An Accidental Statistician

by George E P Box

  We made numerous trips to Pensacola, which, in the 1950s, was largely pine forests and undeveloped coastline. During our free time, we enjoyed the Gulf of Mexico, which offered a beautiful place to swim and eat fresh seafood. Frank was a great cook and a jazz aficionado, and my consulting visits were enlivened by jazz band parties at his house, which were attended by friends who played various instruments. I did my best to keep up on the guitar.

  Stu and I had learned that sometimes things on the road went smoothly and sometimes they did not. A plane that was supposed to fly sometimes didn't fly, and once, when I thought I was taking a plane to Decatur, Alabama, I ended up in Decatur, Georgia. Stu once told me a story that helped when things did not go according to plan. It went like this: A couple had twin boys. One was an incurable pessimist, while the other was a total optimist. On their birthday, the parents resolved to cure them of these peculiarities. They took the pessimist to a room with every kind of present a boy could want. They took the optimist to a deserted stable that contained nothing but horse manure and told him that his present was in there. After about an hour, they checked on the boys. They found the pessimist in tears. He didn't understand the instructions for his toys, and some he had broken. When the couple looked for the optimist, they found him wandering around the stable with a happy smile on his face, saying, “There's got to be a pony in here some place.”

  That phrase sometimes came in handy.

  In the late 1950s, Stu Hunter, Cuthbert Daniel, and I decided that a new journal was needed to meet the needs of those who applied statistics in technology (Figure 6.2). The first half of the twentieth century had shown the value of statistics to scientific research, thanks largely to Fisher and Walter Shewhart. The momentum continued with the beginning of the Gordon Research Conference on Statistics in Chemistry and Chemical Engineering in 1951, and the start of the American Society for Quality Control (ASQC) in 1952. Applied statisticians were still a rare breed, but with the postwar growth in industry, there was growing interest in the application of statistics to technology.

  Figure 6.2 Stu Hunter, me, and Cuthbert Daniel.

  In 1957, some months after I had arrived in Princeton, Professor John Whitwell of Princeton's Chemical Engineering Department invited me to give a talk on iterative experimentation at the Gordon Conference, which he was chairing that year. At the conference, there was informal discussion about the need for a new journal. Later that year, Horace Andrews, who taught statistics at Rutgers and who also headed the Education Committee of the Chemical Division of the ASQC, asked me to develop a course on statistical methods for process development. Stu Hunter, Cuthbert Daniel, and I planned the course together and once again discussed the prospective journal. We broached the subject with members of the ASQC in 1958, and out of our discussions came a prospectus calling for a “new journal to present applications of statistics in the physical and engineering sciences.”

  We decided that the journal should be a joint project between the ASQC and the American Statistical Association (ASA), with the governing body containing a number of members from each institution. The idea was that the ASQC would ensure that the new journal kept its feet on the ground while the ASA would guarantee high quality.

  To start the journal, we needed about $10,000. The ASQC immediately came up with $5,000, but the ASA was hesitant to provide funds. So Stu, Cuthbert, and I put on a special course. We raised the $5,000 and gave it to the ASA.

  The first issue came out in 1959 and bore the subtitle “A Journal of Experimentation in the Chemical and Other Physical and Engineering Sciences.” Stu was the first editor, and R. A. Fisher, who suggested the name Technometrics, contributed a paper, “Mathematical Probability in the Natural Sciences.”7

  I had no teaching duties at Princeton, but in 1959, the Chemical Engineering Department asked me, as a favor, to teach a course on experimental design. They said that the class would be for graduate students and that I did not have to give any exams or grades. Despite this, at the end of the semester, I got a phone call asking what grade I had given to a student called William Gordon Hunter. I said, “I thought you said I didn't need to give any grades.” They then told me that Bill Hunter was not a graduate student but an undergraduate in chemical engineering with special permission to take the graduate course. (Bill later told me that in order to take the class he had had to seek authorization from five deans!)

