Youden, William John

From Encyclopedia of Mathematics
Jump to: navigation, search
Copyright notice
This article William John Youden was adapted from an original article by Harry H. Ku and Joan R. Rosenblatt, which appeared in StatProb: The Encyclopedia Sponsored by Statistics and Probability Societies. The original article ([ StatProb Source], Local Files: pdf | tex) is copyrighted by the author(s), the article has been donated to Encyclopedia of Mathematics, and its further issues are under Creative Commons Attribution Share-Alike License'. All pages from StatProb are contained in the Category StatProb.

William John YOUDEN

b. 12 April 1900 - d. 31 March 1971

Summary. Beginning with the balanced incomplete block designs known as Youden Squares, W. J. Youden created many designs tailored to the needs of the physical and engineering sciences.

Jack Youden, the great communicator of statistical ideas and practicies in non-statistical terms, was born on April 12, 1900, in Townsville, Australia. He came to the U.S.A. at the age of seven and was trained as a chemist (Ph.D., Columbia University, 1924). A few years into his career, however, he became convinced that statistical methods are indispensable in all scientific work, for efficiency and validity. His contributions as a "missionary" for statistics in scientific research were so impressive that the statistical societies gave his name to three series of awards and prizes:

(i) The Youden Memorial Lecture, presented at the Annual Fall Technical Conference sponsored by the Section on Physical and Engineering Sciences of the American Statistical Association (ASA) and the Chemical and Process Industries Division and the Statistics Division of the American Society for Quality Control (ASQC).

(ii) The Youden Prize, awarded by the ASQC for the best expository paper on statistical methods or philosophy that appeared in "Technometrics during the previous year.

(iii) The W.J. Youden Award in Interlaboratory Testing, given each year by the ASA.

Youden's contributions to statistical methods include innovative experiment designs, elegant procedures for displaying the results of interlaboratory comparisons of measurement and test methods, and a stream of techniques tailored for use to improve the quality of scientific and engineering measurements. He was a pioneer in the application of twentieth-century Fisherian small-sample methods to the planning and analysis of experiments in the physical sciences. Following a brief outline of Youden's professional career, we describe a few highlights.

From 1924 to 1948 he was on the staff of the Boyce Thompson Institute for Plant Research in Yonkers, New York. In about 1928 he and Frank Wilcoxon began using Statistical Methods for Research Workers by R.A. Fisher, and soon began contributing to statistical science. Youden took leave during the academic year 1937-38 to work with Fisher at the Galton Laboratory, University College, London. During 1942-45, he served as an operations analyst with the U.S. Army Air Corps.

From 1948 until his retirement in 1965, Youden was a senior staff member of the Applied Mathematics Division at the National Bureau of Standards (NBS) in Washington, D.C.; he continued this affiliation as a Guest Researcher after his retirement. At the NBS, the U.S. national laboratory for physical measurement standards, Youden produced more experiment designs, developed interlaboratory testing procedures and his "ruggedness" test, wrote Statistical Methods for Chemists (Youden, 1951) and other books, and from 1954 through 1959 published 36 columns under the title "Statistical Design" in "Industrial and Engineering Chemistry.

More complete biographical accounts are given in (Eisenhart and Rosenblatt, 1972), (Eisenhart, 1976), (Ku, 1978), (Cornell, 1992), and in a special issue of the Journal of Quality Technology (JQT) dedicated to Youden (Lasater, 1972). The JQT issue contains a nearly complete bibliography of Youden's publications, reprints of several of his papers and other materials, and a "Summary and Index for 'Statistical Design'" compiled by Mary G. Natrella that describes his columns in Industrial and Engineering Chemistry. Eisenhart (1976) provides the definitive scholarly account and completes the bibliography.

Youden was often heard telling a "client" in consultation, or an audience at one of this well-attended lectures, that he was a ``chemist", implying that he was really not a statistician. Nevertheless, while he may have been all chemist for his first few years at Boyce Thompson, the seed of his transformation to statistician was planted early when he obtained a copy of the first edition of Fisher's "Statistical Methods for Research Workers, and seized the opportunity to apply the methods in experiments in the field and in the greenhouse. Evidence of this began to appear in his publications in 1931.

