NBS Handbook 91: Experimental Statistics [1] was first published in 1963. The material for the book was originally commissioned and printed in a limited edition by the U.S. Army as a series of five Army Ordnance Pamphlets OSRDDP 20-110-114. The publication was prepared in the Statistical Engineering Laboratory (SEL) of NBS under a contract with the former Office of Ordnance Research. Although originally intended for the needs of the Army, it proved to be equally useful to research and development groups, both within and outside the government.

The Handbook is organized in five sections; namely, 1. Basic Statistical Concepts and Analysis and Interpretation of Measurement Data

2. Standard Techniques for Analysis and Interpretation of Enumerative and Classificatory Data

3. The Planning and Analysis of Comparative Experi

ments

4. Special Topics

5. Tables

It is a monumental work which brings together under one cover the combined experience and expertise of the Statistical Engineering Laboratory. Mary Gibbons Natrella was principal author with overall responsibility for the entire publication, but there are contributions on polynomial and multivariable relationships, sensitivity testing, use of transformations, and expression of uncertainties by other members of the SEL. Chapters 1, 20, and 23 were written by Churchill Eisenhart, founding father of the SEL; Chapter 6 was written by Joseph Cameron, who later became Chief of SEL, and Chapter 10 is based on material prepared by Mary Epling. Some original tables were prepared by Paul Somerville; Norman Severo assisted with Section 2, and Shirley Young Lehman helped with the collection and analysis of examples.

Mary Natrella had a special gift for elucidating difficult statistical concepts, and these expositions are the strength of the book. The workbook style of the volume probably accounts for its popularity and acceptance by statisticians and non-statisticians alike. It is replete with examples; the page for each example is divided, with the statement of the problem and recommended solution on the left-hand side and detailed step-by-step calculations on the right-hand side. Mary

Fig. 1. Mary Gibbons Natrella.

Natrella also believed in attention to detail. The Foreword states that "some procedures in the Handbook have been explained and illustrated in detail twice: one for the case where the important question is whether the performance of a new material, product, or process exceeds an established standard; and again for the case where the important question is whether its performance is not up to the specified standard."

The Handbook was an immediate success at NBS, in the Army, and throughout the Department of Defense. It eventually received wide acclaim in other government agencies, industry, and universities. Churchill Eisenhart was fond of quoting a statistician who said that "the best thing about the Handbook is that it is correct."

The Handbook is recognized for its deep and longlasting impact on the application of statistics to the planning and analysis of scientific experiments. It was reprinted in 1983 for commercial sale by Wiley Interscience as part of its Selected Government Publications series. In 1985, the American Society for Metals published a condensation of four chapters on planning and

analysis of comparative experiments as part of the Statistics Section of Volume 8 of the 9th edition of the ASM Handbook. It has been NIST's second-best selling publication, after the Handbook of Mathematical Functions, which is covered elsewhere in this volume. The material is still current after more than thirty years, and this year alone it received close to forty journal citations as measured by the Science Citation Index.

NIST still receives requests for this book, and its contents are the basis for training courses taught by the Statistical Engineering Division (SED) and companies such as SEMATECH that are involved in technology development. It has proved such an inspiration that a few years ago Patrick Spagon of the Statistical Methods Group of SEMATECH approached SED with a proposal for updating and recreating the book with examples directed towards the semiconductor industry. That proposal has evolved into a publication for the World Wide Web [2] that is currently under development by a

team that includes: James Filliben, William Guthrie, Alan Heckert, and Carroll Croarkin of SED; Paul Tobias, head of the Statistical Methods Group, and Chelli Zey of SEMATECH; Barry Hembree of AMD; and Ledi Trutna, a private consultant.

Mary Natrella joined the Statistical Engineering Laboratory of NBS as a mathematical statistician in April 1950 after Churchill Eisenhart noticed her work as a sampling inspection expert in the U.S. Navy's Bureau of Ships. At the Navy, she worked on a team that developed the now famous MIL-STD-105A, Sampling Procedures and Tables for Inspection by Attributes (1950), which was to become government wide standard. Her "Report of Proceedings of the Subcommittee for Preparation of MIL-STD-105A," issued as a companion document to the standard, was distributed to government groups developing sampling inspection plans, as well as to professional and technical organizations, and was still in demand in the 1970s.

