Springer Series in Statistics
Advisors: P. Bickel, P. Diggle, S. Fienberg, U. Gather, I. Olkin, S. Zeger Springer Series in Statistics
Alho/Spencer: Statistical Demography and Forecasting. Andersen/Borgan/Gill/Keiding: Statistical Models Based on Counting Processes. Atkinson/Riani: Robust Diagnostic Regression Analysis. Atkinson/Riani/Cerioli: Exploring Multivariate Data with the Forward Search. Berger: Statistical Decision Theory and Bayesian Analysis, 2nd edition. Borg/Groenen: Modern Multidimensional Scaling: Theory and Applications, 2nd edition. Brockwell/Davis: Time Series: Theory and Methods, 2nd edition. Bucklew: Introduction to Rare Event Simulation. Cappé/Moulines/Rydén: Inference in Hidden Markov Models. Chan/Tong: Chaos: A Statistical Perspective. Chen/Shaol/Ibrahim: Monte Carlo Methods in Bayesian Computation. Coles: An Introduction to Statistical Modeling of Extreme Values. Devroye/Lugosi: Combinatorial Methods in Density Estimation. Efromovich: Nonparametric Curve Estimation: Methods, Theory, and Applications. Eggermont/LaRiccia: Maximum Penalized Likelihood Estimation, Volume I: Density Estimation. Fahrmeir/Tutz: Multivariate Statistical Modelling Based on Generalized Linear Models, 2nd edition. Fan/Yao: Nonlinear Time Series: Nonparametric and Parametric Methods. Ferraty/Vieu: Nonparametric Functional Data Analysis: Models, Theory, Applications, and Implementation Fienberg/Hoaglin: Selected Papers of Frederick Mosteller Frühwirth-Schnatter: Finite mixture and markov switching models. Ghosh/Ramamoorthi: Bayesian Nonparametrics. Glaz/Naus/Wallenstein: Scan Statistics. Good: Permutation Tests: Parametric and Bootstrap Tests of Hypotheses, 3rd edition. Gouriéroux: ARCH Models and Financial Applications. Gu: Smoothing Spline ANOVA Models. Györfi/Kohler/Krzyz.ak/Walk: A Distribution-Free Theory of Nonparametric Regression. Haberman: Advanced Statistics, Volume I: Description of Populations. Hall: The Bootstrap and Edgeworth Expansion. Härdle: Smoothing Techniques: With Implementation in S. Harrell: Regression Modeling Strategies: With Applications to Linear Models, Logistic Regression, and Survival Analysis. Hart: Nonparametric Smoothing and Lack-of-Fit Tests. Hastie/Tibshirani/Friedman: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Hedayat/Sloane/Stufken: Orthogonal Arrays: Theory and Applications. Heyde: Quasi-Likelihood and its Application: A General Approach to Optimal Parameter Estimation. Huet/Bouvier/Poursat/Jolivet: Statistical Tools for Nonlinear Regression: A Practical Guide with S-PLUS and R Examples, 2nd edition. Ibrahim/Chen/Sinha: Bayesian Survival Analysis. Jolliffe: Principal Component Analysis, 2nd edition. Knottnerus: Sample Survey Theory: Some Pythagorean Perspectives. Kolen/Brennan: Test Equating: Methods and Practices. Kotz/Johnson (Eds.): Breakthroughs in Statistics Volume I. Kotz/Johnson (Eds.): Breakthroughs in Statistics Volume II. Kotz/Johnson (Eds.): Breakthroughs in Statistics Volume III. Küchler/Sørensen: Exponential Families of Stochastic Processes. Kutoyants: Statistical Influence for Ergodic Diffusion Processes. Lahiri: Resampling Methods for Dependent Data. Le Cam: Asymptotic Methods in Statistical Decision Theory. Le Cam/Yang: Asymptotics in Statistics: Some Basic Concepts, 2nd edition. Liu: Monte Carlo Strategies in Scientific Computing. Longford: Models for Uncertainty in Educational Testing. (continued after p. 660) Stephen E. Fienberg David C. Hoaglin Editors
Selected Papers of Frederick Mosteller Stephen E. Fienberg David C. Hoaglin Department of Statistics Abt Associates Inc. Carnegie Mellon University 55 Wheeler Street 5000 Forbes Avenue Cambridge, MA 02138 Pittsburgh, PA 15213 [email protected] [email protected]
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987654321 springer.com Preface
Both of us have had the good fortune to work closely with Frederick Mosteller and learn from him throughout our professional careers. We have been inspired by his creative approach to statistics and its applications and we, along with countless others, have benefited from reading his papers and books. Through this volume we hope to share the variety and depth of Mosteller’s writings with a new generation of researchers, who can build upon his in- sights and efforts. In many ways this volume of selected papers can be viewed as a companion to an earlier volume that we assembled with William Kruskal and Judith Tanur, A Statistical Model: Frederick Mosteller’s Contributions to Statistics, Science, and Public Policy, Springer-Verlag (1990), and Fred’s forthcoming autobiography, which will also be published by Springer-Verlag. This volume contains a reasonably complete bibliography of Mosteller’s papers, books and other writings. Several of these, which Fred co-authored with his friend and long-time collaborator John Tukey, are included in the multi-volume Collected Works of John W. Tukey (CWJWT). Conveniently, the bibliography in CWJWT tells whether a paper appears in one of those vol- umes. CWJWT includes papers P10, P70, P133, and P142 from the Mosteller bibliography. We say that the bibliography is “reasonably” complete because we know that Fred continues to work on projects and to collaborate on revi- sions of books. We chose the papers for this volume to give a broad perspective on Fred’s work, ranging from statistical theory through applications in a variety of do- mains, and reflecting his long and varied career. We iterated with Fred over a period of a couple of years until we had a collection that captured the nature of his contributions and also fit within a single volume. Each paper reflects one or more aspects of Fred’s approach to statistical research and its appli- cation, and the papers often reflect his general philosophy on how one should go about doing good science. In preparing the papers for this volume, we scanned the original, converted the resulting image to text, and transformed the text into input for LATEX. By careful proofreading we have tried to ensure that each paper is faithful to vi Preface the original. We have, however, corrected typographic errors in the original papers when we encountered them (not often) and occasionally made other straightforward changes. Also, we have restructured some tables, because of incompatabilities in page size and layout. We are deeply indebted to a number of others who contributed to the preparation of the volume, including Cleo Youtz, Marjorie Olson, and Jessa Piaia at Harvard University, and especially to those who actually prepared parts of the LATEX document over the 15 years we have been slowly working on this volume: Valerie Baddon (at York University), Howard Fienberg, Valerie Lenhart, John Clark, Heather Wainer, and Heidi Sestrich (all at Carnegie Mellon). Heather in particular has valiantly worked with us to ensure that the format and content were indeed correct and as consistent as feasible, given the diversity of the original publications and their format styles, and she helped immeasurably in the reproduction of the figures from the original papers.
