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One example of this claim from the Statistics How To website:

Abraham Wald’s Naval Work

In World War II, statistician Abraham Wald tried to determine how to minimize bomber losses. Prior to Wald’s work, researchers from the Center for Naval Analysis analyzed bombers that came back with damage and recommended that the damaged areas be reinforced on all bombers. However, they didn’t take into account that only the surviving aircraft came back; the bombers that did not survive likely had damage to other, more critical areas. Wald recognized that survivorship bias played a part in the Center for Naval Analysis’s decision and recommended basically the opposite–the reinforcement of areas that had not been hit on the surviving aircraft.

Is there proof that this historical incident actually happened? The question is specifically about Abraham Wald overriding a previous report from the Center for Naval Analysis.

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    For the record, it seems undeniable that Wald did work in this area. I can't find the report it supposedly "overrides". – Is Begot Sep 17 '15 at 16:15
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    Much the same claim is made in the UK for Patrick Blackett and his operational research team, recommending armour-plating of undamaged parts of aircraft – Henry Sep 18 '15 at 1:07
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    I was in the middle of writing a comment on the just-deleted answer: pages 63-65 of the linked reprint of 1943 memoranda give an example similar to the OP's of using probability/statistics to determine which areas of an aircraft are more vulnerable. Nowhere can I find a mention of whatever previous ideas these formulas might have replaced. Could still be a response to them, of course. – Dan Getz Jan 30 '16 at 15:46
  • @DanGetz I'll restore the answer, I'm adding more info. It was the military generally that reinforced areas where returning planes were damaged, not SRG which wasn't part of the military, according to SRG's founder Wallis. – DavePhD Jan 30 '16 at 16:17
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Firstly, Wald did not work for the Center for Naval Analyses or its predecessor organizations Antisubmarine Warfare Operations Research Group (ASWORG), Operations Research Group (ORG) or Operations Evaluation Group (OEG). Instead, he worked for the Statistical Research Group at Columbia University. The Center for Naval Analyses merely published his work many years later, and didn't exist as such until 1962.

A good history of what occurred is found in Breakthroughs in Statistics: Foundations and Basic Theory, which is also consistent with Abraham Wald's own description, as published in his book Sequential Analysis.

Quoting from pages 249-250 of "Breakthroughs in Statistics..."

the Applied Mathematical Panel of the U.S. Office of Scientific Research and Development established a Statistical Research Group at Columbia University on July 1, 1942. The purpose of the Group was to advise the Defense Department on statistical methods for experiments that were being conducted on a vast scale of war production. Allen Wallis headed the group with Harold Hotelling and Jacob Wolfowitz as its founding members. Wald, Harold Freeman, and Milton Friedman, among others, joined a few months later. In late March 1943, Wallis discussed the following problem with Friedman [presents highly mathematical problem]

This lead Wallis and Freidman to the following conjecture [more mathematics] Wallis and Friedman approached Wald in early April 1943. Wald was initially unenthusiastic, but phoned 2 days later to admit that their conjecture was, indeed, correct.

So, basically the OP is saying other members of the group erred, when in fact they formed the basis of Wald's work.

More particularly, concerning planes, Willis, the head of the group stated:

"The military was inclined to provide protection for those parts that on returning aircraft showed the most hits" Quoting "The Statistical Research Group, 1942-1945" Journal of the American Statistical Association, Volume 75, pages 320-330 (alternative link).

So, yes Wald was going against the earlier convention, but not against a previous recommendation of the group.

For additional information, in 1980 a reprint of Wald's original 1943 work was republished and the full 100 page text is available A REPRINT OF "A METHOD OF ESTIMATING PLANE VULNERABILITY BASED ON DAMAGE OF SURVIVORS"

  • I'm not sure if this answers the question of whether there existed a recommendation by the Center for Naval Analysis (or a similar organization) to reinforce the damaged areas on bombers. – JonathanReez Jan 30 '16 at 14:28
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    @JonathanReez The problem was originally presented to the group in the context of ordnance testing (shells). The group was recommending wastefully large sample sizes in ordnance testing. Captain G. L. Schuyler pointed out that this was flawed. Wallis and Freidman came up with their conjecture, and Wald further developed the idea and applied it to other areas. The statement in the OP would be correct if it referred to the group making wasteful recommendations about ordnance testing. See letter quoted on page 324 of Decision Theory: Principles and Approaches – DavePhD Jan 30 '16 at 14:54

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