# Frank Yates

### Born: 12 May 1902 in Manchester, England

Died: 17 June 1994 in Harpenden, England

**Frank Yates**'s mother was Edith Wright and his father was Percy Yates. Percy was a seed merchant as was Edith's father. Edith and Percy Yates had five children, with Frank being the eldest with four younger sisters. His interest in mathematics came early [1]:-

He was educated at Wadham House, a private school where the mathematics master was both an excellent mathematician and teacher who encouraged Frank into this direction. He obtained a scholarship to Clifton College in 1916. Four years later he was awarded a scholarship to study at St John's College, Cambridge. He graduated with First Class Honours in 1924 after doing very well at university but never looking like the outstanding scholar that he later became.An uncle's gift of a table of five-figure logarithms led to the young, precocious Yates becoming interested in mathematics.

After two years teaching mathematics in secondary schools, he decided that he wanted to put his mathematical skills to more practical use, and anyway he was tired of trying to teach people who did not want to learn, so he joined the Gold Coast Survey as mathematical advisor [2]:-

Because of ill health he decided to try to obtain a post back in England. Back in England, but before obtaining a job, he married Margaret Forsythe Marsden in Lancaster on 2 November 1929. Margaret was a chemist and the daughter of a civil servant. By chance Yates met R A Fisher and, after applying to him for a post, he was appointed assistant statistician at Rothamsted Experimental Station in August 1931. When Fisher was appointed to a chair in University College London in 1933, Yates became Head of Statistics at Rothamsted. He held this post until he retired in 1968. During the ten years from 1958 until his retirement he was also deputy director of Rothamsted.Here began a deep appreciation of Gaussian least squares, and a lifelong love of the slide rule and other aids to efficient, well-organized, and accurate arithmetic.

In 1933 Yates and his wife obtained a divorce and he married again on 14 July 1939 to Prascovie (Pauline) Tchitchkine. Pauline's father was Vladimir Choubersky who was a railway engineer, and like Yates she was divorced, having been married to Alexis Tchitchkine. Pauline died in 1976 and after this Yates married for a third time, to Ruth Hunt in 1981. Yates was 79 years old at the time but they still enjoyed 13 years of marriage; Ruth died in 1999.

Yates worked on experimental design, often collaborating with Fisher. Together they proved a longstanding conjecture on 6 × 6 Latin squares in 1934. Yates introduced the 'continuity correction' in 1934 and published an extremely important volume of statistical tables jointly with Fisher in 1936. Also in 1936 he published work on incomplete block designs which proved very influential in designing biological experiments. Yates' monograph on factorial design published in 1937 was another important publication. In a paper in the *Proceedings of the Cambridge Philosophical Society* in 1939, Yates discussed the Behrens-Fisher test of the significance of the difference of means of pairs of samples independently drawn from normal populations in which the variances are not assumed to be equal. Wilks writes that Yates indicates:-

During World War II he studied food supplies and application of fertilisers to improve crops. This was an important contribution to the war effort and led directly to the government implementing specific policies on imports. He applied his experimental design techniques to a wide range of problems such as control of pests. After 1945 he was to continue to apply his statistical techniques to problems of human nutrition.... why this test yields a smaller percentage of significant differences than would be the case for a t-test involving a pooled estimate of the variance for populations with a fixed variance ratio.

Yates published a major paper on *Systematic sampling* in the *Philosophical Transactions of the Royal Society* in 1948. Wolfowitz writes that Yates:-

In 1949 Yates was appointed to the United Nations Commission on Statistical Sampling and published... discusses various results dealing with one-dimensional systematic sampling. No fully reliable estimate of the sampling error can be obtained from the observations themselves, except that, under certain circumstances, the sum of sets of terms taken alternately positive and negative provides a reasonably satisfactory estimate(which is usually an overestimate). The method of "partial systematic samples," based on short sections of completely enumerated sequences, is proposed for estimating the systematic sampling error.

*Sampling Methods for Censuses and Surveys*[1]:-

A survey Yates wrote in 1951 on the design of experiments... a work which did much to establish sound principles and technical terminology.

*Quelques développements modernes dans la planification des expériences*discussed topics such as: factorial experiments, including a discussion of the weighing problem; the theory of confounding in factorial experiments; fractional replications; split plot designs; balanced and partially balanced incomplete block designs; lattices; lattice squares; and quasi-Latin squares.

Yates became an enthusiastic user of computers writing:-

In 1954 he purchased a computer to assist with the statistical analysis to the data at Rothamsted. He was one of the people who were influential in establishing the British Computer Society, and he was president of the Society in 1960-61. In his Presidential Address Yates pointed out that, as well as making the impossible possible, computers provided speed, thoroughness and a fairly complete mechanisation of techniques for work which would previously have been done by hand. The last of these, Yates suggested, is particularly important for specialists such as biologists. He went on to say that the reluctance of statisticians to use computers was vanishing and they were carrying out computations which were previously impossible, or almost impossibly time consuming to do by conventional methods. Yates remarked that most of the calculations which were possible by hand calculation were still being done that way, probably because no code had been written and made available. He encouraged people to write code to solve standard statistical problems, and emphasised that it should be code which was machine independent.... to be a good theoretical statistician one must also compute, and must therefore have the best computing aids.

Yates was an extremely good Departmental Head. In the address at his memorial service his style in this role was talked about:-

After he retired, he became Senior Research Fellow at Imperial College, London. There he did some lecturing for the first time in his career, without having a great deal of success. In [3] his lecturing is described as follows:-Frank Yates's method of managing his department was a remarkable one, in that it was totally invisible. There were almost no rules, apart from that which insisted that no scientific paper left the department without being read, and usually greatly improved, by him.

The Royal Society of London, to which he was elected in 1948, awarded him their Royal Medal in 1966 in:-He was not an ideal lecturer, for he lacked concern for comprehensive formal presentation and preferred to talk about general ideas.

He was also a member of the Royal Statistical Society and received their Guy medal in 1960. He was president of the Society in 1967-68.... recognition of his profound and far-reaching contributions to the statistical methods of experimental biology.

**Article by:** *J J O'Connor* and *E F Robertson*

**February 2005**

**MacTutor History of Mathematics**

[http://www-history.mcs.st-andrews.ac.uk/Biographies/Yates.html]