Stephen E. Fienberg December 24, 2005 David C. Hoaglin Contents
Preface ...... v Frederick Mosteller—A Brief Biography Stephen E. Fienberg ...... 1
Bibliography ...... 7 1. Unbiased Estimates for Certain Binomial Sampling Problems with Applications M.A. Girshick, Frederick Mosteller, L.J. Savage ...... 57 2. On Some Useful “Inefficient” Statistics Frederick Mosteller ...... 69 3. A k-Sample Slippage Test for an Extreme Population Frederick Mosteller ...... 101 4. The Uses and Usefulness of Binomial Probability Paper Frederick Mosteller, John W. Tukey ...... 111 5. The Education of a Scientific Generalist Hendrik Bode, Frederick Mosteller, John W. Tukey, Charles Winsor ....147 6. Remarks on the Method of Paired Comparisons: I. The Least Squares Solution Assuming Equal Standard Deviations and Equal Correlations Frederick Mosteller ...... 157 7. Remarks on the Method of Paired Comparisons: II. The Effect of an Aberrant Standard Deviation When Equal Standard Deviations and Equal Correlations Are Assumed Frederick Mosteller ...... 163 viii Contents
8. Remarks on the Method of Paired Comparisons: III. A Test of Significance for Paired Comparisons when Equal Standard Deviations and Equal Correlations Are Assumed Frederick Mosteller ...... 167
9. An Experimental Measurement of Utility Frederick Mosteller, Philip Nogee ...... 179
10. A Mathematical Model for Simple Learning Robert R. Bush, Frederick Mosteller ...... 221 11. A Model for Stimulus Generalization and Discrimination Robert R. Bush, Frederick Mosteller ...... 235 12. The World Series Competition Frederick Mosteller ...... 251 13. Principles of Sampling William G. Cochran, Frederick Mosteller, John W. Tukey ...... 275 14. Stochastic Models for the Learning Process Frederick Mosteller ...... 295
1 15. Factorial 2 : A Simple Graphical Treatment Frederick Mosteller, D.E. Richmond ...... 309 16. A Comparison of Eight Models Robert R. Bush, Frederick Mosteller ...... 317 17. Optimal Length of Play for a Binomial Game Frederick Mosteller ...... 333 18. Tables of the Freeman-Tukey Transformations for the Binomial and Poisson Distributions Frederick Mosteller, Cleo Youtz ...... 337 19. Understanding the Birthday Problem Frederick Mosteller ...... 349 20. Recognizing the Maximum of a Sequence John P. Gilbert, Frederick Mosteller ...... 355 21. The Distribution of Sums of Rounded Percentages Frederick Mosteller, Cleo Youtz, Douglas Zahn ...... 399 22. The Expected Coverage to the Left of the ith Order Statistic for Arbitrary Distributions Barry H. Margolin, Frederick Mosteller ...... 413 Contents ix
23. Bias and Runs in Dice Throwing and Recording: A Few Million Throws Gudmund R. Iversen, Willard H. Longcor, Frederick Mosteller, John P. Gilbert, Cleo Youtz ...... 417
24. An Empirical Study of the Distribution of Primes and Litters of Primes Frederick Mosteller ...... 435 25. A Conversation About Collins William B. Fairley, Frederick Mosteller ...... 445 26. Statistics and Ethics in Surgery and Anesthesia John P. Gilbert, Bucknam McPeek, Frederick Mosteller ...... 457 27. Experimentation and Innovations Frederick Mosteller ...... 473 28. New Statistical Methods in Public Policy. Part I: Experimentation Frederick Mosteller, Gale Mosteller ...... 487 29. Classroom and Platform Performance Frederick Mosteller ...... 499 30. The Clinician’s Responsibility for Helping to Improve the Treatment of Tomorrow’s Patients Bucknam McPeek, John P. Gilbert, Frederick Mosteller ...... 513 31. Innovation and Evaluation Frederick Mosteller ...... 515 32. Combination of Results of Stated Precision: I. The Optimistic Case Frederick Mosteller, John W. Tukey ...... 531 33. Combination of Results of Stated Precision: II. A More Realistic Case Frederick Mosteller, John W. Tukey ...... 549 34. Allocating Loss of Precision in the Sample Mean to Wrong Weights and Redundancy in Sampling with Replacement from a Finite Population J.L. Hodges, Jr., Frederick Mosteller, Cleo Youtz ...... 575 35. Reporting Clinical Trials in General Surgical Journals John D. Emerson, Bucknam McPeek, Frederick Mosteller ...... 583 x Contents
36. Compensating for Radiation-Related Cancers by Probability of Causation or Assigned Shares Frederick Mosteller ...... 597
37. Methods for Studying Coincidences Persi Diaconis, Frederick Mosteller ...... 605
38. A Modified Random-Effect Procedure for Combining Risk Difference in Sets of 2 × 2 Tables from Clinical Trials John D. Emerson, David C. Hoaglin, Frederick Mosteller ...... 623 39. The Case for Smaller Classes and for Evaluating What Works in the Schoolroom Frederick Mosteller ...... 643 40. Frederick Mosteller and John W. Tukey: A Conversation Moderated by Francis J. Anscombe ...... 647 Frederick Mosteller—A Brief Biography
Stephen E. Fienberg
Carnegie Mellon University
Frederick Mosteller celebrated his 89th birthday this year (2005) but re- mains professionally active and involved in several research projects. For an extensive review of many of his contributions, see the special volume A Sta- tistical Model [5], prepared in his honor. John Tukey’s biography of Fred (as he is known to his friends, collaborators, colleagues, and students) in that volume is especially noteworthy.
Fred was born Charles Frederick Mosteller in Clarksburg, West Virginia, on December 24, 1916.1 The family later moved to the Pittsburgh area, where Fred attended Schenley High School and later Carnegie Institute of Technol- ogy (now Carnegie Mellon University). In college, he was interested in mathe- matics and, in particular, in combinatoric problems. This inclination led him to the statistician Edwin C. Olds, who in turn steered Fred into the field of statistics. Fred completed his Sc.M. degree at Carnegie Tech in 1939 and then enrolled at Princeton University to work on a Ph.D. with Samuel Wilks. In ad- dition to participating with Wilks and others in a wartime research group (see the discussion in [17]), Fred assisted Wilks in his role as editor of the Annals of Mathematical Statistics. Fred received the ASA Samuel S. Wilks Award in 1986. At Princeton Fred also began his lifelong interaction and collaboration with John Tukey, described in part in [3] and in their joint interview in Sta- tistical Science [14].
Fred met his wife, Virginia (1917–2000), when he was a college freshman (she rode the same streetcar that Fred took from Wilkinsburg to the campus each day), and they were married in 1941, just as the statistical war research 1This is a birth-date he shares with my mother, and a birthday—same day but different year—he shares with David Wallace, a collaborator of Fred’s. One of Fred’s favorite probability examples has been the well-known birthday problem, see [8]. This event also links to another of Fred’s preoccupations, the statistical analysis of coincidences [4]. 2 Stephen E. Fienberg effort was gearing up. Fred accepted a position in the Department of Social Relations at Harvard University in 1946, and he remained on the faculty of the university in various positions (see below) for the rest of his career. Fred and Virginia moved to their home in Belmont after the birth of their son Bill in 1947. Their daughter Gale was born in 1953.
Fred became Professor of Mathematical Statistics at Harvard in 1951 and led the effort to create the Department of Statistics, which opened in 1957. He served as the department’s first chair, from 1957 to 1969. I remember my first meeting with Fred in the fall of 1964 as I was entering graduate school. Fred took me to lunch at the Harvard Faculty Club, where he insisted that I try the horse steak. As I was busy chewing, he shared with me some handwritten notes from Tukey on assessing probability assessors, a problem that was to be my first project as one of Fred’s research assistants. Although we wrote up the results of that effort as a joint technical report, I confess it was not until a collaboration on the topic with Morrie DeGroot, some 18 years later, that I came to understand and appreciate Fred’s and John’s insights into the problem.
As I was completing my Ph.D. under Fred’s supervision in 1968, he or- ganized a group of us to write a book built around the recent developments in categorical data analysis, especially linked to the use of log-linear models. This project ultimately produced Discrete Multivariate Analysis: Theory and Practice [1]. He was the guiding light behind the project and our constant editor and sometimes contributor, but in typical fashion he insisted that only Yvonne Bishop, Paul Holland, and I be listed as “authors.” Ultimately, he agreed to let us acknowledge his efforts by listing him as a “collaborator” on the title page.
During his years in the Statistics Department, Fred formally supervised 17 Ph.D. dissertations, but he served on the committees of countless others in Statistics, Social Relations, and other parts of Harvard. Over the years he was always available to offer comments on works in progress and unpublished manuscripts, and wise students took advantage of his generosity.
Fred later served as chair of two other departments, Biostatistics and Health Policy and Management, both in the School of Public Health, and he also taught courses in the Harvard Law School and the John F. Kennedy School of Government. On retirement in 1987, Fred maintained his office in the Department of Statistics, where he continued with his usual array of multi- disciplinary projects, almost as if nothing had changed. At the end of 2003, he dismantled his office and relocated to the Washington, D.C. area.
Fred’s bibliography is astounding; it contains 65 books, nearly 350 pa- pers in books and journals, 41 miscellaneous publications, and 26 reviews. Frederick Mosteller—A Brief Biography 3
And, not surprisingly, many of these were coauthored or coedited by over 200 other individuals. My personal favorite is Fred’s classic 1964 book with David Wallace, Inference and Disputed Authorship: The Federalist [15], which was republished in 1984 in expanded form [16]. The intriguing analyses of The Federalist Papers presented by Mosteller and Wallace include one of the first major uses of Bayesian methods, and they provide an early exposition of Laplace’s method for approximating distributions.
