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\noindent{\bf W. Edwards DEMING}\\
b. 14 October 1900 - d. 20 December 1993
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\noindent{\bf Summary.} Long recognized as a leading proponent of
statistical sampling and approaches to quality improvement, Deming led
major efforts to bring statistical approaches and methods to bear on
problems in government, science and industry.
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William Edwards Deming was born in Sioux City, Iowa, USA,
and died at the age of 93 in Washington, D.C.
Deming was active to the end of his life; he spoke at the Joint
Statistical Meetings in San Francisco in the summer of 1993, and he
had presented a four-day seminar on quality management as recently as
December 7-10 in the Los Angeles area. At the time of his death,
Deming was arguably the most famous living statistician.

Deming studied at the Universities of Wyoming (B.S. 1921) and Colorado
(M.S. in Mathematics and Physics, 1924) before going to Yale
University, where he received his doctorate in Physics in 1928. From
1927 through 1939 he held an appointment as Mathematical Physicist in
the Bureau of Chemistry and Soils of the U. S. Department of
Agriculture (USDA).  Deming was instrumental in arranging lecture
series at the USDA. Fisher (q.v.) spoke in 1936, but the more
influential series was one presented in April 1937 by Jerzy Neyman (q.v.).
Deming arranged the publication of Neyman's lectures as a mimeographed
book, Lectures and Conferences on Mathematical Statistics (USDA, 1938;
2nd ed. 1952), one of the earliest and most widely read American
textbooks on mathematical statistics. Deming also lectured on least
squares, and he assisted Shewhart (q.v.) in the 1939 publication of his
lectures as well.

Subsequently, from 1939 to 1945, he was Head
Mathematician and Advisor in Sampling to the U.S. Bureau of Census,
where among his innovations was the application of Shewhart's quality
control ideas to the Census's coding and cardpunching operations, and
the introduction (with F. Stephan) of the Deming-Stephan algorithm for
the iterative proportional fitting of contingency tables. During
1942-45, at the instigation of W. Allen Wallis, Deming was actively
involved with Holbrook Working in arranging a highly successful series
of short courses on the use of statistics in support of the war
effort. In 1945, Deming moved to a position as Advisor in Sampling in
the Bureau of the Budget. 

Deming's great international fame arose from his work on the
re-establishment of Japanese industry after the Second World War. From
1947-50, Deming had been assigned to General Douglas MacArthur's
Supreme Command of the Allied Powers in Tokyo, as Advisor in Sampling
Techniques, and he remained to consult with the Union of Japanese
Scientists and Engineers (JUSE) for two years after that. It was a
most agreeable arrangement for both sides. Deming had come upon
Shewhart's methods of quality control in 1928 and had written and
spoken about them on many occasions; in Japan he found an eager
audience. Post-war Japan by 1950 had a reputation for such poor
quality products that it eagerly embraced Deming and statistical
control methods, both for the substance of the methods and the
symbolism of Deming as an icon of American values. In 1950 JUSE
established the Deming Prize for excellence in quality control, and
the prize has been awarded annually since 1951. Deming's contributions
to quality improvement in Japanese industry became the ``stuff'' of
legends and in the later decades of his life the story was retold in
many ways by many different authors (e.g., see Mann, 1987).

Thereafter, although he held various adjunct teaching positions
(including at New York University (NYU) and at Columbia University)
he worked out of his Washington, D.C. home as a private consultant. He
conducted frequent multi-day seminars in the U.S. and overseas on
managerial methods. He insisted upon the involvement of top-level
management in his programs, and he attacked the use of production
quotas and performance criteria, emphasizing cooperative problem
solving. His approaches to management were reduced to a 14-point
philosophy (e.g., see Deming, 1986) and promulgated by many others in
the United States and abroad.

