An Accidental Statistician

by George E P Box

  Hill had a great sense of humor. When he gave his first address as president of the Royal Statistical Society in 1950, he explained that he hadn't known what to say, so he had consulted the addresses of past presidents to get some ideas. He saw that a very early past president (the RSS was 150 years old) had received a request that the Society determine the amount of horse manure deposited each day on the London streets. The president had written a careful letter in which he made it clear that while members of the Society would be glad to analyze the data, they should not be expected to collect it.

  When I first knew George Barnard, he had a house on Barnes Common by Thames. Especially at night, the house had a miasma of mystery of the late Victorian period. The bathrooms in particular dated from that time, and I was especially fascinated by the shower in one of them. This was a glass box, and when you closed the door and turned it on, you were attacked by multiple squirters that came at you from all directions. These had the peculiarity that some were boiling hot while others were stone cold. It was an excruciating experience. I think I must have learned how to turn the shower on but not how to turn it off. Certainly on the one occasion when I used it, I must have left it running all night. The Barnards were very nice about it, but everywhere downstairs was flooded with water. Armed with mops and buckets, it took all the adults and children most of the day to get it reasonably dry. I think George forgave me, but I suspect that Mary never quite did.

  Later, George and Mary Barnard had a beautiful house known as “Mill House,” close to Brightlingsea, on the Thames estuary. They spent much time and labor fixing it up. I remember visiting unexpectedly when it had been raining hard, and the fixing up process was in its early stages. In particular, the roof of the passage that led to the kitchen leaked. George was away in Canada, and Mary was thoroughly cursing him.

  Brightlingsea had been a favorite haunt of King Edward the Seventh, who kept his yacht there, and it was still a favorite place for sailors. On one occasion, I was visiting with my two children who were quite young, Helen being perhaps six, and Harry four. At some point, George had acquired a small boat with an outboard motor. The children and I climbed into the boat with George who was having trouble starting the motor. He gave a very hard tug on the line, but because he was concentrating on the engine at the back of the boat, he didn't see where he was going, and suddenly the motor roared into life. We charged a bollard at great speed, and the children were thrown into the bottom of the boat. After a bit, George tried again. But this time, we hit someone else's boat with the same result. Picking herself up once more, Helen remarked to Harry, “I hope it doesn't go on like this all day.”

  I stayed with George and Mary at Mill House from time to time, enjoying the lovely garden and fish pond. The house contained various gadgets due to George. I remember in particular an elaborate system of rubber tubes in our room that came with typewritten instructions as to how, by a series of maneuvers, it was possible to get hot water.

  One day I went for a walk with George along the bank of the Thames and George suddenly said, “Do you realize that we are at a National Monument?” I could see nothing but a great deal of mud, but George explained that this was the site of a Roman Oyster Bed. I had no reason to doubt him.

  1 Fisher himself liked our ideas and suggested the name “Technometrics” for a new journal that might publish this kind of work.

  2 G. E. P. Box and K. B. Wilson, “On the Experimental Attainment of Optimum Conditions,” Journal of the Royal Statistical Society, Series B, Vol. 13, 1951, pp. 1–45.

  3 G.E.P. Box and D.R. Cox, “An Analysis of Transformations,” Journal of the Royal Statistical Society, Pt. B, Vol. 26, 1964, pp. 211–252.

  4 The paper was issued as part of the British Doctors Study conducted from 1951 to 2001. See R. Doll and A.B. Hill, “The Mortality of Doctors in Relation to Their Smoking Habits: A Preliminary Report,” British Medical Journal, Vol. II, 1954, pp. 1451–1455.