A partial list of Fred’s varied methodological research interests includes publications on inefficient statistics, sampling, Bayesian methods, paired comparisons, the jackknife, statistics in sports, contingency table analysis, exploratory data analysis, randomized experiments, robustness and meta- analysis and research synthesis.
Depending on how one measures collaboration, John Tukey is Fred’s most extensive collaborator; but others prominent on the list include Thomas Chalmers, John Gilbert, David Hoaglin, Bucknam McPeek, and Fred’s long- time research assistant, Cleo Youtz. Other collaborators of note include John Bailar, Bill Cochran, Persi Diaconis, Milton Friedman, Bill Kruskal, Pat Moynihan, Jimmie Savage, Judy Tanur, Allen Wallis, Sam Wilks, Charlie Winsor, and Gale Mosteller (his daughter). And I am pleased to be included on the list.
Beginning in the 1950s, Fred helped lead an effort to bring probability and statistics to American high schools. He was instrumental in producing teacher’s manuals, and this involvement led to one of the early elementary statistics texts, Probability with Statistical Applications [13]. Fred used a ver- sion of this book as the text for his pioneering 1961 televised course on NBC’s Continental Classroom, which introduced him to students across the nation, young and old. Many textbooks on varied topics followed. When the Ameri- can Statistical Association set up a joint committee with the National Council of Teachers of Mathematics (NCTM) in the 1960s to change the statistical content of the secondary school mathematics curriculum, Fred led the effort once again. He helped to organize, and goaded others into contributing to, the preparation of the ASA-NCTM Committee’s early products, including the 4- volume collection Statistics by Example [9, 10, 11, 12] and Statistics: A Guide to the Unknown [17], which has now appeared in multiple forms and multiple editions.
Fred has always been an organizer, and this talent was recognized by many different societies and other organizations that came to Fred for help with projects, as well as to fill leadership positions. Among the societies he has led as president are (in approximately chronological order): the Psychometric Society, the American Statistical Association, the Institute of Mathematical Statistics, the American Association for the Advancement of Science, and the 4 Stephen E. Fienberg
International Statistical Institute. In the 1960s, he served as Chairman of the Board of Directors of the Social Science Research Council and later as Vice- chair of the President’s Commission on Federal Statistics, which led to the creation of the Committee on National Statistics at the National Research Council (NRC). At the NRC and elsewhere he has served on so many statis- tical and interdisciplinary committees and task forces that one observer [6, p. 87] was led to remark: Applied mathematicians are of course essential in most assessments, for help in designing tests, auditing calculations, and assisting in the drawing of conclusions. Much of this is routine craftwork. But one unusual, crucial role should be recognized. It is my guess that statisti- cians Frederick Mosteller (Harvard) and John Tukey (Princeton) have served on or assisted more technical committees than anybody else alive.... Itisnotjusttheirability to manipulate numbers that keeps these experts in demand, but sensibility in thinking through questions of macro-experimental design: how inquiries should be cast, what ev- idence and logic are applicable, how discrimination can be increased, how uncertainties and sensitivities should be probed, what inferences are allowable from evidence. Mosteller and Tukey outlined this role in an article in 1949 in which they called for education of “scientific generalists” who would master “science, not sciences” [2]. The products of many of these activities are mentioned in the bibliography that follows.
Recognition of his accomplishments has come in many forms. Fred has received honorary degrees from the University of Chicago (1973), Carnegie Mellon University (1974), Yale University (1981), Wesleyan University (1983), and Harvard University (1993). He is also an honorary fellow of the Royal Sta- tistical Society, an honorary member of the International Statistical Institute, and an elected member/fellow of the American Academy of Arts and Sciences, the American Philosophical Society, the Institute of Medicine, and the Na- tional Academy of Sciences. He has served as the Committee of Presidents of Statistical Societies’ R.A. Fisher Lecturer, and has been honored in numerous other ways.
By the age of 89, most people have long since retired and turned to pas- toral pursuits. Yet, though Fred has been officially retired for eighteen years, he remains remarkably active. Nonetheless I recall being at least partially surprised when, perusing the table of contents of a 2002 issue of Statistics in Medicine a few years ago, I came across a paper by Lincoln Moses, John Buehler, and guess who [7], on one of Fred’s longstanding research interests, meta-analysis; this was a reminder that we needed to continually update the bibliography that follows until this volume was sent to press! Frederick Mosteller—A Brief Biography 5
Fred will remain a role model for statisticians and other scientists whom he has mentored, taught, and otherwise influenced over the years. It is our hope that reprinting a selection of his contributions to statistics in a single volume will help his work similarly to influence new generations of researchers.
References
1. Y.M.M. Bishop, S.E. Fienberg, and P.W. Holland (with contributions by R.J. Light and F. Mosteller). Discrete Multivariate Analysis: Theory and Practice. MIT Press, Cambridge, MA, 1975. 2. H. Bode, F. Mosteller, J.W. Tukey, and C. Winsor. The education of a scientific generalist. Science, 109:553–558, 1949. [Paper 5 in this volume] 3. D.R. Brillinger. John W. Tukey: The life and professional contributions. Annals of Statistics, 30:1535–1575, 2002. 4. P. Diaconis and F. Mosteller. Methods for studying coincidences. Journal of the American Statistical Association, 84:853–861, 1989. [Paper 37 in this volume] 5. S.E. Fienberg, D.C. Hoaglin, W.H. Kruskal, and J.M. Tanur, editors. A Statisti- cal Model: Frederick Mosteller’s Contributions to Statistics, Science, and Public Policy. Springer-Verlag, New York, 1990. 6. William W. Lowrance. Modern Science and Human Values. Oxford University Press, New York, 1985. 7. L.E. Moses, F. Mosteller, and J.H. Buehler. Comparing results of large clinical trials to those of meta-analysis. Statistics in Medicine, 21:793–800, 2002. 8. F. Mosteller. Understanding the birthday problem. The Mathematics Teacher, 55:322–325, 1962. [Paper 19 in this volume] 9. F. Mosteller, W.H. Kruskal, R.F. Link, R.S. Pieters, and G.R. Rising, editors. Statistics by Example: Exploring Data. Addison-Wesley, Reading, MA, 1973. 10. F. Mosteller, W.H. Kruskal, R.F. Link, R.S. Pieters, and G.R. Rising, editors. Statistics by Example: Weighing Chances. Addison-Wesley, Reading, MA, 1973. 11. F. Mosteller, W.H. Kruskal, R.F. Link, R.S. Pieters, and G.R. Rising, editors. Statistics by Example: Detecting Patterns. Addison-Wesley, Reading, MA, 1973. 12. F. Mosteller, W.H. Kruskal, R.F. Link, R.S. Pieters, and G.R. Rising, editors. Statistics by Example: Finding Models. Addison-Wesley, Reading, MA, 1973. 13. F. Mosteller, R.E.K. Rourke, and G.B. Thomas, Jr. Probability with Statistical Applications. Addison-Wesley, Reading, MA, 1961. Second Edition, 1970. 14. Frederick Mosteller and John W. Tukey: A Conversation. Moderated by Fran- cis J. Anscombe. Statistical Science, 3 (1988), pp. 136–144. [Paper 40 in this volume] 15. F. Mosteller and D.L. Wallace. Inference and Disputed Authorship: The Feder- alist. Addison-Wesley, Reading, MA, 1964. 16. F. Mosteller and D.L. Wallace. Applied Bayesian and Classical Inference: The Case of the Federalist Papers. Springer-Verlag, New York, 1984. 17. J.M. Tanur, F. Mosteller, W.H. Kruskal, R.F. Link, R.S. Pieters, and G.R. Rising, editors. Statistics: A Guide to the Unknown. Holden-Day, San Francisco, 1972. 18. W.A. Wallis. The Statistical Research Group, 1942-1945 (with discussion). Jour- nal of the American Statistical Association, 75:320–335, 1980. Bibliography
