### BIOGRAPHY 13.1* Ronald A. Fisher* (1890 -1962)

Ronald Aylmer Fisher was born in London, England, and studied mathematics and physics at Cambridge University. He spent his early years indecisively moving about -- working at an investment house, on a farm in Canada, and as a teacher in British public schools. He developed an interest in biometrics, however, and this interest led him, in 1919, to join the staff of the world famous agricultural experiment station at Rothamsted. There he was charged with sorting and reassessing a 66-year accumulation of data on field trials and weather records -- and in the process, he became one of the century's leading statisticians. Early on, he published the epochal *Statistical Methods for Research Workers *(1925), a book that was destined to go through 14 editions in many languages and to become the "bible" for researchers throughout the world. This book was followed by two equally influential works, The *Genetical Theory of Natural Selection* (1930), a book that reconciled Darwinian evolution with Mendelian genetics, and *The Design of Experiments* (1935). These books established Fisher as a top-ranking geneticist as well as statistician. Indeed, prior to his move to Australia late in life, Fisher held long-term positions as professor of eugenics, first at University College, London, and later at Cambridge University.

The works just cited, however, hardly begin to tell the story of Fisher's productivity. Over the course of half a century, he published one paper every two months, and most of them broke new ground! Thus, it is difficult to decide which of his many contributions are the most praiseworthy, and it is surely impossible in a few paragraphs to show how thoroughly the land of statistics is crisscrossed with the footprints of this prolific scholar. He is the pioneer in experimentation who revolutionized the field with randomized blocks, Latin squares, factorial designs, and confounding. (See text Chapter 5 for a discussion of these concepts.) Then he is the man who pushed ahead the theory of estimation (and introduced concepts of unbiasedness, consistency, efficiency, and more) and who made correlation, regression, and analysis of variance (and covariance) what they are today. It was Fisher who erected upon the work of William S. Gosset (Biography 12.1) a comprehensive theory of hypothesis testing based on small samples.
It is not surprising that honors and prizes were heaped upon Fisher throughout his life; he was even knighted in 1952. It is unfortunate that Fisher also became involved in an extraordinarily long-lasting and acrimonious battle with other statisticians concerning the nature of estimation and hypothesis testing.

In his theory of estimation, Fisher introduced the concept of the **fiducial interval**, a range of values that can be trusted, with a specified probability, to contain the value of some parameter. Such an interval might take the form:

Fisher would establish this range *after* a sample had been taken and X bar had been calculated. Given the specific sample result, he would, thus, make a probability statement about the parameter in the form of the fiducial interval and would tell us that we could trust the parameter to lie within that range (the *Latin fiducia* means *trust*) -- *with* a specified probability, depending on the value of *z*. (This view is generally rejected by statisticians today, a fact already implied by the Chapter 12 discussion of *confidence intervals*.)

In subtle but important ways, Fisher's view of hypothesis testing also differed from that of other statisticians, as text Section 13.8 shows. Nevertheless, Fisher's work greatly helped the development of the modern theory of hypothesis testing, and his scientific achievements are in any case so varied and so crucial that nothing can dim their luster or reduce his ranking as one of the greatest scientists of this century.

*Sources: Dictionary of Scientific Biography*, vol. 5 (New York: Scribner's, 1972, pp. 7-11; *International Encyclopedia of Statistics*, vol. I (New York: Free Press, 1978), pp. 352-358. For more information on Fisher, see *Encyclopedia of Statistical Sciences* (New York: Wiley-Interscience, 1982-86), vol. 3, pp. 103-110, or Bennett, J. H. *Collected Papers of R..A. Fisher*. Adelaide, Australia: The University of Adelaide, 1971-74. This five-volume set of more than 300 articles is a monument to Fisher's genius.