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**Twelve British Statisticians**

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### Richard H. Williams, Donald W. Zimmerman,

### Donald C. Ross and Bruno D. Zumbo

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**TABLE OF CONTENTS**

**ACKNOWLEDGEMENTS**

**INTRODUCTION**

**CHAPTER 1**-Karl Pearson: Versatile Statistical Scientist

Overview

Educational Training and Fellowship Activities

The Heart of Karl Pearson’s Versatility

The Controversial Karl Pearson

Concluding Comments

References

**CHAPTER 2**-R. A. Fisher: Contributions to Analysis of Variance and Experimental Design

Overview

Family Background and Early Vocational Choice

Experimental Design

Small Sample Theory and the Various Sampling Distributions

Population Genetics, Evolution Theory, and Eugenics

Controversies with Adversaries

Sir Ronald A. Fisher’s Publications and Honorary Awards

Concluding Comments

References

**CHAPTER 3**-Charles Spearman: Behavioral and Statistical Scientist

Overview

Educational Experience

The Classical Theory of Mental Tests

Factor Analysis

A Two-Factor Theory of Intelligence

Concluding Comments

References

**CHAPTER 4**-Florence Nightingale David: Pioneer Feminist Statistician

Overview

The Four Women Associated with Early History of Statistics

David’s Initial Vocational Frustrations

David’s Reactions to World Class Statisticians

A Sample of David’s Publications

On Entering Administration

Nan Laird’s Interview of Florence N. David

Concluding Comments

References

**CHAPTER 5**-George Udny Yule: Premier British Statistician

Overview

Family Background and Vocational Choice

Is Normality Realistic?

Professional Organizations

Yule’s Textbook

Yule’s Regression Approach

Classical Mental Test Theory

Yule’s Correlation Coefficients

Yule’s Desire to Fly

Statistical Aspects of Literary Style

A Demonstration of Yule’s Research Versatility

Concluding Comments

References

**CHAPTER 6**-Maurice Kendall: Synthesizer and Commentator of Statistics

Overview

Early Childhood and Educational Experience

Kendall Meets Yule

Random Number Generators and Tests for Randomness

Administrative Positions and Honors

Concluding Comments

References

**CHAPTER 7**-George Box: Pioneer in the Forecasting of Time Series

Overview

Educational Training

Box’s Research Contributions

Vocational Experiences

Two Interviews with George Box

Concluding Comments

References

**CHAPTER 8**-Student: Inventor of Small Sample Inferential Statistics

Overview

Student’s Background

How Student Learned Statistics

Student As A Man

Student As A Statistician

Concluding Comments

References

**CHAPTER 9**- Egon Sharpe Pearson: Contributions to Statistical Inference

Overview

Early Years and Educational Training

Egon Pearson As Teacher and Administrator

Reviews of R. A. Fisher’s *Statistical Methods for Research Workers*

Neyman-Pearson Theory of Hypothesis Testing

Egon Pearson’s 30 Year Service As Editor of *Biometrika*

Publications In Honor of His Father

Concluding Comments

References

**CHAPTER 10-** Francis Ysidro Edgeworth: Statistician and Economist

Overview

Educational Training and Vocational Experiences

Francis Bacon and Francis Ysidro Edgeworth

Francis Ysidro Edgeworth’s Research and Publications

Concluding Comments

References

**CHAPTER 11**-Maurice Bartlett: Time Series and Multivariate Statistics

Overview

Educational Training

Vocational Experience

Research Contributions

Concluding Comments

References

**CHAPTER 12**-David Cox: Multivariable Analysis of Failure Rates

Overview

Educational Background

Vocational Experience

Journal and Book Publications

Prizes, Medals, Awards, Memberships, Fellowships, and Knighthood

Concluding Comments

References

**SUMMARY**

**ACKNOWLEDGMENTS**

We are grateful to the Regents of the University of California for permission to reproduce the picture of Egon Sharpe Pearson from the frontispiece of *The Selected Papers of E. S.* *Pearson* (1966).

Thanks to Springer Science and Business Media for permission to reprint three excerpts from Constance Reid’s *Neyman…from Life* (1982). They appear on pages 24-25, 115, and 133 of her book.

We are indebted to John Wiley & Sons, Inc. for permission to reproduce the picture of R. A. Fisher from the set of plates following page 256 in Joan Fisher Box’s *R. A. Fisher*: *The Life of A Scientist* (1978). Thanks also go to this publishing house for permission to reprint two quotations from her book on pages 12-13 and 61.