This bibliography of Frederick Mosteller’s writings generally follows the four categories that Fred has used in his personal bibliography: books, pa- pers, miscellaneous, and reviews. Ordinarily the publications in each category appear in chronological order. We deviate from that ordering to bring together closely related books. We list Fred’s name as it appeared on the publication, usually “Frederick Mosteller.” For works with other authors, we list the names in the order that they appeared on the publication. For publications by a committee or panel, we list the members. If, in addition to being one of the editors of a book, Fred is the author or coauthor of a chapter, we list that chapter under the book but not among the papers. We give any additional information that we have, such as new editions, different printings, and translations. We realize that our information about translations is not complete, nor do we always know of reprinting of papers or chapters. BOOKS B1 Hadley Cantril and Research Associates in the Office of Public Opin- ion Research, Princeton University. Gauging Public Opinion. Princeton: Princeton University Press, 1944. Second Printing, 1947. • Chapter IV. Frederick Mosteller and Hadley Cantril. “The use and value of a battery of questions.” pp. 66–73. • Chapter VII. Frederick Mosteller. “The reliability of interviewers’ rat- ings.” pp. 98–106. • Chapter VIII. William Salstrom with Daniel Katz, Donald Rugg, Fred- erick Mosteller, and Frederick Williams. “Interviewer bias and rap- port.” pp. 107–118. • Chapter XIV. Frederick Williams and Frederick Mosteller. “Education and economic status as determinants of opinion.” pp. 195–208. 8 Bibliography
• Appendix II. Frederick Mosteller. “Correcting for interviewer bias.” pp. 286–288. • Appendix III. Frederick Mosteller. “Sampling and breakdowns: tech- nical notes.” pp. 288–296. • Appendix IV. Frederick Mosteller. “Charts indicating confidence limits and critical differences between percentages.” pp. 297–301. B2 H.A. Freeman, Milton Friedman, Frederick Mosteller, and W. Allen Wal- lis, editors. Sampling Inspection: Principles, Procedures, and Tables for Single, Double, and Sequential Sampling in Acceptance Inspection and Quality Control Based on Percent Defective. New York: McGraw-Hill, 1948. • Chapter 6. Frederick Mosteller and David H. Schwartz. “Use of sam- pling inspection for quality control.” pp. 55–68. • Chapter 13. Frederick Mosteller and David H. Schwartz. “Application of the standard procedure to control sampling.” pp. 135–136. B3 Frederick Mosteller, Herbert Hyman, Philip J. McCarthy, Eli S. Marks, and David B. Truman, with the collaboration of Leonard W. Doob, Dun- can MacRae, Jr., Frederick F. Stephan, Samuel A. Stouffer, and S.S. Wilks. The Pre-election Polls of 1948: Report to the Committee on Analy- sis of Pre-election Polls and Forecasts. New York: Social Science Research Council, Bulletin 60, 1949. • Chapter V. Prepared by Frederick Mosteller. “Measuring the error.” pp. 54–80. B4 William G. Cochran, Frederick Mosteller, and John W. Tukey, with the assistance of W.O. Jenkins. Statistical Problems of the Kinsey Report on Sexual Behavior in the Human Male: A Report of the American Statistical Association Committee to Advise the National Research Council Commit- tee for Research in Problems of Sex. Washington, D.C.: The American Statistical Association, 1954. Two parts of this book were published earlier—papers P31 and P32.
B5 Robert R. Bush and Frederick Mosteller. Stochastic Models for Learning. New York: Wiley, 1955.
B6 A group of the Commission on Mathematics of the College Entrance Ex- amination Board. Introductory Probability and Statistical Inference for Secondary Schools: An Experimental Course. Preliminary edition. New York: College Entrance Examination Board, 1957. Members of the group: Edwin C. Douglas, Frederick Mosteller, Richard S. Pieters, Donald E. Richmond, Robert E.K. Rourke, George B. Thomas, Jr., and Samuel S. Wilks. These names were inadvertently omitted from this edition. Bibliography 9
A revised edition of this volume was published in 1959. B7 A group of the Commission on Mathematics of the College Entrance Ex- amination Board. Teachers’ Notes and Answer Guide: Supplementary ma- terial for the revised preliminary edition of “Introductory Probability and Statistical Inference.” New York: College Entrance Examination Board, 1959. Members of the group: Frederick Mosteller, Richard S. Pieters, Robert E.K. Rourke, George B. Thomas, Jr., and Samuel S. Wilks. B7 and the revised edition of B6 were translated by Professor Marta C. Valincq into Spanish, and published by Comision de Educacion Estadistica del Instituto Interamericano de Estadistica Rosario (Rep. Argentina), 1961. B8 Commission on Mathematics. Program for College Preparatory Mathemat- ics. Report of the Commission. New York: College Entrance Examination Board, 1959. Members of the Commission on Mathematics: Albert W. Tucker, Chairman, Carl B. Allendoerfer, Edwin C. Douglas, Howard F. Fehr, Martha Hildebrandt, Albert E. Meder, Jr., Morris Meis- ter, Frederick Mosteller, Eugene P. Northrop, Ernest R. Ranucci, Robert E.K. Rourke, George B. Thomas, Jr., Henry Van Engen, and Samuel S. Wilks. B9 Frederick Mosteller, Robert E.K. Rourke, and George B. Thomas, Jr. Probability with Statistical Applications. Reading, MA: Addison-Wesley, 1961. Second printing, 1965.
B10 Frederick Mosteller, Robert E.K. Rourke, and George B. Thomas, Jr. Probability with Statistical Applications, Second Edition. Reading, MA: Addison-Wesley, 1970. Extensive revision of B9. World Student Series Edition, Third Printing, 1973, of B10. Pub- lished for the Open University in England. B11 Frederick Mosteller, Robert E.K. Rourke, and George B. Thomas, Jr. Probability and Statistics. Reading, MA: Addison-Wesley, 1961. Official textbook for Continental Classroom. Derived from B9 by abridgment and slight rewriting. Also translated into Turkish. B12 Frederick Mosteller, Robert E.K. Rourke, and George B. Thomas, Jr. Probability: A First Course. Reading, MA: Addison-Wesley, 1961. Derived from B9 by abridgment and slight rewriting. Also trans- lated into Russian. And a Bulgarian translation into Russian. Sofia, Bulgaria: J. Stoyanov, 1975. 10 Bibliography
B13 Frederick Mosteller, Robert E.K. Rourke, and George B. Thomas, Jr. Probability: A First Course, Second Edition. Reading, MA: Addison- Wesley, 1970.
B14 Frederick Mosteller, Robert E.K. Rourke, and George B. Thomas, Jr. Teacher’s Manual for Probability: A First Course. Reading, MA: Addison- Wesley, 1961.
B15 Frederick Mosteller, Robert E.K. Rourke, and George B. Thomas, Jr. In- structor’s Manual to Accompany Probability with Statistical Applications, Second Edition, and Probability: A First Course, Second Edition.Read- ing, MA: Addison-Wesley, 1970.
B16 Frederick Mosteller, Keewhan Choi, and Joseph Sedransk. A Catalogue Survey of College Mathematics Courses. Mathematical Association of America, Committee on the Undergraduate Program in Mathematics, Re- port Number 4, December 1961.
B17 Frederick Mosteller and David L. Wallace. Inference and Disputed Au- thorship: The Federalist. Reading, MA: Addison-Wesley, 1964.
