# Charles Frederick Mosteller

### Born: 24 December 1916 in Clarksburg, West Virginia, USA

Died: 23 July 2006 in Falls Church, Virginia, USA

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**Frederick Mosteller**was known to his friends and colleagues as Fred. His parents were William Roy Mosteller and Helen Kelley. William, from Williamsport, Pennsylvania, started working as a glass blower but gave this up during World War I and became a road builder. He was an intelligent man, but had only a couple of years of high school education. Helen, from Ladoga, Indiana, was keen on education and, after the family moved to the Pittsburgh area when Fred was a baby, she worked as a clerk. Later she became a fulltime housewife caring for the family but still did bookkeeping for the family company.

When Fred was six years old he began attending McNair Elementary School. He was left-handed but his teacher persisted in forcing him to write with his right hand. Beginning school was the first time he had mixed with other children and, probably as a consequence, he went down with all the childhood illnesses one after the other. He missed so much through illness that he began the first grade for a second time. He did not enjoy his first few years at school, performing poorly, but he loved reading and went with his mother to the local library to choose books. His mother tried hard to teach him so that he would perform better at school but it had little effect. He had poor eyesight but hid the fact and it was only discovered when he was ten years old. Changing schools his academic performance slowly improved but he went though a difficult time when his parents divorced following which he continued to live with his mother. After a while they moved to Williamsport to live with Hiram Dangle, Fred's uncle.

Another move, this time to Delaware, saw Fred attend high school there for a year. He became keen on debating but a move to Pittsburg saw him enter Schenley High School where he was taught by a number of outstanding teachers. At this time he became an enthusiast for chess and was a founder member of the Schenley High School chess club which was very successful in competitions. The move to Pittsburg saw him back in contact with his father and he worked during the summers for his father's road construction firm. He won a scholarship to the Carnegie Institute of Technology (now Carnegie Mellon University) and took a broad selection of courses. In his first year he studied engineering drawing, descriptive geometry, English and practical courses which included masonry, carpentry, sheet metal working and welding. In his second year he took courses on calculus, mechanics, French, quantitative analysis, and physical measurements. It was in this last mentioned course that he encountered statistics for the first time. The area of mathematics which he found most interesting was combinatorics, and because of this he approached Edwin Olds, a statistician at the Carnegie Institute. Olds directed Mosteller's interests towards statistics. At this stage he was living with his mother in Williamsport and travelling to the Institute. On these journeys he met Virginia Gilroy, a fellow traveller, and they became good friends. Mosteller graduated from the Carnegie Institute with a B.S. in 1938 and remained there for the academic year 1938-39 undertaking graduate studies. He began working on a Master's thesis on rank correlation coefficients advised by Olds.

Around Christmas 1938 Mosteller was advised to attend a meeting of the Institute of Mathematical Statistics in Detroit. There he attended a talk by William Cochran and met other statisticians such as Samuel Wilks and Harold Hotelling. He discussed with Wilks the possibility of working for his doctorate at Princeton and, after the award of his M.S. in 1939, he went to Princeton having been awarded funds to cover his expenses in return for assisting Wilks edit the

*Annals of Mathematical Statistics*. At Princeton he studied first for a Master's Degree and, in the summer of 1941 before the award of the degree, he married Virginia Gilroy; they had two children, William born in 1947 and Gale born in 1953. Mosteller was awarded an A.M. from Princeton in 1942 and continued to undertake research for a Ph.D. advised by Samuel Wilks. He had already written his first paper [3]:-

The paperWilks's idea was that his students should produce a research paper early on to get them into the swing of such things and also to put Wilks himself in the position of being able to prove to the mathematics faculty, when the question of advancing to the doctoral dissertation came up, that the student could do publishable research. He proposed that I examine the distribution of runs above and below the mean.

