An Accidental Statistician E-Book

George E. P. Box

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 455

Veröffentlichungsjahr: 2013

Beschreibung

Celebrating the life of an admired pioneer in statistics

In this captivating and inspiring memoir, world-renowned statistician George E. P. Box offers a firsthand account of his life and statistical work. Writing in an engaging, charming style, Dr. Box reveals the unlikely events that led him to a career in statistics, beginning with his job as a chemist conducting experiments for the British army during World War II. At this turning point in his life and career, Dr. Box taught himself the statistical methods necessary to analyze his own findings when there were no statisticians available to check his work.

Throughout his autobiography, Dr. Box expertly weaves a personal and professional narrative to illustrate the effects his work had on his life and vice-versa. Interwoven between his research with time series analysis, experimental design, and the quality movement, Dr. Box recounts coming to the United States, his family life, and stories of the people who mean the most to him.

This fascinating account balances the influence of both personal and professional relationships to demonstrate the extraordinary life of one of the greatest and most influential statisticians of our time. An Accidental Statistician also features:

• Two forewords written by Dr. Box’s former colleagues and closest confidants

• Personal insights from more than a dozen statisticians on how Dr. Box has influenced and continues to touch their careers and lives

• Numerous, previously unpublished photos from the author’s personal collection

An Accidental Statistician is a compelling read for statisticians in education or industry, mathematicians, engineers, and anyone interested in the life story of an influential intellectual who altered the world of modern statistics.

Leseprobe

Table of Contents

Title Page

Copyright

Dedication

Foreword

Second Foreword

Preface

Acknowledgments

From The Publisher

Box Titles Published with Wiley

Chapter One: Early Years

Chapter Two: Army Life

The Experimental Station at Porton Down

Chapter Three: ICI and the Statistical Methods Panel

Chapter Four: George Barnard

Chapter Five: An Invitation to the United States

Chapter Six: Princeton

Chapter Seven: A New Life in Madison

Chapter Eight: Time Series

Chapter Nine: George Tiao and the Bayes Book

Chapter Ten: Growing Up (Helen and Harry)

Chapter Eleven: Fisher—Father and Son

Chapter Twelve: Bill Hunter and Some Ideas on Experimental Design

Chapter Thirteen: The Quality Movement

Chapter Fourteen: Adventures with Claire

Chapter Fifteen: The Many Sides of Mac

Chapter Sixteen: Life in England

Chapter Seventeen: Journeys to Scandinavia

Chapter Eighteen: A Second Home in Spain

Chapter Nineteen: The Royal Society of London

Chapter Twenty: Conclusion

Chapter Twenty One: Memories

Index

Copyright © 2013 by John Wiley & Sons, Inc. All rights reserved

Published by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

Box, George E. P.

An accidental statistician : the life and memories of George E.P. Box / George E. P. Box.

pages cm

Includes index.

ISBN 978-1-118-40088-3 (cloth)

1. Box, George E. P. 2. Statisticians\endash United States\endash Biography. I. Title.

QA276.157.B69A3 2013

519.5092–dc23

[B]

2012040251

This book is dedicated to my students, with whom

it was my privilege to work, and who became my friends.

Foreword

Virginia Woolf wrote about a character with a mind that “kept throwing up from its depths, scenes, and names, and sayings, and memories and ideas, like a fountain spurting over.” George Box is the embodiment of that active mind. Dinner with George is a spurting of stories, poems, songs, and anecdotes about his work and his friends. An Accidental Statistician jumps you into that fountain of ideas. It is great fun even if books about statistics and science are normally absent from your reading list.

No doubt many readers think, as I once did, that the subject is difficult and dull. Here we have a charming and colorful storyteller who quotes Yogi Berra in a discussion on the analysis of variance; has Murphy, of Murphy's Law fame, ringing the alarm when there is an opportunity to make things better; and explains an experiment with critical variables named “banging” and “gooeyness.” There are stories about composite designs, time-series forecasting, Evolutionary Operation, intervention analysis, and so on, but they are not mathematical, and most include personal anecdotes about people who were involved in their invention and original application. You learn about statistics and science and, simultaneously, meet a literal Who's Who of statisticians and scientists, and the Queen of England as well.

I met George Box in 1968 at the long-running hit show that he called “The Monday Night Beer Session,” an informal discussion group that met in the basement of his house. I was taking Bill Hunter's course in nonlinear model building. Bill suggested that I should go and talk about some research we were doing. The idea of discussing a modeling problem with the renowned Professor Box was unsettling. Bill said it would be good because George liked engineers. Bill and several of the Monday Nighters were chemical engineers, and George's early partnership with Olaf Hougen, then Chair of Chemical Engineering at Wisconsin, was a creative force in the early days of the newly formed Statistics Department. I tightened my belt and dropped in one night, sitting in the back and wondering whether I dared take a beer (Fauerbach brand, an appropriate choice for doing statistics because no two cases were alike). I attended a great many sessions over almost 30 years, during which hundreds of Monday Nighters got to watch George execute an exquisite interplay of questions, quick tutorials, practical suggestions, and encouragement for anyone who had a problem and wanted to use statistics. No problem was too small, and no problem was too difficult. The output from George was always helpful and friendly advice, never discouragement. Week after week we observed the cycle of discovery and iterative experimentation. We saw real examples that, “All models are wrong, but some are useful.” We saw how statistics is a catalyst for scientific method, and how scientific problems catalyze ideas for doing statistics. What a treat.

