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University College London, 1933–1943

In 1933, Fisher became the head of the Department of Eugenics at University College London. In 1934, he become editor of the Annals of Eugenics (now called Annals of Human Genetics).

In 1935, he published The Design of Experiments, which was "also fundamental, statistical technique and application... The mathematical justification of the methods was not stressed and proofs were often barely sketched or omitted altogether.... led H.B. Mann to fill the gaps with a rigorous mathematical treatment". In this book Fisher also outlined the Lady tasting tea, now a famous design of a statistical randomized experiment which uses Fisher's exact test and is the original exposition of Fisher's notion of a null hypothesis.

The same year he also published a paper on fiducial inference and applied it to the Behrens–Fisher problem, the solution to which, proposed first by Walter Behrens and a few years later by Fisher, is the Behrens–Fisher distribution.

In 1936, he introduced the Iris flower data set as an example of discriminant analysis.

In his 1937 paper The wave of advance of advantageous genes he proposed Fisher's equation in the context of population dynamics to describe the spatial spread of an advantageous allele, and explored its travelling wave solutions. Out of this also came the Fisher–Kolmogorov equation. In 1937, he visited the Indian Statistical Institute in Calcutta, and its one part-time employee, P. C. Mahalanobis, often returning to encourage its development. He was the guest of honour at its 25th anniversary in 1957, when it had 2000 employees.

In 1938, Fisher and Frank Yates described the Fisher–Yates shuffle in their book Statistical tables for biological, agricultural and medical research. Their description of the algorithm used pencil and paper; a table of random numbers provided the randomness.