selection bias (Wald)

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 ── “During World War II, the Jewish Austro-Hungarian mathematician Abraham Wald demonstrated a remarkable understanding of selection bias.  Wald was asked to examine data on the location of enemy fire hits on bodies of returning aircraft, to recommend which parts of the airplanes should be reinforced to improve survivability.  To this superiors' amazement, Wald recommended adding armor to the locations that showed no damage.   His unique insight was that the bullet holes that he saw in surviving aircraft indicates places where an airplane could be hit and still endure.  He therefore concluded that the planes that had been shot down were probably hit precisely in those places where the persevering planes where lucky enough not to have been hit.”, p.259, Mario Livio, Brilliant blunders, 2013 

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Mario Livio, Brilliant blunders, 2013                                       [ ]

pp.258-259

p.258

   Statisticians always dread selection biases.  These are the distortions of the results, introduced either by data-collecting tools or by the method of data accumulation.  Here are a few simple examples to demonstrate the effect.  Imagine that you want to test an investment strategy by examining the performance of a large group of stocks against twenty (20) years' worth of data.  You might be tempted to include in the study only stocks for which you have complete information over the entire twenty-year period.  However, eliminating stocks that stopped trading during this period would produce biased results, since these were precisely the stocks that did not survive the market. 

p.259

   During World War II, the Jewish Austro-Hungarian mathematician Abraham Wald demonstrated a remarkable understanding of selection bias.  Wald was asked to examine data on the location of enemy fire hits on bodies of returning aircraft, to recommend which parts of the airplanes should be reinforced to improve survivability.  To this superiors' amazement, Wald recommended adding armor to the locations that showed no damage.   His unique insight was that the bullet holes that he saw in surviving aircraft indicates places where an airplane could be hit and still endure.  He therefore concluded that the planes that had been shot down were probably hit precisely in those places where the persevering planes where lucky enough not to have been hit. 

p.259 

   Astronomers are very familiar with the Malmquist bias (named after the Swedish astronomer Gunnar Malmquist, who greatly elaborated upon it in the 1920s).  When astronomers survey stars or galaxies, their telescopes are sensitive only down to a certain brightness.  However, objects that are intrinsically more luminous can be observed to greater distances.  This will create a false trend of increasing average intrinsic brightness with distance, simply because the fainter objects will not be seen. 

p.259 

   Brandon Carter pointed out that we shouldn't take the Copernican principle ── the fact that we are nothing special in the cosmos ── too far.  He reminded astronomers that humans are the ones who make observations of the universe; consequently, they should not be too surprised to discover that the properties of the cosmos are consistent with human existence.  For instance, we could not discover that our universe contains no carbon, since we are carbon-based life-forms.  Initially, most researchers took Carter's anthropic reasoning to be nothing more than a trivially obvious statement. 

   (Brilliant blunders: from Darwin to Einstein ─ colossal mistakes by great scientists that changed our understanding of life and the universe / Mario Livio.,  1. errors, scientific., Q172.5.E77L58  2013, 500─dc23, first Simon & Schuster hardcover edition May 2013, 2013, )

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en.wikipedia.org

   Abraham Wald

   Wald's sequential sampling theory 

p.20  QMJ 94 Fall

He also presented what was, at the time, the very latest research work on the sequential sampling theory of Abraham Wald (see Wald 1947; Wallis 1980).  

(It is a bit ironic that Wald's theory, which had been developed during the war under U.S. Navy sponsorship, was considered classified material until shortly before Deming presented it to the Japanese.)

Despite all the time he allotted to the topic of sampling inspection, despite all his many references to its theory, one can sense that, at the time of these lectures, Deming already had considerable ambivalence about the utility of acceptance sampling.  His lecture is full of warnings and citations of limitations about its use. 

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source:

        what deming told the Japanese in 1950 

        DeminginJapanin1950.pdf

        Peter J. Kolesar, Columbia university

        QMJ 94 Fall 

        

The primary source documents are the published lecture transcripts that Deming considered authentic. 

The transcripts show that Deming introduced to the Japanese a product design cycle of Shewhart that is distinct from the management process that the Japanese later came to call the plan-do-check-act cycle. 

Deming cycle of the plan-do-check-act (PDCA) cycle development, variation, evolution, iteration  

   Figure 2   The Deming/Shewhart design cycle (Deming 1951), p.14

   Figure 3   The Deming PDSA cycle (Deming 1986)., p.15 

   Figure 4   The Mizuno PDCA control circle (Mizuno 1984), p.16  

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