My business is water quality engineering. One night I wanted to discuss a problem that involved a measurement called the Biochemical Oxygen Demand (BOD). George asked whether it would be all right for him to explain this BOD test. He gave as good an explanation as I ever heard. I asked how he happened to know that and learned that at age 16, he took a job as an assistant chemist in a sewage treatment plant. One year before I was born, in 1939, at age 19, he published a paper about oxygen demand in the activated sludge wastewater treatment process, which at the time was new and poorly understood. George's paper can stand with papers on the subject written by some famous Wisconsin engineers who worked on the problem at about the same time. In the 1990s, 55 years later, George and I worked on forecasting the dynamics of activated sludge process performance using multivariate nonstationary time series. Imagine that from a world-famous statistician who was one of the earliest researchers on this widely used wastewater treatment process.

George and I have one bit of unfinished piece of business. A 20-foot-tall civil war soldier guards the stone arch entrance to Fort Randall Park, which is next to the engineering building and the statistics building at the University of Wisconsin—Madison. George had thought for some time that the soldier should have a medal. In 1993, we found a suitable brass medal in a sidewalk stall near Hyde Park, London, but our plan to hang it around the soldier's neck was never fulfilled. I now believe that the medal should stay with George as an award of merit for memoir writing. He deserves it. (And we two old friends do not have to climb the soldier.)

Last night, May 10, 2012, my wife and I had dinner with George and Claire at their house in Shorewood Hills. He said, “The memoir is finished.” I asked, “What's your next project. It's hard to picture you not doing some writing every day.” He answered, “I 'm thinking of a paper about Fisher's idea on multiplicative effects in experiments.”

An Accidental Statistician is finished, but apparently George is not. That is good news. Thank you, George.

P. Mac Berthouex

Emeritus Professor

University of Wisconsin

Second Foreword

It is a pleasure to welcome this autobiography of an extraordinary scholar and gentleman: George Edward Pelham Box. My intersection with George Box's long and active statistics career begins in the summer of 1952, when I was a research associate at the Aberdeen Proving Grounds, MD, working for Dr. Frank Grubbs. Dr. Grubbs and I together read George Box's wonderful paper on response surface experimentation,1 and I recall how we both marveled at its simplicity … obvious of course now that the message was offered! Originality and elucidation are the signs of Box's genius. On returning that September to my graduate studies at the Institute of Statistics, NC State, in Raleigh, I learned that George Box had agreed to come to Raleigh for a year as a visiting Research Professor. In January 1953, I became his first graduate student.

It's a pleasure to read about George's boyhood. His father worked hard to provide a modest family environment in a society that offered advantaged youths the greatest opportunities. We learn how George, through the good fortune of meeting alert teachers, uncovered his talents as a writer and more modestly in mathematics. He starts his young adult life as an assistant chemist collecting data on wastewater treatment, and it is here that his career as a statistician begins. And what a career it proved to be!

One of George Box's distinguishing characteristics is that he only occasionally published a paper as a sole author. This memoir introduces us to a host of his students and research associates, and it provides colorful vignettes of these many wonderfully varied personalities who became his co-authors. Some ten years ago, a group of his students gathered together a compendium of his papers covering the statistical fields of quality, experimental design, control, and robustness.2 Both neophytes and savants have found the exposition within these many papers superb. Of course, there are also his co-authored textbooks on experimental design,3 time series analysis,4 Bayesian inference,5 and control,6 wherein elucidation of the subject's theory and application repeatedly prove both original and illuminating. For George Box, the acronym “KISS” translates into “Keep It Sophisticatedly Simple.”

I found one recollection of George Box's early statistical experiences particularly fascinating. Near the end of World War II, the British came into possession of German explosive shells containing unknown deadly gases. George was part of the small group that first determined the spectacular deadliness of tiny concentrations of these new reagents (actually nerve gases). They were never employed in warfare, but had portions been dropped over major cities, the population consequences could easily have rivaled those of Hiroshima and Nagasaki. To have been present working along that thin boundary keeping the world from additional disaster is impressive.

We learn, too, of those whom George Box considered his mentors and hear tales of his early collaborations with others well known among the statistical fraternity. And throughout this autobiography, we become aware of Box's broad contributions to modern statistical theory and practice. His papers and books have vastly expanded awareness of Bayesian methods and time-series modeling. We find the production of information-laden data to be a statistical specialty that enhances scientific progress as it moves from initial conjecture through experimentation and data analysis, leading on to new conjecture. And beyond statistically formal matters, we also capture his deep appreciation for the mind's ability, or better still that of a collection of minds, to give birth to new models and not usual conjectures. It seems that George Box's advice to all those pondering a problem is to be sure to think out of the box.

J. Stuart Hunter

Professor Emeritus

Princeton University

1 “On the Experimental Attainment of Optimum Conditions” Box, G. E. P. and Wilson, K. B. (1951) Jour. Royal Stat. Soc. Series B, 13, 1–45.

2Box on Quality and Discovery: George Tiao, Søren Bisgaard, William J. Hill, Daniel Peña, Stephen M. Stigler. (2000) John.Wiley & Sons.

3Statistics for Experimenters: Box, G.E.P, Hunter, William G. and Hunter, J. Stuart (1978) John Wiley & Sons.

