# Yule, G. Udny

# Yule, G. Udny

George Udny Yule (1871-1951), British statistician, was the only child of Sir George Udny Yule, an Indian civil servant, and the nephew of Sir Henry Yule, a distinguished Orientalist and traveler. He was educated at Winchester and at University College, London, where he graduated in engineering in 1892. Feeling that engineering was not his metier, he tried experimental physics and spent a year at Bonn in research under Hertz on electric waves in dielectrics. Yule’s first four published papers, in fact, dealt with this subject. But physics also failed to hold his interest. In his mature work there is little evidence of his background, except at the end of his life, when the philological gifts of his family became manifest in his studies of literary vocabulary.

When Yule returned to London in 1893, Karl Pearson was beginning to form his famous statistical unit at University College. Having known Yule as a student and divined something of his talents, Pearson offered him a demonstratorship (a kind of junior lectureship), which Yule promptly accepted. He held this post for six years, but the salary was scarcely a living wage, and in 1899 he resigned to earn his bread and butter as secretary to an examining body in London. His separation from University College, however, was more formal than real: in particular he gave, from 1902 to 1909, a series of lectures that formed the basis of his *Introduction to the Theory of Statistics* (1911). This rapidly diffused his reputation throughout the scientific world; 50 years later, after two revisions by M. G. Kendall, it was still a standard text.

In 1912 the University of Cambridge decided to create a lectureship in statistics. Yule was offered the lectureship and accepted it. Apart from the interruption of World War i (during which he acted as director of requirements at the Ministry of Food), he spent the rest of his life at St. John’s College, Cambridge. He was promoted from lecturer to reader (the equivalent of the American assistant professor) and continued as reader until his retirement in 1930. At that point he was physically fit enough to learn to fly, but shortly afterward he was grounded and, indeed, virtually confined to college by a partial heart block. After some years of relative inactivity he took a new lease on life, producing in 1944 his *Statistical Study of Literary Vocabulary;* but his health continued to decline, and he died of heart failure in 1951.

Honors came to him in a steady stream. He received the gold medal of the Royal Statistical Society in 1911, was elected a fellow of the Royal Society in 1922, and was president of the Royal Statistical Society from 1926 to 1928. He was also elected to various foreign societies, and his *Introduction to the Theory of Statistics* was translated into several languages.

Yule’s contributions to the development of theoretical statistics were extensive and profound. They may be classified into four main groups, corresponding roughly in time to his period in London (1893-1912), the war interval (1913-1919), his heyday at Cambridge (1920-1931), and his final studies (1938-1946).

When Yule joined Pearson in 1893, the science of statistics as it became known in the middle of the twentieth century scarcely existed. Pearson was beginning his series of memoirs on frequency curves and on correlation. The practical applications of this work lay mainly in biology, and he made occasional forays into social medicine. Yule was an ideal complement. He took the theory of correlation, then in a rather elementary state, and in two basic memoirs (1897 and 1907) laid the foundations of the theory of partial correlation and of linear regression for any number of variables *[see*multivariate analysis, *articles on*correlation]. Yule’s method almost immediately became standard practice. Characteristically, Yule’s theoretical studies of regression were accompanied by practical studies, notably on the relationship between pauperism and outrelief (i.e., relief given outside institutions by local authorities).

From problems of relationships among measurable variables Yule was led to the parallel problems among attributes—i.e., those qualities that form the basis of classification on a nonmeasured basis, such as sex, inoculation against disease, or eye color. This in turn led him to revive Boole’s logic of class frequencies (1901) and to develop a theory of association, culminating in a fundamental paper (1912). The work was illustrated by studies of smallpox and vaccination. These interests led to the formation of a lifelong friendship with the epidemiologist Major Greenwood. Their joint work on the interpretation of inoculation statistics (1915), now almost a textbook commonplace, was a landmark in medical statistics.

Yule’s second period, 1913-1919, short as it was, produced two basic papers in collaboration with Greenwood. In the first (1917), Yule produced a theoretical scheme to account for the so-called negative binomial distribution, for which fresh applications were still being discovered nearly 50 years later. In the second (1920), the authors discussed compound distributions, with particular reference to industrial accidents. In the light of later elaborations these early attempts seem simple. But the simplicity is that of genius, and if it is the first step that counts, Yule must be credited with a great many first steps. The 1917 paper contains the beginnings of what in later hands became an important class of stochastic processes.

The third period saw the full exercise of Yule’s abilities. Some earlier studies in Mendelian inheritance emerged in a mathematical theory of evolution (1924), which attracted no attention from geneticists but introduced some J-shaped frequency distributions that later proved of great interest in other subjects. Likewise, his interests in vital statistics, a subject on which he lectured for many years, culminated in a paper (1925) on the growth of population and the factors that control it. His greatest work, however, undoubtedly lay in his papers on time series (1926; 1927).

