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\noindent{\bf Ronald Aylmer FISHER}\\
b. 17 February 1890 - d. 29 July 1962
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\noindent{\bf Summary.}
R. A. Fisher transformed 
the statistics of his day from a modest collection of useful ad hoc 
techniques into a powerful and systematic body of theoretical concepts and 
practical methods.  This achievement was all the more impressive because at 
the same time he pursued a dual career as a biologist, laying down, together 
with Sewall Wright and J. B. S. Haldane, the foundations of modern 
theoretical population genetics.
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Ronald Aylmer Fisher, arguably
the greatest statistician of this (or any 
century)
was born in Hampstead, England.  After attending Harrow,
he studied at Gonville and Caius College, Cambridge from 1909 to 1913;  later
returning to Cambridge first as a Fellow, and then as Professor of Genetics.
He died in Adelaide, Australia.
	Fisher made profound contributions to both theoretical and applied
statistics, and to population genetics.  His career divides naturally into
five periods:  1913 - 1919 (held several minor commercial and teaching
positions);  1919 - 1933 (resident statistician at Rothamsted);  1933 - 1943
(Galton Professor of Eugenics, University College, London);  1943 - 1957
(Arthur Balfour Professor of Genetics, University of Cambridge);  and 1957 -
1962 (retirement).  Throughout his life he received many awards and honors,
including the Weldon Memorial Medal (1928), election to Fellowship of the
Royal Society (1929), and honorary degrees from Harvard University (1936) and
the University of Chicago (1956).
	Fisher's mathematical genius was already evident during his student 
days at
Cambridge.  During these years he also gained his first exposure to Mendelian
genetics and the English eugenics movement;  his interest in statistical
inference was intimately connected to these biological interests, and in later
years his output was almost always evenly divided between the two areas.
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\noindent{\bf Initial Contributions, 1913 - 1919}

During his first years after
graduation from Cambridge, Fisher published two papers of outstanding
significance:  one on the small sample distribution of the sample correlation
coefficient (1915;  CP 4);  the other  linking the Mendelian and Darwinian
approaches to genetics (1918;  CP 9).  (References to Fisher's papers are to
the date of publication and their number in his Collected Papers [=CP]
(Bennett, 1971-1974).)
	During this initial period Fisher was strongly influenced by the work of
William Sealy Gossett (``Student") (q.v.), impressing the later by producing a
rigorous mathematical derivation for Student's $t$-distribution (in his paper
Student had only guessed the form of the distribution on the basis of its
first four moments).  Encouraged by this first success, Fisher turned to the
correlation coefficient.  Earlier studies by Pearson (q.v.), Filon, Gosset, 
and Soper
had given approximate, large sample expressions for the mean and standard
error of the sample correlation coefficient $r$.  Using geometric insights
(representing the outcome of a random sample as a single point in an $n$-
dimensional space, in a mathematical tour-de-force Fisher was able to derive
the exact, small-sample distribution of $r$.  Although Karl Pearson accepted
Fisher's paper for publication in his journal {\it Biometrika}, two years 
later a
``cooperative study" by Pearson and his associates appeared criticizing
Fisher's paper on several grounds.
	Although relations between Fisher and Pearson remained cordial in the
immediate aftermath, Pearson rejected another paper of Fisher submitted to
{\it Biometrika} and this, together with the rejection of Fisher's Mendelian 
paper
by Royal Society (Pearson had been one of the referees to give a negative
report), ultimately led Fisher to a sharp deterioration in relations between
the two.  Pearson, nevertheless, recognizing Fisher's obvious abilities,
offered him a position in his University College London statistical
laboratory, but Fisher recognized the incompatibility of their personalities;
and when a competing offer came from Rothamsted, an agricultural research
station in the English countryside, Fisher readily accepted it.
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\noindent{\bf Rothamsted:  1919 - 1933}

Fisher's days at Rothamsted were his among his
happiest and most productive.  Enjoying for the first time a secure position,
he was surrounded by appreciative and supportive colleagues, and had access
both to important problems and extensive statistical compilations of data that
needed analysis.  In his element at last, Fisher began to develop an
extraordinary range of statistical methods fitted into a theoretical
superstructure: during the next fifteen years he produced a flood of papers
unparalleled either before or after.  These fell into four main categories:
statistical tests of significance and distribution theory, contributions to
theoretical statistics and estimation theory, fiducial inference, and the
design of experiments.