4Time Series Analysis: Forecasting and Control: Box, G.E.P and Jenkins, Gwilym M. (1970) Holden Day.

5Bayesian Inference in Statistical Analysis: Box, G.E.P. and Tiao, George C. (1973) Addison Wesley.

6Statistical Control by Feedback and Adjustment: Box, G.E.P. and Lucño, Alberto (1997) John Wiley & Sons

Preface

There is a story about a very tall man who was walking with his four-year-old son to pick up a newspaper. He suddenly realized that his son was having difficulty keeping up with him. He said, “Sorry, Tommy, am I walking too fast?” And the boy said, “No, Daddy, I am.”

Now this account can be viewed in two ways: as an amusing story, or joke or, as illustrating the essence of scientific discovery. The boy's view of the situation was correct but not obvious. The father's view was obvious but wrong.

So it is perhaps no coincidence when humor and scientific insight come together. Good science is a form of wit, of seeing the joke that nature is playing on us.

At 93, I can look back on quite a few examples.

The Box family circa 1895. From left clockwise, Uncle Bertie, my grandfather and grandmother, my father, Aunt Daisy, Uncle Pelham, and Aunt Lina.

Acknowledgments

For much of the time that this memoir was being written, I have been quite ill. This has placed an enormous burden on my wife, Claire, who herself has been ill during much of this time. Had it not been for her devoted help, so generously given, this memoir could never have been written. This help has been realized by a practical, ingenious, and well-trained mind. Whenever there is a crisis, she has not only known what to do, she has done it with cheerful understanding and expertise.

In addition, I am especially grateful to:

Bovas Abraham

Judy Hunter

David Bacon

Stu Hunter

Ford Ballentyne

Brian Joiner

Ernesto Barrios

Tim Kramer

Mac Berthouex

Kevin Little

Sue Berthouex

Alberto Luceño

Claire Box

Merve Muller

Joan Box

Vijay Nair

Helen Box

Lars-Erik Öller

Harry Box

Judy Pagel

Robin Chapman

Daniel Peña

Norman Draper

José Ramírez

Conrad Fung

Marian Ros

Larry Haugh

Xavier Tort

Margaret Homewood

John Sølve Tyssedal

Brent Nicastro for his permission to use various photographs.

And to Judith Allen, my friend.

From The Publisher

To those of you who do not know George Edward Pelham Box well, suffice it to say that he is a titan in the field of statistics. He is a self-taught statistician who utilized his experience and knowledge of statistics to create unique contributions to many areas particularly in process improvement. And, he is a nice guy, to boot. He rarely—if ever—needs an introduction. His very presence is our present.

This book is being published in the year of George's ninety-fourth birthday as a memoir of his life, his friends, and his contributions. We know that, during his academic tenure, he wrote over 2000 journal articles; published twelve books for Wiley alone (see list below) resulting in over a quarter-of-a-million copies sold worldwide; and was responsible for helping to get Technometrics, a joint publication of the American Society for Quality and the American Statistical Association, off the ground.

We also know from first-hand experience that George is a true gentle-man, a loving father, and a dedicated husband. He has influenced the lives, in no small way, of everyone he has touched, from young aspiring statisticians to experienced editors-in-chief. When you see a grin on his face, you know that he is about to espouse a bit of wisdom mixed-in with a tad of advice and always with a joke. He most often accomplishes what he sets out to achieve, without fanfare or accolade. He is probably the most unforgettable character a graduate student or editor-in-chief has ever had the experience and pleasure to know.

Two people have assisted George in the production of this book. They include his loving wife of twenty-seven years, Claire Box, and his friend and research assistant, Judith Allen, both of whom supported him as he wrote this book.

The management and staff of Wiley commend Dr. Box for all that he has done to enrich the world of statistics, both here and abroad. We wish him continued “presence” and the peace of mind that he will always remain a titan in the written word and in our hearts for generations to come.

Box Titles Published with Wiley

Evolutionary Operation: A Statistical Method for Process Improvement

Box-Draper, 1969

Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building

Box-Hunter-Hunter, 1978

Empirical Model-Building and Response Surfaces

Box-Draper, 1986

Bayesian Inference in Statistical Analysis

Box-Tiao, 1992

Statistical Control: By Monitoring and Feedback Adjustment

Box-Lucno, 1997

Evolutionary Operation: A Statistical Method for Process Improvement

Box-Draper, 1998

Statistics for Experimenters: Design, Innovation, and Discovery, 2nd Edition

Box-Hunter-Hunter, 2005

Improving Almost Anything: Ideas and Essays, Revised Edition

Box-Friends, 2006

Response Surfaces, Mixtures, and Ridge Analyses, 2nd Edition

Box-Draper, 2007

Time Series Analysis: Forecasting and Control, 4th Edition

Box-Jenkins-Reinsel, 2008

Statistical Control by Monitoring and Adjustment, 2nd Edition

Box-Lucno-Paniagua Quiñones, 2009

An Accidental Statistician: The Life and Memories of George E.P. Box

Box, 2013

“Who in the world am I? Ah, that's the great puzzle.”1

Chapter One

Early Years

Gravesend, where I was born, is about 25 miles east of London on the River Thames. The river there is about a mile across, and at that time ships from all over the world came by on their way to the London docks. As a ship would come up the river, three tugs would hurry across to its side and accompany it while it moved on. From the first of these, you could watch the pilot climb aboard; then, from the second, the health officer; and finally the customs officer. There were occasionally large vessels coming from the Far East, Australia, New Zealand, or India that could not travel further, and so they were moored in the middle of the river. Thus, Gravesend was very much concerned with the sea, and people such as pilots, lightermen, and customs and health officials abounded (Figure 1.1).