Thanks to *The Annals of Human Genetics* for permission to reprint the picture of William Sealy Gosset from volume 9, part 1 of the frontispiece of the 1939 *Annals of* *Eugenics*.

The *Institute of Mathematical Statistics* and *Statistical Science* were quite helpful in giving permission to reproduce the pictures of George E. P. Box and Florence Nightingale David, the former in volume 2, page 240 (1987), and the latter in volume 4, page 236 (1989) of *Statistical Science*.

Blackwell Publishing gave us permission to reproduce pictures of the following three British statisticians:

Sir David Roxbee Cox-His picture appeared as the frontispiece in the *Journal of the* *Royal Statistical Society*, Series A, *144*(3), 1980.

Maurice Stephenson Bartlett-His picture appeared as the frontispiece in the *Journal of the* *Royal Statistical Society*, Series A, *130*(4), 1967.

Francis Ysidro Edgeworth-His picture is from the facing page 238 in *Annals of the Royal* *Statistical Society*, 1934-1934, 1934 ESS sup 54-55.

We are grateful to the Regents of the University of California for permission to reproduce the picture of Egon Sharpe Pearson from the frontispiece of *The Selected Papers of E. S.* *Pearson* (1966).

Thanks to Springer Science and Business Media for permission to reprint three excerpts from Constance Reid’s *Neyman…from Life* (1982). They appear on pages 24-25, 115, and 133 of her book.

We are indebted to John Wiley & Sons, Inc. for permission to reproduce the picture of R. A. Fisher from the set of plates following page 256 in Joan Fisher Box’s *R. A. Fisher*: *The Life of A Scientist* (1978). Thanks also go to this publishing house for permission to reprint two quotations from her book on pages 12-13 and 61.

Thanks to *The Annals of Human Genetics* for permission to reprint the picture of William Sealy Gosset from volume 9, part 1 of the frontispiece of the 1939 *Annals of* *Eugenics*.

The *Institute of Mathematical Statistics* and *Statistical Science* were quite helpful in giving permission to reproduce the pictures of George E. P. Box and Florence Nightingale David, the former in volume 2, page 240 (1987), and the latter in volume 4, page 236 (1989) of *Statistical Science*.

Blackwell Publishing gave us permission to reproduce pictures of the following three British statisticians:

Sir David Roxbee Cox-His picture appeared as the frontispiece in the *Journal of the* *Royal Statistical Society*, Series A, *144*(3), 1980.

Maurice Stephenson Bartlett-His picture appeared as the frontispiece in the *Journal of the* *Royal Statistical Society*, Series A, *130*(4), 1967.

Francis Ysidro Edgeworth-His picture is from the facing page 238 in *Annals of the Royal* *Statistical Society*, 1934-1934, 1934 ESS sup 54-55.

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**INTRODUCTION**

This slim volume provides a brief description of the lives and scientific contributions of twelve British Statisticians—Karl Pearson, R. A. Fisher, Charles Spearman, Florence Nightingale David, George Udny Yule, Maurice G. Kendall, George E. P. Box, William Sealy Gosset (“Student”), Egon Sharpe Pearson, Francis Ysidro Edgeworth, Maurice Stevenson Bartlett, and David Cox. The book is written in a non-mathematical manner to make it accessible to a wider reading audience.

The Pearson product-moment correlation coefficient is named in honor of Karl Pearson. In addition to studying mathematics and German he took a law degree. He and his wife co-founded the Men and Women Club that was designed to permit free discussion among men and women. His 18 publications in *Philosophical Transactions of the Royal Society* provided contributions in theoretical as well as substantive areas.

Some scientists view Fisher’s work in population genetics and evolutionary theory as being as important as his innovations in statistics. R. A. Fisher introduced pioneering work in the analysis of variance and covariance. These inferential statistical techniques are central tools in much empirical, scientific work. He also laid the groundwork for multivariate statistical analysis. Fisher derived important sampling distributions for correlations and regression coefficients. His publications swept across many substantive disciplines. His work in experimental design, including the idea of randomization, is monumental. It should be mentioned that Fisher was a controversial man and sometimes clashed with fellow scientists.

Charles Spearman developed fundamental models in factor analysis, mental test theory, and theories of intelligence. His two-factor theory contained a general factor of intelligence together with certain specific factors. This theory of the intellect is still used as the basis for hierarchical models. His achievements were based on both statistical procedures and empirical psychological studies.

