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\noindent{\bf George Udny YULE}\\
b. 18 February 1871 - d. 26 June 1951
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\noindent{\bf Summary.} Yule's coefficient of association, Yule's paradox
(later called Simpson's paradox) and the Yule process all perpetuate the name of a pioneer
statistician who also contributed to Mendelian theory and time-series
analysis.
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George Udny Yule was born in Beech Hill, near Haddington, Scotland. He
came from an old-established family of army officers,
civil servants and orientalists. Both his father and his uncle had been
knighted. He was educated at Winchester College from where, at the age
of only 16, he transferred to University College, London, to study
engineering. Karl Pearson (q.v.), then Professor of Applied Mathematics, was
beginning to develop his own interest in statistics, and in 1892 offered
Yule a post as demonstrator. In 1896 Yule was appointed Assistant Professor
of Applied Mathematics, a post he held for three years until he resigned it
in favour of more remunerative employment.

His continuing interest in statistics, however, led to his appointment as
Newmarch Lecturer in Statistics at University College in 1902, a post which
he held concurrently with his other work until 1909 and which led to the
publication of the book which made his name, {\it An Introduction to the Theory
of Statistics}. The first edition appeared in 1911 [4] and during his
lifetime there were thirteen further editions. The eleventh edition was the
first to be jointly undertaken with M.G. Kendall [7], and by the time of the
fourteenth and last edition of Yule and Kendall, 1950, Kendall's own
two-volume {\it The Advanced Theory of Statistics} was already establishing
itself. It, and its present-day descendants, still bear the marks of Yule's
pioneering effort.

In 1912 a Lectureship in Statistics was established for Yule by the
University of Cambridge, to be held in the Faculty of Agriculture, and
this, coupled with a Fellowship at St John's College from 1922, provided
him with congenial employment (save for the war years) until 1931 when he
retired, by then Reader in Statistics. At that stage he bought an
aeroplane and learnt to fly. He kept up his College teaching
until the second war, and died in Cambridge in 1951.

A major topic of Yule's early statistical work was pauperism, and he
concentrated on the way administrative reforms reduced observed rates.
He distanced himself from standard eugenic interpretations.

Yule played an important part in the affairs of the Royal Statistical
Society, of which he was honorary secretary for twelve years and
subsequently President (1924-26). He was elected a Fellow of the Royal
Society in 1922.

Yule's main contributions in the theoretical field were concerned with
regression and correlation, association in contingency tables, Mendelian
genetics, epidemiology and time series. In the Pearsonian fields of
regression and correlation he gave more prominence than his mentor to the
former, perhaps easing the path towards R.A. Fisher's (q.v.) invention of the
analysis of variance.

Yule's studies of the correlation of continuous variables led him, in 1900
[1], to study measures of association for discrete variables, in particular
the cross-ratio $c$ (``odds ratio") in a $2\times2$ contingency table and its
transform $Q = (1-c)/(1+c)$, now known as ``Yule's coefficient". This led to
an altercation with Pearson in which Pearson's capacity for acrimonious and
ill-directed criticism was displayed, in marked contrast to Yule's gentler
mode of expression. Even Fisher, who as a young man had also felt the
sharpness of Pearson's pen, was later moved to remark ``Pearson attacked
Yule's work at one time much more violently than ever he did mine". In 1903
[3] Yule, making use of his understanding of partial correlation, described
what was much later to be termed ``Simpson's paradox", in which the pairwise
associations at two levels in a $2\times2\times2$ table can be seemingly incompatible
with the marginal association. In his work on association, all his
numerical examples were drawn from biology.

In Mendelian genetics, Yule [2] was the pioneer in suggesting that the
observed correlations between parent and offspring could be accounted for
by multifactorial Mendelian inheritance, as Fisher fully acknowledged in
his classic treatment of the correlation between relatives in 1918.
In 1914, in collaboration with F.L. Engledow, Yule invented the method of
minimum $\chi^2$ for estimating a genetic recombination fraction, and the
following year, with M. Greenwood, he was the first to recognize that there
was something wrong with Pearson's $\chi^2$ test of association in respect of
the degrees of freedom used, as Fisher was later to prove. He introduced
the simple birth process of stochastic theory (the ``Yule process") in
connection with evolution in 1924 [5]. He also introduced the correlogram
of a time series and laid the foundations of the theory of autoregressive
processes. His name is remembered in the ``Yule-Walker equations" which provide
least squares estimators of the parameters of an autoregressive process.

F. Yates ended his Royal Society obituary notice of Yule with
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``We may ...
justly conclude that although Yule did not fully develop any completely new
branches of statistical theory, he took the first steps in many directions
which were later to prove fruitful lines for further progress. ... In the
biological field ... his work provided a corrective to many of the errors
committed by the biometric school, and served to spread the use of
statistical methods amongst biologists who might otherwise have been wholly
repelled by them. He can indeed rightly claim to be one of the pioneers of
modern statistics".
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\noindent{\bf References}

\noindent
[1] Yule, G.U. (1900). On the association of attributes in statistics: with
illustrations from the material of the Childhood Society, \&c. {\it
Philosophical Transactions of the Royal Society of London
(A)}, {\bf 194}, 257-319.

\noindent
[2] Yule, G.U. (1902). Mendel's Laws and their probable relations to
intra-racial heredity. {\it New Phytologist}, {\bf 1}, 193.

\noindent
[3] Yule, G.U. (1903). Notes on the theory of association of attributes in
statistics. {\it Biometrika}, {\bf 2}, 121-134.

\noindent
[4] Yule, G.U. (1911). {\it An Introduction to the Theory of Statistics}.
Griffin, London.

\noindent
[5] Yule, G.U. (1924). A mathematical theory of evolution, based on the
conclusions of Dr J.C.Willis. {\it Philosophical Transactions of the
Royal Society of London (B)}, {\bf 213}, 21.

\noindent
[6] Yule, G.U. (1927). On a method of investigating the periodicities of
disturbed series, with special reference to Wolfer's sunspot numbers.
{\it Philosophical Transactions of the Royal Society (A)}, {\bf 226}, 267-298.

\noindent
[7] Yule, G.U. and Kendall, M.G. (1937). {\it An Introduction to the Theory of
Statistics}. Griffin, London.
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\noindent{\bf Bibliography}

\noindent
Yule, G.U. (1971). {\it Selected Papers of George Udny Yule}. A. Stuart and
M.G. Kendall (eds.). Griffin, High Wycombe. (This contains, in
particular, a reprinting of Kendall's obituary article from {\it
Journal of the Royal Statistical Society, Series A}
{\bf 115}(1952), 156-161.)
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\hfill{A.W.F. Edwards}

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