  I was perplexed about what to do, so they said I could give him an oral exam. Up to that time, I had not taken much notice of Bill, but at the oral exam, he really surprised me with his knowledge. Princeton had a grading system of 1 through 7, with 7 being the highest grade. When I informed the office that Bill had received a 7, they said that was good because he would now graduate summa cum laude. Bill had told me that he planned to go to Illinois for a year to get a Master's degree in chemical engineering. After that, he wanted to do a Ph.D. with me at the University of Wisconsin.

  1 Notice that to say that a result is statistically significant does not mean that it is important.

  2 This is a reference to a procedure called “Winsorizing” in which, in an endeavor to remove “outliers,” the largest and smallest observations are omitted.

  3 Donald Behnken, letter to author, April 6, 1984.

  4 G.E.P. Box and D.W. Behnken, “Some New Three Level Designs for the Study of Quantitative Variables,” Technometrics, Vol. 2, No. 4, 1960, pp. 455–475.

  5 R.A. Fisher, Statistical Methods for Research Workers, Oliver & Boyd, Edinburgh, 1925.

  6 F. Wilcoxon, “Individual Comparisons by Ranking Methods”, Biometrics Bulletin, Vol 1, 1945, pp. 80–83. Reprinted in the Bobbs-Merrill Reprint Series in the Social Sciences, S-541.Also contained in the pamphlet by Frank Wilcoxon and Roberta A. Wilcox, Some Rapid Approximate Statistical Procedures, Insecticide and Fungicide Section, Stamford Research Laboratories, American Cyanamid Co., 1964.

  7 See D.M. Steinberg and S. Bisgaard, “Technometrics: How It All Started,” redOrbit.com, March 10, 2008.

  “Digging for apples, your honor!”

  Chapter Seven

  A New Life in Madison

  I enjoyed my stay at Princeton and was to receive a full professorship there. But sadly in 1959, I had gone through a divorce, and Jessie and Simon had returned to England. I was to marry Joan Fisher, and to spare her some of the inevitable gossip, I decided to leave Princeton. Sam Wilkes, the head of the department, very much wanted me to stay at Princeton. He argued that in a year or two, this would all be forgotten. I felt adamant about leaving, however, and sought a job elsewhere. I found out that Columbia, Chicago, and Berkeley were interested, but at Wisconsin, there was the attractive possibility of starting a new department.

  So what else happened so that I ended up in Madison? I think it went like this: Henry Scheffé, with whom I had worked at STRG, was on the faculty of the Statistics Department at Berkeley. He believed that to be a good statistician, you needed more than good mathematics. Henry had read my papers and gave a seminar at Berkeley called, “Some Bright Ideas of G.E.P. Box.” Meanwhile, Professor Rudolph Langer, mathematician and director of the Mathematics Research Center (MRC) at Wisconsin, had been looking for talent for the MRC. Langer, whose search was for statisticians as well as for mathematicians, knew and respected Henry, and I believe it was Henry who first told Langer about me.

  At Madison there was a loosely associated group of perhaps 200 people called the “Division of Statistics.” All you needed to be a member of this group was to have some interest in the subject of statistics. The group's members had decided that it wanted to set up a statistics department at Madison, and the idea was that if I came and formed a department, I could begin by being employed part time at the MRC.

  I was invited to give two seminars, one on some technical problem and the other on what I would do if I were asked to start a new department. My plan was to have a central statistics group, plus joint appointments in agriculture, engineering, medicine, and business. The next day the d
ean told me, “The committee liked your ideas and wants you to come and put them into practice.”

  What was remarkable was that I was appointed to initiate and head the department as a full professor even though I had never had an academic appointment at any university. At North Carolina, I was called a “visiting research professor.” At Princeton, I had been a “senior research associate.”

  The new department was not to be started until the beginning of the academic year in September 1960. In the months that intervened, I worked at the Math Research Center and planned the new department. We needed additional funding, and Dean Erwin Gaumnitz of the Business School was instrumental in helping the department get its financial legs. The accommodation for the new statistics department was modest at first. We were housed in a Quonset hut, which was one of many erected to provide housing for the influx of returning soldiers who enrolled at the University after World War II. The hut was near the lake, and from time to time, it flooded. At first there were just me and a secretary occupying the hut and getting wet.