{\it a. Statistical tests of significance and distribution theory}.  Fisher's
mathematical skills and geometric insights enabled him to tackle a wide
variety of distributional problems, extending the work of Gosset on the $t$-
distribution (for whom Fisher had a life-long admiration).  One of the most
important of these was the distribution of the chi-squared statistic,
determining the appropriate number of degrees of freedom if the cell
probabilities depended on one or more estimated parameters. Fisher proceeded
(in a series of five papers published over the seven year period 1922-1928) to
attack Pearson's use of the chi-squared statistic to test homogeneity, on the
(entirely correct) grounds that Pearson had systematically employed an
incorrect number of degrees of freedom).  The result was a heated dispute, to
which Fisher repeatedly returned (CP 19, 31, 34, 49, 62, 188).
	Other, less controversial but equally fundamental distributional
results
obtained by Fisher during this period included his paper on testing the
significance of regression coefficients (1922, CP 20), the $F$ distribution
(1924, CP 36), the independence of the sample mean and variance from a normal
population (1925, CP 43), the sampling distribution of the multiple
correlation coefficient (1928, CP 61)

{\it b.  The theory of estimation}.  At the same time as he made major 
strides in
distribution theory, Fisher began to craft a systematic theory of estimation,
introducing the basic concepts of sufficiency (192, CP 12), consistency, and
efficiency (1922, CP 18; 1925, 42).  The method of maximum likelihood was
advanced as the practical realization of these three goals;  and the entire
structure laid out systematically in Fisher's epochal {\it Statistical 
Methods for
Research Workers} (1st ed., 1925).  The book illustrated Fisher's genius for
the apt example, systematic exposition of efficient computational technique,
and ruthless suppression of mathematical justification or derivation.  The
last chapter of the book, involving the estimation of a genetic linkage
parameter, is a masterpiece of exposition;  using five competing methods of
estimation, the advantages and ease of use of the method of maximum likelihood
estimation are contrasted with other, less efficient, more eclectic, or more
cumbersome  modes.
	Throughout his life Fisher remained an ardent supporter of the method of
maximum likelihood, but his views regarding it evolved.  His initial 1922
paper argued its large sample merits, but the 1925 paper began to argue that
it had small sample advantages as well, and introduced the concept of
information loss (as well as the method of scoring).

{\it c.  Fiducial inference}. 	Pearson was also an exponent of Bayesian 
methods, and
Fisher's rejection of inverse methods and his ultimate development of fiducial
inference as an alternative to them was thus yet another assault on the
Pearsonian edifice.  
	It is in many ways ironic that Fisher's first paper on fiducial 
inference,
``Inverse Probability" (1930, CP 84), contains little that is controversial.
In it Fisher introduced the probability integral transformation, and observed
that this transformation often provides a pivotal quantity that can be
inverted to obtain interval estimates having any prespecified coverage
frequency.  It was only later, after Fisher attempted to extend the argument
to include multiparameter estimation, that difficulties arose.
	In 1935 Fisher (CP 125) illustrated the use of a simultaneous fiducial
distribution with two examples, one of which was the notorious Behrens-Fisher
problem:  to estimate the difference in the means $m_1$ and $m_2$ of two normal
populations, given that the variances ${s_1}^2$ and ${s_2}^2$ of the two 
populations are
unknown. Few could have predicted then that it would generate a debate lasting
several decades.  Fisher's solution was almost immediately questioned by
Bartlett, who noted that unlike the examples involving the $t$-statistic,
standard deviation, and correlation coefficient, the interval estimates for 
$m_2 - m_1$ advocated by Fisher gave rise to tests with inappropriate levels of
significance, in terms of frequencies involving repeated sampling from the
same initial population.
	Unlike Fisher's many other original and important contributions to
statistical methodology and theory, fiducial inference never gained widespread
acceptance, despite the importance that Fisher himself attached to the idea.
Instead, it was the subject of a long, bitter, and acrimonious debate within
the statistical community;  and although Fisher's impassioned advocacy gave it
viability during his own lifetime, it quickly exited the theoretical
mainstream after his death.  Considerable confusion always existed about the
exact nature of the fiducial argument;  and the entire subject came to have an
air of mystery. Fiducial inference never developed during Fisher's lifetime
into a coherent and comprehensive theory, but remained a collection of
examples, insights, and goals, added to and modified over time;  and the
polemical nature of the debate on both sides rendered much of the resulting
literature opaque.

