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William Gemmell Cochran
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Rutherglen, Scotland
Orleans, Massachusetts, USA
Biography
William Cochran was the son of Thomas Cochran (1875-1943) and Jean Willock Gemmell (1878-1949), known as Jeannie. Thomas had been born in Camlachie, Glasgow, on 21 June 1875, the son of Oliver Cochran and Isabella Coventry Duncan. In the 1891 Scottish Census, Thomas is living with his parents at 18 Union Place, Rutherglen, Lanarkshire, Scotland and is working as a railway clerk. Thomas was the eldest of his parents seven children, with siblings Oliver (age 13), John (age 12), Isabella (age 10), Alexander (age 7), David (age 3) and Andrew (age 2). Jeannie had been born in Bridgeton, Glasgow, on 15 June 1878, the daughter of William Gemmell and Jane Willock. Thomas and Jeannie were married at the Royal Institute of Fine Art, Blythswood, Glasgow on 29 June 1906. They had two sons, Oliver Cochran, born in Rutherglen on 24 February 1908 and William Gemmell Cochran, the subject of this biography, born in Rutherglen on 15 July 1909. William Cochran was known as Willie to his family but later in life was known as Bill to his friends and colleagues.Oliver Cochran provided information about his brother's childhood for the biography [45]:-
Oliver has colourful recollections of their childhood. At age five, Willie (pronounced Wully), as he was known to family and friends, was hospitalised for a burst appendix, and his life hung in the balance for a day. But soon he was home, wearying his family with snatches of German taught him by a German patient in his nursing-home ward. Willie had a knack for hearing or reading something and remembering it. Oliver recalls that throughout his life, Willie would walk or sit around reciting poems, speeches, advertisements, music hall songs, and in later life oratorios and choral works he was learning.His childhood was happy but the family lived in difficult conditions. Their home had only one bedroom which the parents slept in, and the two boys had to sleep in a room which was also where the family cooked and ate. He had to walk over a mile to his local school, doing that walk four times a day since he came home for lunch. When he was sixteen years old the family moved to a better home and life became easier. Cochran won many prizes when at school, not only mathematics prizes and medals but also prizes in his other subjects. He was highly competitive and always aimed to be first. He attended Gourock High School and Glasgow High School, winning the mathematics medal from both, the first in 1924 and the second in 1927 [45]:-
Willie had no absorbing hobbies as a boy, although he dabbled in many things. Cycling, hiking, and walking in the hills were his chief physical activities. Later, studying and reading became primary. His scholastic prowess won him many books as prizes and created an extensive home library.Cochran took the University of Glasgow Bursary Competition in 1927 and he was placed first. This Competition was open to all pupils in Scotland and required students to take papers in a wide variety of subjects; Cochran took papers on English, Latin, mathematics, natural philosophy (as physics was called at that time, and still was when I [EFR] was a student in Scotland in the 1960s), and chemistry. The award of a bursary allowed him to take his first degree at the University of Glasgow which certainly would not have been possible without this financial support. He was awarded an M.A. in mathematics and physics in 1931. It was, and still is, the tradition that Scottish universities award an MA as a first degree where English, and other, universities award a B.A. He won the Logan Medal for the best student in the Faculty of Arts and won the George A Clark Scholarship to study mathematics at Cambridge. This scholarship had been funded by George Aitken Clark (1823-1873), a Scottish manufacturer; it was awarded by the University of Glasgow and funded four years of study. Cochran was accepted to study the mathematical tripos at St John's College Cambridge.
At Cambridge he took the standard tripos courses, attending lectures by G H Hardy and Abram Besicovitch as well as having Ebenezer Cunningham, Max Newman and Sydney Goldstein as advisors at St John's College. He also chose, as an elective course, John Wishart's course in mathematical statistics, then proceeded to take a practical course in the School of Agriculture. Although Cochran was renowned as a very hard worker, he did find time at Cambridge to have other interests. He [85]:-
... was a member of the St Johns Music Club, sang in the choir, and attended concerts.He also played badminton once a week with Anton Hales (1911-2006), a fellow mathematical tripos student who became a leading geophysicist. They always followed their game with tea and oatcakes.