Florence Nightingale David’s contributions opened the door to women desiring a career in Statistics, and she was justly rewarded for her achievements. She generated 100 publications. One that is likely to interest both beginners and sophisticates is her 1962 book, *Games, Gods, and Gambling*. Students flocked to Dr. David’s popular lectures.

George Udny Yule conducted early work in time series and contingency table analysis. He is viewed as one of the pioneers of modern statistics. The highlight of his publications is probably the book, *An Introduction to the Theory of Statistics*, which went through 14 editions and appeared in five languages. Yule also investigated statistical aspects of literary style. Legend has it that he told Spearman the fundamental equation of mental test theory, X=T+E.

Maurice G. Kendall made contributions to nonparametric correlational techniques, random walk theory, random number generators and tests for randomness. He published many books, some of them highly respected. A sample of these volumes is *Advanced Theory of Statistics* (two volumes), *Geometrical Probability*, and *Time Series.*

George E. P. Box has published numerous academic and industrial journal articles as well as a good number of books and teaching materials. He holds both Ph.D. and D.Sc. degrees in mathematical statistics from the University of London. Dr. Box has made important research contributions to statistical quality control, Bayesian statistics, and analysis of time series.

William Sealy Gosset (“Student”) developed the Student’s t-test and related small sample statistics while working for the brewery of Arthur Guinness Sons & Company of Dublin. This was a major breakthrough as until then the only statistical techniques available were those applicable to rather large sets of data. At the request of the brewery, he published all of his papers, many of which appeared in *Biometrika*, under the pseudonym “Student.” In his later publications he tried to omit mathematical concepts and he would ask colleagues and friends to view him as a non-mathematician.

Egon Sharpe Pearson was a versatile statistical scientist. Since his father was Karl Pearson, he had an impressive tradition to carry on. Egon was a leading statistician. And he did important editorial work as Managing Editor of *Biometrika* for three decades. His research in developing the Neyman-Pearson theory of hypothesis testing was important to statistical inference. When his father retired he took over as Chairman of the Department of Applied Statistics at University College, London. He was a noted historian of statistics as well as a skilled teacher.

Francis Ysidro Edgeworth possessed a mind with great intellect. Although his formal education was in modern and ancient languages, as well as law, he learned a great deal of mathematics, statistics, probability, logic and related disciplines on his own. There is a great deal which is puzzling as to how he did this. Sometimes there were friends or colleagues who stimulated him, such as Francis Galton or Karl Pearson. He never married and might have been lonely, except for the intellectual stimuli that surrounded him. Vocationally he was very stable. He was appointed to the Drummond chair of Political Economy at Oxford and was chosen as a fellow of All Souls in 1891, and retained both until his retirement. Similarly, he became the initial editor of the *Economic Journal* in the same year and remained in an editorial capacity until retirement. Sometimes he had controversies regarding priority of research findings, especially with Karl Pearson.

Maurice Bartlett, like several of the other British statisticians in this book, was very good in mathematics. He lived a long and productive life, excelling in teaching, research, and administration. His most well known statistical finding was the test for homogeneity of variance in the analysis of variance. He was elected to many fellowships, medals, foreign associateships and honorary memberships, and the University of Chicago and the University of Hull awarded him honorary doctorates. His research contributions spanned 55 years. Bartlett’s research interests in statistics and related disciplines covered a wide range of topics including statistical theory and methods, population and epidemic models, stochastic processes, time series analysis, and multivariate analysis.

David Cox’s research interests are in inferential theoretical and applied statistics, biostatistics, and applied probability. The applications that he especially focuses on are in the physical, biological, and social sciences. His best-known research contribution is the proportional hazards model, which has numerous applications in the analysis of survival data.

Both the references and the mathematical notation in this book follow the manual of style of the American Psychological Association.

**CHAPTER 1**

**Karl Pearson: Versatile Statistical Scientist**

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*Overview*: This chapter displays the versatility of Karl Pearson, focusing not only on his contributions to statistics and other quantitative disciplines but also on his research and publications in religion, politics, literary criticism, philosophy of science, Darwinism, biology, history, free thought, evolution, genetics, socialism, anthropology, eugenics, and emancipation of women. Being the chairman of a first class academic department and the managing editor of a major journal, Pearson sometimes used his power to the detriment of other important scientists, such as R. A. Fisher and Jerzy Neyman, and this chapter also brings out this unfortunate characteristic of his personality.

