Leon Isserlis
and the *JRSS* review of the 1^{st}
edition of * Statistical Methods for Research Workers*

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

Introduction

*
Statistical Methods for Research Workers* (1925) was probably the
most influential statistics book of the 20^{th} 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:

- E.
S. Pearson’s review in
*Science Progress.* - Student’s
review in the
*Eugenics Review.* - Harold
Hotelling’s review in
*JASA.* - W.
P. Elderton’s review in the
*Journal of the Institute of Actuaries* *Nature*review*BMJ*review

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.

*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)**

- The first edition of
*Statistical Methods for Research Workers*is available on Christopher Green’s*Classics in the History of Psychology*website.

·
*Journal of
Agricultural Science*, **11**, (2),
107-135.

·
*Philosophical Transactions of the Royal Society*, *B*, **213**,
89-142.

·
*American Mathematical Monthly*, **38**, 335-338.** ***JSTOR*

·
*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,

- J.
Aldrich (2010)
__Figures from the History of Probability and Statistics.__For many of the important figures and references on the History of Statistics.

- 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 *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 3^{rd} edition ** **(*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* (*Journal of the Royal Statistical Society*,
**89**, 145-146. *JSTOR*

* *

*Statistical Methods for Research Workers*. By

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 χ^{2} 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.