Leon Isserlis and the JRSS review of the 1st edition of R. A. Fisher’s Statistical Methods for Research Workers


John Aldrich, University of Southampton, UK. (home) August 2005/April 2019.



R. A. Fisher’s Statistical Methods for Research Workers (1925) was probably the most influential statistics book of the 20th century. It presented for the first time in book form Fisher’s work on maximum likelihood, t-tests (including applications to regression), the z-transformation of the correlation coefficient, the analysis of variance, randomisation and blocking in the design of experiments, etc. The first edition is available on Christopher Green’s Classics in the History of Psychology website.


I have noticed seven reviews of the first edition. One appears here and the other six are available as follows:


All the reviews are worth consulting for each gives a different perspective on the book. See these other sites for further literature and links.


Leon Isserlis reviewed Fisher’s Statistical Methods for the Journal of the Royal Statistical Society. The statisticians the society represented were economic and social statisticians and “research workers” in biology published elsewhere. However, Fisher published three papers in the journal in 1922-4 and the journal reviewed his book. A decade later the society broadened its ‘state-istics’ agenda and welcomed work on agriculture and industry and on mathematical statistics.


Leon Isserlis (1881-1966), like Fisher and Karl Pearson, studied mathematics at Cambridge.  He was born in the Ukraine in a family with a long line of distinguished rabbis; one of his ancestors was Moses Isserles of Cracow.  He came to England with his widowed mother, elder brother and two sisters just before his eleventh birthday. He won a scholarship to the City of London School mother and went on to Christ’s College Cambridge. On leaving Cambridge, he was appointed head of mathematics at West Ham Municipal Technical Institute (one of the ancestors of the modern UEL). From 1912 to –15 Isserlis also studied statistics under Karl Pearson. His early papers appeared in Biometrika but later Isserlis associated more with statisticians than with biometricians. From 1920 to his retirement he worked as statistician to the Chamber of Shipping.


Isserlis and Fisher

Isserlis’s main interest in statistical theory was in the exact distribution of sample moments. With his Russian background his unique contribution to British statistics was to bring Russian work to the attention of British statisticians; the comment in his review on Fisher’s neglect of Chebyshev’s work is characteristic. Fisher had first used Chebyshev polynomials in a paper written in 1920 and published in 1921 in the Journal of Agricultural Science. In the JRSS Current Notes, Anon (1920) remarks of a method used in an Italian paper that “the method, due to Tchebycheff is not often adopted by English statisticians.” The following year the use of Tchebycheff in a work by Esscher is noted:  this “provides a somewhat simpler method of proof than that to be found in the textbooks, but does not appear to recognize the fact that the process itself has often been used before.” The statisticians and Fisher came together at a meeting of the Statistical Society (see Yule (1921)*) when Isserlis’s friend, Major Greenwood, described Esscher’s work; Greenwood was probably responsible for the Current Notes entries. In 1925 Fisher (p. 98) looked back, “The most convenient orthogonal functions to use are those developed by Esscher in respect to mortality, and independently by the present author.” The charge of Isserlis was echoed by Grove (1930) and Fisher (1930) answered by saying he had never put forward the technique as his own discovery because it was obvious—“no mathematician considering the same problem … could have failed to introduce orthogonal functions…” Besides nothing was to be gained now from reading Chebyshev! Chebyshev (and perhaps Isserlis) remained a sore point with Fisher. In a letter to Aitken in November 1932 he wrote, “The fact is that it has always been a cheap way of maintaining a shaky reputation for expert knowledge, to quote some foreigner unknown to most of one’s countryman, as of the highest importance. Russians have done long and fruitful service in this respect, owing to their admirably inaccessible language. When you find me browbeating an audience with Japanese authorities, you will recognise the first signs of decrepitude.” 


Isserlis had a long association with the Royal Statistical Society and Fisher had a long dis-association. Fisher’s relations with the society soured when it would not publish a paper of his in 1923; see Box (1978, pp. 86-7 and Bennett pp. 76-7). In 1935 a reconciliation was in prospect when Fisher presented a paper to a meeting of the society. Bowley proposed the vote of thanks and Isserlis seconded it (pp. 57-9). However no reconciliation was achieved. Fisher replied, “The acerbity, to use no stronger term, with which the customary vote of thanks has been moved and seconded … does not, I confess surprise me.”


* The discussion of Yule (1921) may also contain the germ of Fisher’s jibe quoted by Isserlis in his review viz. “Not only does it take a cannon to shoot a sparrow, but it misses the sparrow.” Edgeworth had said, “Mr. Yule was not open to the sarcasm which a distinguished statistician [Harald Westergaard in JRSS 1918] had directed against his mathematical colleagues, that they shot at sparrows with a cannon.”



References (Fisher)


·         R. A. Fisher (1921) Studies in Crop Variation. I. An Examination of the Yield of Dressed Grain from Broadbalk, Journal of Agricultural Science, 11, (2), 107-135.

·         R. A. Fisher (1925) The Influence of Rainfall on the Yield of Wheat at Rothamsted. Philosophical Transactions of the Royal Society, B, 213, 89-142.

·         R. A. Fisher (1931) A Letter from R. A. Fisher to the Editor (in Recent Publications), American Mathematical Monthly, 38, 335-338. JSTOR

·         R. A. Fisher (1935) The Logic of Inductive Inference, with discussion, Journal of the Royal Statistical Society, 98, 39-82. JSTOR.



References (other)


·         J. Aldrich (2010) Mathematics in the London/Royal Statistical Society 1834-1934 Journal Electronique d'Histoire des Probabilités et de la Statistique for Fisher’s relations with the RSS.