B18 Frederick Mosteller and David L. Wallace. Applied Bayesian and Classical Inference: The Case of the Federalist Papers. New York: Springer-Verlag, 1984. Second Edition of B17. A new chapter dealing with authorship work published from about 1969 to 1983 was added in the second edition. A new, lengthy Analytic Table of Contents replaced the original Table of Contents. B19 Panel on Mathematics for the Biological, Management, and Social Sci- ences. Committee on the Undergraduate Program in Mathematics, Math- ematical Association of America. Tentative Recommendations for the Un- dergraduate Mathematics Program of Students in the Biological, Manage- ment and Social Sciences. Berkeley, CA: CUPM Central Office, 1964. Panel members: John G. Kemeny, Chairman, Joseph Berger, Robert R. Bush, David Gale, Samuel Goldberg, Harold Kuhn, Frederick Mosteller, Theodor D. Sterling, Gerald L. Thompson, Robert M. Thrall, A.W. Tucker, and Geoffrey S. Watson. B20 Frederick Mosteller. Fifty Challenging Problems in Probability with Solu- tions. Reading, MA: Addison-Wesley, 1965. Also translated into Russian, 1975. A second edition of the Russian translation was published in 1985. For this edition, Frederick Mosteller provided a new problem, “Distribution of prime divisors.” Bibliography 11
B21 Frederick Mosteller. Fifty Challenging Problems in Probability with Solu- tions. New York: Dover, 1987. Reissue of B20. B22 Panel on Undergraduate Education in Mathematics of the Committee on Support of Research in the Mathematical Sciences of the National Research Council. The Mathematical Sciences: Undergraduate Education. Washington, D.C.: National Academy of Sciences, 1968. Panel members: John G. Kemeny, Grace E. Bates, D.E. Christie, Llayron Clarkson, George Handelman, Frederick Mosteller, Henry Pollak, Hartley Rogers, John Toll, Robert Wisner, and Truman A. Botts. B23 John P. Bunker, William H. Forrest, Jr., Frederick Mosteller, and Leroy D. Vandam, editors. The National Halothane Study: A Study of the Possi- ble Association between Halothane Anesthesia and Postoperative Hepatic Necrosis. Report of the Subcommittee on the National Halothane Study, of the Committee on Anesthesia, Division of Medical Sciences, National Academy of Sciences–National Research Council. National Institutes of Health, National Institute of General Medical Sciences. Washington, D.C.: U.S. Government Printing Office, 1969. • Part IV, Chapter 1. Byron W. Brown, Jr., Frederick Mosteller, Lincoln E. Moses, and W. Morven Gentleman. “Introduction to the study of death rates.” pp. 183–187. • Part IV, Appendix 3 to Chapter 2. Frederick Mosteller. “Estimation of death rates.” pp. 234–235. • Part IV, Chapter 3. Yvonne M.M. Bishop and Frederick Mosteller. “Smoothed contigency-table analysis.” pp. 237–272. • Part IV, Chapter 8. Lincoln E. Moses and Frederick Mosteller. “Af- terword for the study of death rates.” pp. 395–408. B24 The President’s Commission on Federal Statistics. Federal Statistics: Re- port of the President’s Commission, Vol. I. Washington, D.C.: U.S. Gov- ernment Printing Office, 1971. Members of the Commission: W. Allen Wallis, Chairman, Freder- ick Mosteller, Vice–Chairman, Ansley J. Coale, Paul M. Densen, Solomon Fabricant, W. Braddock Hickman, William Kruskal, Robert D. Fisher, Stanley Lebergott, Richard M. Scammon, William H. Shaw, James A. Suffridge, John W. Tukey, and Frank D. Stella. The Staff: Daniel B. Rathbun, Executive Director, Paul Feldman, Deputy Executive Director, and Norman V. Breckner, Assistant Director. B25 The President’s Commission on Federal Statistics. Federal Statistics: Re- port of the President’s Commission, Vol. II. Washington, D.C.: U.S. Gov- ernment Printing Office, 1971. 12 Bibliography
• Chapter 6. Richard J. Light, Frederick Mosteller, and Herbert S. Winokur, Jr. “Using controlled field studies to improve public policy.” pp. 367–398.
B26–B31 Judith M. Tanur and members (Frederick Mosteller, Chairman, William H. Kruskal, Richard F. Link, Richard S. Pieters, and Gerald R. Rising) of the Joint Committee on the Curriculum in Statistics and Probability of the American Statistical Association and the National Council of Teach- ers of Mathematics, editors.
These comprise essays by many authors, and the same essay may appear in more than one of the books.
B26 Statistics: A Guide to the Unknown. San Francisco: Holden-Day, 1972.
B27 Second edition of B26. San Francisco: Holden-Day, 1978. With Erich L. Lehmann, Special Editor. Re-issued: Monterey, CA: Wadsworth & Brooks/Cole, 1985.
B28 Third edition of B26. Judith M. Tanur, Frederick Mosteller, William H. Kruskal, Erich L. Lehmann, Richard F. Link, Richard S. Pieters, and Gerald R. Rising, editors. Pacific Grove, CA: Wadsworth & Brooks/Cole, 1989. Translated into Spanish: La Estad´ıstica: Una gu´ıa de lo descono- cido. Madrid: Alianza Editorial, 1992. B29 Statistics: A Guide to Business and Economics. San Francisco: Holden- Day, 1976. With E.L. Lehmann, Special Editor.
B30 Statistics: A Guide to the Biological and Health Sciences. San Francisco: Holden-Day, 1977. With E.L. Lehmann, Special Editor.
B31 Statistics: A Guide to Political and Social Issues. San Francisco: Holden- Day, 1977. With E.L. Lehmann, Special Editor.
• Frederick Mosteller. “Foreword.” pp. viii–x. Also in second edition, pp. ix–xi; third edition, pp. ix–x; and in Statistics: A Guide to Business and Economics, pp. viii–x. • Lincoln E. Moses and Frederick Mosteller. “Safety of anesthetics.” pp. 14–22. Also in second edition, pp. 16–25; third edition, pp. 15–24; and in Statistics: A Guide to the Biological and Health Sciences, pp. 101– 110. • Frederick Mosteller and David L. Wallace. “Deciding authorship.” pp. 164–175. Also in second edition, pp. 207–219; third edition, pp. 115– 125; and in Statistics: A Guide to Political and Social Issues, pp. 78–90. Bibliography 13
• John P. Gilbert, Bucknam McPeek, and Frederick Mosteller. “How fre- quently do innovations succeed in surgery and anesthesia?” In second edition, pp. 45–58. Also in Statistics: A Guide to the Biological and Health Sciences, pp. 51–64. • John P. Gilbert, Richard J. Light, and Frederick Mosteller. “How well do social innovations work?” In second edition, pp. 125–138. Also in Statistics: A Guide to Political and Social Issues, pp. 47–60.
B32 Frederick Mosteller and Daniel P. Moynihan, editors. On Equality of Ed- ucational Opportunity: Papers deriving from the Harvard University Fac- ulty Seminar on the Coleman Report. New York: Random House, 1972. • Chapter 1. Frederick Mosteller and Daniel P. Moynihan. “A pathbreak- ing report.” pp. 3–66. • Chapter 8. John P. Gilbert and Frederick Mosteller. “The urgent need for experimentation.” pp. 371–383. B33 Frederick Mosteller and Robert E.K. Rourke. Sturdy Statistics: Nonpara- metrics and Order Statistics. Reading, MA: Addison-Wesley, 1973.
B34 Frederick Mosteller and Robert E.K. Rourke. Solutions Manual for Sturdy Statistics: Nonparametrics and Order Statistics. Reading, MA: Addison- Wesley, 1973.
B35–B38 Frederick Mosteller, William H. Kruskal, Richard F. Link, Richard S. Pieters, and Gerald R. Rising, editors. The Joint Committee on the Cur- riculum in Statistics and Probability of the American Statistical Associa- tion and the National Council of Teachers of Mathematics. Reading, MA: Addison-Wesley, 1973.
Parts of these books were translated into Japanese, 1979.
B35 Statistics by Example: Exploring Data. (with the assistance of Martha Zelinka) • Set. 2. Frederick Mosteller. “Fractions on closing stock market prices.” pp. 9–13. • Set 7. Frederick Mosteller. “Collegiate football scores.” pp. 61–74. • Set 8. Frederick Mosteller. “Ratings of typewriters.” pp. 75–78. B36 Statistics by Example: Weighing Chances. (with the assistance of Roger Carlson and Martha Zelinka) • Set 7. Frederick Mosteller. “Stock market fractions.” pp. 67–69. • Set 10. Frederick Mosteller. “Ratings of typewriters.” pp. 81–94. • Set 11. Frederick Mosteller. “Collegiate football scores.” pp. 95–111. • Set 12. Frederick Mosteller. “Periodicities and moving averages.” pp. 113–119. 14 Bibliography
B37 Statistics by Example: Detecting Patterns. (with the assistance of Roger Carlson and Martha Zelinka) • Set 9. Frederick Mosteller. “Transformations for linearity.” pp. 99–107. B38 Statistics by Example: Finding Models. (with the assistance of Roger Carl- son and Martha Zelinka) • Set 4. Frederick Mosteller. “Escape-avoidance experiment.” pp. 35–39. B39 Panel on Weather and Climate Modification, Committee on Atmospheric Sciences, National Research Council. Weather & Climate Modification: Problems and Progress. Washington, D.C.: National Academy of Sciences, 1973. Members of the panel: Thomas F. Malone, Chairman, Louis J. Battan, Julian H. Bigelow, Peter V. Hobbs, James E. McDonald, Frederick Mosteller, Helmut K. Weickmann, and E.J. Workman. B40 Yvonne M.M. Bishop, Stephen E. Fienberg, and Paul W. Holland, with the collaboration of Richard J. Light and Frederick Mosteller. Discrete Multivariate Analysis: Theory and Practice. Cambridge, MA: MIT Press, 1975. Paperback edition, 1977.