Figure 1.1 Pilot leaving Terrace Pier, Gravesand, Original by Anthony Blackman.

My grandfather, also named George, was a grocer and an “oil and color” merchant—that is, one who sold paint. My father, Harry, was the youngest boy. My father's oldest brother, whom we called “Uncle Bertie,” attended private school and took degrees in theology and semitic languages at Oxford. He became a rector, wrote a number of esoteric and scholarly books, and was rarely heard from again.

In 1892, Pelham, the second son, was lured under false pretenses to make his fortune in the United States. He was about 20 when he got off a train in Nebraska to find nothing but the howling wind, but he later returned and stayed in the United States, becoming a citizen and eventually working for the railroad in Chicago. When he retired, he moved to Florida where he had a small citrus grove.

Over the years, my family fell on increasingly difficult times. My father had hoped to go to engineering school, but by the time he was a young man, the family had little money and he had few career choices. Two sons had already left, so my father stayed and found work as a “clothier's assistant.” He had a hard life. When I was growing up, he still worked in a tailor shop, at Tilbury docks, across the river from Gravesend. To get to work from our house on Cobham Street, he had to walk about a mile to the Town Pier at the bottom of High Street, cross on the ferry, walk some more, get on a train that took him to Tilbury docks, and then walk again to get to the shop. In the evening, he would face the same journey in reverse, sometimes in the pouring rain. He was poorly paid—two pounds ten shillings a week was barely a living wage.

Because people had to use coal for heating and cooking, the resulting fog could sometimes be so thick that objects four or five feet away were invisible. My father got across the river then in a small boat. On foggy days, lightermen (who transferred goods between ships and docks) made extra money by taking people across.

When I was about nine, I learned to use stilts, and walking on these, I would meet my father at the end of our road. He would sometimes have a pennyworth of roasted chestnuts in a paper bag that he would share with me.

From the time I was about five years old, I sometimes went with him to Tilbury. I liked perching myself at the very front of the ferry and watching it cut through the water. My father had a friend called Mr. Launder who kept a tobacconist and barber shop at Tilbury docks. Mr. and Mrs. Launder, who did not have any children, liked for me to come and visit them. I provided some entertainment to the people waiting at the barber shop by reciting poetry. I remember one poem that began, “Great Wide Beautiful Wonderful World,” and a line I liked was “World, you are beautifully dressed.” I enjoyed poetry and tried writing some myself.

Despite his hard life, my father was a happy man. With the help of my sister Joyce, he would frequently organize picnics and parties. Our parties were not like parties now. There were no alcoholic drinks. (It wasn't that we were teetotalers; we just didn't have any money.) We gathered around the piano and sang sentimental Victorian songs; most of these sound pretty silly now. We also played all kinds of party games: musical chairs, hunt the slipper, “murders,” and so forth. In addition, we performed plays of our own invention. And there were mysteries when my father demonstrated the power of the magic wand.

When we wanted to go somewhere for a picnic, we walked. Cars were for rich people. Although we did not have a car, we did have a “barrow,” which we pushed. This was my father's invention. It could be steered with two pieces of rope, and in the back, it carried supplies: cricket bats and picnic things. We would walk with the barrow to some pretty place we liked, perhaps about three or four miles away.

The countryside was lovely. Cobham village was only four miles away, and the church and the two pubs there were old, unspoiled, and beautiful. One pub was called the Dickens Inn because Charles Dickens had written some of his books there, and he chose this locale for some of his stories. In his book Great Expectations (1860, Chapman & Hall), you will find, for example, that the prison ship from which the convict Magwitch escaped was just below Gravesend, and it was near Gravesend, that Magwitch was finally caught. Close at hand inland was the village of Meopham (pronounced “Meppam”), with a fine cricket field, and a lovely place for picnics called the Happy Valley. There we sat in the grass, made a fire for cooking and heating water for tea, and we sometimes played cricket.

My mother had a difficult life, with such meager resources, trying to provide for a family. She fed and cared for not only our immediate family but also for various relatives who lived with us while I was growing up. And she also had to contend with my father, whose kindness and generosity knew no bounds. I am afraid her life was often one of quiet desperation.

But it was not all gloomy. Sometimes we went to the park on Windmill Hill, where we would play and my parents would have a beer at the pub that backed up to the park. On other occasions, my mother and my father would go out together in the evening, perhaps to see a movie, and my sister Joyce would take care of my brother and me (Figure 1.2).

Figure 1.2 Growing up, Clockwise from left to right, me, my brother Jack, and my sister Joyce.

Joyce was ten years older than me. Her mother, my father's first wife, had died in an influenza epidemic. Joyce could always come up with an exciting game, and we often played cowboys and Indians. Joyce had a lot of responsibility within the family but was a very good sport about it. In addition to watching over my brother and me, she was also my father's chief helper around the house. My father was a wonderful handyman, and this was fortunate because we had so little money. He could do most things that others hired people to do: roof mending, gas fitting, paper hanging, and so on. But every now and again, he and Joyce quarreled and Joyce would run downstairs very upset and say, “I won't help him anymore!” After about ten minutes, my father would come downstairs and apologize. Then they would make up and things would go along quietly for a bit (Figure 1.3).