The paper Youden (1937; reprinted in Lasater, 1972) was the first in which he introduced new experiment designs. The new class of rectangular designs, termed "Youden Squares" by Fisher and Yates in the first edition, 1938, of their book of tables, was found immediately to be of broad utility in biological and medical research generally, and to be of great value in scientific and engineering experimentation connected with research and development.

The description of Youden's work as operations analyst during World War II (Miser 1992) was entitled ``Craft in Operations Research", but could as well be called ``craft in applied statistics". Youden directed groups of civilian scientists seeking to understand and improve bombing accuracy, first in Britain and later in the Pacific area, and was awarded the Medal of Freedom in 1946. According to Miser, stories are legion among the members of the Operations Research Group of the Eight Bomber Command in England about Yourden's exceptional skills in the invention of novel, and adaption of standard, tools of experiment design and analysis, and his gifts in divining the best way (officially or unofficially) to get people to adopt his suggestions. Miser's account is summarized in a series of nine ``lessons", for example, ``When timely results are important, simple forms of analysis can be useful", and ``It is worth a great deal to shape one's explanatory theory into a form in which it speaks clearly, easily, and forcefully to operational people". Youden's expository and persuasive skills are a recurrent theme in any account of his work.

In 1948, Youden accepted Churchill Eisenhart's invitation to join the newly established Statistical Engineering unit at the National Bureau of Standards. At the NBS, Youden was one of the first to recognize and to capitalize on important differences between experimentation in biological and agricultural sciences on the one hand and in the physical sciences on the other. Of paramount importance, he noted, is the difference in the magnitude of the error of measurement in the two areas.

Exploiting the precision of physical measurements, and responding to the challenges presented by practical aspects of experimental work, Youden developed several new kinds of designs. One group, ``chain block designs", took advantage of special circumstances of spectographic determinations of chemical elements carried out by comparing spectrum lines recorded on photographic plates (Youden and Connor, 1953). Experiments involving pairs of measurements (blocks of size two) arose in the NBS thermometer, meter-bar, and radium-standards programs. This led to the development of ``calibration designs" where only differences (or ratios) are observed for readings on two objects in blocks of size two (Youden and Connor, 1954). With J.S. Hunter, Youden developed ``partially replicated Latin squares" to check whether the usual requirements for a Latin square design have been met (Youden and Hunter, 1955).

The high degree of precision with which physical scientists can repeat their measurements, with the same instrumentation set-up and within a short period of time, sometimes lures them into claiming an unwarranted confidence in their results and neglecting the vagaries of other components of error such as day-to-day variation, differences among nominally idential instruments and standards, and possible systematic errors that are not obvious "a priori. Youden spared no effort in his lectures and writings to impress upon his audiences that a realistic estimate of experimental error could be obtained only through "hidden replication", that is, that a measure of precision should not be calculated from a series of straightforward repetitions, but from discrepancies between the measured values and the corresponding adjusted values derived under conditions specified by a careful design. In searching for unsuspected sources of systematic errors, he advised the experimenter, contrary to the time-honoured tradition of ``varying one factor at a time", to a vary several factors at a time by proper planning, such that the effect of each factor can be measured with better precision than in the traditional way while using the same number of measurements (Youden, 1961). This 1961 paper introduced the ``ruggedness test", for investigating the sensitivity of a method of measurement with respect to recognized sources of systematic error and changes of conditions likely to be encountered in practice.

By his publications and by his examples, Youden contributed significantly to the achievement of objectivity in experimentation and in the setting of more exacting standards for drawing scientific conclusions. His last major address, as retiring President of the Philosophical Society of Washington in 1968, was devoted to exposition of schemes for incorporating investigations of systematic errors into experimental determinations of fundamental physical constants. The plea for explicit efforts by scientists to accumulate objective evidence for the description of the precision and accuracy of their work was entitled ``Enduring Values" (Youden, 1972).