B41 John P. Bunker, Benjamin A. Barnes, and Frederick Mosteller, editors. Costs, Risks, and Benefits of Surgery. New York: Oxford University Press, 1977. • Chapter 9. John P. Gilbert, Bucknam McPeek, and Frederick Mosteller. “Progress in surgery and anesthesia: Benefits and risks of innovative therapy.” pp. 124–169. • Chapter 10. Bucknam McPeek, John P. Gilbert, and Frederick Mosteller. “The end result: Quality of life.” pp. 170–175. • Chapter 23. John P. Bunker, Benjamin A. Barnes, Frederick Mosteller, John P. Gilbert, Bucknam McPeek, and Richard Jay Zeckhauser. “Summary, conclusions, and recommendations.” pp. 387–394. B42 William B. Fairley and Frederick Mosteller, editors. Statistics and Public Policy. Reading, MA: Addison-Wesley, 1977. • Frederick Mosteller. “Assessing unknown numbers: Order of magnitude estimation.” pp. 163–184. • John P. Gilbert, Richard J. Light, and Frederick Mosteller. “Assessing social innovations: An empirical base for policy.” pp. 185–241. • William B. Fairley and Frederick Mosteller. “A conversation about Collins.” pp. 369–379. B43 Frederick Mosteller and John W. Tukey. Data Analysis and Regression: A Second Course in Statistics. Reading, MA: Addison-Wesley, 1977. Also translated into Russian, 2 volumes. Moscow: Statistika Pub- lishers, 1983. Bibliography 15
B44 Committee for a Planning Study for an Ongoing Study of Costs of Environment-Related Health Effects, Institute of Medicine. Costs of En- vironment-Related Health Effects: A Plan for Continuing Study. Washing- ton, D.C.: National Academy Press, 1981. Members of the Committee: Kenneth J. Arrow, Chairman, Theodore Cooper, Ralph C. d’Arge, Philip J. Landrigan, Alexander Leaf, Joshua Lederberg, Paul A. Marks, Frederick Mosteller, Evelyn F. Murphy, Robert F. Murray, Don K. Price, Frederick C. Robbins, Anne A. Scitovsky, Irving J. Selikoff, Herman A. Tyroler, Arthur C. Upton, and Richard Zeckhauser. B45 David C. Hoaglin, Richard J. Light, Bucknam McPeek, Frederick Mosteller, and Michael A. Stoto. Data for Decisions: Information Strategies for Pol- icymakers. Cambridge, MA: Abt Books, 1982. Paperback: Lanham, MD: University Press of America, 1984. B46 The National Science Board Commission on Precollege Education in Mathematics, Science, and Technology. Educating Americans for the 21st Century: A Plan of Action for Improving Mathematics, Science and Tech- nology Education for All American Elementary and Secondary Students so that Their Achievement is the Best in the World by 1995. Washington, D.C.: National Science Foundation, 1983. Members of the Commission: William T. Coleman, Jr., Co-Chair, Cecily Cannan Selby, Co-Chair, Lew Allen, Jr., Victoria Bergin, George Burnet, Jr., William H. Cosby, Jr., Daniel J. Evans, Pa- tricia Albjerg Graham, Robert E. Larson, Gerald D. Laubach, Katherine P. Layton, Ruth B. Love, Arturo Madrid II, Frederick Mosteller, M. Joan Parent, Robert W. Parry, Benjamin F. Payton, Joseph E. Rowe, Herbert A. Simon, and John B. Slaughter. • A Report to the American People and the National Science Board. • Source Materials. B47 David C. Hoaglin, Frederick Mosteller, and John W. Tukey, editors. Un- derstanding Robust and Exploratory Data Analysis. New York: Wiley, 1983. Translated into Portuguese: Analise Exploratoria de Dados. Tec- nicas Robustas. Lisbon: Novas TecnoLogias, 1992. Also translated into Chinese, (by Zhonglian Chen and Deyuan Guo), Beijing: China Statistics Publishing House, 1998. Wiley Classics Library Edition, 2000. • Chapter 9. David C. Hoaglin, Frederick Mosteller, and John W. Tukey. “Introduction to more refined estimators,” pp. 283–296. B48 Frederick Mosteller, Stephen E. Fienberg, and Robert E.K. Rourke. Begin- ning Statistics with Data Analysis. Reading, MA: Addison-Wesley, 1983. 16 Bibliography
B49 Joseph A. Ingelfinger, Frederick Mosteller, Lawrence A. Thibodeau, and James H. Ware. Biostatistics in Clinical Medicine. New York: Macmillan, 1983. Italian edition: Biostatistica in Medicina, translated by Ettore Marubini. Milano: Raffacello Cortina Editore, 1986.
B50 Second edition of B49, 1987. The second edition has two new chapters—one on life tables, the other on multiple regression. B51 Lincoln E. Moses and Frederick Mosteller, editors. Planning and Analysis of Observational Studies, by William G. Cochran. New York: Wiley, 1983. At the time of his death, William G. Cochran left an almost completed manuscript on observational studies. Lincoln E. Moses and Frederick Mosteller edited and organized the manuscript, and Planning and Analysis of Observational Studies is the result. B52 Oversight Committee on Radioepidemiologic Tables, Board on Radiation Effects Research, Commission on Life Sciences, National Research Coun- cil. Washington, D.C.: National Academy Press, 1984. Members of the Committee: Frederick Mosteller, Chairman. Jacob I. Fabrikant, R.J. Michael Fry, Stephen W. Lagakos, Anthony B. Miller, Eugene L. Saenger, David Schottenfeld, Elizabeth L. Scott, John R. Van Ryzin, and Edward W. Webster; Stephen L. Brown, Staff Officer, Norman Grossblatt, Editor. • Assigned Share for Radiation as a Cause of Cancer: Review of As- sumptions and Methods for Radioepidemiologic Tables. Interim Re- port. • Assigned Share for Radiation as a Cause of Cancer: Review of Ra- dioepidemiologic Tables Assigning Probabilities of Causation. Final Report. B53 David C. Hoaglin, Frederick Mosteller, and John W. Tukey, editors. Ex- ploring Data Tables, Trends, and Shapes. New York: Wiley, 1985. • Chapter 5. Frederick Mosteller and Anita Parunak. “Identifying ex- treme cells in a sizable contingency table: probabilistic and exploratory approaches.” pp. 189–224. • Chapter 6. Frederick Mosteller, Andrew F. Siegel, Edward Trapido, and Cleo Youtz. “Fitting straight lines by eye.” pp. 225–239. B54 Committee for Evaluating Medical Technologies in Clinical Use, Division of Health Promotion and Disease Prevention, Institute of Medicine. As- sessing Medical Technologies. Washington, D.C.: National Academy Press, 1985. Bibliography 17
Members of the Committee: Frederick Mosteller, Chairman, H. David Banta, Stuart Bondurant, Morris F. Collen, Joanne E. Fin- ley, Barbara J. McNeil, Lawrence C. Morris, Jr., Lincoln E. Moses, Seymour Perry, Dorothy P. Rice, Herman A. Tyroler, and Donald A. Young. Study Staff: Enriqueta C. Bond, Barbara Filner, Caren Carney, Clifford Goodman, Linda DePugh, Naomi Hudson, and Wallace K. Waterfall.