  “The time has come, ‘the walrus said,’ to talk of many things. Of shoes and ships and sealing wax, of cabbages and kings…”

  Chapter Five

  An Invitation to the United States

  I was happy with what I was doing at ICI, and I had had no thought of academia. But in the course of solving practical problems, I had come up with a number of ideas for the development of statistical methods and had published them. In 1952, I was surprised to receive a letter from North Carolina State University at Raleigh, which had established one of the first departments of statistics in the United States.1 The letter was from Miss Gertrude Cox, who famously ran the Institute of Statistics with departments on both the Raleigh and Chapel Hill campuses. It was an invitation to spend a year at Raleigh as a “Visiting Research Professor.”

  I later found out how this came about. J. Stuart Hunter, then a graduate student at Raleigh, had worked during the summer vacation at the Army Research Office (ARO) (Figure 5.1). Stu had seen the paper I had written at ICI with K. B. Wilson in 1951, which concerned the experimental determination of optimal process conditions. He showed this to Frank Grubbs, who was in charge of ARO, and Frank proposed to Gertrude that she use some ARO funds to invite me over. The ICI board of directors gave me a year's leave of absence, but they made it clear that they wanted me back.

  Figure 5.1 George Box, Ralph Hader, and Stu Hunter.

  At that time, I had not submitted my Ph.D. thesis. People told me that, although this didn't matter much in England, in the United States, everyone was supposed to have a Ph.D. I had already written my thesis, much of which had appeared in already published papers. So I had my examination just a few days before I was to leave for the United States on the Queen Mary. My examiners, E. S. Pearson, H. O. Hartley, and M. S. Bartlett didn't mention statistics but chatted with me about the comparative advantages of going to America by air or by sea. When I asked if I'd passed, they said, “Yes, of course.”

  At ICI I was attached to a group called the Miscellaneous Chemicals Division. It included various activities such as X-ray Crystallography that didn't fit anywhere else. Our boss was Dr. S. H. Oakeshott. When the board decided I could go to the United States, Oakeshott asked me to come and see him. He said, “Now we'll need to give you some money to get to North Carolina because it's on the west coast of the United States and it's a long train ride.” I told him, “No, it's in the east.” We had a discussion, and finally I remembered the words to the song “The Chattanooga Choo Choo.” I sang some of the words to him:

  You reach the Pennsylvania station ‘bout a quarter to four,

  You read a magazine and you're in Baltimore

  Dinner in a diner

  Nothing could be finer

  Then to eat your ham and eggs in Carolina

  [Citation: Harry Warren and Mack Gordon, 1941; first recorded by Glenn Miller and His Orchestra in 1941.]

  I said, “So you see, it's got to be on the east coast.” He was a very nice man of the “old school tie” type, and he didn't seem to follow me, but eventually we got out a map and he realized that I was right.

  Jessie and I left Southampton on the Queen Mary in the middle of winter. When we first arrived at the dock, there was great excitement on board with cameras and lights everywhere. It turned out that Sir Winston Churchill was crossing to see President Eisenhower. Two or three members of his family and a number of important people were there to see him off. There was much flashing of cameras and general commotion, but eventually he was ushered away. Jessie and I had been watching all of this from close to the top of the gangway. We too decided to move on, but didn't know our way around the ship. We found ourselves walking down a narrow corridor where we could just see two people walking toward us from the other end. It turned out to be the Captain and Churchill. To get past them, we had to go stomach to stomach.

  Not long after we put to sea, we noticed members of the crew setting up ropes by all the stairs and passages. I asked if they were expecting rough weather and they allowed that this might be the case. The ste
ward suggested that the best chance of avoiding sea sickness was to stay up on deck in the open air. On deck where there was a bar and, usually, dancing. After it got rough, I saw one couple attempting to dance, but the floor was rising and falling at strange angles and they had to give it up. One interesting phenomenon was to see a drink creep up one side of the glass and then down and up the other side.

  The storm became dramatic. I got up on deck and wedged myself in the highest place I could find, facing forward. We cut through huge waves, the enormous ship diving deep into the water and then flying up with an immense volume of water breaking over its prow.

