Student’s review of the 1st edition of
John
Aldrich,
Introduction
“Student” was the pen name of William Sealy Gosset MacTutor Wilkipedia (1876-1937), a brewer of Guinness in Dublin and the pioneer in the analysis of small samples. Gosset had studied with Karl Pearson, the biometrician and leading statistician of the time. Although Pearson helped with the 1908 paper, he was used to working with large samples and doubted the value of small sample analysis. The controversy and disputes, to which Student alludes to in the review, were primarily between Pearson and Fisher and began about 10 years later. In a letter of April 3rd 1922 Gosset told Fisher “In most of your differences with Pearson I am altogether on your side and in some cases I have agreed to differ from him long ago.”
Of the established statisticians Gosset was the closest to Fisher. They were in regular touch from Fisher’s joining Rothamsted in 1919, though they met rarely and communicated by letter. Only a few of Fisher’s letters have survived but the development of his ideas can be traced through Gosset’s letters reacting to them. Student was the least “innocent” of the reviewers of the Statistical Methods for, not only had he been kept informed of the development of Fisher’s ideas, he had read the book in proof. Gosset sent Fisher a long letter with corrections and comments on October 20th 1924. Some of the comments are repeated in the review, including his opinion of the unsuitability of Example 1 and his practical objections to randomisation. On the latter he wrote, “You would want a large lunatic asylum for the operators who are apt to make mistakes enough even at present.” He continued, “If you say anything about Student in your preface you should I think make a note of his disagreement with the practical part of the thing: of course he agrees in theory.” Later in the 1930s the two would publicly disagree about randomisation.
The biographies by Egon Pearson and Box treat the relationship between Gosset and Fisher. Both draw heavily on the Letters but the Pearson volume is the more useful for indicating Student’s input into the Methods and for tracing the later disagreements between Fisher and Gosset. 2008 is the centenary of Student’s famous paper and Zabell (2008) and his commentators discuss how it influenced Fisher.
- 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) “
- For a very brief
account of how Fisher transformed Student’s z-test into the t-test
see the entry on Student’s t distribution in Earliest known uses of some
of the words of mathematics.
- Letters from W. S. Gosset
to
- Joan Fisher
- E. S. Pearson (1990)
‘Student’, A Statistical Biography
of William Sealy Gosset, Edited and
Augmented by
- S. L. Zabell (2008) On Student’s 1908 paper “The probable
error of a mean,” with comments by S. M. Stigler, J.
Aldrich, A. W. F. Edwards, E. Seneta, P. Diaconis & E. L. Lehmann and rejoinder from Zabell, Journal
of the American Statistical Association, 103, 1-20.
- Gosset was also drawn into a controversy between Fisher
and Egon Pearson that was prompted by Pearson’s
review of the 2nd edition of the Statistical Methods. See
E.
S. Pearson’s Reviews of Fisher’s SMRW.
- For more on Student
and his relations with Fisher see the Student section of A Guide to R. A.
Fisher.
- For Karl Pearson see Karl
Pearson: A Reader's Guide.
- Student, Fisher and
Pearson all appear in Figures
from the History of Probability and Statistics (534 KB) This also has references on the history of Statistics
In all there were 6 major reviews
of the 1st edition of the Statistical Methods. The other 5 are also available on the web.
- Leon
Isserlis’s review in the Journal of the Royal Statistical
Society.
- E.
S. Pearson’s reviews in the
journal Science Progress.
- Nature
review (anonymous)
- BMJ
review (anonymous)
- Harold
Hotelling’s review in the Journal
of the American Statistical Association.
All are worth looking at as they emphasise different facets of the book
________________________________________________________________________
Student’s review (Eugenics Review, 18,
(1926), 148-150.)
Fisher,
Owing to his connection with
large scale experimental work it happened that the reviewer was one of the
first to draw attention of Biometricians to the fact that a special technique
is required in dealing with ‘small’ samples, by which is meant samples so small
that the statistical constants of the population cannot be replaced by those of
the samples without appreciable error.
Further,
it was the incompleteness, from the mathematical standpoint, of his solution of
one of the fundamental problems which first drew Dr. Fisher’s attention to the
subject and it is therefore with particular pleasure that he welcomes the
publication of Statistical Methods for
Research Workers, the first book on Statistics which deals mainly with this
special technique.
Dr.
Fisher is not himself occupied to any great extent in experimental work, but as
Chief Statistician to the Rothamsted Experimental
Station he is in close touch with experiments carried out both in the field and
in the various laboratories of that institution, and it is in response to this
stimulus that the book has been written.
We
must not, therefore, consider it as a text-book but rather as a summary of the
author’s own work; and the proverbial aloofness of the text book from
controversy, and often it is to be feared from current practice, is not to be
expected: in fact it must be admitted that while no one disputes the fact that
Biometrical methods must be modified, there is still controversy as the exact
nature of the most suitable modification for the purpose.