B55 John C. Bailar III and Frederick Mosteller, editors. Medical Uses of Statis- tics. Waltham, MA: NEJM Books, 1986. • Introduction. John C. Bailar III and Frederick Mosteller. pp. xxi–xxvi. • Chapter 8. James H. Ware, Frederick Mosteller, and Joseph A. In- gelfinger. “P values.” pp. 149–169. • Chapter 13. Rebecca DerSimonian, L. Joseph Charette, Bucknam McPeek, and Frederick Mosteller. “Reporting on methods in clinical trials.” pp. 272–288. • Chapter 15. Frederick Mosteller. “Writing about numbers.” pp. 305– 321. Italian edition: L’Uso della Statistica in Medicina. Roma: Il Pensiero Scientifico Editore, 1988. Translated by Giovanni Apolone, Antonio Nicolucci, Raldano Fossati, Fabio Parazzini, Walter Torri, Roberto Grilli. B56 John C. Bailar III and Frederick Mosteller, editors. Medical Uses of Statis- tics, second edition. Boston: NEJM Books, 1992. • John C. Bailar III and Frederick Mosteller. “Introduction.” pp. xxiii– xxvii. • Chapter 10. James H. Ware, Frederick Mosteller, Fernando Delgado, Christl Donnelly, and Joseph A. Ingelfinger. “P values.” pp. 181–200. • Chapter 16. John C. Bailar III and Frederick Mosteller. “Guidelines for statistical reporting in articles for medical journals: Amplifications and explanations.” pp. 313–331. • Chapter 17. Rebecca DerSimonian, L. Joseph Charette, Bucknam McPeek, and Frederick Mosteller. “Reporting on methods in clinical trials.” pp. 333–347. • Chapter 20. Frederick Mosteller. “Writing about numbers.” pp. 375– 389. • Chapter 21. John C. Bailar III and Frederick Mosteller. “Medical tech- nology assessment.” pp. 393–411. • Chapter 22. Katherine Taylor Halvorsen, Elisabeth Burdick, Graham A. Colditz, Howard S. Frazier, and Frederick Mosteller. “Combining results from independent investigations: Meta-analysis in clinical re- search.” pp. 413–426. 18 Bibliography
B57 Frederick Mosteller and Jennifer Falotico–Taylor, editors. Quality of Life and Technology Assessment, monograph of the Council on Health Care Technology, Institute of Medicine. Washington, D.C.: National Academy Press, 1989. • Jennifer Falotico-Taylor, Mark McClellan, and Frederick Mosteller. “The use of quality-of-life measures in technology assessment” (in- cluding “Twelve applications of quality-of-life measures to technology assessment”). pp. 7–44. • Jennifer Falotico-Taylor and Frederick Mosteller. “Applications of quality-of-life measures and areas for cooperative research.” pp. 116– 118. B58 David C. Hoaglin, Frederick Mosteller, and John W. Tukey, editors. Fun- damentals of Exploratory Analysis of Variance. New York: Wiley, 1991. • Chapter 1. John W. Tukey, Frederick Mosteller, and David C. Hoaglin. “Concepts and examples in analysis of variance.” pp. 1–23. • Chapter 2. Frederick Mosteller and John W. Tukey. “Purposes of an- alyzing data that come in a form inviting us to apply tools from the analysis of variance.” pp. 24–39. • Chapter 3. Frederick Mosteller and David C. Hoaglin. “Preliminary examination of data.” pp. 40–49. • Chapter 7. Frederick Mosteller, Anita Parunak, and John W. Tukey. “Mean squares, F tests, and estimates of variance.” pp. 146–164. • Chapter 9. Constance Brown and Frederick Mosteller. “Components of variance.” pp. 193–251. • Chapter 10. Thomas Blackwell, Constance Brown, and Frederick Mos- teller. “Which denominator?” pp. 252–294. • Chapter 11. John W. Tukey, Frederick Mosteller, and Cleo Youtz. “As- sessing changes.” pp. 295–335. B59 Committee to Review the Adverse Consequences of Pertussis and Rubella Vaccines, Division of Health Promotion and Disease Prevention, Insti- tute of Medicine, Christopher P. Howson, Cynthia J. Howe, and Harvey V. Fineberg, editors. Adverse Effects of Pertussis and Rubella Vaccines. Washington, D.C.: National Academy Press, 1991.
B60 Thomas D. Cook, Harris Cooper, David S. Cordray, Heidi Hartmann, Larry V. Hedges, Richard J. Light, Thomas A. Louis, and Frederick Mosteller. Meta-Analysis for Explanation: A Casebook. New York: Russell Sage Foundation, 1992. • Richard J. Light and Frederick Mosteller. “Annotated bibliography of meta-analytic books and journal issues.” pp. xi–xiv. B61 Kenneth S. Warren and Frederick Mosteller, editors. Doing More Good Than Harm: The Evaluation of Health Care Interventions. New York: Bibliography 19
Annals of the New York Academy of Sciences, 703, New York Academy of Sciences, 1993. • Frederick Mosteller. “Some evaluation needs.” pp. 12–17. B62 Howard S. Frazier and Frederick Mosteller, editors. Medicine Worth Pay- ing For: Assessing Medical Innovations. Cambridge, MA: Harvard Uni- versity Press, 1995. • Chapter 1. Howard S. Frazier and Frederick Mosteller. “The nature of the inquiry.” pp. 3–8. • Chapter 2. Frederick Mosteller and Howard S. Frazier. “Evaluating medical technologies.” pp. 9–35. • Chapter 11. Georgianna Marks, Frederick Mosteller, Marie-A. McPher- son, and Grace Wyshak. “The contributions of lenses to visual health.” pp. 157–172. • Chapter 17. Frederick Mosteller and Howard S. Frazier. “Improving the health care system.” pp. 245–259. • Chapter 18. Frederick Mosteller and Howard S. Frazier. “Innovation- specific improvements.” pp. 260–274. • Chapter 19. Howard S. Frazier and Frederick Mosteller. “Recommen- dations for change.” pp. 275–280.
B63 Committee for Guidance on Setting and Enforcing Speed Limits, Trans- portation Research Board, National Research Council. Managing Speed: Review of Current Practice for Setting and Enforcing Speed Limits,Spe- cial Report 254. Washington, D.C.: National Academy Press, 1998.
B64 Committee on Equivalency and Linkage of Educational Tests, Board on Testing and Assessment, Commission on Behavioral and Social Sciences and Education, National Research Council, Michael J. Feuer, Paul W. Holland, Bert F. Green, Meryl W. Bertenthal, and F. Cadelle Hemphill, editors. Uncommon Measures: Equivalence and Linkage Among Educa- tional Tests. Washington, D.C.: National Academy Press, 1999.
B65 Frederick Mosteller and Robert Boruch, editors. Evidence Matters: Ran- domized Trials in Education Research. Washington, D.C.: Brookings In- stitute Press, 2002.
PAPERS P1 Frederick Mosteller. “Note on an application of runs to quality control charts.” Annals of Mathematical Statistics, 12 (1941), pp. 228–232.
P2 Frederick Mosteller and Philip J. McCarthy. “Estimating population pro- portions.” Public Opinion Quarterly, 6 (1942), pp. 452–458. 20 Bibliography
P3 Louis H. Bean, Frederick Mosteller, and Frederick Williams. “Nationali- ties and 1944.” Public Opinion Quarterly, 8 (1944), pp. 368–375.
P4 M.A. Girshick, Frederick Mosteller, and L.J. Savage. “Unbiased estimates for certain binomial sampling problems with applications.” Annals of Mathematical Statistics, 17 (1946), pp. 13–23. Reprinted in The Writings of Leonard Jimmie Savage—A Memo- rial Selection, edited by a committee. Washington, D.C.: The American Statistical Association and The Institute of Mathemat- ical Statistics, 1981. pp. 96–106. P5 Frederick Mosteller. “On some useful ‘inefficient’ statistics.” Annals of Mathematical Statistics, 17 (1946), pp. 377–408.
P6 Cecil Hastings, Jr., Frederick Mosteller, John W. Tukey, and Charles P. Winsor. “Low moments for small samples: A comparative study of order statistics.” Annals of Mathematical Statistics, 18 (1947), pp. 413–426.
P7 Frederick Mosteller. “A k-sample slippage test for an extreme population.” Annals of Mathematical Statistics, 19 (1948), pp. 58–65.
P8 Frederick Mosteller. “On pooling data.” Journal of the American Statis- tical Association, 43 (1948), pp. 231–242.
P9 Frederick Mosteller and John W. Tukey. “The uses and usefulness of bino- mial probability paper.” Journal of the American Statistical Association, 44 (1949), pp. 174–212.
P10 Hendrik Bode, Frederick Mosteller, John W. Tukey, and Charles Winsor. “The education of a scientific generalist.” Science, 109 (June 3, 1949), pp. 553–558.
