforcement.

He said: Save the reinforcement for the engines, where the bullet holes aren't. Wald not only noticed the selection bias in this data, he reasoned from it. Wald said that the data shows that the RETURNING planes are those with the holes in the fuselage. The implication is not that the German fire finds the fuselage more easily but that the planes with holes in the engine don't return. It is an observation about the vulnerability of the engine, and the survivability of hits to the fuselage.

That turned the matter around neatly. It is a great story.

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