Cochran was a Wrangler (First Class student) in the 1933 Mathematical Tripos and continued studying at Cambridge for a doctorate. His first two papers, published in 1934, show the influence of two of his lecturers, namely Goldstein and Wishart. The first of the two papers, The flow due to a rotating disc, was influenced by Goldstein and considers the steady motion of an incompressible viscous fluid due to an infinite rotating plane lamina. The other 1934 paper The distribution of quadratic forms in a normal system, with applications to the analysis of covariance contains what today is known as "Cochran's Theorem". It has the following Abstract:-
Many of the most frequently used applications of the theory of statistics, such for example as the methods of analysis of variance and covariance, the general test of multiple regression and the test of a regression coefficient, depend essentially on the joint distribution of several quadratic forms in a univariate normal system. The object of this paper is to prove the main-relevant results about this distribution. As an application of these results, the theory involved in the method of analysis of covariance will be investigated.Frank Yates writes about this paper in [90]:-
Although elegant mathematically, it is perhaps doubtful whether his results were of much practical value; certainly, as Cochran himself recognised in his paper, they did nothing to resolve the question of exact tests of significance in analyses of covariance, which had been bothering Wishart, and which was the practical motivation for the paper.In 1934 R A Fisher left Rothamsted Experimental Station to accept the Galton chair at University College, London and Frank Yates became head at Rothamsted. Cochran was offered the vacant post but he was still not finished his doctoral course at Cambridge. Yates later wrote (see [85]):-
... it was a measure of good sense that he accepted my argument that a PhD, even from Cambridge, was little evidence of research ability, and that Cambridge had at that time little to teach him in statistics that could not be much better learnt from practical work in a research institute.Cochran accepted the post at Rothamsted where he worked for five years on experimental designs and sample survey techniques. During this time he worked closely with Yates. He also had the chance to work with Fisher who was a frequent visitor to Rothamsted. Yates writes [90]:-
Cochran came to Rothamsted at an opportune time. Fisher's new ideas on experimental design and analysis, which had been developed in the 1920s and with which I was particularly involved in my work at Rothamsted, were finding increasing recognition at other research institutes, both in the United Kingdom and overseas. Cochran worked closely with me in their further development and in their application to the research problems of Rothamsted, and through our association with agronomic research workers in overseas dependencies to the problems of tropical agriculture.At Rothamsted, Cochran met Betty Irene May Mitchell (1910-2002) who was an entomologist. Betty had been born in Beckenham, Kent, the daughter of Forbes Tarrant Mitchell, a Carpet Warehouseman, and his wife Alice May Dance. On 17 July 1937, Cochran married Betty at St Columba's Church of Scotland, Pont Street, London; they lived at 70 Luton Road, Harpenden, Hertfordshire. William Cochran sailed from Southampton to New York on the Normandie, departing 5 October 1938. He was on his way to the Iowa Statistical Laboratory, in Ames, Iowa, which had been established at the Iowa State College in 1933 by George W Snedecor. Snedecor had already published two works which would become classics, Calculation and Interpretation of Analysis of Variance and Covariance (1934) and Statistical Methods (1937). Cochran travelled alone to the United States since his wife was expecting their first child. On 26 October 1938 the Cochrans' first child was stillborn at the Nursing Home in Harpenden. Betty Cochran went to join her husband at Ames, sailing from Southampton to New York on the Aquitania arriving on 9 December 1938.
Cochran and his wife left the United States sailing from New York on the ship Washington to Plymouth, England arriving on 25 January 1939. He had already agreed to return to the University of Iowa to teach during the 1939-40 academic session but as an imminent war seemed increasingly impossible to avoid, he felt that leaving Europe at such a time was not the right thing to do. Torn between breaking his promise to Iowa or leaving his country at a critical time, he eventually decided that he must keep his promise. Before leaving Britain, the Cochrans went to Glasgow to visit Cochran's relations. William and Betty Cochran sailed on the ship Montrose from Greenock, Scotland to Quebec, Canada departing on 26 August 1939. They gave their UK address as 11 Hampden Terrace, Glasgow. While at Ames, the Cochrans' two children were born; Elizabeth (born 25 April 1940) and Alexander Charles (born 24 April 1942).
From autumn 1939, with a permanent position of professor at Ames, Iowa, Cochran's task was to develop the graduate programme in statistics within the Mathematics Department. His first two lecture courses were on sample surveys and experimental design. These would be developed over the following years until they formed the basis of his two classic books.
For extracts from reviews of Cochran's books see THIS LINK.