Figure 1.3 My father and Joyce.

In 1926, a man called Alan Cobham became famous when he flew from England to Australia and back, landing his plane in the River Thames in front of the Houses of Parliament. He was promptly knighted. Later, Sir Alan formed Cobham's Flying Circus, a group of fliers that went around England showing off their skills and giving plane rides to the public.

In the early 1930s, Cobham's Flying Circus was performing in a field close to Gravesend and Joyce and I went to watch. Plane rides were part of the show, and to my astonishment, Joyce said, “Come on, Pel, let's go up in an airplane!” I said, “But Joyce, it's five shillings!” Five shillings seemed a huge amount of money. “Just this once,” she answered, and so up we went in this small plane and thrilled to the views of town and countryside. Although it wasn't a very long flight, it was my first and I never forgot it.

Joyce worked at Woolworth's, where she eventually became an overseer. I realized much later how she had contributed substantially to the family budget for many years and, in particular, how her sacrifice had made it possible for my brother Jack and me to get an education. I know if she had had the chance, she would have done just as well.

My brother Jack was three years older than me. He could not have been more than 13 when he became very interested in amateur (ham) radio. He designed and built a transmitter, and as he couldn't apply for a ham radio license until he was 17, for some years, he had a “pirate” station. The town had many ham radio enthusiasts, and they used to communicate with others throughout the world. When you made a contact, you exchanged “QSL cards.” These were decorated postcards showing your amateur station's designated call sign in large letters (G6BQ in my brother's case). You might be particularly proud, for example, of a QSL card from some remote part of China. The cards were often used by hams to decorate the walls of their “shacks.” Jack used a small shed that my father had constructed at the back of the house for his shack. Thinking about it now, my father, sister, and I formed a cohesive group. Jack was always happy with his radio (Figure 1.4).

Figure 1.4 Jack's radio.

Behind the houses on Cobham Street, there was an extensive area of allotments. These were rectangular plots of land that you could rent for growing vegetables. They also proved useful for erecting antenna poles to achieve long-range radio contact. Erecting an antenna pole was quite a task, so friends and other hams came and helped. Reception depended to some extent on the direction in which the antenna was pointing, so Jack managed to persuade a number of allotment holders to allow poles to be erected on their plots so that he had antennas facing in all directions. From the nearby railway station, you could see the various antennas, and stories got around, especially during the Cold War, about their purpose. I remember one ham radio colleague complaining to me about the number of Jack's poles. He said, “I don't mind helping him with one pole, but he wants them all over the place.”

There was a scheme to take over the allotments to build a car park for the many people who took the train to London. This plan didn't suit Jack, and for weeks he went around collecting signatures opposing the car park, arguing disingenuously that the allotments were needed to grow food. His scheme worked for a number of years, but I have seen in a recent photograph that the car park is now firmly established.

When I was about ten I came a cross a book called The Boy Electrician.2 The fascinating thing about it was that it was a “can do” book. The apparatus and experiments that the author described could all be constructed from components which were readily available. He told for example how to make an electric bell or burglar alarm, a morse telegraph, an experimental wireless telephone and an electric motor.

From the first day I saw it, the book was seldom in the library. I had a friend, Jim Tatchol, who was equally interested and we spent hours together making, or trying to make, the things in the book. In doing so we learned a great deal. We were also fortunate in having a very sympathetic physics teacher who after school spent hours with us helping to make things work.

When I was about eleven years of age, I used The Boy Electrician to build myself a crystal set. With this I would listen to the BBC on headphones after I went to bed. From about 10 p.m. until midnight, the station transmitted live dance music from one or another of the big hotels in London. They all had dance bands, one of the most famous being the Savoy Hotel Orpheons. Others were named for the dance bandleaders: Jack Payne, Harry Roy, Geraldo, and so on. I can still sing many of the songs that were popular then. My antenna was looped around the ceiling, and I could get good reception provided that my brother was not on the air.

The establishment of the BBC as an independent entity was largely due to its first director, Sir John Reith, to whom we remain forever grateful. Sir John, however, was very religious, so on Sundays, the station carried only religious programs. On those days, we listened instead to Radio Luxemburg and Radio Paris, which were commercial stations that carried special programs in English. I can still remember the jingles that accompanied the commercials, such as:

We are the Ovaltineys,

Little boys and girls;

Make your request, we'll not refuse you,

We are here just to amuse you.

Would you like a song or story?

Will you share our joys?

At games and sports we're more than keen;

No merrier children could be seen,

Because we all drink Ovaltine,

We're happy girls and boys!

[Citation: Harry Hemsley, “We Are the Ovaltineys,” 1935; theme song on Radio Luxembourg show, “The Ovaltineys Concert Party” from 1935 to 1940.]

My family lived in a rather large, semidetached house at 52 Cobham Street, which as I mentioned, we often shared with relatives and friends. When I was small, there was Mr. Strickland, a lodger, who lived downstairs in the basement. My mother told me that as a child I walked in my sleep and on one occasion had walked down three-and-a-half flights of stairs and said to Mr. Strickland, “Go away, Stricky, I'm in the middle of a dream.” After Mr. Strickland died, we took over the two basement rooms for a kitchen and dining room.

