Harold Hotelling’s review of the 1^st edition of R. A. Fisher’s Statistical Methods for Research Workers

John Aldrich, University of Southampton, UK. (home) Most recent changes April 2019.

Introduction

Ronald Fisher’s Statistical Methods for Research Workers (1925) is considered by many to be the most influential statistics book of the twentieth century. Yet according to Fisher’s biographer, “The book did not receive a single good review.” Box (1978, p. 130). It is debateable whether Box’s generalisation applied to all the British reviews but it certainly did not apply to the review by the American statistician, Harold Hotelling (1895-1973). His review was also probably the most consequential of the lot.

British reviews of the first edition

I have noticed 6 British reviews of the 1^st edition of the Statistical Methods. They are available online as follows.

• E. S. Pearson's reviews in Science Progress and Nature
• Leon Isserlis’s review in the Journal of the Royal Statistical Society.
• Student’s review in the Eugenics Review.
• Nature review (unsigned)
• W. P. Elderton’s review in the Journal of the Institute of Actuaries
• BMJ review (unsigned)

Hotelling’s review

Hotelling reviewed the book on his own initiative and was so impressed that he became Fisher’s earliest fan. Some spectators found Hotelling’s enthusiasm excessive. Arne Fisher, the Danish-American actuary, disapproved of “adoring disciples.” See Arne to Ronald: correspondence p.310.

Reading Fisher’s book did not change those of the reviewers who were established statisticians—like Student and Isserlis—but it did change Hotelling and Hotelling was important. Arrow & Lehmann (2005: 11) write, “It is no exaggeration to state that during the 1930s and early 1940s, Hotelling nearly single-handedly brought American statistics into the modern age and laid the foundation for the extraordinary development of the subject after the Second World War.”

Harold Hotelling

Harold Hotelling completed a PhD at Princeton on topology supervised by Oswald Veblen. He soon switched to statistics and he encountered Fisher’s work very early in his career. He tried unsuccessfully to get Fisher to visit Stanford in 1928 and 1929 (Stigler, 1999) and instead he went to Rothamsted as a voluntary worker for the second half of 1929. Hotelling was the most mathematically sophisticated of the early reviewers and he did not complain, as the other reviewers did, about the difficulty of the book. Yet he saw a need for a Statistical Methods with proofs and in the early years discussed with Fisher their collaborating on such a work. In the event there was no joint work, nor a theory book by either of them. Hotelling was also the first to attempt a rigorous development of Fisher’s maximum likelihood theory: see Stigler (2008).

Hotelling was a distinguished economic theorist and so it is appropriate that the National Academy of Science memoir was a joint effort from statistician Erich Lehmann and Kenneth.Arrow, a Hotelling student and Nobel laureate in Economics.

Hotelling’s reviews of the first seven editions of the Statistical Methods

Hotelling did not only review the first edition of the Statistical Methods but he kept publicising Fisher’s book through the 1930s by reviewing new editions.

• 1^st edition: Journal of the American Statistical Association 1927, 22, 411-412. JSTOR
• 2^nd edition: Journal of the American Statistical Association 1928, 23, 346. JSTOR
• 3^rd edition: Journal of the American Statistical Association 1930, 25, 381-382. JSTOR
• 4^th edition: Journal of the American Statistical Association 1933, 28, 374-375. JSTOR
• 5^th edition: Journal of the American Statistical Association 1935, 30, 118. JSTOR
• 6^th edition: Journal of the American Statistical Association 1937, 32, 218-219. JSTOR
• 7^th edition: Journal of the American Statistical Association 1939, 34, 423-424. JSTOR

After his visit to England in 1929 Hotelling wrote two pieces on the condition of statistics in Britain. Both emphasised the importance of Fisher.

• British Statistics and Statisticians Today, Journal of the American Statistical Association 1930, 25, 186-190. JSTOR
• Recent Improvements in Statistical Inference, Journal of the American Statistical Association 1930, 26, 79-87. JSTOR

Hotelling wrote a piece to mark the silver anniversary of the appearance of the Statistical Methods

• Harold Hotelling (1951) The Impact of R. A. Fisher on Statistics, Journal of the American Statistical Association, 46, 35-46. JSTOR

Hotelling also publicised Fisher’s The Design of Experiments by reviewing the first two editions.

