**William Youden**'s family were originally from Britain. His father was also named William John Youden and he was an engineer who had been born in Dover. Youden's mother, Margaret Hamilton, came from Carluke in Scotland. Although Youden was born in Australia, his family returned to England he was two years of age. For five years they lived in Dover, then when Youden was seven they emigrated to the United States.

Arriving in Connecticut in 1907, Youden's family soon moved to the Niagara Falls. There he attended school but after a few years the family were on the move again, this time taking up residence in Rochester. Youden was sixteen years old when he began to live in Rochester and he was nearing the age to begin his university education. Indeed, he entered the University of Rochester in the following year and studied chemical engineering.

When he entered university in 1917 World War I was in progress, and Youden had a break from university for three months in 1918 while he served in the Army. He returned to complete his studies for a B.S. which was awarded in 1921. In September 1922 Youden entered Columbia University to study, first for his Master's Degree which was awarded in 1923, then for his doctorate which was awarded in 1924. Both these postgraduate degrees were in chemistry.

So far we have seen nothing which might indicate why Youden would be the right person to include in this history of mathematics archive. In fact up to this time Youden had shown no interest in statistics, the area to which he would eventually make a major contribution. After obtaining his doctorate in 1923 he obtained a post with the Boyce Thompson Institute for Plant research as a physical chemist.

Youden did not become interested in statistics for a few years. In fact over the first few years that he worked at the Institute Youden became more and more disillusioned with the way that measurements were made in biology. At one point he was so upset by the methods used that he considered resigning his position. However, in 1928 he obtained a copy of Fisher's *Statistical Methods* which had been published three years earlier. This book opened up a new world for Youden who now saw that he had the perfect opportunity to carry out agricultural experiments which could be set up using the new experiment designs put forward by Fisher.

In 1931 Youden published his first paper on statistical methods. It marks [1]:-

In his work during the 1930s on the statistical design of experiments, Youden introduced new methods based on balanced incomplete block designs. Youden made Fisher aware of these methods in 1936 and Fisher called the new experiment designs 'Youden squares' in his work on... the beginning of Youden's "missionary" efforts to acquaint research workers with statistical methods of value in their work.

*Statistical tables*published jointly with Yates in 1938. Youden published a paper in 1937

*Use of incomplete block replications in estimating tobacco mosaic virus*which used his new rectangular experimental arrangements. He introduced further designs in a paper which appeared in 1940.

In [5] Preece surveys Youden squares. His own summary of what is contained in this papers follows:-

Youden squares played an important role in World War II being used for experimental trials in engineering and other scientific projects. During World War II Youden worked for the military as a operations analyst. He spent some time in Britain undertaking war work, mainly investigating the factors which control the accuracy of bombing. He also spent time in India, China, and the Marianas carrying out similar work.Youden squares were introduced in the1930s as designs for experimentation on plants. We discuss their mathematical properties and their enumeration. Cyclic and partly cyclic methods of generating Youden squares are given particular attention. Some balanced Graeco-Latin designs that incorporate Youden squares are discussed; these have statistical interest because of their potential for use as designs for orchard experiments, and some have mathematical interest because of their role in the construction of Graeco-Latin squares.

In 1948 Youden, by now recognised as a leading statistician as well as a chemist, joined the National Bureau of Standards. In that position he again was deeply involved in devising experimental arrangements for a wide range of different tasks from spectral analysis to thermometer and other instrument calibration.

In 1974, three years after his death, Youden's final book was published. He had completed the manuscript of *Risk, choice and prediction* shortly before his death and this text was aimed at school children. Youden wrote in the introduction that the book was aimed at anyone:-

... who wants to learn in a relatively painless way how the concept and techniques of statistics can help us better understand today's complex world.

**Article by:** *J J O'Connor* and *E F Robertson*