An Accidental Statistician

by George E P Box

  During the years I spent at Princeton, the STRG did some excellent research, producing many publications. Members of the group, many of whom came as visitors, included Stu Hunter, Don Behnken, Colin Mallows, Geoff Watson, Merve Muller, Norman Draper, Henry Scheffé, Martin Beale, and H. L. “Curly” Lucas. Henry, who was from Columbia University, was an important visitor. He was concerned with our physical, as well as our mental, well-being—he insisted that we all go swimming every lunch time and led us to the pool. Stu, who was a permanent member, recalls driving John Tukey's rusty station wagon to meet Colin Mallows at the boat in New York City, and in a moment of excitement, Colin put his foot through the floor of the car.

  When we first set up the group, it was housed in the Theobald Smith House on the Forrestal Campus. This address foxed some of our correspondents. In particular, we received a request for a report that was addressed to “The Old Bald Smith.” I found a photograph of a distinguished looking elderly bald man, and we framed it, hung it on the wall, and claimed that “Old Bald Smith” was our founder. You need tradition to be respectable.

  Later the group moved to two houses on Nassau Street that were to be made into one. When I signed off on the plans before I visited England, I noticed that one thing to be done was the removal of a first floor closet. Upon my return, I noticed that the closet was still there, and when I pointed this out, I was told that they had kept the closet because it was the only thing that was holding up the bathroom on the second floor. Much as Francis Scott Key had been inspired by the events of his time, the closet prompted Collin Mallows and I to write the following ditty:

  If you're walking by the Gauss House

  And look inside the door,

  You will see a little closet

  And you'll ask “Now what's that for?”

  All the members of the group will come hurrying along,

  They'll stand round in a Normal curve

  And sing this little song:

  “It's the closet that holds up our john,

  The basis that all rests upon.

  Without it the structure would all tumble down,

  It's the closet that holds up our john!

  We called the building on Nassau Street the “Gauss House” because of our admiration for the great mathematician, Carl Friedrich Gauss, and we nailed up an appropriate sign. But this led to a misunderstanding because there had been a famous Princeton dean, Christian Gauss. One day it was raining hard and on leaving our building Merv Muller encountered an elderly lady sheltered by an umbrella who was staring at our sign. She said, “Dean Gauss never lived in that house!” Despite the fact that he had no umbrella and was getting very wet, Merve explained the misunderstanding and described at some length the many accomplishments of Carl Friedrich Gauss. Unmoved, the lady exclaimed, “I don't care what you say; Dean Gauss never lived in that house!”

  In the mid-1950s, one of the topics of interest was the modeling of chemical reaction mechanisms described by differential equations. This required nonlinear estimation and a great deal of computing. I got together with a professor of engineering, and we found that by pooling some of our research funds, we could rent an IBM 650 machine. Judged by today's standards, this machine was painfully slow and had very limited memory, but at that time, it was the last word in computers. We needed to get permission from the Dean to use our money for this purpose. He said that he wouldn't try to stop us, but that we were being very foolish. He explained that they had made a survey of all the people interested in computing at Princeton and had found that with such a “very powerful machine,” all the University's needs for a whole year would be satisfied in one afternoon of computing time! As we suspected, this was a mistaken view. Within a few months' time, our rented machine was used 24 hours a day. Our group used it during the day and made it available free to anyone who wanted to use it at any other time.

  I had attended my first Gordon Research Conference on Statistics in 1953, while I was at North Carolina. The Gordon Research Conference was named for Professor Neil Gordon, a chemist at Johns Hopkins who had become discontented with the habit that “big shot” researchers had of presenting their papers at scientific meetings and then disappearing. He felt that opportunity for informal discussion with colleagues was essential. In the 1930s, the conference was held on Gibson Island, in Chesapeake Bay, and all the participants were marooned there for a week. However, the idea of the conference soon spread to other topics and locations. Thus, the Gordon Research Conferences on Statistics in Chemistry and Chemical Engineering began in 1951 and continued through the summer of 2005. For many of those years, it was held on the campus of New Hampton School, a private boarding school that was beautifully situated in a small New Hampshire village.

  The conference lasted five days, and statisticians, chemists, and chemical engineers came from all over the country. Many flew into Boston where there was a bus waiting to drive them to New Hampshire. Don Behnken and I often drove together. He later recalled our “automobile trips to the Gordon Conference, forking left and forking right with an average of a punch line or a song every two miles [and] some memorable walks and conversations at the same conference.”3

  I had become close friends with Don and his wife, Neeta, while I was at Princeton. Don had served in the U.S. Navy from 1943 to 1946. He had undergraduate degrees in physics from Dartmouth and Yale and an MBA from Columbia. In 1956 he had enrolled in the Ph.D. program at Raleigh. His friend, Sig Andersen, urged him to study with me, but by then I was at Princeton. Undeterred, Don spent two summers working with me at Princeton on the understanding that he would qualify for his Ph.D. at Raleigh. In 1960, we produced what came to be called Box–Behnken designs, which are experimental designs for response surface methodology.4 These use only three levels for each variable and allow the fitting of important models with few experimental points.