  The Math Department at Madison was anxious to get rid of the statistics courses that it had offered in the past. I had little formal teaching experience when I came to Madison, but there were parallels between what I had to do in the classroom and what I had done in the Army and at ICI. There I had worked closely with scientists to use statistics to help solve problems and I had given occasional talks about problem solving. A flier would be posted and a small group—perhaps six or seven people—showed up to listen. I also taught a night class at Salford Technical College, halfway between Blakely and Sale, where I lived. I suppose events of this kind prepared me, to some extent, to teach in a university classroom.

  Once I got to Madison, it was my first duty to teach the course the “Advanced Theory of Statistics.” I issued mimeographed notes each week, and as a student of Egon Pearson, initially I taught Neyman–Pearson theory. However, after I left University College, partly because of research I had done on what happened when standard assumptions were not true, and partly from what I thought was common sense, I had found a Bayesian approach much more convincing. So I found that my teaching of this course became more and more Bayesian with every week that passed.

  From the beginning, I wanted my students to know that they were at the forefront of a movement in which statistics played a vital role in scientific inquiry. I wanted them to understand that statistics was a catalyst to learning and discovery that had many useful applications in the science and engineering fields. Moreover I wanted them to take their ideas out of the classroom, to discuss and to argue them, and to meet industrial statisticians who could explain how they solved problems.

  No beginning teacher could have had a more promising group of students. George Tiao, Bill Hunter, and Sam Wu were among my first students, and by 1963, all three had taken their PhDs at Wisconsin. Dean Wichern, who came later in the 1960s, became a professor in the business school in 1969. Other students from that first decade, such as Duane Meeter, David Bacon, and Paul Newbold, went on to teach at universities in the United States., Canada, and England. John Wetz, Bill Hill, David Pierce and Jake Sredni found employment in industry or government. I have said many times that as a student, George Tiao was my bell weather: Whenever he looked worried, I examined the blackboard to see what I had done wrong.

  I did not realize that when David Bacon was my student, he enjoyed scribbling some of my odd remarks and unusual turns of phrase in the margins of his lecture notes. He recently sent me some of these, which he has preserved since the 1960s:

  Fisher is being a bit “shirty” here [(in specifically denying the legitimacy of assuming locally uniform prior distributions in the absence of prior knowledge).]

  Likelihood methods are like a very intelligent but nondiscriminating child.

  Good research these days is simply a moving of one blinker three degrees to the right.

  There may be some forlorn and shipwrecked brother who is traveling at the same speed as I am.

  None of this is a hanging matter.

  Whenever we see virtue rewarded, we are completely surprised.

  At this point, I don't want any chemical engineers to spit on the floor and walk out.

  You think that because an F-test shows significance, you can draw conclusions about the contours? Not on your Nelly!

  What we need at this point is a blackboard that can be erased!

  [Said during a Monday night beer session…], I am so angry at the College of Letters and Science that I have forgotten what I was going to say.

  Ah Jeffreys, poor Jeffreys! Can't we then have Lady Bella?

  Data cannot always speak for themselves.

  In model building, by and large, it's easier to get things into the act than out of the act—and people too, for that matter.

  [Working his way through a rather detailed derivation…]Take care not to get your nose caught in the tram lines.

  Now we move from the sublime to the gor blimey.

  [As George is about to launch into a detailed derivation…] Now, like the beginning of the English radio program “Living with Mother,” “Are you sitting comfortably? Then let us begin.”

  I had better say this again because one chap in the back row looks as if he's been hit over the head with a sledge hammer.

  Most of the members of the Institute of Mathematical Statistics have never seen a model, don't want to see a model, and couldn't care less about data. If you want to see some of these people, they'll be here in a couple of weeks. Be kind to them. Remember that that they are human beings, you know.