Richard L Anderson (1915-2003), who became a professor of statistics at North Carolina State University and the University of Kentucky, writes [2]:-
Professor Cochran's lectures were gems of clarity, conciseness and rigour, interspersed with many real-world examples. In addition, he was a fountain of information on how to tackle seemingly insolvable problems. When he came to Iowa State, I was well on my way with research on the distribution of the serial correlation coefficient. One day in the winter of 1940, I presented my up-to-then results to the seminar we often held after tea; the distribution theory (based on characteristic functions) was so complicated that closed-form solutions seemed intractable for . The next morning I found on my desk a short note from W G C, which went something like this: "I believe you might find my article on the distribution of quadratic forms helpful." This referred to Cochran's Theorem, published in 1934. I suppose what he really meant was that if I had stayed awake in class, I would have tried it out before then. In any event Cochran's Theorem was the solution to all my problems.Frank Yates writes [90]:-
Cochran's appointment to Iowa State greatly furthered the spread of sound experimental techniques in agriculture and biology in America. For the first time he was involved in teaching and rapidly showed his abilities in this direction. His stay at Ames saw the genesis of his book on experimental design and analysis, in collaboration with Gertrude Cox, who had already been collecting examples illustrating the Fisherian techniques. This was eventually published in 1950 and rapidly became the standard textbook on the subject. He also did much to popularise the use of quasi-factorial and lattice designs for varietal trials and published a number of papers on them.Geoffrey S Watson (1921-1998) quotes Alexander McFarlane Mood's thoughts on Cochran in [85] [Note: Mood (1913-2009) was a statistical consultant and professor at Iowa State for many years and received several awards for his work in statistics]:-
Almost from the day he arrived [at Ames] [Cochran] was the pre-eminent statistical consultant in the U.S. He was marvellous at it and to my judgment in a class by himself. No one else had the breadth of experience with data from so many fields of statistical investigation; no one else had such universal knowledge of statistical techniques; probably no one else was such a comprehensive reader of statistical journals. ... The courses at Ames, although taught in the mathematics department, were quite unmathematical. Somehow, people introduced to statistics by Snedecor's book developed very good insights as to how to partition, purely arithmetically, sums of squares associated with very elaborate designs. Even the advanced sampling and design courses used essentially no mathematics or probability theory or mathematical statistics.In Yates' quote above, he writes of Cochran's collaboration with Gertrude Cox. Let us quote Cochran's own thoughts on this from [19]:-
Gertrude and I were on the faculty of the Statistical Laboratory at Iowa State College during the years 1938-40. ... In 1940 she had a paper in the 'Annals' on the construction of balanced incomplete blocks, and we had a joint paper with R C Eckhardt on lattices and triple lattices. She was also assembling her series of typed, mimeographed notes on standard designs. Each note indicated the kind of experiment for which the design was suitable and gave an example of its use, with the arithmetic needed to do the analysis and summarise the results. These notes led to the book 'Experimental Designs', published in 1950. I don't remember when or how we decided to write a book; the suggestion may have come from Walter Shewhart, who was then advising Wiley's on a series of books on statistics. Our division of labour was easily agreed upon. Since Gertrude disliked the job of writing even more than I did, she took responsibility for the experimental plans, and I took primary responsibility for the descriptive text and any hidden theory.In 1943 Cochran was seconded to Samuel Wilks' research team at Princeton where he was involved in war work examining probabilities of hits in naval warfare. By 1945 he was working on bombing raid strategies. Anderson writes in [19]:-
In 1945 he was asked to serve on a select team of statisticians to evaluate the efficacy of the World War II bombing raids. This was only the first of many blue-ribbon committees on which he was to serve. Cochran was instrumental in persuading me to join the Princeton group. I remember with pleasure the Sunday afternoon teas at the Cochran-Mood residence; the two families occupied one of Princeton's huge houses. It was there that I discovered that Cochran was an excellent badminton player. I could never understand how a man could be so good at badminton and so terrible at tennis. Later I was to discover in Raleigh that he and Betty were also barn-dance enthusiasts.Cochran joined the newly created North Carolina Institute of Statistics in 1946, again to develop the graduate programme in statistics. The Cochrans' third child, Theresa, was born in North Carolina in 1946. While at North Carolina, Cochran was on the Organising Committee which set up the Biometric Society. He wrote in [17]:-
In the founding of the Biometric Society, a wise decision was taken to regard biometry as roughly synonymous with quantitative biology and as a discipline requiring the cooperation of biologists, mathematicians, and statisticians. ... The Biometric Society has the opportunity to play an important role in the future development of biometry. [The] reminder that our society is an experiment in cooperation, and one where success will be difficult to attain, is wise. I hope that the scope of the Society will continue to be conceived broadly and that biologists and mathematicians will have their share of responsibility in determining our future activities. Finally, I hope that we will set an example in international cooperation.From 1949 until 1957 he was at Johns Hopkins University in the chair of biostatistics. Here he was more involved in medical applications of statistics rather than the agricultural application he had studied earlier. From 1957 until he retired in 1976 Cochran was at Harvard. His initial task was to help set up a statistics department, something which he had a great deal of experience with by this time. He had almost become a professional at starting statistics within universities in the USA.