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**Educational Training and Fellowship Activities**

In the year 2006 Karl Pearson is best remembered for his research in statistics, where he developed the formula for the product-moment correlation coefficient (rho) and introduced the chi square statistic. Occasionally it is recalled that he took a degree in law and wrote a book on the philosophy of science titled *The Grammar of Science* (1892). The last two items, taken together with his statistical contributions, might give one a glimpse of his intellectual versatility. The main purpose of the present chapter is to display this versatility and elaborate on it in a fully comprehensive way. A secondary purpose is to reveal an unfortunate feature of Pearson’s personality—viz., that he used his professorial and administrative potency to advocate his own research ideas, inhibit those he did not approve of, and insult and intimidate statistical scientists from different philosophical camps.

Karl Pearson was born in London on March 27, 1857 and he died at Coldharbour, Surrey on April 27, 1936. His father was a successful Barrister and this may have led him to attain a law degree. Karl was educated at home until he turned nine, and then studied at University College, London for seven years.

In his early years he displayed a wide array of interests and a strong intellectual thrust. He frowned upon authority figures, which he viewed as being misdirected, and took delight in argumentation. He graduated Third Wrangler in Mathematics Tripos in 1879 from Kings College, Cambridge and was awarded a flexible fellowship. It extended six years and gave him great freedom regarding scholarly work and travel.

Karl Pearson studied law in London and was called to the bar in 1881. In 1882 he took a master’s degree. During his Fellowship years he studied at the Universities of Berlin and Heidelberg, spending a great deal of time in the Black Forest, studying and writing. Germany was always one of his favorite countries. The disciplines he focused on were philosophy, biology, metaphysics, Roman law, mediaeval and renaissance German literature, physics, and Darwinism. After a period of serious study he became fluent in German and well versed in German literature. Karl Pearson was indeed a Germanophile. Legend has it that he was offered a college post in a German Department, but there is some debate on this point.

On returning to England he became engaged in activities that involved the ideas of Karl Marx, Spinoza, and Martin Luther. He also returned to King’s College where he wrote papers on certain mathematical topics.

Karl Pearson was appointed Professor of Applied Mathematics and Mechanics at University College, London in 1884 and this college was to be his home base for the rest of his life. He became department head in Applied Mathematics in 1907. For four years he lectured in Geometry. He conducted research in biometry and evolutionary theory from 1891 to 1906 with Rafael Weldon, Professor of Zoology and Comparative Anatomy. As requested by Francis Galton, who was a polymath, Pearson became the first Galton Professor in Eugenics in 1911 and retained that title until his retirement in 1933.

Karl Pearson and Maria Sharpe were married in 1890 and they had two daughters, Sigrid and Helga, and one son, Egon. The couple met at the Men and Women Club, which was co-founded by Pearson, and designed to permit free discussion among men and women. Maria died in 1928 and the following year he married Margaret Child, a colleague at University College.

**The Heart of Karl Pearson’s Intellectual Versatility**

By perusing Karl Pearson’s academic studies in London and in Germany, one can sense the broad scope in his interest patterns. We now look more closely at his writings, his research, and his publications. He published 18 papers with the title “Mathematical Contributions to the Theory of Evolution,” all of them with different subtitles. They were all published in *Philosophical Transactions of the Royal Society*. R. A. Fisher also made strong contributions to evolution theory. The foundation of the system of Pearson Curves appears in these publications. Suspicious of the assumption of normality, he explored a number of other possible frequency distributions. Substantively, his publications dealt with problems in genetics, anthropology, biology, eugenics, evolution, etc. Statistically, they provided theoretical contributions to kurtosis, the coefficient of contingency, the correlation ratio, tetrachoric and biserial correlations, product moment correlation (rho), chi square, the normal curve and other distributions, multiple correlation and regression, partial correlation, scedasticity, the coefficient of variation, and the standard deviation. He coined this latter term and employed the Greek letter sigma to denote its population parameter. His equation for the biserial is the very one that is currently used (1909). Pearson contended that he was the one who named the LaPlace-Gaussian curve the “normal curve,” which he later viewed as unfortunate because it seemed to imply that all other curves were abnormal (Pearson, 1920, p. 25). In Pearson’s first fundamental paper on correlation, “Mathematical Contributions to the Theory of Evolution: III. Regression, Heredity, and Panmixia” (1896), he derived the formula which we now call the “Pearson product-moment correlation coefficient,” although Francis Galton was first to conceptualize it. And he gave the coefficients of the multiple regression equation in terms of the zero order correlation coefficients.