Deming's great gifts were enormous energy and an early keen sense of
the broad applicability of statistical methods in government, science,
and industry. The ideas he is associated with came from many sources:
quality control from Shewhart, statistical methods from Fisher and
Neyman, sampling techniques from Stephan and Hansen. But the mixture
of these and the forceful way he melded them to a philosophy of
management were his own. He also had a great interest in the
history of statistics, and in 1940 he arranged for the reprinting of
two original papers by Thomas Bayes (q.v.), adding his own commentary to
Bayes's paper on divergent series.

Deming married Agnes Bell in 1922, and she died eight years later. In
1932 he married Lola E. Shupe, who had been a co-author on a number of
physics articles with Deming and later helped him with calculations
for his research. She died in 1986.

Deming was awarded the President's National Medal of Technology in
1987, but characteristically Deming was unwilling to cancel a
previously arranged managerial seminar in Detroit; the medal was
received from President Reagan on his behalf by his two daughters at a
White House Rose Garden ceremony. Deming was the President of the
Institute of Mathematical Statistics in 1945.
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\noindent{\bf Deming on Least Squares and the Adjustment of Data}

In 1934, Deming published, jointly with the UC Berkeley Physicist
Raymond T. Birge, an influential paper ``On the Statistical Theory of
Errors.''  This review paper brought the methods of Fisher, Neyman and
Pearson (q.v.), and Jeffreys (q.v.) to a broad audience of American physical
Scientists. It was reprinted with additional notes in 1937 by the
Graduate School of the USDA, and it served effectively as a textbook
for over a decade. In correspondence with Deming, Fisher was generally
quite complimentary, although in a 1940 letter to Maurice Frechet (q.v.)
about Deming and Birge, Fisher complained that he found ``these
writers very often obscure.'' This material also made its way into
Deming's mimeographed lecture notes on least squares which first
appeared in 1938, which he later turned into the 1943 book on the
adjustment of statistical data.

Deming worked with Frederick Stephan on what was an crucial problem
for the Bureau of the Census, how to adjust a sample table of counts
to have the same marginal totals that were available for the
population. In 1940, the Bureau implemented the first sample long form
and needed to have the sample data consistent with that from the
complete census long form for selected marginals.  Their answer, which
they published in a 1940 paper, was to apply least squares to minimize
the weighted sum of squared discrepancies between the adjusted
frequencies and the sample frequencies, subject to the marginal
contraints using Lagrange multipliers.  They weighted the individual
squared discrepancies by the inverse of the sample cell counts (thus
using a chi-square-like metric).  Their method could be viewed as a
form of post-sratification which generalized ratio
adjustment, an approach which handles one set of margins only.  This
method generalized to three and higher dimensions where adjustments
were made for one way and even two-way totals, but the solution of the
normal equations proved computationally daunting.  Thus Deming and
Stephan suggested an approximation which they described as the method
of iterative proportions, which successively rescaled the sample data
by a proportional adjustment to have the correct margins and iterated
until convergence.  This approximate method proved workable and soon
became the method of choice at the Census Bureau under the label
``raking.''  Deming included a chapter on this method in his 1943
book.

Stephan, after some further interaction with Deming, published a
second paper on the topic in 1942, in which he proposed an alternative
iterative method that actually produced the least squares solution for
this problem and noted that the method of iterative proportions did
not actually solve the least squares problem and that there was no
proof of convergence for more than two dimensions.  There the problem
lay, until Yvonne Bishop, in work on the National Halothane Study (see
Bishop, 1969), noted that the method of iterative proportions solved
the loglinear model estimation problem for contingency tables.  At
about the same time several others found various ways to exploit the
algorithm (e.g., see the uses and related references presented in
Bishop, et al., 1975).
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\noindent{\bf Deming on Sampling and its Applications}
 
Deming's work on sampling went beyond that linked to the statistical
adjustment of data and methods worked on while he was at the Bureau of
the Census.  His books on sampling (1950) and the design of business
research (1960) both had considerable impact on the applications of
sampling beyond government, as did his expository articles on sampling
such as Deming (1968). He wrote about nonsampling errors, and he
applied the notion of capture-recapture to human populations (Sekar
and Deming, 1948), linking the approach to sampling and stratification.
After the method had been promulgated by others at the Bureau of the
Census and elsewhere, he worked with the demographer Nathan Keyfitz to
extend capture-recapture ideas to multiple recaptures, but without making
the link to loglinear models and his method of iterative proportions.

