# Notable Advances in Statistics: 1919-1943

British geneticist and statistician R. A. Fisher began working at the Rothamsted (Agricultural)
Experimental Station in 1919. The Station is located just north of London on quite
variable soil as a result of past experimentation. He saw an immediate need for careful
experimental designs. While at the Rothamsted, he “almost single-handedly created the foundation for modern
statistical science.”^{3}

He promoted statistics as a mathematical science and early on provided mathematical
rigor to the Student t-test. While analyzing crop experiments, he conceived the analysis
of variance (ANOVA) and the F-distribution. Then he developed and tied together the
concepts of sufficiency, consistency, efficiency, maximum likelihood, and Fisher information.
Fisher first published his revolutionary book, *Statistical Methods for Research Workers* in 1925, it continuing through many editions. Among other influences, that book led
to wide-spread use of the P-value and significance tests.

Fisher moved to University College London in 1933. His 1935 book, *Design of Experiments*, presented fundamental statistical techniques that greatly influenced statistical
practice. (Some commonly accepted experimental-design nomenclature such as randomized
block and split plot designs stem from his earlier closeness to agronomic research.)
The book included Fisher’s view of a null hypothesis and introduced Fisher’s exact
test and other permutation tests. He advanced the theory and application of linear
discriminant analysis. By 1940, Fisher was located at the University of Cambridge,
where he applied statistics to the study of genetics.

In 1924, Walter Shewhart invents the control chart. In 1930, the journal *Annals of Mathematical Statistics* began publication by the Institute of Mathematical Statistics. In the mid-1930s,
J. H. Gaddum and C. I. Bliss devised the probit analysis method for conducting regression
analyses of binary data. Under the guidance of W. E. Deming, the 1940 U.S. Census
used statistical quality control techniques to improve the process of tabulating and
summarizing the results. It was the first use of statistical methods of quality improvement
in an office environment.

Meanwhile, the Polish statistician Jerzy Neyman was making tremendous advances in statistical sampling. His books on statistics and experimentation were widely read. He was especially interested in randomized sampling and his work on stratified sampling and purposive selection proved ground-breaking. In collaboration with Egon Pearson, the statistical world was treated to the Neyman-Pearson Lemma and the decision theoretic view of inference, including errors of Type I and Type II. Neyman extended his hypothesis testing framework by introducing confidence intervals. In 1938, Neyman left Poland and joined the statistics group at the University of California, Berkeley.

Probability theory also made great strides during this period. Well known Economist,
John Maynard Keynes published *A Treatise on Probability* in 1921. He argued against the subjective approach because he felt there should be
an objective relationship between knowledge and probabilities. In response, Frank
P. Ramsay presented his views on utility and advocated subjective probability leading
to Bayesian analyses. In 1933, the Russian mathematician Andrey Nikolaevich Kolmogorov
published his book *Foundations of the Theory of Probability*, which presented the modern axiomatic basis for probability theory.

New methods and new sources of information made it possible to measure the impact of U.S. President F. D. Roosevelt’s "New Deal" policies. Along with the increased government activity during the Great Depression of the 1930s, the number of statisticians in U.S. government service in 1938 was eight times the number in 1930. Politicians in the 1930s were kept in check by the new businesses of political consulting and public opinion polling, the single most important forces in American democracy since the rise of the party system. Political consulting is the business of managing the opinions of the masses. Public opinion surveying is the business of finding out the opinions of the masses. Political consultants tell voters what to think; pollsters ask them what they think. The purpose of fascist propaganda was to control the opinions of the masses and deploy them in service of the power of the state.

The American public opinion industry began as democracy’s answer to fascist propaganda.
The real innovation in public opinion measurement was a method that had been devised
by social scientists in the 1920s, which was to use statistics to estimate the opinions
of a vast population by surveying a statistically representative sample. Polling proponents explained, “you take sections of voters, check new trends against
past performances, establish percentage shift among different voting strata, supplement
this information from competent observers in the field, and you can accurately predict
an election result.”^{6}

By WWII, statistics had become a key component of man’s search for knowledge. Statisticians produced practical, sophisticated theory and techniques for collecting, interpreting, and presenting data, designing studies and experiments, and assessing the uncertainty in conclusions. The war created an even larger need for advances in statistical thinking and for people who could apply the new ideas. In 1942, a War Powers Act granted the president authority over “special investigations and reports of census or statistical matters.”

As WWII hit England in the late 1930s, the British asked the epidemiologist Major
Greenwood to create a statistical basis on which the domestic logistical operations
of the war effort could be built. Also, the British government set up a statistical
arm of the civil service, the “S Branch,” in which the statisticians provided reliable
data and forecasts on manpower, rationing, taxation, and social insurance, the later
of which led to Britain’s universal healthcare system. Alan Turing used advanced Bayesian
statistics to crack the German Enigma code. Many young British mathematicians were
assigned to statistical duties because, as the prominent statistician D. R. Cox explained,
“the naive assumption was that if you were good enough to get a degree in mathematics,
you could pick up statistics in a week or two.” Some of Britain’s most influential
statisticians got their start through such WWII assignments. An interesting side-note is that the eminent statistician R. A. Fisher was not directed
to war work; it seems he was unfairly suspected of fascist leanings.^{9}

As it prepared for inevitable involvement in WWII, the U.S. War Department in 1940 initiated a project on the application of statistical methods to the quality control of materials and manufactured products. A committee that included H. F. Dodge and W. E. Deming developed three standards that were approved as American Defense Emergency Standards in 1941. Later, in the early 1950s, they were accepted as official standards by the American Society of Quality Control. There were a variety of similar accomplishments during WWII. Statisticians across the country became engaged in the war effort. American statisticians, along with their colleagues in Britain and other allied countries, created major advances in areas such as statistical decision theory, statistical quality control, operations research, and sequential analysis, the later topic led by Abraham Wald in the U.S. and Peter Armitage in Britain.

Advances in Stat during Era 4

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(Last revised: 2021-04-17)