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\noindent{\bf Egon Sharpe PEARSON}\\
b. 11 August 1885 - d. 12 June 1980
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\noindent{\bf Summary.} Egon Pearson continued and developed his father, 
Karl's, pioneering work in
teaching and research in statistics at University College London and, with
Neyman, made fundamental contributions to the theory of hypothesis testing.
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Egon Sharpe Pearson, the son of Karl Pearson (q.v.), was born in Hampstead
(London) and died in Midhurst, Sussex. His education took him from
Winchester College to Trinity College, Cambridge where he
graduated in mathematics. He then moved into his father's
department at University College, London in 1921 and remained
there, apart from wartime service in the Ministry of Supply,
until his retirement in 1960. Advancement was rapid and he was
promoted to Reader in 1933, when his father retired, and to
Professor in 1935. From 1933 he was also head of one of the two
departments into which Karl Pearson's department had been divided
on his retirement; R.A. Fisher (q.v.) headed the other.

     Like many sons who have followed in the footsteps of famous
fathers, it could not have been easy for Egon to establish a
distinctive academic identity. Indeed, there was a strong element
of continuity between the old regime and the new. He took over
the editorship of {\it Biometrika} from his father in 1936 and
continued in that role until 1966 by which time the journal had
been in the hands of the two Pearsons for the whole of the 65
years since its founding.

   {\it Biometrika} has always been a vehicle for the publication of
statistical tables, many computed at University College. In the
pre-computer era, such tables were the essential infra-structure
of practical statistics. They required an immense amount of
calculation and Egon Pearson contributed extensively to this
enterprise. The Biometrika Trust published many such tables and
the most useful were brought together, and widely disseminated,
in the two volumes edited jointly with H.O. Hartley: {\it Biometrika
Tables for Statisticians} Volumes I and II.

     Computation was also a key element in the Pearsonian
approach to teaching statistics. The many hours spent with
Brunsviga calculators left its mark on generations of students.
Subsequent developments in computing soon made the skills it
imparted obsolete, but first hand experience of handling data was
a more durable element.

     As a lecturer Egon Pearson was hesitant in delivery but his
presentation was liberally illustrated with examples and
enlivened with allusions to the historical origins of the methods
he described. A particular feature, shared with his father, was
the use of geometrical representations to reveal the essential
structure of a problem. This was also the subject of his
presidential address to the Royal Statistical Society in 1955.

     Egon Pearson also shared with his father a deep interest in
the history of probability and statistics. In {\it Biometrika} there
was a long-running series of historical papers leading to a
volume of collected papers, edited jointly with M.G. Kendall. Two
major memoirs on his father were brought together in {\it Karl
Pearson, An Appreciation of his Life and Works}, (CUP, 1938) while
Egon's last publication, two years before his death, was an
edition of his father's lectures on {\it The History of Statistics in
the 17th and 18th Centuries}. 

     Egon Pearson's main contribution, however, owed little to
the departmental tradition but followed the arrival, in 1925, of
Jerzy Neyman (q.v.).  By that time R.A. Fisher had laid the foundation
of estimation theory and significance testing but Neyman and
Pearson felt that more account needed to be taken of alternative
hypotheses. Over the decade 1928-38 the Neyman-Pearson theory
took shape, focusing on the concept of the power of a test.
Pearson thought that the germ of this idea had been contained in
correspondence with W.S. Gossett (q.v.) but he also remarked once that
the concept of power  had come to him while looking over a farm
gate. Even to those who subscribe to other approaches to
inference, this contribution remains one of the landmarks of
statistical theory.

     The `Neyman-Pearson' theory of hypothesis testing was
launched with two {\it Biometrika} papers in 1928 running to almost 100
pages. Five years later there followed a major memoir of 48 pages
in the {\it Philosophical Transactions of the Royal Society} and a
lesser, but still substantial, paper in the {\it Proceedings of the
Cambridge Philosophical Society}. The tour de force was completed
in a three-part contribution, in 1938, to the short-lived
{\it Statistical Research Memoirs} published by the Statistics
Department at University College. These papers are included in
the {\it Joint Statistical Papers} of J. Neyman and E.S. Pearson
published  by Cambridge University Press and the University of
California Press in 1966.