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The SEL was a pioneering group dedicated to application in the physical sciences of the statistical methods developed by R. A. Fisher, J. Neyman, and E. S. Pearson in England and Walter Shewhart in the United States. Mary Natrella served as a consultant on statistical planning and analysis of experiments to NIST scientists, and her training course on "Statistics of Measurement" was heavily attended for many years. Her most notable publication is Handbook 91, which was 7 years in preparation and required all her talents as teacher and consultant. During this time, Mary also contributed several sections to NBS Special Publication 300 [3] and worked with Carroll Brickenkamp and Steve Hasko of the NIST Office of Weights and Measures on NBS Handbook 133: Checking the Net Contents of Packaged Goods [4], which has been adopted by the National Conference on Weights and Measures. She performed her last service for the Statistical Engineering Division by serving as Acting Division Chief for the 2 years prior to her retirement in 1986.

The 1980's brought the culmination of Mary's career, with recognition on many fronts. She was elected a Fellow of the American Statistical Association (ASA) in 1981. In 1982, she received the Department of Commerce's Superior Federal Service Award. She was a long-time member of American Society for Testing Materials (ASTM) Committee E-11 on Quality and Statistics. In 1984, for her work as chairman of Subcommittee E11.03 on Statistical Analysis and Control Techniques, she was awarded the Society's Award of Merit, which carries the designation of Fellow.

In the year 2000 Mary Natrella has been further honored by the establishment of an endowed scholarship fund which will provide $1000 scholarships each year for two students to attend the Quality and Productivity Research Conference (QPRC). The scholarships were established by the Quality and Productivity section of the American Statistical Association, under the chairmanship of Veronica Czitrom of Lucent Technologies, with funds donated by Mary's husband, Joseph V. Natrella, and the QPRC Steering Committee. The purpose is to honor Mary's 36 years as author, teacher, and consulting statistician and her many contributions to the statistical community.

Prepared by M. Carroll Croarkin.

Bibliography

[1] Mary Gibbons Natrella, Experimental Statistics, NBS Handbook 91, National Bureau of Standards, Washington, DC (1963); reprinted 1966.

[2] Paul Tobias and Carroll Croarkin (eds.), NIST/SEMATECH Engineering Statistics Handbook, (http://www.itl.nist.gov/ div898/handbook/index.html), National Institute of Standards and Technology (1999).

[3] Harry H. Ku (ed.), Precision Measurement and Calibration: Statistical Concepts and Procedures, NBS Special Publication 300, Vol. 1, National Bureau of Standards, Washington, DC (1969).

[4] C. S. Brickenkamp, S. Hasko, and M. G. Natrella, Checking the Net Contents of Packaged Goods, NBS Handbook 133, Third Edition, National Bureau of Standards, Gaithersburg, MD (1988).

The Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables [1] was the culmination of a quarter century of NBS work on core mathematical tools. Evaluating commonly occurring mathematical functions has been a fundamental need as long as mathematics has been applied to the solution of practical problems. In 1938, NBS initiated its Mathematical Tables Project to satisfy the increasing demand for extensive and accurate tables of functions [2]. Located in New York and administered by the Works Projects Administration, the project employed not only mathematicians, but also a large number of additional staff who carried out hand computations necessary to produce tables. From 1938 until 1946, 37 volumes of the NBS Math Tables Series were issued, containing tables of trigonometric functions, the exponential function, natural logarithms, probability functions, and related interpolation formulae. In 1947, the Math Tables Project was moved to Washington to form the Computation Laboratory of the new National Applied Mathematics Laboratories of NBS. Many more tables subsequently were published in the NBS Applied Mathematics Series; the first of these, containing tables of Bessel functions [3], appeared in 1948.

On May 15, 1952, the NBS Applied Mathematics Division convened a Conference on Tables. Milton Abramowitz of NBS, who had been a member of the technical planning staff for the Math Tables Project, described preliminary plans for a compendium of mathematical tables and related material. Abramowitz indicated that the Bureau was in need of both technical advice and financial support to carry out the project. With the support of the National Science Foundation (NSF), a two-day Conference on Tables was held at the Massachusetts Institute of Technology on September 15-16, 1954, to discuss the prospects for such an undertaking. Twenty-eight persons attended, including both table producers and users from the science and engineering community. The report of the conference concluded that

"an outstanding need is for a Handbook of Tables for the Occasional Computer, with tables of usually encountered functions and a set of formulas and tables for interpolation and other techniques useful to the occasional computer."