*Note on an application of runs to quality control charts*was published in the

*Annals of Mathematical Statistics*in 1941. In [6] Mosteller contrasts the style of Wilks's supervision compared with that of Olds:-

[After his first paper was published, Mosteller thought that he could work on the problem of up and down runs for his doctoral thesis but, after producing quite an extensive collection of results, he saw that similar results which in fact went further than his had just been published in a paper by Jacob Wolfowitz. He began to work on a new thesis topic but, partly because he was now doing work for the War Department in New York as his contribution to the United States war effort after the country had entered World War II, things only progressed slowly. In New York he also worked for the Office of Public Opinion research [3]:-Samuel Wilks]was a very different man from Edwin Olds. When Edwin Olds wanted you to do something you didn't have any misunderstanding about that job. He just told you. When Wilks wanted you to do something, it was hard to catch it. You had to be alert for it. He would hint around, "It would be nice if somebody did something of a certain kind." You had to grasp that he meant you. Coming from Olds it was a little hard for me to make it out sometimes.

Although Wilks was Mosteller's official thesis advisor, he was greatly assisted by Tukey [6]:-Shortly after World War II concluded in August1945, Virginia and I returned to Princeton. Except for some special mop-up work I did for Mina Rees to help in closing out the work of the Applied Mathematics Panel, I worked on my thesis and on other research papers that had emerged during our stay in New York.

John Tukey and Samuel Wilks were running a very active statistics seminar at Princeton and Mosteller presented work to this seminar which led to useful discussions. He presented his doctoral thesisJohn[Tukey]became essentially the advisor on the thesis. I went around to John from time to time and asked him for some suggestions. He always did two things: Took a pass at the problem I asked him about and then he'd always suggest something else, something entirely different to work on. And I gradually got an important idea out of that experience which was that it's important to get out of ruts and into some new activity that may turn out to be more beneficial than the ruts you are already in and can't handle. So I owe John a great deal for that.

*On some useful "inefficient" statistics*to Princeton and was awarded a Ph.D. in 1946, publishing the results of his thesis in a paper in the

*Annals of Mathematical Statistics*. At this time he began joint work with John Tukey and others which led to a number of papers written with various coauthors:

*Unbiased estimates for certain binomial sampling problems with applications*(1946);

*Low moments for small samples: A comparative study of order statistics*(1947) and

*The uses and usefulness of binomial probability paper*(1949). After completing work for his thesis at Princeton, Mosteller was appointed as a lecturer in the Social Relations Department at Harvard University. He was promoted to professor in 1951 and, two years later, became acting head of the Department of Social Relations. In 1957 the Statistics Department was set up at Harvard and Mosteller, who had been a leading figure in its creation, became its first chairman.

It was at Harvard that Mosteller became interested in applying statistical techniques to assist in healthcare. Caroline Richmond writes [33]:-

His career at Harvard reflected this interest in healthcare. He served as Chairman of the Department of Biostatistics from 1977 to 1981 and during these years (actually in 1978) he was named Roger I Lee Professor. He then served as Chairman of the Department of Health Policy and Management from 1981 to 1987. This last position was near the end of his career, for he retired and was made Professor Emeritus in 1988. However, this did not in any way mark an end to his research activities for he continued to keep daily office hours in the Department of Statistics until 2003 when he moved to Virginia to be near his children.Mosteller did much to assess the effectiveness of treatments and contributed greatly to substantive understandings of what works to improve health. He was a pioneer in meta-analysis and systematic reviewing techniques. In a classic study he compared the results of cumulative meta-analyses of randomised clinical trials of treatment for myocardial infarction with the advice being offered in medical textbooks. The results were sobering.

