An Accidental Statistician

by George E P Box

  I invited him in to share a pot of tea and we discussed the virtues of the blue Denby jug that held the milk. I said, and it sounds pretentious now as I repeat it, “There is a kind of truth in good design.”

  And that was it. I'd given the password. My use of the word TRUTH, admitted me to the inner circle.

  In the next few hours I discovered that Harry was on a QUEST, a quest for certainty, proof, truth. He would have no truck with metaphysics or mysticism or any religious dogma or doctrine. He could find no basis for belief in God.

  He was a student of Science and Mathematics. He looked to Mathematics for truth—that led him to Philosophy—and he found, in his words, “Certainty, both in Philosophy and Mathematics, is currently unavailable.”

  He found this intolerable and a challenge. Over the last few years he has been hammering out what he called his “proposed System of Deductive Proof in Philosophy.” His aim: To put the TRUTH back into Mathematics. To put the TRUTH back into Philosophy,” remembering the words of another mathematician: “If the premises are right, so will be the conclusions.” He believed his system would challenge all known systems and change the basis of human thought forever.

  But now there was a problem, nothing to do with the difficulties of the task.

  He was, as I've shown, a man with a purpose, a mission you might say, but that did not include hurting people.

  He had no time for bigots and fundamentalists of course, but it was leading respected scholars who were his target: Tarski, Polkinghorne etc.— not your average church-goer, not his family, not his friends, many of whom had firm religious faith.

  He was seriously concerned about the impact his findings would have on them.

  I used to remind him that there is a long history of religious doubt—even before Richard Dawkins, even before Charles Darwin himself—but still he worried.

  He was like no one else—truly eccentric, single-minded—sometimes too direct for comfort, wise and naive at the same time; strangely, unnervingly innocent—childlike.

  I was with him—was it really only ten days ago?—when the young consultant registrar, after a long and patient questioning, armed with X-rays, and grey with anxiety, asked Harry's permission to be frank.

  “Of course – please.”

  He was frank—gentle, but totally frank.

  There was a pause, then, Harry beamed at the young man, slapped the table twice, saying “Excellent! Excellent!”

  …I saw it as Harry's recognition of a difficult job well and thoroughly done—step-by-step analysis and then the deduction.

  “If the premises are right, so will be the conclusions.”

  TRUTH, based on evidence.

  “I've had a very interesting day,” he said, and later, “We've come to the end of the road, haven't we?”

  It was, I thought later, another stage of the experiment…

  This man was now facing mortal illness in the same spirit—a scientist in another phase of the Experiment we call Life—in another area of the great Laboratory—still looking for the TRUTH.

  Isn't that a good way to die?

  —and a good way to live!

  And how glad I am to have known him.

  [Citation: With kind permission in a letter to George E.P. Box from Mrs. M.E. Homewood (UK) sometime in 2008.]

  “There goes Bill!”

  Chapter Twelve

  Bill Hunter and Some Ideas on Experimental Design

  Bill Hunter arrived in Madison to begin his Ph.D. in the fall of 1960 after working during the summer in Whiting, Indiana. He had enjoyed the job so much that he had written asking whether it was possible to start classes a week after the semester began. I wrote back telling him that no, this would not be possible, so Bill arrived just before classes started (Figure 12.1).

  Figure 12.1 Stu Hunter, me, and Bill Hunter.

  Bill was on a fast track from the day he came to Madison. He completed a brilliant thesis1 in 1963. Soon after, we offered him an assistant professorship in the Statistics Department. From the beginning, he was an excellent teacher and did some first-class research. As a result, he became an associate professor in 1966, and a full professor in 1969, meaning that he had gone from graduate student to full professor in eight years.

