The Statistical Research Group, 1942-1945: RejoinderAuthor(s): W. Allen WallisSource: Journal of the American Statistical Association, Vol. 75, No. 370 (Jun., 1980), pp. 334-335Published by: American Statistical AssociationStable URL: http://www.jstor.org/stable/2287454 .

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Rejoinder W. ALLEN WALLIS

I am interested in, pleased by, and in agreement with the comments by Anscombe and Kruskal that my paper stimulated. They do not provoke a true rejoinder, only a few comments.

I am disposed to defend, though not without limit, ir- relevance in academic research. In some ways, the most valuable contribution that universities can make and one that is unique to universities is to support research and scholarship that are not subject to tests of relevance. Re- search that is clearly relevant is supported by many other institutions, including profit-dependent and vote-depen- dent institutions. But the life of the mind has an intrinsic value of its own. At the least, its products are relevant to a clearer or deeper intellectual understanding, if only of logical implications and relations. And who can say what may be the relevance and practical applications of in- tellectual understanding and of the processes through which it is obtained?

Anscombe's strictures on work that is "highly technical and narrow in scope," academic, and not "relevant to anything" bring to mind Alfred Marshall's "general rule that in discussions on method and scope, a man is nearly sure to be right when affirming the usefulness of his own procedure, and wrong when denying that of others" (Marshall 1907, p. 771).

The kind of work that SRG did is not the whole of sta- tistics. Far from it. Indeed, from one viewpoint-the viewpoint appropriate to academic institutions but to few if any others-it was peripheral: the interface, in con- temporary jargon, between the heartland of statistics and the real world. To many, much of the work that Wald did, that Wolfowitz did, and that Savage did, other than dur- ing their participation in SRG, typifies highly technical academic work deficient in relevance. But their contribu- tions to SRG's work were clearly based on their back- grounds in this academic work, and the same has been true subsequently of students of theirs working in various branches of statistics. Their own later academic work- for example, Wald's work on decision theory-was in turn influenced by their work at SRG.

Wald's work on decision theory had begun before his association with SRG. When Savage first joined SRG, I introduced him to Wald at lunch one day. Wald dis- cussed some of his ideas on decision theory and Savage, who was a former research assistant of VonNeumann's, remarked that he knew a rather obscure paper that would interest Wald, namely, VonNeumann's 1928 paper on games. Wald laughed and said that some of his ideas were

based on that paper. It is a highly technical and academic paper.

These remarks to the contrary notwithstanding, I agree strongly with Anscombe's emphasis on the value in sta- tistical training of fairly deep exposure to one or more fields in which people are struggling to unlock nature's secrets and are interested in statistics not for its own sake but as an implement. Indeed, the preceding remarks but- tress his position.

Kruskal has performed an extraordinarily useful feat in elucidating Hotelling's SRG work on multivariate quality control. Any student setting out to master that work will find Kruskal's exposition invaluable.

Finally, a legend that has had some currency concern- ing Hotelling's work at Dahlgren: For his first visit, Hotelling was told that a station wagon to Dahlgren would leave the main Navy building in Washington at 8:00 a.m. Someone else told him 8:30 a.m. He arrived at 8:15, missing the station wagon by 15 minutes. This led to much joking about statisticians drowning in streams only three feet deep on the average. Actually he had started in time to be confident of arriving by 7:45 a.m., but had encountered an extraordinary delay of more than half an hour. Nevertheless, the legend lives on. I do not expect this note to slay it, any more than I expect my paper to slay the legend about Wald's work being given a security classification and snatched away from him be- cause he lacked a security clearance. Many will feel with Parson Weems, the originator of the story about George Washington and the cherry tree, that "If it isn't true, it ought to be." Or is the remark by the parson merely one that he ought to have made, but didn't?

A postscript: In the course of reviewing the history of SRG, I was reminded of some ingenious work by Wald that has never seen the light of day. Arrangements have now been made for its publication, although the form and place are yet undecided.

Wald wrote a series of memoranda on estimating the vulnerability of various parts of an airplane from data showing the number of hits on the respective parts of planes returning from combat. The vulnerability of a part (engine, aileron, pilot, stabilizer, elevator, etc.) is defined as the probability that a hit on that part will re- sult in destruction of the plane (fire, explosion, loss of power, loss of control, etc.). The military was inclined to provide protection for those parts that on returning

? Journal of the American Statistical Association June 1980, Volume 75, Number 370

Invited Papers Section

334

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Wallis: The Statistical Research Group, 1942-1945 335

planes showed the most hits. Wald assumed, on good evidence, that hits in combat were uniformly distributed over the planes. It follows that hits on the more vulner- able parts were less likely to be found on returning planes than hits on the less vulnerable parts, since planes re- ceiving hits on the more vulnerable parts were less likely to return to provide data. From these premises, he de- vised methods for estimating the vulnerability of vari- ous parts.

Although Wald's work on estimating vulnerability has never been published, I have learned through the Center for Naval Analyses (CNA), an affiliate of the University of Rochester, that his methods have been used by both the Navy and the Air Force. The CNA has undertaken to

prepare an article for publication, either presenting Wald's memoranda or giving an expository account of them. While the work does not relate to central issues of statistics comparable with Wald's work on sequential analysis and decision theory, it does represent an inter- esting and ingenious piece of work by one of the greatest figures in the history of American statistics and certainly should be published-as it will be soon.

REFERENCES

Marshall, Alfred (1907), Principles of Economics (5th ed.), New York: Macmillan.

VonNeumann, John (1928), "Zur Theorie de Gesellschaftsspiele," Mathematische Annalen, 100, 295-320.

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