A significant fraction of NBS work is related to the development and interlaboratory comparison of measurement and testing procedures. The ``Youden plot" procedure was designed to provide simple but forceful interpretation of the results obtained in several laboratories ostensibly using the same test method (Youden, 1959; reprinted in Lasater, 1972).

Youden proposed that each laboratory make determinations on two specimens, chosen to have slightly different values of the quantity to be measured, avoiding the possibility that systematic differences between laboratories might be different at different magnitudes of the measurand (a phenomenon called ``interaction" by statisticians). The Youden plot displays one point for each laboratory, the value for the first specimen plotted against that for the second. If the laboratories differ only because of small measurement errors, the points will fall within a roughly circular area. As is more often the case, however, the systematic differences between laboratories cause the points to spread out along a line with 45-degree slope so that laboratories that tend to obtain low values and those that tend to obtain high values are easily identified. This procedure is widely used in programs for proficiency testing of laboratories.

Youden had a talent for reducing a complicated idea to its essentials and then expressing the idea through simple language. He worked hard at it. He was highly successful in convincing his audience, specialists in other fields, of the reasonableness and usefulness of a statistical idea, omitting all unnecessary details, formulas, and statistical terms. For example, in his book for high school students, "Experimentation and Measurement (Youden, 1962), the word ``statistics" does not appear once! But the book is about the use of statistical design and analysis in physical experiments that can be performed readily by students.


[1] Selected works of Youden:
[2] (1937). Use of incomplete block replications in estimating tobacco-mosaic virus. Contributions from Boyce Thompson Institute, 9, 50-57.
[3] (1951). Statistical Methods for Chemists. John Wiley and Sons, New York, N.Y., 126 pages.
[4] (1953). The chain block design (with W.S. Connor). Biometrics, 9, 127-140.
[5] (1954). New experimental designs for paired observations (with W.S. Connor). J. Res. Nat. Bur. Standards, 53, 191-196.
[6] (1955). Partially replicated Latin squares (with J.S. Hunter). Biometrics, 11, 399-405.
[7] (1959). Graphical diagnosis of interlaboratory test results. Industrial Quality Control, 15, No.11, 24-28.
[8] (1961). Systematic errors in physical constants. Physics Today, 14, No.9, 32-42.
[9] (1962). Experimentation and Measurement. Vistas of Science Series, National Science Teachers Association, Washington, D.C., 128 pages. Reprinted by the National Bureau of Standards as NBS Special Publication 672, 1984.
[10] (1972). Enduring values. Technometrics, 14, 1-11.
[11] Biography and bibliography of Youden:
[12] Eisenhart, Churchill, and Joan R. Rosenblatt (1972). W.J. Youden, 1900-1971. Annals of Mathematical Statistics, 43, 1035-1040.
[13] Lasater, H.A. (ed.) (1972). Journal of Quality Technology, 4, 1-67.
[14] Eisenhart, Churchill (1976). William John Youden. Dictionary of Scientific Biography, Charles C. Gillispie, ed., Scribner's, New York, Vol.14, pp. 552-557.
[15] Ku, Harry H. (1978). W.J. Youden. International Encyclopedia of Statistics (W.H. Kruskal and J.M. Tanur, eds.), The Free Press, New York, N.Y., pp.1257-1261.
[16] Cornell, John A. (1992). W.J. Youden - The man and his methodology. ASQC Statistics Division Newsletter, 13, No.2, 9-18.
[17] Miser, Hugh J. (1992). Craft in operations research. Operations Research, 40, 633-639.

Reprinted with permission from Christopher Charles Heyde and Eugene William Seneta (Editors), Statisticians of the Centuries, Springer-Verlag Inc., New York, USA.

How to Cite This Entry:
Youden, William John. Encyclopedia of Mathematics. URL:,_William_John&oldid=52901