As a child, my best buddy was my maternal grandmother. I used to sit on her bed, and she told me stories and read to me. This was when I first heard what is still my favorite book, Alice in Wonderland. Except for the kitchen, the rest of the house was not heated, but there was always a fire in Grandma's room and I used it to make hot buttered toast for both of us. When she died and I couldn't find her, an aunt told me that she had “gone to live with Jesus.” I said, “I don't want her to live with Jesus. I want her to live with me.”

Aunt Lina, my father's sister, lived in a room on the ground floor of our house when I was about ten years old. (She is pictured at lower right in the 1893 Box family photo locates in the Preface.) Aunt Lina read a lot, but she was stone deaf. I could only communicate with her by writing things down, and she enjoyed this. I must have realized how lonely her life was because I taught both of us sign language, and from then on, we communicated with our hands. One game that greatly amused her was when the family was gathered around the table for a meal. I would sign a funny message with my fingers, such as “Uncle So and So makes a terrible noise when he's drinking soup,” and she would go into fits of laughter. The joke was, of course, that normally she was entirely cut off from what was being said, but this message only she and I could understand.

After I went to grammar school, I had a friend, Cyril Jones, whose parents had a car. One day we drove down to a place called Tudely-cum-Caple near Dover to see Aunt Daisy, who was my father's other sister. She and her husband had a small holding that did not look very prosperous. Soon after this, her husband died and Aunt Daisy came to live with us. She also was deaf, but not totally, and she had a very primitive hearing aid. She liked to dance, and I was frequently recruited as a partner (Figure 1.5). Like my father, she was a happy person and liked to play the piano and sing.

Figure 1.5 Dancing with Aunt Daisy.

And then there was Uncle Willy, who was actually my father's first cousin. He lived 12 miles away in Gillingham and, to my mother's dismay, would turn up unexpectedly and expect to be fed. He had money, which we didn't, so we did our best not to offend him. He had worked for the Admiralty on airship design and had helped design the airship R33, which crashed. He had also been on a trip up the Amazon River, and he had composed a long lecture, “One Thousand Miles Up the Amazon,” which he illustrated with lantern slides. He endlessly rehearsed this at our house, consulting my father on the text. I can remember my father coming home from a hard day's work and my mother's cry of despair, “Uncle Willy's here.” He was very mean with his money, and I recall him telling my mother how he had once saved a penny by changing buses on his way to see us.

Uncle Willy eventually died, and we inherited his musical instruments, which included a banjo, a guitar, a violin, an organ, and a player piano. My father could produce a tune from almost any musical instrument, but what he liked best was what we called the organ, which was really a souped-up harmonium.

Willy had been a keen photographer, so we also inherited a very nice set of lenses. As a boy, I very much wanted a camera, but we didn't have any money to buy one. I saw an advertisement for a new newspaper, The Daily Herald, that was to begin publication. To encourage circulation, they printed a coupon with each issue and after you had collected 100 consecutive coupons, you could get a free camera. My father was already receiving a different paper, the Daily Chronicle—we called it the Daily Crocodile—which was more aligned with his political views. With his typical kindness, he switched to the new paper (although he much preferred the other), during the time it took to collect the coupons and I got my camera.

I used Uncle Willy's lenses to build an epidiascope projector so that I could put on “shows” of the photos that I took of family picnics and outings (Figures 1.6 and 1.7). I built it of wood, painted the inside black, and used two 100-Watt bulbs that heated up to the point that those in attendance experienced some rather strong fumes. To make it a proper show, I hung a white sheet on the wall for a screen. I also wrote and projected commentary cards to accompany the photos that said things like, “Hello Uncle Jack and Aunt Maggie. Many happy returns of the day.”

Figure 1.6 A family picnic. From left to right, my brother Jack, his wife Gladys, Joyce with her husband Alfred, and cousin Vera.

Figure 1.7 Uncle Jack and my father bringing tea from a local house to the rest of us picnicking at Happy Valley.

My father also inherited some money, but here Uncle Willy's meanness was catastrophic. To save money, he had not employed an attorney to help him write his will. Instead he had purchased a form for sixpence. The will said that his money was to be divided into six parts, one of which was to a charity. On the strength of this, my father bought the house for which we had previously been paying rent. However, one of the intended recipients of the proceeds of the will had died and the lawyer for the charity disputed the will. The lawyers for the various parties argued about this until most of the money was gone, leaving my father a debt that was a great worry to him.

In England, an elementary education was available to all but you were taught very little—mostly how to read and write and to do simple arithmetic. The classes were very large, and you left when you were 14 years old, usually to get a menial job. There was no possibility of escape unless your parents could pay for you to go to a grammar or secondary school, which of course mine couldn't. It was possible to get a scholarship, but there weren't very many of these. The class system based on money was heavily entrenched.

Mr. Spencer, the headmaster of the elementary school I attended, by some means or other, became aware of a poem I had written. To check me out, he told me to sit at a table next to his desk and write poetry. I wrote four poems. After this, he had me stay after school to prepare under his guidance for the scholarship examination.