In many ways Mosteller's contributions are too broad to give anything other than the briefest of overviews in this biography. His bibliography contains 65 books, around 350 papers in journals and conference proceedings, 41 other publications and 26 reviews, so we can look only at a few highlights. One of the highly significant publications by Mosteller (with co-author David L Wallace) was the book

*Inference and Disputed Authorship: The Federalist*(1964). William Kruskal writes [26]:-

George Tiao writes [37]:-The book might well be regarded by historians as an application of statistics to settling longstanding disputes about authorship of the Federalist papers, but for Mosteller, Wallace, and most of the book's statistical readers, the Federalist focus of the book provided a specific, fascinating historical context in which to compare Baysian and frequentist modes of statistical analysis.

In 1955, in collaboration with Robert Bush, Mosteller published... this work represents a significant contribution to statistics. In particular, it shows how a real classification problem can be analyzed and what are the difficulties involved. After reading the book, one cannot help to have the feeling that it is this type of study which makes statistics a fascinating subject in its own right.

*Stochastic Models for Learning*. Vajda writes [38]:-

We should mention another related area in which Mosteller did not apply statistics but rather he sought to raise the profile of statistics, namely in high school teaching. His efforts to see school children get some experience with ideas from probability and statistics saw him write teaching manuals and textbooks. For example, in collaboration with R E K Rourke and G B Thomas, he publishedIt is natural that psychologists should try to find out how we learn, or that teachers should want to know how our learning could be improved. The authors of this book wish to contribute to just one aspect of this wide field. It is their view that learning is probabilistic, in that events change the probability of responses. One gathers that not all professional psychologists agree, but to a mathematical statistician the concept is of intriguing interest.

*Probability: A First Course*in 1961. Freda Conway writes [15]:-

This text formed the basis for a televised course that he gave in the same year making him well-known to school pupils across the United States. Also in 1961 the same authors published an extended version of this book under the titleUsing only high school algebra and no calculus, they develop the subject from probability, permutations and combinations, through set theory to frequency distributions and statistical inference. Such a treatment necessarily limits the type of statistical problem which can be discussed: frequency distributions are limited to discrete variables and estimation problems only involve proportions. On the other hand probability is well worth studying for its own sake and this approach to statistics is both logical and mathematically satisfying.

*Probability with Statistical Applications*.

Mosteller had many collaborators but the person with whom he published most often was John Tukey. One of their joint works was the book

*Data Analysis and Regression. A Second Course in Statistics*(1977). Edward Haertel writes [23]:-

However, reviewing the same book, R L Holder is critical [24]:-Mosteller and Tukey systematically develop a range of techniques for exploring real data, mostly by hand. In the course of presenting these techniques, they offer new perspectives on the formulation of statistical and data analytical problems, the nature of uncertainty and the need for cross-validation, the need for multiple analyses of the same data, ways in which the data can guide the analysis, the importance of robust and resistant measures, and similar practical and philosophical problems. The stated purpose of the book is to teach attitudes and approaches, and to provide tools for their implementation.

Mosteller received a long list of honours of which we can only mention a selection. He was awarded honorary degrees from the University of Chicago (1973), Carnegie-Mellon University (1974), Yale University (1981), Wesleyan University (1983) and Harvard University (1991). He was elected to the National Academy of Sciences, the American Philosophical Society, the American Academy of Arts and Sciences, and the Royal Statistical Society. He won several prizes including the Myrdal Science Award (1973), the Paul Lazarsfeld Prize for Applied Social Research (1979); the Samuel S Wilks Award from the American Statistical Association (1986); the R A Fisher Award (1987); the Surgeon General's Medallion (1988); and the Rossi Award (2005). He was president of the Psychometric Society (1957-1958), the American Statistical Association (1967), the Institute of Mathematical Statistics (1974-1975), and the American Association for the Advancement of Science (1980).I welcome the attempt that the authors have made to encourage common sense and thought in data analysis and regression but regret that they chose to mix a highly individual view of statistics with an objective that their book should be read by all. It has produced a text which is generally unrepresentative and confusing for students yet too verbose and loosely argued for a more advanced readership.

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

**List of References** (38 books/articles)

**Mathematicians born in the same country**

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