·         J. Aldrich (2010)  A Guide to R. A. Fisher. For Fisher generally,

  • Anon, (1920) Current Notes, Journal of the Royal Statistical Society, 83, (2), 328.
  • Anon, (1921) Current Notes, Journal of the Royal Statistical Society, 84, (2), 306.

·         J. H. Bennett (1983) (ed.)  Natural Selection, Heredity, and Eugenics. Including Selected Correspondence of R. A. Fisher with Leonard Darwin and Others. Oxford: Clarendon Press.

·         Joan Fisher Box (1978) R. A. Fisher: The Life of a Scientist, New York: Wiley.

·         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. For a perspective on Fisher’s book.

·         Frederik Esscher (1920) Ueber die Sterblichkeit in Schweden 1886-1914, No. 23 of Serie II. Meddelanden frdn Lunds Astronomiska Observatorium, Lund.

·         V. Farewell, T. Johnson & P. Armitage (2006) ‘A Memorandum on the Present Position and Prospects of Medical Statistics and Epidemiology’ by Major Greenwood, Statistics in Medicine, 25, 2167-2177. (Describes Greenwood’s great esteem for Isserlis and for the Russian school.)

·         Charles C. Grove (1930) Statistical Methods for Research Workers 3rd edition  (R. A. Fisher), American Mathematical Monthly, 37, 547-550.  JSTOR

  • Anders Hald (1998) A History of Mathematical Statistics from 1750 to 1930, New York: Wiley. Chapter 25 has a history of orthogonal polynomials.

·         J. O. Irwin (1966), Leon Isserlis, M.A., D.Sc. (1881-1966), Journal of the Royal Statistical Society A, 129, 612-616. JSTOR

·         L. Isserlis (1927) Two Notes on Certain Expansions in Orthogonal and Semi-Orthogonal Functions: I Note on Chebysheff’s Interpolation Formula (Note II is by Romanovsky), Biometrika, 19, 87-99. JSTOR

·         M. G. Kendall (1967) Leon Isserlis, 1881-1966, Revue de l'Institut International de Statistique / Review of the International Statistical Institute, 35, 105-106. When Isserlis retired from the Chamber of Shipping Kendall replaced him.

·         G. U. Yule (1921) On the Time-Correlation Problem, with Especial Reference to the Variate-Difference Correlation Method, with discussion, Journal of the Royal Statistical Society, 84, 497-537. JSTOR








L.I. (1926) Review of Statistical Methods for Research Workers (R. A. Fisher), Journal of the Royal Statistical Society, 89, 145-146.  JSTOR


Statistical Methods for Research Workers. By R. A. Fisher, M.A, 232 pp. Edinburgh: Oliver and Boyd, 1925. Price 15s. net.


This book is No. 3 of the Biological Monographs and Manuals, edited by F. A. E. Crow and D. Ward Cutler and, as indicated by the Editors’ preface, has a dual aim. It is intended on the one hand, to provide an authoritative record of achievement in a particular branch of biological investigation and, on the other hand, to give the author an opportunity of expressing the results of his own researches in a more extended form. On the whole the second aim seems dominant, and we have presented a very full account of the statistical methods favoured by the author and of the conclusions he has reached on topics some of which are still in the controversial stage. Much is lacking if the book is to be regarded as an authoritative record of achievement in statistical method apart from Mr. Fisher’s own contributions. The explanation may be found in the author’s preface where he says, “Little experience is sufficient to show that the traditional machinery of statistical processes is wholly unsuited to the needs of practical research. Not only does it take a cannon to shoot a sparrow, but it misses the sparrow.” The task of reviewing the book is not made any easier by the fact that it is apparently addressed to the intelligent biologist, who is assumed to be able to [p. 146] handle mathematical formulae, but is spared the exercise of following a mathematical proof. We thus find in the earlier chapters excellent, if dogmatic statements about binomial distributions, Poisson’s series and the normal law, to which no exception can be taken by those who work the “traditional machinery.” Side by side with these statements we find others equally dogmatic about maximum likelihood and similar topics without warning to the non-mathematical reader that he is no longer on terra firma. In the sections in the earlier chapters dealing with distributions, goodness of fit, independence and so forth, the author explains clearly the use and meaning of the χ2 test and provides simple tables for the purpose. Chapter V, on means and regression coefficients, is full of good matter, but the author, here as elsewhere, is very economical in his references to earlier work. A notable example is his description of the technique of fitting regression lines by least squares, so that each new approximation is a mere extension of the earlier stages. In this description there is no reference to Tchebysheff's work. A clear account of the usefulness of the product-moment coefficients is given in Chapter VI. Mr. Fisher's sympathies are obviously with Mendelian methods, and the following quotation is therefore interesting: “but even with organisms suitable for experiment and measurement, it is only in the most favourable cases that the several factors causing fluctuating variability can be resolved, and their effects studied by Mendelian methods. Such fluctuating variability, with an approximately normal distribution, is characteristic of the useful qualities of domestic plants and animals; and although there is strong reason to think that inheritance in such cases is ultimately Mendelian, the biometrical method of study is at present alone capable of holding out hopes of immediate progress.”

            This chapter deals also with the partial correlation and with the transformation devised by the author, z =   which simplifies the study of the distribution of r in small samples. Chapter VII is devoted to the study of intra-class correlations and their sampling errors, and a final chapter deals with the analysis of variance. Here the author uses the ideas underlying the correlation ratio but dismisses the ratio itself as a descriptive statistic the use of which is extremely limited. The book will undoubtedly prove of great value to research workers whose statistical series necessarily consist of small samples, but will prove a hard nut to crack for biologists who attempt to use it as a first introduction to statistical method.