{\it d.  Design of experiments}.  The abundance of agricultural data 
available at
Rothamsted led Fisher by a direct and natural route to the analysis of
variance;  and his first paper on this subject appeared as early as 1923 (CP
32).  This initial effort suffered from a number of defects:  Fisher had not
tabulated the $F$ distribution, nor did he yet appreciate fully the crucial role
of randomization.  But progress came quickly:  Fisher's address the next year
to the 1924 International Congress of Mathematicians in Toronto (CP 36)
described the relationship between the $z$ =: 1/2 ln $F$, chi-squared, normal, 
and $t$-distributions; and passages from the 1925 edition of {\it Statistical 
Methods
for Research Workers} emphasized the importance of randomization in ensuring
the validity of tests of significance.  During this period Fisher developed in
rapid succession the basic elements of design:  blocking, factorial designs
(1926, CP 48), Latin squares, confounding, and partial confounding, and the
analysis of covariance.  This work was summarized in Fisher's classic book 
{\it The
Design of Experiments} (1935), another masterpiece of exposition containing the
celebrated example of the lady tasting tea (Chapter 2:  ``The Principles of
Experimentation, Illustrated by a Psycho-Physical Example").
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\noindent{\bf Professor of Eugenics, University College London, 1933 - 1943}


Ironically, Fisher's move to London and a Professorship marked the beginning
of a period of increasing controversy in his life, in particular the dispute
with Neyman (q.v.).  Before his dispute with Neyman, Fisher had engaged in other
statistical controversies, crossing swords with Arthur Eddington, Harold
Jeffreys (q.v.), and Karl Pearson. He had been fortunate in his previous 
choice of
opponents:  Eddington conceded Fisher's point;  Jeffreys was cordial in
rebuttal;  and Pearson labored under the disadvantage of being wrong.  But in
Neyman Fisher faced an opponent of an entirely different character.
	Neyman left Poland at the beginning of 1934 in order to assume a 
permanent
academic position at University College London.  Shortly after his arrival in
England, Neyman read a paper before the Royal Statistical Society (on 19 June
1934) dealing in part with the fiducial argument, and reformulating Fisher's
theory in terms of what Neyman called ``confidence intervals".
Neyman described introducing his theory of confidence intervals as an
alternative description and development of Fisher's theory of fiducial
probability, permitting its extension to the several parameter case.
Fisher, one of the paper's discussants, in turn referred to Neyman's work as a
``generalization" of the fiducial argument, but pointed to the problem of a
possible lack of uniqueness in the resulting probability statements if
sufficient or ancillary statistics were not employed.  Confidence intervals,
Fisher thought, make statements which, although mathematically valid, are of
only limited inferential value;  but that they had some value he conceded in a
footnote.  In 1935, shortly after this, relations between the two broke down
after Fisher's discussion of Neyman's 1935 JRSS paper (read 28 March).
Neyman's paper had been critical of some of Fisher's most important work in
the design of experiments, although the attack was indirect and  towards
Fisher himself the tone of the paper was one of almost studied politeness.
Fisher's discussion was sharply critical of Neyman, both in substance and
tone; and Neyman did not hold back in response.
	Closely linked to his criticisms of Neyman's confidence intervals were
Fisher's emerging views on the nature of conditional inference.   There were
already hints of this in some of his earlier papers (in particular, CP 42),
but the issue first clearly arose in his papers in the 1930s.  In his 1934
classic ``Two new properties of mathematical likelihood" (CP 108), Fisher
introduced the concept of the recovery of information using conditioning;  and
in his 1934 address to the Royal Statistical Society (CP 108), he turned to
the conditional analysis of the two-by-two table and the use of the exact
test.  In both cases, as throughout his career, the examples advanced beyond
the supporting theory, and no general prescription or rationale for
conditioning was provided.
	In his papers of the 1930's, Fisher was just beginning to grapple with 
these
issues, and his comments are at times brief, fragmentary, even tentative. It
is symptomatic of the uncertainty he must have felt at this period in his life
that in 1941 he made the extraordinary concession that Jeffreys, ``whose
logical standpoint is very different from my own, may be right in proposing
that ``Student's' method involves logical reasoning of so novel a type that a
new postulate should be introduced to make its deductive basis rigorous"
(1941, CP 181,  p. 142).   
	But when referring to Neyman, no such concession was possible.  By 1945
Fisher's view had hardened,  and he labeled the criterion that ``the level of
significance must be equal to the frequency with which the hypothesis is
rejected in repeated sampling of any fixed population allowed by hypothesis"
as an ``intrusive axiom, which is foreign to the reasoning on which the tests
of significance were in fact based" (1945, CP 203,  p. 507).
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\noindent{\bf Professor of Genetics, University of Cambridge: 1943 - 1957}