Fig. 1. Portrait of Milton Abramowitz.

(Note that here the term computer refers to a person performing a calculation by hand.) The report recommended that NBS manage the production of the Hand book and that NSF provide financial assistance. The conference elected the following committee to carry out its recommendations: P.M. Morse (Chair), M. Abramowitz, J.H. Curtiss, R.W. Hamming, D. H. Lehmer, C.B. Tompkins, and J.W. Tukey. The committee was successful in persuading both NBS and NSF to support the project, and it began officially in December of 1956.

The Mathematics Division of the National Research Council also had an interest in mathematical tables. Since 1943, they had been publishing a quarterly journal entitled Mathematical Tables and Other Aids to Computation (today known as Mathematics of Computation). To provide technical assistance to NBS, as well as independent oversight for NSF, the NRC established a Committee on Revision of Mathematical Tables. Its members were P. M. Morse (Chair), A. Erdélyi, M. C.

Gray, N. C. Metropolis, J. B. Rosser, H. C. Thacher, Jr., John Todd, C. B. Tompkins, and J. W. Tukey. This group of luminaries in the fields of applied mathematics and physics provided guidance to NBS throughout the project to produce the Handbook.

Milton Abramowitz, who was then Chief of the Computation Laboratory of the NBS Applied Mathematics Division, led the project. Abramowitz was born in Brooklyn, NY, in 1915. He received a B. A. from Brooklyn College in 1937 and an M. A. in 1940. He joined the NBS Math Tables Project in 1938 and in 1948 received a Ph.D. in Mathematics from New York University. Abramowitz' dedication, enthusiasm, and boundless energy led to substantial progress in the project during its first year. The proposed outline for the Handbook called for a series of some 20 chapters, each with a separate author. Authors were drawn from NBS staff and guest researchers, as well as external researchers working under contract. Most chapters would focus on a particular class of functions, providing formulas, graphs, and tables. Listed formulas would include differential equations, definite and indefinite integrals, inequalities, recurrence relations, power series, asymptotic expansions, and polynomial and rational approximations. Material would be carefully selected in order to provide information most important in applications, especially in physics. Consequently, the higher mathematical functions, such as Bessel functions, hypergeometric functions, and elliptic functions, would form the core of the work. Additional chapters would provide background on interpolation in tables and related numerical methods for differentiation and quadrature.

Philip J. Davis of NBS first prepared Chapter 6, on the gamma and related functions, to serve as a model for other authors. This chapter portrayed the telegraphic style that is a hallmark of the Handbook, i.e., the material is displayed with a minimum of textual description. In the course of developing his chapter, Davis became interested in the history of the topic. This led to a historical profile published in 1959 [4], which won the prestigious Chauvenet Prize for distinguished mathematical exposition from the Mathematical Association of America.

The Handbook project occurred during the period when general-purpose electronic computing machinery was first coming into use in government research laboratories. (Early computer development of SEAC at NBS is described elsewhere in this volume.) Nevertheless, most of the tables in the Handbook were generated by hand on desk calculators. However, even at that time it was clear to the developers of the Handbook

that the need for tables themselves would eventually be superseded by computer programs which could evaluate functions for specified arguments on demand.

By the summer of 1958, substantial work had been completed on the project. Twelve chapters had been completed, and the remaining ones were well underway. The project experienced a shocking setback one weekend in July 1958 when Abramowitz suffered a heart attack and died. Irene Stegun, who was Assistant Chief of the Computation Laboratory, took over management of the project. Stegun, who was born in Yonkers, NY in 1919, had received an M. A. from Columbia University in 1941, and joined NBS in 1943. The exacting work of assembling the many chapters, checking tables and formulas, and preparing the work for printing took much longer than anticipated. Nevertheless, the Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables was finally issued as Applied Mathematics Series Number 55 in June 1964 [1]. The volume, which is still in print at the U.S. Government Printing Office and stocked by many bookstores and online booksellers, is 1046 pages in length. The chapters and authors are as follows.