Karl Pearson produced over 300 publications in his career. Although he attended especially to studies of heredity and evolution he also conducted research in areas such as alcoholism, mental deficiency, mental illness, and tuberculosis, as well as meteorology and astronomy. (Lord, 1995)

Books edited or authored by Karl Pearson also display his scholarly versatility. In the time period between 1922 and 1934 he edited volumes of the incomplete beta and gamma functions and tables for statisticians and biometricians.

Francis Galton was Karl’s mentor and his best friend. When Galton died, he began research on a four volume biography of Galton titled, *The Life, Letters, and* *Labours of Francis Galton* which took him many years to write (1914-1930). Karl Pearson also wrote an obituary of Galton which was published in *Nature* (1911).

Pearson produced two volumes, which were quite different from his purely statistical works. They are philosophical or sociological in nature and are titled: *The Chances of Death and Other Studies in Evolution* (two volumes, 1897) and *The Ethic of Free Thought and Other Addresses and Essays* (1901). Many of the sections in these two books are from a lecture or an essay or a reprint.

*The Grammar of Science* (1892) is perhaps Karl Pearson’s *magnum opus*. Vladimir Lenin reacted to this book by saying that it showed integrity and consistency and displayed great precision of expression. (Lenin, 1939) It should be mentioned that Lenin disagreed with some of Pearson’s ideas.

In 1915 Jerzy Neyman, who was to become a world-class statistician, read this pilosophy of science book of Karl Pearson’s. He grew very exited about the book and his wife, Olga, said that Karl Pearson was constantly on his mind. He shared the book with fellow students and they too were strongly impressed.

Years later Neyman recalled that: “We were a group of young men who had lost our belief in orthodox religion, not from any sort of reasoning, but because of the stupidity of our priests. [But] we were not freed from dogmatism and were prepared in fact to believe in authority, so long as it was not religious.

“The reading of *The Grammar of Science*…was striking because…it attacked in an uncompromising manner all sorts of authorities…At the first reading it was this aspect that struck us. What could it mean? We had been unused to this tone in any scientific book. Was the work ‘de le plague’ [something of a hoax] and the author a ‘canaille’ [scoundrel] on a grand scale…? But our teacher, Bernstein, had recommended the book; we must read it again.” (Reid, 1982, pp. 24-25). It is of interest to note that when the 23-year-old Albert Einstein formed a study group called the Olympia Academy with his two younger friends, he recommended that the first book they read was Karl Pearson's *The Grammar of Science*.

George Udny Yule described Karl Pearson as a philosopher, poet, and historian as well as a statistician. (Lord, 1995). Although Yule held a position as demonstrator awarded by Pearson, they differed on certain statistical matters.

Years later Neyman would initiate a research project with Karl Pearson’s son, Egon, which would lead to the important Neyman-Pearson Theory of Hypothesis Testing.

In October of 1884, Karl Pearson was asked to edit and provide a preface to the incomplete manuscript, *The Common Sense of the Exact Sciences*. The author, William Kingdon Clifford, had died prematurely and some additional sections had to be added to complete the work. Pearson successfully brought the work to conclusion. It was reissued in 1946 and Bertrand Russell, who praised both Clifford’s original production and Pearson’s editorial work, wrote a new preface. He said the book diminished his bewilderment concerning geometries that differed radically from that of Euclid.

Just before the turn of the nineteenth century the Syndics of the University Press requested that Karl Pearson edit and complete the unfinished manuscript, *A History of* *the Theory of Elasticity and of the Strength of Materials from Galilea to Lord Kelvin* (two volumes). The deceased author, Isaac Todhunter, had left volume two incomplete, and a great deal of editorial work was needed. Each volume was a thousand pages in length. Pearson successfully completed the task in 1893.

Karl Pearson was co-founder, with Francis Galton and Walter Weldon, of the journal *Biometrika* in 1900. Pearson was its editor from its inception until he died in 1936. His son, Egon Sharpe Pearson, who was a well-known statistician in his own right, took over the editorship at that time and mentored it until almost 1966. This journal publishes studies of the statistical study of Biology. They formed it because the Royal Society refused to publish papers that combined Biology with Mathematics. The reader desiring additional early biographical information on Karl Pearson cannot do better than Egon Sharpe Pearson’s *Karl Pearson: An Appreciation of Some Aspects of His Life and* *Work* (1938). Egon’s work, however, is uniformly positive, which, perhaps, is to be expected.

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