  During the first several years I worked at ICI, I taught statistics two nights a week at Salford Technical College to earn a bit of extra income. The college was about halfway between ICI, at Blackley, and my home in Sale, so I would work a full day at ICI, eat dinner at a greasy spoon restaurant, and go directly to the college to teach the class. The course concerned the design of experiments. I wrote out my notes, dittoed them, and circulated them to the class in advance so that the students could listen, rather than write. These notes also formed a basis for later courses I taught, and for my contributions to the second book for ICI, called the Design and Analysis of Industrial Experiments, otherwise known as “Big Davies,” after its editor, published in 1954. The latter book, and my notes, were very useful when Bill Hunter, Stu Hunter, and I began writing Statistics for Experimenters in the early 1960s.

  As I have said, in the 1950s, statistics was subsumed by mathematics at most universities and received little respect as a field. The incentive to use it in science and industry came from industry itself, not from the college campus. The intention of the book was to introduce its application to a wider public. Stu and I made a good beginning when I moved to Wisconsin in 1959, and he came the following year. In 1962, however, Stu took a job at Princeton and duties at our respective institutions made collaboration more difficult. Stu continued to make further contributions when he became the department's first statistician in residence.

  Bill Hunter had a joint appointment with the departments of Statistics and Engineering, and later his office was on the fifth floor of the School of Engineering; you could tell which room was his from outside of the building because he had pasted the pages of the New York Times on the window to keep the sun out. We often used Bill's office while we were working on Statistics for Experimenters. One of our bigger challenges was that some of our collaboration occurred during the Watergate hearings in the summer of 1973. The hearings, which kept the nation spellbound, regularly lured us from our work to watch the television in the nearby student union. There we were joined by numerous others who found it difficult to resist the unfolding story and its cast of characters. There were the testimonies of John Dean, H.R. Haldeman, and John Ehrlichman, among others, all presided over by the courtly Senator Sam Ervin, a man who possessed remarkable eyebrows.

  We continued our work on the book well after the Watergate hearings were over. Finally, in 1978, we sent it off to Wiley, our publisher. Shortly before that, I wrote to my daughter, Helen, who was a senior at Culver. “The house is (almost) unimaginable because over the last several months it has been littered with Galleys, Page Proofs, Indexes and all the etceteras. BE IT KNOWN that today not only has Box (Hunter)2 been sent off for the last time but ‘Fisher The Life of a Scientist’ by Joan Fisher Box has also been sent off for the last time. Next time we see them they will be bound books!”

  One of the best descriptions of the long process that yielded our book, and of Bill's role in it, comes from Conrad Fung, who was a master's degree student as the book was in progress:

  I met Bill Hunter in the Fall semester of 1975 when I transferred into his course Statistics 424… It was ‘Statistics for Experimenters’ taught from mimeographed notes by Box, Hunter, and Hunter, that students could purchase from Mary Arthur in the Statistics Department office. The book would ultimately be published in 1978; we students who continued in the department over the years had the privilege of seeing the book take final form—including the evolution of all the half-normal plots that were in the manuscript when we took the course, into full normal plots when the book was published.

  Bill later told the story that he himself had learned from similar notes two decades before, when he got permission…to attend George's graduate seminar on exp
erimental design at Princeton. … They were dittoed notes in that case, but had the same + and − signs ‘marching down the page,’ as Bill described them. He said that little did he know then, as a student, that he was learning from a book of which he was to become one of the authors. And upon publication in 1978, he said, he broke into doggerel:

  The three wrote the book page by page

  So that statistics would become all the rage.

  But when it came back from the binding,

  They made a great finding:

  At birth, it had reached voting age!2

  The book would never have become a book had it not been for Bea Shube, the exceptional editor at Wiley Publishing. As a woman working in the field of scientific publishing, she was a pioneer. She started at Wiley in the early 1940s and worked there until 1988, and during that time, she shepherded many outstanding books into publication. There is no question that her encouragement and wise suggestions made Statistics for Experimenters a better book. When Bea retired in 1988, I was fortunate that Wiley had Lisa Van Horn to take her place, and she and I worked together for over 20 years, beginning with the 1997 paper edition of Evolutionary Operation. In 2004, she oversaw the second edition of Statistics for Experimenters and a book of collected articles, Improving Almost Anything, in 2006. Lisa also edited the second editions of Response Surfaces in 2008 and of Statistical Control in 2009. Her input was unusually perceptive, and it was always a joy to work with her. Steve Quigley, the associate publisher at Wiley, oversaw the publication of all of these books, and he and I remain close friends.