  After Don received his Ph.D., he went to work as a statistician for American Cyanamid in Norwalk, Connecticut. Later I became a consultant for Don's company, which gave me a chance to work with him and visit his family. Don was a wonderful sailor, and I spent a many weekends on his boat. Once, when his family was not with us, Don and I passed the weekend sailing and telling jokes. Behnken claimed 106 were mine and 30 were his.

  On another occasion, when his family was on the boat with us, we took a picnic to an island in Long Island Sound. Soon after we had arrived, a serious storm blew up and we rushed to get ourselves and the picnic things into the dinghy and back to the anchored boat. It was a matter of minutes before the dinghy swamped, and the adults and children all set to bailing furiously as we fought through the waves and just managed to reach safety.

  Don and I continued both the banter and more serious shoptalk at the Gordon conferences. As Neil Gordon had intended, the conference provided free time for informal exchanges of this kind. Although mornings and evenings were reserved for formal presentations and discussion, the afternoons were open. There were many beautiful places for walking, and close by was a place to swim. Spouses (in those days mostly wives) were invited, and there were activities specifically for them. The food was particularly good, with lobster being the traditional fare of the final evening. On the last night there was always a skit. Below is an excerpt from one in which I played an aberrated version of myself.

  The scene is the office of the senior professor George, at the University of Little Marsh in Radison. The faculty, who are not well endowed, have pulled their last resources together to send a junior faculty member, young Professor John, off to the Gordon Research Conference to learn about new things. We see young Professor John come into the office of Professor George.

  George: Who are you young man? I don't recognize you!

  John: I am an assistant professor.

  George: Which department?

  John: Your department, Sir!

  George: Ah well, okay, what do you want young man? Asking for a raise I suppose…

  John: Well, we agreed that we meet here and I report ab
out the Gordon Research Conference. Will the Dean come around?

  George: Yes, he'll come a bit later. He is messing around somewhere.

  John: This conference was most confusing! First I thought I had come to the wrong conference, that one on zoology. They only talked about milking fish patties and on how to convert pesticides into hair growth agents. But after a while they went into more specifics and taught us how to run experiments.

  George: But we know that, don't we?

  John: Yes but they had some strange ideas about experimentation. Instead of changing one factor at a time, they change them all together!

  George: Most unscientific! That is ridiculous! You all remember my famous experiments supported by the Southern Neural Fundamentalists Network (SNAFU), in which I refuted once and for all this theory of sexual reproduction, the details of which I won't even repeat here—it's too disgusting. For these experiments I used two rabbits, a doe and a buck. They said that a doe and a buck would produce little rabbits, but I proved them wrong. Here Professor George shows a series of overhead projections.

  George: Thus they were forced to accept the alternative hypothesis

  continues: that little rabbits are brought by little storks and hidden under gooseberry bushes… Oh, here comes our queer old Dean. We are listening to this young man—what did you say your name was?—reporting from the Gordon Research Conference.

  Dean: Oh yes, here you are, young John!

  George: They had some very strange ideas of changing all experimental factors together and I reminded them about our rabbit reproduction research.

  Dean: Yes, and your famous flea research!

  George: Yes, again I've proven them wrong! I took a flea. I banged the table and it jumped. I banged the table again, and it jumped again.

  John: That's a replication.

  George: Nonsense! I just did it again. Well, I cut the legs off the fleas and I banged the table and it did not jump. I banged the table again and it did not jump.

  John: That's replication again!

  George: You hold your tongue, young man! What I proved was that when you remove the legs of a flea, it loses its sense of hearing!

  And so on.

  One very interesting man who regularly attended the Gordon Conferences was Frank Wilcoxon (Figure 6.1). I looked forward to seeing him and his wife Freddie on these occasions. In particular, I fondly recall that they would often invite me for an aperitif before dinner.

  Figure 6.1 Dr. Frank Wilcoxon.

  Born in 1892, Frank had had an adventurous youth before receiving his Ph.D. in physical chemistry at the age of 32. In the mid-1920s, he had a postdoctoral fellowship at the Boyce Thompson Institute for Plant Research where he worked on the use of copper compounds in fungicides. It was at the Institute that he and his colleagues, among them Jack Youden, studied Fisher's Statistical Methods for Research Workers, published in 1925.5

  In 1943 Frank began to work for American Cyanamid, where he led a group at the insecticide and fungicide laboratory. It was at American Cyanamid that Frank's main interest moved from chemistry to statistics, and in 1945, he wrote a paper that shook the field.6 The background to this was that Frank's lab was required to test a large number of synthetic substances, comparing them for effectiveness with the previously best-known product. Frank had to check all these comparisons for statistical significance, and there were a very large number of these to do. The standard statistical test was Gosset's t-test, and unfortunately, with the primitive calculators of the 1940s, this took a long time. So Frank invented a quicker test. To determine the level of significance you in effect simply noted the overlap between the two samples and consulted a table that Frank had calculated.