I remember that during the oral exam I happened to say the word “chimney,” which I pronounced “chimley.” The examiner asked, “How do you spell chimley?” I spelled it correctly, so he said, “Well why do you say chimley?” I passed, and soon after I went to the new school, which was called the County School for Boys. I started in the second form, at age ten (Figure 1.8). There was another boy of about my age whose name was also Box (Ronald Box). He was on his bicycle when, unfortunately, he was hit by a truck and killed. The whole school of about 500 boys gathered together in the auditorium each morning with the youngest boys at the back. The headmaster announced from the platform that I had been killed. This, I think, was the only time that he said nice things about me. I am told that I walked all the way from the back to just below the platform and said, “Please, Sir, I'm not dead.”

Figure 1.8 Second form at Gravesend County School. I am the first left in the back row.

My brother Jack and I were among the very few scholarship boys in the school. Although almost all of the students came from families that had more money than mine did, I made friends. But there was one student whose mother would not allow me in the family home when her son and I played together. By contrast, the mother of my friend, “Ginger” Harris, thought I was a good influence on her son. I was never particularly strong, but I made up for my lack of physical prowess by inventing games that the other boys enjoyed.

The second form started immediately with French, Latin, English grammar, English literature, physics, and chemistry. We also began mathematics—first algebra and then geometry—and we began calculus in the upper fourth form. My first math teacher nobody liked. He was sarcastic and unresponsive to questions. But later we had a different math teacher, Mr. Marshall, who for some obscure reason was nicknamed “Banners.” He was genuinely anxious that everyone in the class understand the lessons, and he was tireless in explaining difficult points. With his guidance, I quickly moved ahead in the class.

I remember one incident with Banners when one of the boys had brought his pet mouse to school in a little box. During class he was showing his mouse to a friend when it jumped loose and started to run about in the front of the room. Banners pursued it with the pointer, and after a number of near misses, the mouse took refuge under a radiator. The little boy who was owner of the mouse remarked, “Please, Sir: that's my mouse!” Banners replied very apologetically, “Oh I beg your pardon. I didn't know it was a private mouse.”

Unfortunately, before I could go to the new grammar school, I had been subjected to a “health examination” and it was decided (on what grounds I never understood) that I had to have drops in my eyes for six months. As a result, for much of the first year, I couldn't see what was written on the blackboard and had difficulty reading the printed page. I missed such things as the beginning of French, algebra, and English grammar. My father did his best to help and wrote out my homework for me as I dictated. It took a very long time to catch up with my studies, so whereas in elementary school I had been close to the top of my class, at the new school, I had to get used to being close to the bottom. By age 16, when one or two of the boys got to go to a university, I was not among them.

During all this time, Mr. Spencer from the elementary school remained my friend. He was also head of the Sunday school, and our house was on the way to his, so each week after Sunday school, we would walk home together and we discussed just about everything.

One thing I made which was a success was what was called a shocking coil, which was a watered down version of an induction coil. This consisted of a core, which was made of slives of iron wire, and this was wrapped with primary and secondary insulated copper wires.

Each year at our school there was a “prep fair” that raised money for the town hospital. My project for the fair was to make a shocking coil. The coil had two handles, one of which was in a tub of water. The other handle was held by the “client” who was visiting the fair. The client paid sixpence, which was dropped into a locked box. At the bottom of the tub were coins.

The client would reach into the tank to pickup some of the coins, but I had a dial under the table that was connected to a rheostat, and as the customer grasped for the coins, I turned up the dial which gave the person a substantial shock. No one managed to get any of the money until this woman came along, and when it was her turn to reach into the tank, I turned up the dial as usual, but she wasn't the least affected by the shock.

She took all of my coins and she deposited these into the locked hospital box. This left me with no coins with which to lose more clients. Finally Banners, the math master, gave me some money so that I could continue.

I wasn't much good at learning French, but a boy in my class called Newton was, and he wrote a play in French. The French teacher liked it and decided that we should put it on in the school auditorium with parents invited. I had a small part as an “Englishman who didn't know much French,” which suited me very well. The French teacher and his wife were very kind, and while rehearsing the play, we had refreshments at their house.

Because my lack of French limited my participation as an actor, I wanted to help all I could in other ways. For example, in the play, someone got shot. I found a realistic-looking toy gun for the actor to flourish, and after much experimentation, I found that a hollow pencil box struck against a plywood panel sounded very much like a pistol shot. I had to watch carefully to synchronize it with what was happening on stage to make it sound genuine.

There was one scene where people were sitting around a table having dinner. To make this look real, I persuaded my brother Jack to ride his bicycle to get six helpings of fish and chips. He arrived a bit early, and the intense smell of the fish and chips was evident for a long time in the theater before and after the actual scene.