  Over the years, the department was situated in four locations. After the brief stint in the Quonset hut, we moved to a nice house on Johnson Street. I was sitting in my office one day when a man came in and started knocking on the wall. I asked him what he was doing, and he said he was checking where the joists were. When I asked, “Why are you doing that?” his response was, “Well, as you know, we are knocking down this house next week.” I immediately called someone in the University, and I was told, “Oh no, Professor Box. That house is scheduled for eventual demolition, but this is not likely to happen for another year or two.” With relief I put down the phone, but after about 15 minutes, it rang again. An agitated voice on the other end of the line said, “You were right! Can you start getting out this afternoon?”

  Next we were accommodated over Tiedemann's Drug Store on University Avenue. It must have previously been a rooming house because it had a lot of bathrooms. (The baths turned out to be handy places for the graduate students to park their bicycles.) The room we used for seminars was an L-shaped room, useful when we had an uninteresting seminar speaker because one could take refuge around the corner.

  Dean Young (later chancellor) came to see me when we were at Tiedemann's. I asked him how you got a new building. He said, “You get in the queue.” I said, “How do you jump the queue?” He replied, “You get matching funds from somewhere.” We applied for National Science Foundation money, and when they came on a tour of inspection, June Maxwell, our secretary, enlarged the pages of some of our reports and hung them on the wall in strategic places. To emphasize our need, she also arranged that bits of plaster fell from the wall as people passed by.

  In 1964, the University formed a Computer Science Department. They didn't have a senior figure to lead the way, so they got Professor Steve Kleene of the Mathematics Department to be temporary chairman. Kleene was a brilliant mathematician and a world-famous logician, as well as a charming man. Steve and I met and found we shared the belief that statistics and computer science could interact and complement each other. So our pitch to various possible funding sources was based on this idea. We talked to a number of funding agencies, and we finally got some money from the National Science Foundation. (When we were talking to the granting agencies, I might have been too verbose, because Steve Kleene rather pointedly told me a story about two men listening to a speaker, and after about five minutes, one said to the other, “Let's gi
ve him twenty dollars.” After ten minutes, he said, “Let's give him five dollars.” After twenty minutes, he said, “Let's not give him anything at all.” I took the hint.)

  We planned a building in which statistics and computer science offices would alternate so as to maximize the chance that people from the two disciplines would talk and work with each other. Also, there was a single lounge where they might discuss problems over coffee. Unfortunately, time proved our plan a miserable failure: Statisticians and computer scientists were not interested in talking to each other. After a while, computer science had the rooms rearranged into two separate blocks. Computer science expanded at a much greater rate than statistics, and in 2003, the statisticians were evicted to their current quarters, offices in a building that had been the old hospital.

  One day, soon after the Computer Science Department got started, the new chairman came to my office to ask me about the regulations for the master's and Ph.D. degrees. I said, “What regulations?” He explained that an inquiry had revealed that a new department had to prepare various documents setting out requirements for degrees and so forth, and these had to be approved by appropriate committees. I had not done any of these things, so I couldn't help him. I felt that I had been entrusted with starting a department of statistics and I had assumed that I could develop it my own way. My rules for the Ph.D. exam, for example, were based on those at the University of London, which simply said that a candidate should submit an original thesis and the examiners could then (1) pass the candidate; (2) submit the candidate to any examination or examinations, written or oral; or (3) fail the candidate. Later on the Ph.D. regulations in the Department of Statistics were changed and became a long rigmarole like those of other departments. I am not really sure, therefore, that some of our early Ph.D.s were legal, although we produced some fine statisticians.

  Both Joan and I are British citizens so before leaving England to come to the United States in 1959, we obtained alien registration cards. This entitled us to many of the privileges of a U.S. citizen, but getting such a card was not easy. We had to fill in the largest form I've ever seen. You had to answer a great many questions, like, “Are you now, or have you ever been, a member of the New York Photographic Society?” (You were left to fantasize on what they did in the dark room.)