On an Absolute Criterion... (1912)
Early Research
In April 1912, while still a student, Fisher published his first mathematical paper ‘On an Absolute Criterion for Fitting Frequency Curves,’ introducing what would become known as the method of maximum likelihood (a method of estimating the parameters of a probability distribution by maximizing a likelihood function, so that under the assumed statistical model the observed data is most probable.) He would continue to refine this method for a further 10 years.
On display:
- ‘On an Absolute Criterion for Fitting Frequency Curves’ / R.A. Fisher. Fisher Papers. Series 2: Collected Papers, 1. This paper was developed out of his study of the theory of errors
After Graduation
On the Stability of Veering Flight. [undated]
Paid work was not forthcoming after graduation. His real interests were in the eugenical and statistical work which were only combined at the Galton Laboratory, but Fisher had failed to win recognition from Professor Karl Pearson. He enjoyed the farming life but was without the capital to invest. He was offered a job at an aircraft factory when they saw his ready grasp of their problems but he did not feel that aircraft design would satisfy him permanently and he turned it down (despite writing a short mathematical treatment of a practical flying problem ‘On the Stability of Veering Flight.’) As war seemed likely, he marked time with his Officer’s Training Corps and Territorial Army Training until he could join the regular army.
He worked for a short time as a statistician for the Mercantile and General Investment Company in London. In 1914, at the advent of World War I, he volunteered for the army but was rejected multiple times due to his poor eyesight. As his contribution to the war, he taught physics and mathematics at private schools, including Rugby and Bradfield College in Kent, and on the HM Training ship Worcester.
In 1919 Fisher unsuccessfully applied for various positions, including at Cairo University and in New Zealand, and he failed to win a Cambridge Fellowship. He was seriously considering farming before he was introduced to Dr E.J. Russell who was visiting Cambridge looking for staff for the Rothamsted Experimental Station.
On display:
- Undated paper ‘On the Stability of Veering Flight.’ Fisher Papers. Series 13 [undated]
Cambridge University Eugenics Society
Mendelism and Biometry (1911)
As a Freshman, Fisher had purchased the newly published Mendel’s Principles of Heredity and in 1911 he gave a 15 minute talk to the Cambridge University Eugenics Society on ‘Mendelism and Biometry,’ which suggested the two seemingly incompatible sciences could be combined to study the phenomenon of inheritance.
Fisher had been one of the founders of the University of Cambridge Eugenics Society. This led to a friendship with Leonard Darwin, son of Charles Darwin and President of the Eugenics Education Society. The Society published the Eugenics Review for which Fisher would write many pieces. Darwin’s financial, intellectual and emotional support was important to Fisher, especially in the early part of his career when he was an obscure schoolteacher whose contributions were largely rejected by professionals.
On display:
- Fisher's copy of his 1911 paper on ‘Mendelism and Biometry’, with his ms corrections. Fisher Papers. Series 12: Papers on Eugenics
First Genetics Papers
The Correlations... [1918]
Also in 1915, Fisher made his first contribution to the theory of sexual selection in the paper ‘The Evolution of Sexual Preference’ and in 1918 published the landmark paper ‘The Correlation Between Relatives on the Supposition of Mendelian Inheritance’ which introduced variance and further vindicated Mendelism and biometry or quantitative genetics. The paper was originally submitted to the Royal Society of London Transactions in 1916 but the reviewers (including Karl Pearson) had difficulty understanding it and it was put aside. It was eventually published in the Transactions of the Royal Society of Edinburgh in 1918, with financial assistance from Leonard Darwin.
Fisher’s new ideas and his mathematical approach to biological questions were often met with incomprehension and sometimes downright resistance. Fisher had a quick temper and became involved in some rather bitter feuds. His ability to ‘see’ the answers to complex mathematics problems was both a blessing and a curse as most people could not follow the logic of his arguments without detailed proofs. The books he would later write were landmarks in biology and statistics, but often had to be explained by more ‘user friendly’ scientists before they became widely understood.
On display:
- Fisher’s first genetics paper, ‘The Correlations to be Expected Between Relatives on the Supposition of Mendelian Inheritance,’ published in the Transactions of the Royal Society of Edinburgh [1918]. Fisher Papers. Series 2: Collected Papers, 9
W.S. Gosset and R.A. Fisher
Fisher with W.S. Gosset as a student
Fisher’s investigation of the distributions of sampling statistics began when he came across a paper ‘On the Probable Error of the Mean’ by W.S. Gosset (known under the pseudonym of ‘Student’) which attempted to deal with standard deviation and small samples which were more subject to error than large sample work.
Fisher began corresponding with ‘Student’ in 1915 and he improved Student’s original “z”-distribution (for assessing the statistical significance of the difference between two sample means) as a “t”-distribution. He also developed a distinction between sample and population means.
The correspondence continued until 1924 in friendship and collaboration, although they quarrelled in the last year over randomisation. After Gosset’s death in 1937 he reviewed and added a summary to the collected correspondence which was later published privately. Unfortunately, only a few of Fisher’s letters had survived.
On display:
- Photograph: Fisher with ‘Student’ [Gosset]. Fisher Papers. Series 25.1: Family album c1900-55
- Letter from Marjory Gosset, 8 November 1937, following Gosset’s death. Fisher Papers. Series 24: Cuttings book re [early] career
- Volume 1: ‘Letters from W.S. Gosset to R.A. Fisher. 1915-1936.’
5 volumes. [The Letters were published for private circulation in 1962] Fisher Papers. Series 6: Letters from W.S. Gosset to R.A. Fisher, vol. 1
Professor Karl Pearson (1857-1936), first Galton Chair of Eugenics
Frequency Distribution... (1915)
Karl Pearson founded the world’s first statistics department at University College London and established it as a serious branch of science.
Fisher was at first Pearson’s protégé and in 1915 published Fisher’s ‘Frequency Distribution of the Values of the Correlation Coefficient in Samples from an Indefinitely Large Population’ in Biometrika, which Pearson edited. The paper established a new era in the exact theory of sampling distributions and led to a feud with Karl Pearson. Pearson continued his own work on the issue with four of his assistants and in 1917 published ‘the cooperative study’ which contained a criticism of Fisher’s method of maximum likelihood and labelled it inverse inference, which Fisher had gone out of his way to avoid. Fisher pledged never to send another paper to Biometrika. Pearson then ignored Fisher’s much of Fisher’s work and subsequent papers were withdrawn from the Royal Society’s consideration because of the tension between the two statisticians.
In 1919, Pearson offered Fisher a job in his department with restrictive conditions, but Fisher declined and accepted the position at Rothamsted.
On display:
- ‘Frequency Distribution of the Values of the Correlation Coefficient in Samples from an Indefinitely Large Population’ Biometrika (1915). Fisher Papers, Series 2: Collected Papers 4