  When I was still in England, I bought some records at bargain prices from a shop that had been damaged by fire. One of these I particularly liked was a song by Cole Porter called “Experiment,” sung, I think, by Gertrude Lawrence. I thought it might be an appropriate anthem for our book. But Bill had never heard of it, and no one else he knew in the United States had ever heard of it either. This was strange because Cole Porter was, of course, American. We knew that if we wanted to use the song in the book, we would have to get permission from whomever owned the copyright. So when Bill was going to England one summer, he decided to track the song down. After several dead ends, he went to the British Institute of Recorded Sound. He asked an old gentleman at the main desk if he knew anything about the song. The man promptly stood up and sang it. When Bill asked why the song was unknown in the United States, the man explained that it was in a 1933 show, Nymph Errant, that had been tried out in London and had flopped. So it had never appeared in the United States. In the show, the song is part of a commencement address. We included only the chorus on the first page of Statistics for Experimenters II. Here is the song in its entirety:

  Before you leave these portals to meet less fortunate mortals,

  There's just one final message I would give to you.

  You all have learned reliance on the sacred teachings of science

  So I hope through life you never will decline in spite of philistine defiance

  To do what all good scientists do.

  Experiment.

  Make it your motto day and night.

  Experiment and it will lead you to the light.

  The apple on the top of the tree is never too high to achieve,

  So take an example from Eve, experiment.

  Be curious, though interfering friends may frown,

  Get furious at each attempt to hold you down.

  If this advice you only employ, the future can offer you infinite joy

  And merriment.

  Experiment and you'll see.

  [Citation: Cole Porter, “Experiment,” from the London stage musical, “Nymph Errant,” 1933.]

  Statistics for Experimenters is now in its second edition and has sold over 163,000 copies. I was particularly delighted when it was translated into Spanish by my friends in Barcelona and Madrid.3 My friend Ernesto Barrios was immensely helpful with the technical revision of the second spanish edition. Ernesto had been one of the longer running Ph.D. students in the Statistics Department. He wrote a very good thesis, but when I encouraged him to take the exam so that he could graduate, he always argued that there were parts of his dissertation that he wanted to improve. He did eventually go back to Mexico, in 2005, and is a professor of statistics at the Instituto Tecnológico Autónomo de México.

  In the second edition, we added on the inside covers, more than 60 aphorisms, some our own, and some from other authors. Among them were:

  All models are wrong; some models are useful.

  It's better to solve the right problem approximately than the wrong problem exactly. (John Tukey)

  Experiment and you'll see! (Cole Porter)

  Question assumptions!

  One must try by doing the thing; for though you think you know, you have no certainty until you try. (Sophocles)

  Designing an experiment is like gambling with the devil: Only a random strategy can defeat all his betting systems. (R.A. Fisher)

  You can see a lot by just looking. (Yogi Berra)

  Common sense is not common.

  When running an experiment the safest assumption is that unless extraordinary precautions are taken, it will be run incorrectly.

  When Murphy speaks, listen.

  Certain words should be used sparingly. These include should, could, would, ought, might, can't, and won't.