Beginning in the 1950s, Deming referred to himself professionally as a
``Consultant in Statistical Surveys,'' and he consulted widely with
those in government and in industry. He was among the first
statisticians to testify as an expert witness in court about the
results of sample surveys.  He wrote on this topic as early as 1954,
and he included an example drawing on this work in his 1960 book.

In 1958 Deming presented a Special Invited Address on "Principles of
Professional Statistical Practice" at the Boston meeting of the
Institute of Mathematical Statistics (see Deming, 1965).  This was one
of the first papers to appear in the statistical literature which
emphasized the professional ethics associated with the practice of
statistics, and much of what he wrote then and subsequently on the
topic served as the foundation for codes of ethics developed both by
the American Statistical Association and the International Statistical
Institute.
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\begin{thebibliography}{3}

\bibitem{0}   
 Bishop, Y.M.M. (1969). Full contingency tables,
logits, and split contingency tables.  {\em Biometrics}, {\bf 27},
545--562.

\bibitem{1}  Bishop, Y.M.M., Fienberg, S.E., and Holland, P.W.  (1975).
{\em Discrete Multivariate Analysis: Theory and Practice}. MIT
Press, Cambridge, MA.

\bibitem{2}  Deming, W. E. (1943).  {\em Statistical Adjustment
of Data.} Wiley, New York.

\bibitem{3}  Deming, W.E. (1950). {\em Some Theory of
Sampling.} Wiley, New York. 

\bibitem{4}  Deming, W.E. (1960). {\em Statistical Design in
Business Research}.  Wiley, New York. 

\bibitem{5}  Deming, W.E. (1965). Principles of Professional
Statistical Practice.  {\em Annals of Mathematical Statistics}. {\bf
36}, 1883--1900.

\bibitem{6}  Deming, W.E. (1968). Sample surveys: The field.
In {\em International Encyclopedia of the Social Sciences}, Vol. {\bf 13},
594--612.

\bibitem{7}  Deming, W. E.  (1986).  {\em Out of the Crisis}.
MIT Center for Advanced Engineering Study, Cambridge, MA. 

\bibitem{8}  Deming, W.E., and Birge, R.T. (1934).  On the
Statistical Theory of Errors. {\em Review of Modern Physics}, {\bf
6}, 119--161.

\bibitem{9}  Deming, W. E. and Stephan, F.F. (1940). On a least
squares adjustment of a sampled frequency table when expected
marginal totals are known.  {\em Annals of Mathematical Statistics},
{\bf 11}, 615--630.

\bibitem{10}  Mann, N.R. (1987).  {\em The Keys to Excellence,} (2nd
ed.) Prestwick Books.

\bibitem{11}  Neyman, J. (1952 [1938]). {\em Lectures and
Conferences on Mathematical Statistics and Probability}. The
Graduate School, U. S.  Department of Agriculture, Washington, DC.
(The 1952 edition is an expanded and revised version of the original
1938 mimeographed edition.)

\bibitem{12}  Sekar, C.C. and Deming, W.E.
(1948).  On a method of estimating birth and death rates and the
extent of registration.  {\em Journal of the American Statistical
Association}, {\bf 44}, 101--115.

\bibitem{13}  Shewhart, W.A. (1939).  {\em Statistical Method from
the Viewpoint of Quality Control}. The Graduate School, U. S.
Department of Agriculture, Washington, DC.

\bibitem{14}  Stephan, F.F. (1940). On a least squares method of
adjusting sample frequency tables when expected marginal totals are
known.  {\em Annals of Mathematical Statistics}, {\bf 13}, 166--178.
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\hfill{Stephen E. Fienberg and Stephen M. Stigler}
\end{thebibliography}

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