  In 1950, Frank began work at the Lederle Laboratories Division at American Cyanamid. There he began a statistical consulting group that he ran until he retired in 1957. In 1960, he took on a half-time distinguished lectureship at the newly formed Department of Statistics at Florida State University and taught until he died on November 18, 1965.In January 1967, I joined others who gave lectures at a conference in Tallahassee in Frank's memory. Franks wife, Freddie, was there, as were numerous colleagues. Frank and Freddie had been avid bicyclists, but as he aged, Frank began to ride a motorcycle, which you can see in the photo in Figure 6.1.

  Cuthbert Daniel also attended the Gordon Conference regularly. He was born a maverick in 1904 and remained one his entire life. He was a chemical engineer who had never attended a course on statistics, but who had read Fisher's Statistical Methods for Research Workers, which his wife Janet had brought home as part of her studies in biochemistry. Cuthbert was among the first to employ factorial experiments in industry. He invented a simple graphical method for analyzing data from such designed experiments. His method also detected suspect data values. From the 1940s through the mid-1980s, he worked as an industrial statistical consultant for Union Carbide, Proctor and Gamble, U.S. Steel, E.R. Squibb, and others and regularly came up with highly original and useful ideas.

  Cuthbert did not suffer fools gladly and had a hearing aid with a cord and a switch that he sometimes rather pointedly turned off. He had a remarkable sense of humor and drily pretended to be overawed by theoreticians. He was liable to say, in the middle of his own talk, “Alright so far!” I remember once, during a very mediocre presentation that we had to listen to, Cuthbert whispered to me, “George, there's less in this than meets the eye.”

  On another occasion on the lawn after a meeting, I was asked by someone about the method of least squares. I said, “Well, you see you have a vector x representing the input variables,” and I moved my left hand to point to the direction of this imaginary vector, “and another vector y representing the data,” and I moved my other hand to point to the direction of the output vector. At that point, Cuthbert, as he was walking past, said, “Let me hold that one for you George.”

  Cuthbert could be dramatically informal. One evening when we were consulting in Pittsburgh, he suggested going to see a play in which his sister was appearing. It was some distance away, and I forget how we got there, but at the end of the play, it was far from clear how we were going to get back. Cuthbert solved the problem by saying to two people in a car, “Are you going to Pittsburgh?” When they said, “Yes,” he got into the back of their car, opened the door for me to do likewise, and told them where he wanted to go. I think the middle-aged man and his wife were terrified. They must have thought that we were gangsters, but they took us there. Cuthbert thanked them, and we got out.

  I have in my possession some wonderful letters that Cuthbert wrote to me in the mid-1950s, some addressed “Dear E.P.” One begins:

  Dear George,

  Apparently even a semi-annual letter to you strains my capacities. But here I am. It is a sticky day and so I am boycotting the national convention of ASQC and catching up on my home work. I want you to answer this half-normal plot thing. Please don't think you can get rid of me, or even change our friendship by casting me into outer darkness, saying—Ye are a Fisherian, or something repulsive like that.

  Cuthbert remained my friend until he died in August 1997 at the age of 92.

  For many years, Stu Hunter and I were frequently on the road together, often as industrial consultants for the same company, and when we taught week-long short courses for industry in various places in the United States and Europe. It was at a Gordon Conference that Stu and I met Dr. Frank Riordan. Frank, who was a chemical engineer at Chemstrand, was faced with a very difficult challenge. The DuPont Company had previously had a monopoly on the manufacture of nylon and had consequently been sued for constraint of trade. After many years of litigation, the following solution was agreed upon in 1951: DuPont would build a second nylon plant at Pensacola, Florida, using all their expertise, with a capacity to match the DuPont plant.

  Frank was an engineer responsible for process improvement in the new company. Since DuPont had been making nylon for many years, he knew that to compete with them would be tough. He bel
ieved, however, that by using data analysis and statistical experimental design to solve problems, he could make up the difference. So he invited Stu Hunter and me to come on board as consultants.

  When the new plant was built, it was immense, extending over 2,000 acres. The plan was that DuPont would start up the new plant and then, on a certain date, they would hand it over to the new company, which would be called Chemstrand and would be affiliated with Monsanto. After this, DuPont and Chemstrand would be competitors. One story that went the rounds was told by the new plant superintendant. He was looking over the plant a few days before production was scheduled to start when he met a process worker who asked him who he was. He said, “I'm the plant superintendant.” The process worker looked at the huge plant that stretched away in the distance as far as the eye could see and said thoughtfully, “Jeez, if you don't screw up you've really got it made.”

  Frank had a small but impressive technical staff of chemists and engineers, and for several years, we met with him and his group regularly. Together we solved many problems, usually with the help of carefully planned experiments. I remember one problem very vividly. At one point Chemstrand's nylon cord, used in the manufacture of automobile tires, was not as good as DuPont's. Salesmen complained, and we feared we would lose this market to DuPont. No one in the company wanted to tackle the problem, so it was left to Frank's group. Frank put a sign on his door that said, “Calhoun.” The joke was about a boys' school football team that got involved in an exceedingly rough game. The coach kept shouting, “Give the ball to Calhoun! Give the ball to Calhoun!” Eventually a call came back, “Calhoun says he don't want the ball!”