Fisher's
return to Cambridge, although a professional triumph, was marked by personal
tragedy:  irreconcilable differences led to permanent separation from his
wife, and shortly after, in December 1943, his son George was killed in the
war.  Fisher's output of scientific papers continued unabated, but although
these still contained much of interest, there was nevertheless for the most
part a clear decline in their depth and insight relative to his best earlier
work, save for the  occasional exception, such as ``Dispersion on a sphere"
(Fisher, 1953; CP 249).  His book {\it The Theory of Inbreeding} (1949) has 
been
described by his own daughter as ``remarkable for being peculiarly his own
formulation without reference to, or comparison with, what others had
published on that subject" (Box, 1978, p. 417).
	In the 1950s, sensing that the tide had turned against his theory of 
fiducial
inference, Fisher returned to the subject in his 1956 book, {\it Statistical
Methods and Scientific Inference} (SMSI, 1956).  Fisher's treatment of
probability in SMSI revealed an important shift in his view of the nature
probability.  In his papers before World War II, Fisher had described prior
distributions as referring to an objective process by which population
parameters were generated;  writing for example in 1921, that the problem of
finding a posterior distribution ``is indeterminate without knowing the
statistical mechanism under which different values of [a parameter] come into
existence" (1921, CP 14, p. 24), and that ``we can know nothing of the
probability of hypotheses or hypothetical quantities" (p. 35).
	In contrast, in the 1950's Fisher espoused a view of probability much 
closer
to the personalist or subjectivistic one:  ``probability statements do not
imply the existence of [the hypothetical] population in the real world.  All
that they assert is that the exact nature and degree of our uncertainty is
just as if we knew [the sample] to have been one chosen at random from such a
population" (1959, CP 273, p. 22).  None of the populations used to determine
probability levels in tests of significance have ``objective reality, all being
products of the statistician's imagination" (1955, CP 261, p. 71;  cf. SMSI,
p. 81 ).  In the 1st and  2nd editions of SMSI, Fisher referred to ``the role
of subjective ignorance, as well as that of objective knowledge in a typical
probability statement" (p. 33).  Thus, although Fisher remained publicly anti-
Bayesian, after World War II he was in fact much closer to the ``objective
Bayesian" position than that of the frequentist Neyman.
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\noindent{\bf Retirement:  1957 - 1962}

Fisher did not retire from his Professorship of
his own accord, but due to an imposed age requirement at Cambridge (although
he continued on at Gonville and Caius, elected President of the College in
1957).  In his last years, he traveled extensively, visiting Michigan State
University in the Fall of 1957, and later both returning to the United States
and visiting Japan, India, Belgium, France, and Italy.  Controversial to the
end, after becoming a scientific consultant for the British Tobacco
Manufacturers Standing Committee he repeatedly expressed skepticism both in
invited lectures and in print regarding the statistical evidence then
available regarding the causal connection between smoking and lung cancer.
	In 1959 Fisher moved to the University of Adelaide in Australia, 
spending
much of his remaining time there.  It was here that he was diagnosed as having
cancer in the summer of 1962;  and although the operation (on July 21) was
judged a success, eight days later Fisher died suddenly of a post-operative
embolism.
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\noindent{\bf Literature} 