In his earlier work on correlation Yule had been puzzled by the high correlations that were noted between unrelated quantities observed over a course of time. For example, suicide rate was highly correlated with membership in the Church of England, and more recently, in the same category, there has been observed in Sweden a remarkable correlation between the fall in birth rate and the decline in the population of storks. Yule called these “nonsense-correlations” and successfully set out to explain them. Incidentally, in so doing, he frightened economic statisticians off correlation analysis for two or three decades. He then proceeded to discuss time series in terms of their internal correlations, devising the correlogram for the purpose. In his papers on sunspots, he effectively laid the basis of what is known as the theory of “autoregressive” time series *[see* Time series]. In later hands this has developed into a large and complicated subject, but no one has ever surpassed Yule’s peculiar blend of insight, theoretical analysis, and insistence on practical application.

His illness over the years 1931-1938 prevented the publication of any serious research. Toward the end of that period, however, he became interested in the statistical characteristics of prose style, with particular reference to questions of disputed authorship. His earlier work concerned sentence length, but he later turned to noun frequency. The master had not lost his touch: once more his work formed the basis of extensive further research by others, and his technique was applied in such an unrelated field as bacteriology. But he himself had finished and, as his health steadily failed, set himself to wait for the end, which came in his 81st year.

Yule’s outstanding contribution to statistics results not so much from any one quality as from his combination of qualities. He was not a great mathematician, but his mathematics was always equal to the task. He was not trained in economics or sociology, but his wide knowledge of human relationships enabled him to write with insight on both subjects. He had the precision, the persistence, and the patience of a true scientist but never lost sight of the humanities. He was a kindly, genial, highly literate, approachable man who refused to embroil himself in the controversies that mar so much of statistical literature. Above all, he had the flair for handling numerical data that characterizes the truly great statistician.

M. G. Kendall

[For *the historical context of Yule’s work, see the biography of*pearson. *See also*linear hypotheses, *article on*regression; statistics, Descriptive, *article on*association.

## WORKS BY YULE

*There is no collected edition of Yule’s works. A complete bibliography is given in* Kendall 1952.

1897 On the Significance of Bravais’ **Formulae for Regression &c.,** in the Case of Skew Correlation. Royal Society of London, *Proceedings* 60:477-489.

1901 On the Theory of Consistence of Logical Class-frequencies, and Its Geometrical Representation. Royal Society of London, *Philosophical Transactions* Series A 197:91-133.

1907 On the Theory of Correlation for Any Number of Variables, Treated by a New System of Notation. Royal Society of London, *Proceedings* Series A 79: 182-193.

(1911) 1958 *An Introduction to the Theory of Statistics.* 14th ed., rev. & enl. London: **Charles Griffin. → M. G. Kendall** has been a joint author since the eleventh edition, 1937. The two most recent editions were revised by Kendall.

1912 On the Methods of Measuring Association Between **Two Attributes.** *Journal of the Royal Statistical Society* 75:579-652. → Contains ten pages of discussion.

1915 Greenwood, Major; and Yule, G. Udny The Statistics of Anti-typhoid and Anti-cholera Inoculations, and the Interpretation of Such Statistics in General. Royal Society of Medicine, Section of Epidemiology and State Medicine, *Proceedings* 8, part 2:113-194.

1917 Greenwood, Major; and Yule, G. Udny On the Statistical Study of Some Bacteriological Methods Used in Water Analysis. *Journal of Hygiene* 16:36-54.

1920 Greenwood, Major; and Yule, G. Udny An Inquiry Into the Nature of Frequency Distributions Representative of Multiple Happenings With Particular Reference to the Occurrence of Multiple Attacks of Disease or of Repeated Accidents. *Journal of the Royal Statistical Society* 83:255-279.

1924 A Mathematical Theory of Evolution, Based on the Conclusions of Dr. J. C. Willis, F. R. S. Royal Society of London, *Philosophical Transactions* Series B 213: 21-87.

1925 The Growth of Population and the Factors Which Control It. *Journal of the Royal Statistical Society* 88:1-58.

1926 Why Do We Sometimes Get Nonsense-correlations Between Time-series?—A Study in Sampling and the Nature of Time-series. *Journal of the Royal Statistical Society* 89:1-64.

1927 On a Method of Investigating Periodicities in Disturbed Series, With Special Reference to Wolfer’s Sunspot Numbers. Royal Society of London, *Philosophical Transactions* Series A 226:267-298.

1944 *The Statistical Study of Literary Vocabulary.* Cambridge Univ. Press.

## SUPPLEMENTARY BIBLIOGRAPHY

Kendall, M. G. 1952 G. Udny Yule 1871-1951. *Journal of the Royal Statistical Society* 115:156-161. → Contains a complete bibliography.

Yates, F. 1952 George Udny Yule 1871-1951. Volume 8, pages 309-323 in Royal Society of London, *Obituary Notices of Fellows.***Cambridge: The Society. → Contains a bibliography on pages 320-323.**

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