  In August 1984, I received a note from Emily Peterson, Chancellor Irving Shain's secretary, asking whether I would be able to join the Chancellor and some special visitors from England for lunch two months hence, on Oct. 18 or 19. I checked my schedule and realized that I was to attend a conference in New Mexico during that time so I wrote back sending my regrets. Ms. Peterson replied immediately, explaining that there was now a chance that the British visitors would be coming to Madison on Friday, Oct. 12 instead, and would I be available then? I was free that day, so I answered in the affirmative. In September, Ms. Peterson wrote confirming that I was to join the Chancellor and his English guests at noon on Oct. 12 at “L'Etoile,” Madison's finest restaurant, which was across the street from the state capitol building.

  On the appointed day, I drove from the west side of town to the restaurant on the capitol square, which is in the center of Madison's famed isthmus. The isthmus is a narrow and congested part of town where parking is very scarce. As I approached the area, traffic became backed up and access to some of the streets was blocked. I suddenly remembered that this was the day Walter Mondale and Geraldine Ferraro were coming to Madison for a huge rally in the run-up to November's presidential election. There was absolutely nowhere to park, and by now I was sure I would be late. Finally I found a parking spot blocks away from the restaurant and hastily made my way to L'Etoile.

  I arrived breathless at the restaurant and looked around for Chancellor Shain and his guests. They were nowhere in sight. What I saw instead was a large group of my past graduate students, some of whom had come from great distances. It dawned on me that this was a “setup.” Conspiring with the chancellor and his secretary, Bill had invited my students to Madison to celebrate my 65th birthday. I was completely stunned and delighted.

  [Citation: Emily A. Peterson, letter to author, September 19, 1984.]

  What behind-the-scenes chaos arose when I canceled the first meeting with the fabricated Englishmen I do not know, but doubtless there was some. Needless to say, there was much merriment and we had a wonderful reunion. Bovas Abraham had helped with the plot, which included asking various students and colleagues, including a number who could not be there, to write letters recounting memories and offering best wishes. These letters were beautifully bound into a leather volume that was presented to me at the gathering. Twenty-five years letter, they still give me great pleasure. The writers were:

  Bovas Abraham Hannes Ledolter

  Sig Andersen Kevin Little

  Dave Bacon Greta Ljung

  Steve Bailey John MacGregor

  Don Behnken Paul Newbold

  Gina Chen Lar
s Pallesen

  Larry Haugh Dave Pierce

  Bill Hill Jake Sredni

  Bill Hunter David Steinberg

  Stu Hunter Ruey Tsay

  Hiro Kanemasu John Wetz

  Dean Wichern

  Below is part of Bill's letter:

  My first day in Madison was memorable. I arrived on a Saturday, to register at the last possible moment. I was working that summer in Whiting, Indiana for John Gorman, and did not want to leave. I was having a lot of fun working there, on such things as nonlinear estimation. You came breezing through the department (which, as you recall, was in the house on Johnson Street) about lunch time and asked if I had any plans for lunch. I said no, and you invited me to join you and Gwilym. I then sat in the back of your VW van as you gave him a tour of Madison, which included the zoo.

  You stopped at El Rancho for some things for dinner, and, before I knew it, I was having dinner with all of you. There was champagne, which came out of the newly opened bottle in an overly vigorous way, which got everything, tablecloth and all, wet. Napkins were pushed under the tablecloth, which gave the otherwise formal setting, a somewhat casual and definitely lumpy appearance. As I recall, the champagne was a last-minute idea as an addition to the menu, and the bottle was not sufficiently chilled. In any event, a fine time was had by all, and the evening went on to songs by you and Gwilym. I think you both had guitars, and at one point you were singing statistical songs, impromptu efforts in rhyme, with you and Gwilym taking turns.

  It was a magical day. About 2 am I left. As I was walking away in the night I thought to myself, ‘What a splendid day. It was wonderful. When I tell anyone about it, they won't believe it. Neither will I. I should have a momento. The champagne bottle is a possibility. That would be nice to have.' I turned around, returned, knocked on the door. You looked more than a little surprised when you answered the door, because being called on at 2 am is quite unusual. I explained that I’d like to keep the champagne bottle, and you said fine. That was the end of my first day in Madison.