Later I had a small part in a school play, Shakespeare's Macbeth. This was a much more serious affair. My scene occurred at night inside the gates of Macbeth's castle. The audience knows that Duncan, the king, has been murdered, but this is not known to Macduff and Lennox, who are outside the gate knocking to gain admittance. I played the part of the porter who, instead of opening the gate, engages in a long drunken harangue in which he imagines himself porter at the gates of hell. He admits a series of imaginary visitors—a farmer who hanged himself in the expectation of plenty, and so on. Finally he opens the gates to Macduff and Lennox, but the action is further held up when the porter gossips, humorously, with Macduff, a device that effectively increases the tension. At one point Macduff asks the porter, “What three things does drink especially provoke?” to which I replied:

Marry, sir, nose-painting, sleep, and urine. Leachery, sir, it provokes, and unprovokes; it provokes the desire, but it takes away the performance: therefore, much drink may be said to be an equivocator with leachery: it makes him and it mars him; it sets him on, and it takes him off; it persuades him, and disheartens him; makes him stand to and not stand to; in conclusion, equivocates him in a sleep, and giving him the lie, leaves him.3

I was keen on chemistry, and when I left school at 16, I got a job as an assistant to a chemist who managed the sewage treatment plant at Gravesend. I became very interested in the activated sludge process responsible for producing a clean effluent that would not pollute the river, and the first article I ever published was about this topic.4 While at the plant, my goal was to get an external degree in chemistry from London University. I wasn't paid much, but I was allowed two free afternoons a week to go to Gillingham Technical College where I could attend the necessary courses.

To get to Gillingham, if I had the money, I sometimes took the train, but most often I rode my bike 12 miles along the hilly and busy road that passed through Stroud, Chatham, Rochester, and Gillingham. One day my plans almost came to a sudden end when a truck driver's error sent my bicycle and me skidding under his vehicle. His back wheel just missed my head, and my bicycle was a wreck I spent about eight months writing to his insurance company trying to get them to pay to replace it. After months of arguing, they finally did.

To get an external degree in science at London University, you had first to pass the Intermediate Science Exam. After that, with a year or two of further study, you could attempt the Bachelor of Science degree exam itself. I had to go to London to take the intermediate exam, which included a two-day practical exam as well as a week-long written part. My subjects were pure and applied mathematics, physics (heat, light and sound, electricity, and magnetism), and chemistry (organic and inorganic). These were the most difficult exams I ever took, but I passed and they helped me get a grounding in science that has been invaluable ever since.

I believe that it was this basic scientific knowledge that helped me later on to come up with ideas in the development of statistics. It would, I think, be tremendously helpful if, before taking a degree in statistics, there was a requirement to pass a similar preliminary exam in science. A serious mistake has been made in classifying statistics as part of the mathematical sciences. Rather it should be regarded as a catalyst to scientific method itself. Proper preparation for a degree in statistics should be like that for the intermediate science exam described above, which would include running real experiments.

1 All quotations appearing above chapter titles are from Lewis Caroll, Alice's Adventures in Wonderland, originally published in 1865 by Macmillan.

2 Alfred P. Morgan, The Boy Electrician, Lathrop, Lee & Shepard, 1913

3 William Shakespeare, The Complete Works of William Shakespeare, Vol. 2, Garden City, NY: Nelson Doubleday, Inc., nd, p. 799.

4 Ronald Hicks and G.E. Pelham Box, “Rate of Solution of Air and Rate of Transfer for Sewage Treatment by Activated Sludge Process,” Sewage Purification, Land Drainage, Water and River Engineering, Vol. 1, June 1939, pp. 271–278. Hicks was my supervisor but did not take part in writing the article.

“Contrarywise, if it was so, it might be: and if it were so, it would be: but as it isn't, it ain't. That's logic.”

Chapter Two

Army Life

At home in Gravesend, my family congregated for meals and other activities in the basement kitchen. When it had become clear that war was inevitable, my father, who had experienced the First World War, went to the wood yard and bought a number of very large wooden beams with sections of about 8 inches by 8 inches. With these he fortified the walls and ceiling of the downstairs kitchen so that in an air raid we were less vulnerable.

For many months before war was declared in 1939, people in Britain had been warned what to expect: raids of hundreds of enemy planes dropping bombs and poison gas. Everyone had been issued a gas mask that was carried in a cardboard box. At 11 a.m. on September 3, 1939, Prime Minister Neville Chamberlain announced on the radio that we were at war with Germany. Almost immediately the air raid sirens blew, so my family went to the downstairs kitchen, but once there, we realized that we might be short of drinking water. In the kitchen was our zinc bathtub in which each family member took a weekly bath. We hoisted the tub onto the sink and filled it with water from the tap, forgetting how heavy it would become. In our attempt to lift it down, most of the water spilled onto the floor, so apart from everything else, we had a small flood. After about three quarters of an hour, we heard the “all clear” siren. Our first air raid warning had in fact been a false alarm. This was the beginning of the “Phoney War,” a period of about eight months when neither side did very much, at least in terms of a land war.1

As a teenager in the 1930s, I was interested in politics. I was particularly angry at the British government because it seemed they had done nothing to stop Adolph Hitler. His aggressions and absorption of one country after another clearly pointed to a plan for world domination. Six weeks after the war began, I turned 20, the age required at that time for enlistment into the Army. I stopped working on my chemistry degree, went to the nearest enlistment office, which was in Chatham, and joined up.

During my first week in the Army, I was told to read Company Orders each day and to perform any duties required of me. Sure enough, on a long list outside the Company Office, I found my name, and next to it were the words “key man.” I asked somebody what I was supposed to do as the key man, and they explained that at some time during the evening, the bugler would sound the “Buckshee Fire Call.” (This was the fire call followed by two Gs, which meant it was not for a real fire.) When you heard this, you ran down to the Company Office, and when they called your name, you shouted “present.” So I did that, but then I wondered what I was supposed to do as the key man. I asked a junior NCO.2 He said, “When you hear the Buckshee Fire Call you run down to the Company Office and answer your name.” “But,” I persisted,” What am I supposed to do