  The remainder of our crossing was rough, but we finally got to New York, where the authorities came on board to check passports and visas and inspect the chest X-rays that everyone had to present before they were allowed off the boat. We disembarked and had breakfast in New York. This cost eighty cents, an amount that at the time seemed almost ruinous when converted into British currency.

  On the plane flying down to Raleigh from New York, I got into conversation with my neighbor, an Egyptian student. By coincidence we were staying at the same hotel, and we met the next day for breakfast, where we discussed the many different kinds of English spoken in the world. As if to illustrate the point, when I asked the waitress for ham and eggs, she said, “Huh?” I repeated my words with the same result. Finally I pointed to the items I wanted on the menu. My Egyptian friend watched this performance with wide-eyed surprise and then remarked, “If you cannot understand them, how can I?” When the waitress brought my breakfast, in the corner of my plate was a mess of some kind. I took it back to the counter and said, “I didn't order this.” She exclaimed, “Why them's yer grits!” Like french fries in Australia, you got them whether you wanted them or not.

  I was not the only Englishman who had initial difficulty with certain American traditions. When I got to Raleigh, I heard a story about a very large park that was nearby, and during the war, it was made available to British submarine crews to rest up. A number of southern ladies had volunteered to help, and among other things that were offered to the soldiers was iced tea. This was a beverage that was totally unknown in England. It took some time to discover that out of sight of the ladies, the crew had built a fire and used it to heat up the tea, thereby making it drinkable.

  After settling into our new quarters in North Carolina, I became acquainted with Miss Cox (Figure 5.2). She was surprising: What you thought you saw was a pleasant, middle-aged lady who liked to tend her garden and bake cookies. Despite of appearances, she was a ball of fire. She had been a researcher and assistant to Professor George Snedecor at Iowa State, where the latter had founded the first department of statistics at a U.S. university. Snedecor had been asked to suggest a person suitable to head the Department of Experimental Statistics that was being established at North Carolina State, and he came up with the names of five men. When Miss Cox asked, “Why don't you recommend me?” he did, and in 1940, she went to Raleigh. When I got there in 1953, she had organized and was running the Institute of Statistics. This included a department at Chapel Hill, concentrating on theory, as well as the Raleigh department, concentrating on more practical things. She had the support of the governor and was also involved in founding the “Research Triangle,” a joint effort from Raleigh, Chapel Hill, and Duke University. She was one more example demonstrating that a woman can be an inspired leader and a super competent administrator.

  Figure 5.2 Gertrude Cox.

  The following story illustrates her remarkable talents. She had an offer of half a million dollars if she could find matching funds for the other half a million. She asked the help of a famous industrialist who said he would have no difficulty in raising the matching funds. There was a time limit of 12 months, but at the end of 9 months, he had failed to get the money. She said, “Okay, will you let me try?” She approached the faculty and the graduate students and explained her problem. She said, “I want each of you who is doing practical research to write up a ten-minute talk. We'll make the rounds of the big shots and see if we can raise the money.” I helped by contributing a piece on efficient experimentation and was moved to write a little ditty:

  Here we come with whistle and flute,

  Collecting for the Institute

  She got the money!

  What was taught at Raleigh and Chapel Hill was Fisherian statistics: the analysis of variance and other ideas due to Fisher. My research on response surface methods was a natural extension of Fisher's concepts applied, however, to technology rather than to agriculture. My ideas were known to Fisher who was delighted that his kind of statistics was being developed in new areas.

  Unfortunately there was a graduate student who went around saying that people were wasting their time studying Fisherian statistics that had (in his mind) been superceded by response surface methods. Stu Hunter found out about this. He told me that the faculty thought that the student's opinions had come from me, and they were angry about it. Each month Gertrude had a session at her house where matters of interest were discussed, and Stu warned me that I was to be “called over the coals” at the next session. The published account of response surfaces was rather mathematical, but the basic ideas were sensible and easy to understand, so very quickly, I wrote an applied paper called “The Exploration and Exploitation of Response Surfaces” specifically for Miss Cox.2 She studied it before the meeting, and when the criticism started, she intervened and said that she thought these ideas were excellent and didn't in any way conflict with those of Fisher or with what was being taught in the department. She added that she planned to publish my paper in Biometrics, the journal of which she was editor.