{\it Primary Sources}.  Fisher's three books on 
statistical theory
({\it Statistical Methods for Research Workers, The Design of Experiments}, and
{\it Statistical Methods and Scientific Inference}) have gone through many 
editions.
Now individually out of print, they have been reprinted in a single volume by
Oxford (Fisher, 1990);  {\it The Genetical Theory of Natural Selection} (1930)
remains in print thanks to Dover Publications.  Fisher's Collected Papers
(Bennett, 1971 - 1974) remain an invaluable source for the study of Fisher
(although the collection omits most of his book reviews, and scattered other
minor contributions).  Fisher's selected correspondence has also been
published in two volumes, one genetic (Bennett, 1983) and one statistical
(Bennett, 1990).  These are invaluable for understanding the evolution of his
thinking, and sometimes contrast in interesting fashion with his more public
statements of position. Of particular interest is Fisher's correspondence with
Gossett, unfortunately only published privately. 

{\it Secondary Sources}.  The biography of Fisher by his daughter (Box, 1978) 
is an
invaluable source of information regarding Fisher's life and personality; its
scientific discussion provides a useful orientation for further study.  Also
useful is the obituary notice of Yates and Mather (1963).
	There are many appreciations of Fisher's contributions to statistical
science;  but of particular note is the remarkable effort of L. J. Savage
(1976).  The essays in R. A. Fisher:  An Appreciation (Fienberg and Hinkley,
1980), although of variable quality, have considerable value as assessments of
Fisher's contributions from the perspective of later professional
statisticians.  (Outstanding among these is D. L. Wallace, ``The Behrens-Fisher
and Creasy-Fieller Problems", pp. 119-147.)  Gosset's recent statistical
biography (Pearson, 1990) of necessity touches on Fisher throughout.  Among
the numerous appreciations and discussions of Fisher, two of particular
interest are Yates (1951) and Kruskal (1980).
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\begin{thebibliography}{3}

\bibitem{1}  Bennett, J. H. (ed.) (1971-1974). {\it  Collected Papers of R. A. 
Fisher} (5 vols).  University of Adelaide.

\bibitem{2}  Bennett, J. J. (ed.) (1983). {\it Natural Selection, Heredity, 
and Eugenics.
Including Selected Correspondence of R. A. Fisher with Leonard Darwin and
Others}.  Clarendon Press, Oxford. 

\bibitem{3}  Bennett, J. H. (ed.) (1990). {\it  Statistical Inference and 
Analysis:  Selected
Correspondence of R. A. Fisher}.  Clarendon Press, Oxford.

\bibitem{4}  Box, Joan Fisher (1978). {\it R. A. Fisher:  The Life of a 
Scientist}.  Wiley, New
York.

\bibitem{5}  Fienberg, Stephen E. and Hinkley, David V. (1980). {\it R. A. 
Fisher:  An
Appreciation}.  Lecture Notes in Statistics 1, Springer-Verlag, New York.

\bibitem{6}  Fisher, R. A. (1990). {\it Statistical Methods, Experimental 
Design, and
Scientific Inference}.  Clarendon Press, Oxford.

\bibitem{7}  Kruskal, W. (1980).  The significance of Fisher:  a review of R. A. Fisher:
The Life of a Scientist. {\it Journal of the American Statistical Association}
{\bf 75}, 1019-1030.

\bibitem{8}  Pearson, E. S. (1990). {\it `Student':  A Statistical Biography of William Sealy
Gosset} (R. L. Plackett and G. A. Barnard, eds.).  Clarendon Press, Oxford.

\bibitem{9}  Savage, L. J. (1976).  On re-reading R. A. Fisher. {\it
Annals of Statistics} {\bf 3},
441-500 (with discussion).

\bibitem{10}  Yates, F. (1951).  The influence of Statistical Methods for 
Research Workers
on the development of the science of statistics.  {\it Journal of the American
Statistical Association} {\bf 46}, 19-34.

\bibitem{11}  Yates, F. and Mather, K. (1963).  Ronald Aylmer Fisher, 1890-1962.
{\it Biographical Memoirs of Fellows of the Royal Society of London}
{\bf 9}, 91-120.
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\hfill{S.L. Zabell}


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