     At the heart of the theory is the Neyman-Pearson lemma. This
tells us how to find the most powerful test of a simple null
hypothesis against a simple alternative. It shows that, for such
a test, the critical region has a boundary on which the
likelihood ratio is constant. The desired size of the test is
then achieved by an appropriate choice of this constant. If the
null and alternative hypotheses are indexed by a single parameter
for which a sufficient statistic exists, then the test statistic
will be a function of that statistic. If the alternative
hypothesis is composite, consisting of a set indexed by some
parameter, and if the most powerful test for any member of the
family turns out not to depend on which member is chosen, then
the same test statistic will serve for all members of the set.
In that case we have a uniformly most powerful (UMP) test.

     Unfortunately UMP tests seldom exist, and much of the theory
is concerned with how to obtain good tests in their absence. This
is particularly the case when nuisance parameters are present.
Neyman and Pearson introduced such notions as similar regions and
unbiasedness to help deal with these cases, but their lasting
practical legacy is to be seen in the so-called generalized
likelihood ratio test in which unknown parameters are replaced
by their maximum likelihood estimators. This includes, as special
cases, most of the parametric tests in use today.

     These results gave the likelihood function the central place
in testing theory, which it already had in Fisher's point 
estimation theory. It also provided a link with Neyman's later
work on interval estimation and, more generally, with Bayesian
and likelihood approaches to inference.

     A constant theme of the theoretical work of Egon Pearson and
his students was the approximation of sampling distributions
under both the null and alternative hypotheses. Often this was
done within the framework of the Pearson family of frequency
curves devised by his father. The common sampling distributions;
normal, chi-squared, $t$ and $F$, were already members and many more,
which could not be determined exactly, could be approximated by
a Pearson curve by equating moments. The provision of percentage
points for these curves as a function of their skewness and
kurtosis provided a solution of the significance testing problem
for a very large class of cases.

     On the applied side, Egon Pearson made a major contribution
to industrial statistics. This  seems to have been stimulated by
meeting W.H. Shewart (q.v.) and led to the formation by the Royal
Statistical Society of its Industrial and Agricultural Research
Section in 1933 and, most notably, in a handbook on statistical
methods in standardization (BS 600) published in 1935. Wartime
service in the Ministry of Supply gave an impetus to this
interest which continued through membership of committees of the
British Standards Institution.

     Egon Pearson's importance in the development of statistics
is to be seen, perhaps, not so much in his individual
contributions to theory and practice but in the aggregate effect
of his many-sided activities focused in the work of the
Statistics Department  at University College London. Its staff,
students and publications had, and continue to have, world-wide
influence and, significantly, Egon Pearson's leadership spanned
the period when modern statistics was born. His was not the style
of leadership exercised in the public arena but in the sustained
and meticulous attention to the work of publication, teaching and
supervision which underpins the statistical edifice. The regard
in which he was held is reflected in the honours which came his
way, most notably Fellowship of the Royal Society (1966),
President of the Royal Statistical Society (1955-7), its Guy Medal
in Gold (1955), and CBE (1946).
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\noindent{\bf Bibliographical Notes}

\noindent
Obituaries by M.S. Bartlett are given in {\it Biometrika} {\bf 68}
(1981), 1-7 and in {\it Biographical Memoirs of Fellows of the Royal
Society}, (1981), 425-443. The former is followed by an appreciation
by L.H.C. Tippett and both contain full list of publications. A
further obituary is by N.L. Johnson in {\it Journal of the Royal
Statistical Society Series A},
{\bf 144} (1981), 270-1.

\noindent
An 80th birthday tribute by P.G. Moore is in {\it Journal of the
Royal Statistical Society Series A},
{\bf 138} (1975), 129-30.

\noindent
The key publications are reprinted in {\it The Selected Papers of E.
S. Pearson}, Cambridge University Press, 1966 and {\it Joint Statistical
Papers of J. Neyman and E.S. Pearson}, Cambridge University Press
and University of California Press, 1966. Egon Pearson's own
account of the collaboration with Jerzy Neyman is in `The Neyman-
Pearson Story: 1926-34', in {\it Research Papers in Statistics,
Festschrift for J. Neyman}, ed. F.N. David, Wiley, Chichester, 1966,
1-23.

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\hfill{David J. Bartholomew}

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