• 1^st edition: Journal of the American Statistical Association, 1935. 30, 771-772 JSTOR
• 2^nd edition: Journal of the American Statistical Association, 1937. 32, 580-582 JSTOR

References

• The first edition of Statistical Methods for Research Workers is available on Christopher Green’s Classics in the History of Psychology website.
• For a perspective on Fisher’s book see A. W. F. Edwards, (2005) “R. A. Fisher, Statistical Methods for Research Workers, 1925” in I. Grattan-Guinness (ed.) Landmark Writings in Western Mathematics : Case Studies, 1640-1940, Amsterdam: Elsevier.

• Joan Fisher Box (1978) R. A. Fisher: The Life of a Scientist, New York: Wiley.
• Walter L. Smith (1978) Harold Hotelling 1895-1973, Annals of Statistics, 6, 1173-1183. JSTOR

• Adrian C. Darnell (1988) Harold Hotelling (1895-1973), Statistical Science, 3, 57-62. Most of the issue is devoted to Hotelling. Project Euclid.
• Kenneth J. Arrow, & E. L. Lehmann (2005) Harold Hotelling 1895-1973, National Academy of Sciences, 87, 1-15.
• ASA Statisticians in History : Harold Hotelling
• In Memoriam: Harold Hotelling 1895-1973, American Economic Review, 64, 1102-1103. JSTOR.
• Edmund A. Gehan (2005) Harold Hotelling, Encyclopedia of Biostatistics, New York: Wiley.
• New School Harold Hotelling 1895-1973
• Mathematics Genealogy Project: Harold Hotelling.
• John Aldrich (2010) The Econometricians’ Statisticians 1895-1945. History of Political Economy, 42, 111-154. pdf
• Correspondence between Fisher and Hotelling. Online from Adelaide. There are more letters at Columbia University.

· Stephen M. Stigler (1999) The Foundations of Statistics at Stanford, American Statistician, 53, 263–66

• Stephen M. Stigler (2008) The Epic Story of Maximum Likelihood, Statistical Science, 22, (4), 598-620. Project Euclid
• John Aldrich A Guide to R. A. Fisher contains many further references.
• John Aldrich Figures from the History of Probability and Statistics for general background.

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Hotelling’s review of the 1^st edition

Statistical Methods for Research Workers, by R. A. Fisher. Edinburgh and London: Oliver and Boyd. 1925. ix, 239 pp. Journal of the American Statistical Association 1927, 22, 411-412

Most books on statistics consist of pedagogic rehashes of identical material. This comfortably orthodox subject matter is absent from the volume under review, which summarizes for the non-mathematical reader the author's independent codification of statistical theory and some of his brilliant contributions to the subject, not all of which have previously been published.

The theory of probable errors in ordinary use is valid only in the limit as the size of the sample approaches infinity. The author has created most of the existing theory of small samples. It is therefore natural that the book deals largely with methods which must be used where the number of cases is limited and which, he holds, may well be used in general. Common occurrence in economic and other statistics of short series will make the work valuable to a larger class of research workers than the biologists for whom it was primarily intended.

Of particular interest are the methods of evaluating the significance of correlation coefficients drawn from small samples, the tests of significance of differences of means, and the method (p. 125) of fitting a polynomial to a series of observations by adding terms one at a time until the fit is sufficiently good. All these are due entirely, I think, to Mr. Fisher's own researches. Some of the tables, particularly V (A) which gives the values which a correlation coefficient must attain in order to reach certain levels of significance, are indispensable for the worker with moderate-sized samples.

The author (who must not be confused with Arne or Irving Fisher) has an answer to the query as to the singular of “statistics.” A statistic is a quantity such as an average or correlation coefficient which summarizes characteristics of a body of data relevant to a particular inquiry. The criterion of “maximum likelihood” for the derivation of statistics which he invented is illustrated. His position regarding the number of classes with which tables of χ² must be entered is clearly set forth.

Some slight preliminary knowledge of statistical concepts is needed to make the reading smooth. The absence of proofs and the omission of some topics make the book inadequate for mathematical readers, who will find it desirable to read also the author's original papers. If used in a course in mathematical statistics it should be supplemented with these proofs. It would be impossible to combine in such brevity a compendium of sound practical methods with a complete theoretical development. The author's work is of revolutionary importance and should be far better known in this country.

HAROLD HOTELLING

Stanford University