George Box’s passing (see his obituary in the previous issue) brought to my mind something that has long interested me: the enormous boost that World War 2 (hereafter “the War”) gave to Statistics in the United Kingdom, the USA, and elsewhere. This is one of the many paradoxes of war. We all agree that it is terrible and to be avoided to the greatest extent possible, yet it is hard not to concede that wars can bring scientific, technological, industrial, cultural, political, even economic benefits, over and above the purely strategic goals for which wars are fought. Not only was there extremely rapid development of some areas of statistics, especially industrial statistics, but also a large proportion of the leaders in our subject in the 40 years following the War met it for the first time during the War. It seems to me likely that a large proportion of these people, mostly men, would not have become statisticians but for the War. Indeed, Box titled his memoirs An Accidental Statistician, the “accident” being that he was assigned the role of statistician when he was a soldier in the War working on chemical defence.

I can remember being enormously impressed that such an elegant, powerful and eminently practical theory as Abraham Wald’s sequential analysis was developed in wartime. This work fascinated me for several years, particularly the extensions using martingales of Wald’s identities. W. Allen Wallis was the leader of the US east coast Statistical Research Group (SRG) within which Wald worked. In a 1980 JASA paper which I found inspiring, he gave a history of this group and a first-hand account of the origins of Wald’s work. About the four books resulting from the SRG’s work, Wallis wrote, “All have proved influential—Wald’s [Sequential Analysis, 1947] far more than the others, of course.”

Many other wartime discoveries on both sides of the Atlantic have proved influential. In the UK Ministry of Supply’s Scientific Research group SR17 led by George Barnard, one project concerned the operation of a weapon that contained 22 components (factors). Wanted was an experiment with a realistic number of combinations of levels of these factors that was optimum in a suitable sense for estimating the coefficients in a main-effects only model. The result was the path-breaking work of R.L. Plackett and J.P. Burman utilizing the mathematical research of R.E.A.C. Paley on Hadamard matrices. Today their work is seen as the beginning of screening designs, which have become widely used in industry, and are now vigorously promoted as multivariable testing (MVT). Interestingly, writing about this work more than 40 years afterwards, Plackett noted, “An experiment was carried out on the lines proposed, and the interpretation of the data was found to be somewhat difficult.” Presumably the interactions between the 22 factors were not all negligible!

Alan Turing was not a statistician either before or after the War, but during it made several important contributions to our subject, in particular to the use of Bayes factors, log Bayes factors and sequential analysis. These have already become part of Bayesian folklore, and have recently been summarized along with much else in the book The Theory That Would Not Die by Sharon Bertsch McGrayne. Turing’s cryptanalytic method known as Banburismus involved a Bayesian form of sequential analysis pre-dating Wald’s, but details were not made public until decades after the War. It is not easy to get an accurate picture of who knew what in the period 1941–1945, but much relevant material is now available, particularly in books about Turing, articles by I. J. Good, and on the website

Why should we care about these events 70 years ago? Reflecting on them, two key British participants, Barnard and Plackett wrote in 1985 “Peace finally returned, and the statistical scene in the United Kingdom had been completely transformed… No other method would have produced these changes in only six years…There was a large increase in the number of people who knew that statistics was an interesting subject, and they had been given an excellent training free of charge. …Those in charge of higher education realized that an important field had in the past been largely neglected, and during the next twenty years the situation was remedied.”

But it seems to me there is a stronger message. Commenting on Wallis’ 1980 JASA paper, F.J. Anscombe, a member of SR17, wrote, “the heart of Allen Wallis’s message is: ‘What a wonderful thing a statistical research group can be’.” He went on to say, “I believe our subject would be in better shape if we could return to a former tradition—if it were the usual practice for the most exciting new PhD’s to spend several years in a research team that had some definite mission, before, perhaps, re-entering the academic world.”

Many statisticians worked in the War to improve the accuracy of anti-aircraft guns

Photo: Wikimedia Commons