Writing about graduate training in statistics, he writes [15]:-
... that statistics depends primarily on mathematics and mathematicians for its future development. Anyone interested in the progress of statistics cannot but hope that able young mathematicians will continue to be attracted into this field, which offers a wide range of useful and stimulating applications. Such mathematicians need not be regarded as lost or strayed from the fold. For while statistics has as yet contributed relatively little to repay its debt to mathematics, it is to be expected that new points of view and new problems arising in mathematical statistics will in course of time enrich the body of mathematical knowledge itself.Cochran's books became classics and were widely used by scientists in many different disciplines. We present extracts from 74 reviews of his books at THIS LINK.
In particular, Contributions to statistics (1982) contains over 100 research papers by Cochran and the reviews of this book give a good overview of the range of his contributions; see THIS LINK.
The authors of [29] write about Cochran's abilities as a teacher:-
Cochran made friends easily and travelled widely. He was a gifted teacher, noted for the clarity, individuality, and carefulness of his lectures. He could be gruff in his rejoinders to students whose work fell below his high standards, but he was patiently encouraging, too. He was very much loved and revered for helping students and colleagues make substantial progress on seemingly intractable problems. His 40 or so PhD students include many leading applied statisticians. Several hundred admiring friends and associates from the world over attended his retirement banquet at the Harvard Club in Boston in 1976.Barry Margolin writes [63]:-
Cochran possessed a particular gift for absorbing, synthesising, summarising and interpreting new statistical work, and a rare ability to communicate with practicing statisticians and other users of statistics; this is reflected in the more than one dozen expository papers that he wrote, reviewing advances in statistics and discussing the resultant changes in training needs for professional statisticians.Cochran did much to promote statistics within the USA. Anderson in [2] sums up Cochran's contribution as follows:-
Cochran was that rarity, a man with both a keen mind and the desire to use it for the benefit of mankind. His office was always open to the struggling student, nonplussed scientist, or inquiring citizen. We who were benefitted by him offer our sincere thanks. To Betty and the children one can only say that the world is a better place because he was in it for a while.The authors of [45] write:-
Personally, Bill was an unpretentious man with Scottish wit and humour. He was a believer in the fellowship of man, and one of the few things sure to elicit his anger was a bigoted comment. Although he preferred to work by himself rather than to collaborate with others, he was friendly to everyone and liked by all. He and his wife Betty, to the delight of colleagues and students, entertained frequently, and enjoyed square dancing, theatre, music, and travel. Hundreds of statisticians from far-flung places attended Bill's retirement dinner in 1976. The last several years of Bill's life were plagued with a series of medical problems. Nonetheless, after his retirement and his move to his Cape Cod home, he continued to travel, to teach, and to write.Cochran received many honours and awards for his outstanding contributions. He held a Guggenheim Fellowship in 1964. He served as President of the International Statistical Institute, the American Statistical Association, the Institute of Mathematical Statistics, and the Biometric Society. The Royal Statistical Society elected him an honorary fellow in 1959 and he was elected to the National Academy of Sciences in 1974. In 1967 he was awarded the S S Wilks Medal of the American Statistical Association. Although he never completed his doctorate at Cambridge, he was awarded honorary doctorates from the University of Glasgow and Johns Hopkins University.
He died in Cape Cod Hospital in Hyannis, Massachusetts.
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Written by J J O'Connor and E F Robertson
Last Update September 2020
Last Update September 2020