  The story goes that at one point Miss Cox invited both Sir Ronald Fisher and Frank Yates to present a series of lectures at North Carolina. She worked Fisher pretty hard, so he was quite glad when it was Independence Day and he was able to take off on his own with his butterfly net. But one of the graduate students had seen him and thought that now was his chance to get close to Fisher. The student found him and said, “It's a fine day.” Fisher said, “Yes.” The student said, “We get a day off—it's Independence Day.” Fisher said, “Yes.” The student then said, “I suppose you don't celebrate that in England.” At that point Fisher turned on him and said, testily, “No, perhaps we should!”

  Howard Hotelling was a distinguished statistician at Chapel Hill, and at times, he could be a bit pompous. One day he came to the park to attend a department picnic driving a large new car. He asked some graduate students to drive it to a safe parking place where it would not be scratched. There were a lot of trees, and they took a long time to park it. Sometime later, the professor needed his car, but the original team of graduate students was no longer there, so another group took on the job. After a considerable time, they confessed themselves beaten. The car was completely surrounded by trees, seemingly dropped from the sky. For a long time, they were completely baffled (and this, remember, was a group of scholars, all candidates for the degree of doctor of philosophy at one of the finest universities in the country). After a considerable time, there was a breakthrough, and there were those present who felt that they should be awarded their doctorates without further delay. But no theses had been produced with pages that met the exacting requirements of proper margins and numerous signatures, so that plan fell through.

  It seemed to me then, as it does now, that something new in statistics most often comes about as an offshoot from work on a scientific problem. With this in mind, during my year at Raleigh, Stu and I helped a chemical engineer with his investigations. His name was Dr. Frederick Philips Pike. He had a great sense of humor, and we got on famously. He told me that he was a distant relative of Lieutenant Pike who was the original surveyor of Pike's Peak.

  Pike said that as a young man he had been anxious to visit Pike's Peak and had managed to get close to the top in his old car. He was starting on the return journey when someone opened the opposite door and sat down in the passeng
er seat. The newcomer wanted to be taken down the mountain, and it was evident that he was very drunk. So Pike took him along, and as they proceeded, he told Pike about his recent history. He had left home three days previously, and before he had left, he had had a violent quarrel with his wife in which neighbors and relatives had been involved.

  They proceeded for some way in silence, and about halfway down the mountain, his passenger asked Pike what he did. Pike said, “I'm a mind reader.” The drunk said he didn't believe him, so Pike told him the same story that the drunk had previously related to him. As Pike suspected, the passenger had completely forgotten he had told him about this, and he began to eye Pike with deep suspicion. Finally, when Pike had driven him home, his passenger left the car, but then came back very angry and said, “I know what's been going on. There's only one way you could know all this. You must have been carrying on an affair with my wife.” At that point, he seemed dangerous and Pike quickly drove off.

  In Raleigh, every morning on the radio, almost everyone listened to a disc jockey called Fred Fletcher. He was great fun. I remember, for example, that he would often play a request that was a “commercial” for Grandma's Lye Soap.” One verse I remember was about someone who

  Suffered from ulcers, I understand

  Swallowed a cake of Grandma's Lye Soap

  Now has the cleanest ulcers in the land…

  [Citation: Song goes by same title, John Standley and Art Thorson, 1952.]

  If you had anything to sell, Fred would advertize it for you. I remember that for some days, there was a donkey tethered outside the station and Fred would ask for and get food for it while waiting for a purchaser. One day he advertized a piano, and I bought it for 40 dollars. It was thick with beer stains, but it didn't sound too bad.