Nevertheless,
it is the reviewer’s opinion that even if all points which are still in dispute
were conceded to his opponents, we should seldom in practice draw inferences
from our data which would be appreciably different from those which we shall
draw if we follow our author.
One
of Dr. Fisher’s merits is his instance throughout on the fact that all correct methods
of treating statistics which make use of all the available relevant information
must necessarily give the same result, and this has led to a unity of outlook
which has not always been sufficiently emphasised.
In
this he has been helped by what, in anything but mathematics, would be
considered coincidences, such as the fact that the χ2
distribution is identical in form with that of the variance of samples drawn
from a normal population.
The following tabular statement may illustrate better than anything the general arrangement of the book
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Subject Matter |
Tables
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Number
of numerical
examples |
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I |
Introductory. |
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1 |
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II |
Diagrams |
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III |
Distributions, (i) Normal, (ii) Poisson,
(iii) Binomial |
I
& II of probability integral |
6 |
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IV |
Test
of goodness of fit, independence or homogeneity |
III
of χ2. |
8 |
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V |
Test
of significance of means, differences of means and regression coefficients |
IV
of t. |
9 |
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VI |
The
correlation coefficient, partial correlation and the z transformation |
VA of r for zero correlation. VB
r to z for any correlation. |
9 |
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VII |
Intra-class
correlation and the analysis of Variance |
VI
of z for P= .05. |
8 |
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VIII |
Further
applications of the analysis of Variance, experimental planning, the |
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Chapter I is not easy to follow for those unfamiliar with the “jargon” of the science and such readers are advised to skip freely after Section 2, but to return and read it carefully after they have become accustomed to the use and implications of the various terms employed. This advice, however, does not apply to Example 1 which is difficult alike to those unfamiliar either with mathematics or with the higher genetics, for it may be neglected by both classes since it does not illustrate any of the methods exhibited in the later chapters of the book.
Chapters II
& III, excepting sections 17 and 19 which might have been included in
Chapter IV, are mainly descriptive and should be mastered by anyone who wishes
to apply the tests in Chapters IV and V.
Chapters VI,
VII & VIII trace the connection between correlation and the analysis of
variance which is dealt with in a manner particularly convenient for those who
are concerned with the planning and interpretation of Agricultural experiments.
Nevertheless the reviewer sometimes doubts whether Dr. Fisher’s rigid adherence
to the true Gospel of random, if controlled, arrangement will find favour with
those who require a regular system as an aid to method and useful check for the
avoidance of mistakes.
The tables of
mathematical functions are given in skeleton form, and I—VA are
entered contrary to the usual practice by using values of P as argument: they
will be found, however, to be well suited to their purpose and their
compactness conduces to speed in use. They are not, of course, intended to
replace the full tables published elsewhere.
Table VI is
admittedly less complete than the others as it only gives z for the value P=
.05 which the author uses as his ordinary limit of significance.
All seven of
the tables are reprinted at the end of the book and can be opened out so as to
be used while reading any page of the book. They can also be cut out and
mounted on cardboard, either with cloth hinges to fold up like a map, or to
form the outside faces of two triangular prisms which stand up on the table
when in use and one of which can slip inside the other for storage purposes.
In connection
with the c2 test
there is a statement on p. 80 which the reviewer cannot altogether endorse,
when the author states that in cases where χ2 [sic] is
unexpectedly small and P takes such a value as .999; “the hypothesis considered
is as definitely disproved as if P had been .001.”
Now in the
first place there is this fundamental difference between the values .001 and
.999: —while it is generally easy to formulate any number of likely hypotheses
to account for the low value, it is apart from blunders or cheating,
exceptional to find an alternative explanation to account for .999 which is not
itself extremely improbable: in the second place χ2, with small
samples, can only take a limited number of values of which zero, corresponding
to P=1, is not unlikely to occur by chance.
For example,
if twenty pairs of coins be tossed we obtain as the “calculated” distribution
on the hypothesis that heads and tails are equally likely, five cases of two
heads, ten of head and tail and five of two tails. This will actually occur in
the long run rather more than once in twenty five trials; in such cases P=1 but
the hypothesis could not be said to be in any way weakened.
Dr. Fisher’s book will doubtless be found in the
laboratories of those who realise the necessity for statistical treatment of
experimental results, but it should not be expected that full, perhaps even in
extreme cases any, use can be made of such a book without contact either
personal or by correspondence with someone familiar with its subject matter.
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·
Information
on the technical terms used in the review, such as Fisher’s z transformation of
the correlation coefficient, is available on the Earliest Uses pages:
see Probability
& Statistics on the Earliest Uses Pages