P11 Frederick Mosteller and John W. Tukey. “Practical applications of new theory, a review.” • “Part I: Location and scale: tables.” Industrial Quality Control, 6, No. 2 (1949), pp. 5–8. • “Part II: Counted data—graphical methods.” No. 3 (1949), pp. 5–7. • “Part III: Analytical techniques.” No. 4 (1950), pp. 5–8. • “Part IV: Gathering information.” No. 5 (1950), pp. 5–7. P12 Frederick Mosteller. Article on “Statistics” in Collier’s Encyclopedia,circa 1949, pp. 191–195.
P13 Frederick Mosteller and John W. Tukey. “Significance levels for a k-sample slippage test.” Annals of Mathematical Statistics, 21 (1950), pp. 120–123. Bibliography 21
P14 J.S. Bruner, L. Postman, and F. Mosteller. “A note on the measurement of reversals of perspective.” Psychometrika, 15 (1950), pp. 63–72.
P15 Arthur S. Keats, Henry K. Beecher, and Frederick Mosteller. “Measure- ment of pathological pain in distinction to experimental pain.” Journal of Applied Physiology, 3 (1950), pp. 35–44.
P16 Frederick Mosteller. “Remarks on the method of paired comparisons: I. The least squares solution assuming equal standard deviations and equal correlations.” Psychometrika, 16 (1951), pp. 3–9. Reprinted in Readings in Mathematical Psychology, I,editedbyR. Duncan Luce, Robert R. Bush, and Eugene Galanter. New York: Wiley, 1963. pp. 152–158. P17 Frederick Mosteller. “Remarks on the method of paired comparisons: II. The effect of an aberrant standard deviation when equal standard devia- tions and equal correlations are assumed.” Psychometrika, 16 (1951), pp. 203–206.
P18 Frederick Mosteller. “Remarks on the method of paired comparisons: III. A test of significance for paired comparisons when equal standard devia- tions and equal correlations are assumed.” Psychometrika, 16 (1951), pp. 207–218.
P19 Robert E. Goodnow, Henry K. Beecher, Mary A.B. Brazier, Frederick Mosteller, and Renato Tagiuri. “Physiological performance following a hypnotic dose of a barbiturate.” Journal of Pharmacology and Experi- mental Therapeutics, 102 (1951), pp. 55–61.
P20 Frederick Mosteller. “Theoretical backgrounds of the statistical methods: underlying probability model used in making a statistical inference.” In- dustrial and Engineering Chemistry, 43 (1951), pp. 1295–1297.
P21 Frederick Mosteller. “Mathematical models for behavior theory: a brief report on an interuniversity summer research seminar.” Social Science Research Council Items, 5 (September 1951), pp. 32–33.
P22 Frederick Mosteller and Philip Nogee. “An experimental measurement of utility.” The Journal of Political Economy, 59 (1951), pp. 371–404. Reprinted in the Bobbs-Merrill Reprint Series in the Social Sci- ences.
P23 Robert R. Bush and Frederick Mosteller. “A mathematical model for sim- ple learning.” Psychological Review, 58 (1951), pp. 313–323. 22 Bibliography
Reprinted in Readings in Mathematical Psychology, I,editedbyR. Duncan Luce, Robert R. Bush, and Eugene Galanter. New York: Wiley, 1963. pp. 278–288. Reprinted in the Bobbs-Merrill Reprint Series in the Social Sci- ences.
P24 Robert R. Bush and Frederick Mosteller. “A model for stimulus general- ization and discrimination.” Psychological Review, 58 (1951), pp. 413–423. Reprinted in Readings in Mathematical Psychology, I,editedbyR. Duncan Luce, Robert R. Bush, and Eugene Galanter. New York: Wiley, 1963. pp. 289–299. P25 Frederick Mosteller. “Clinical studies of analgesic drugs: II. Some statisti- cal problems in measuring the subjective response to drugs.” Biometrics, 8 (1952), pp. 220–226.
P26 Frederick Mosteller. “The World Series competition.” Journal of the American Statistical Association, 47 (1952), pp. 355–380. Translated into French by F.M.-Alfred, E.C.´ “Utilisation de quelques techniques statistiques au service des parieurs. Pr´esentation et traduction de l’article ‘World Series Competition’ de Fr´ederic Mosteller.” Herm`es, Bulletin de la Facult´edeCommercedel’Universit´e Laval, 1953, #7, pp. 50–64; #8, pp. 29–37. P27 Frederick Mosteller. “Statistical theory and research design.” Annual Re- view of Psychology, 4 (1953), pp. 407–434.
P28 Robert R. Bush and Frederick Mosteller. “A stochastic model with ap- plications to learning.” Annals of Mathematical Statistics, 24 (1953), pp. 559–585.
P29 Henry K. Beecher, Arthur S. Keats, Frederick Mosteller, and Louis Lasagna. “The effectiveness of oral analgesics (morphine, codeine, acetylsalicylic acid) and the problem of placebo ‘reactors’ and ‘non-reactors.’ ” Journal of Pharmacology and Experimental Therapeutics, 109 (1953), pp. 393–400.
P30 Frederick Mosteller. “Comments on ‘Models for Learning Theory.’ ” Sym- posium on Psychology of Learning Basic to Military Training Problems, Panel on Training and Training Devices, Committee on Human Resources Research and Development Board, May 7–8, 1953, pp. 39–42.
P31 William G. Cochran, Frederick Mosteller, and John W. Tukey. “Statisti- cal problems of the Kinsey Report.” Journal of the American Statistical Association, 48 (1953), pp. 673–716. Bibliography 23
P32 William G. Cochran, Frederick Mosteller, and John W. Tukey. “Principles of Sampling.” Journal of the American Statistical Association, 49 (1954), pp. 13–35. Translated into Spanish: “Fundamentos de muestreo.” Estad´ıstica, Journal of the Inter-American Statistical Institute, June 1956, Vol. XIV, No. 51, pp. 235–258. P33 Louis Lasagna, Frederick Mosteller, John M. von Felsinger, and Henry K. Beecher. “A study of the placebo response.”American Journal of Medicine, 16 (1954), pp. 770–779.
P34 Frederick Mosteller and Robert R. Bush. “Selected quantitative tech- niques.” Chapter 8 in Handbook of Social Psychology, edited by Gardner Lindzey. Cambridge, MA: Addison-Wesley, 1954. pp. 289–334. Reprinted in paperback, circa 1969, together with Chapter 9, “At- titude measurement” by Bert F. Green. It was decided to pub- lish these two chapters as a separate book because they were not reprinted in The Handbook of Social Psychology, Second Edition, Vol. I, 1968, Vols. II–V, 1969, edited by Gardner Lindzey and Elliot Aronson. P35 Robert R. Bush, Frederick Mosteller, and Gerald L. Thompson. “A formal structure for multiple-choice situations.” Chapter VIII in Decision Pro- cesses, edited by R.M. Thrall, C.H. Coombs, and R.L. Davis. New York: Wiley, 1954. pp. 99–126.
P36 Frederick Mosteller. Introduction, IV, “Applications.” In Tables of Cumu- lative Binomial Probability Distribution, by the Staff of Harvard Compu- tation Laboratory. The Annals of the Computation Laboratory of Harvard University, XXXV. Cambridge, MA: Harvard University Press, 1955. pp. xxxiv–lxi.
P37 Frederick Mosteller. “Stochastic learning models.” In Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Volume V: Econometrics, Industrial Research, and Psychometry, edited by Jerzy Neyman. Berkeley: University of California Press, 1956. pp. 151– 167.
P38 Frederick Mosteller. “Statistical problems and their solution.” Chapter VI in “The measurement of pain, prototype for the quantitative study of subjective responses,” by Henry K. Beecher. Pharmacological Reviews, 9 (1957), pp. 103–114.
P39 Frederick Mosteller. “Stochastic models for the learning process.” Pro- ceedings of the American Philosophical Society, 102 (1958), pp. 53–59. 24 Bibliography
P40 Frederick Mosteller and D.E. Richmond. “Factorial 1/2: A simple graph- ical treatment.” American Mathematical Monthly, 65 (1958), pp. 735–742.
P41 Frederick Mosteller. “The mystery of the missing corpus.” Psychometrika, 23 (1958), pp. 279–289.
P42 Frederick Mosteller. “Statistical problems and their solution.” Chapter 4inMeasurement of Subjective Responses, Quantitative Effects of Drugs by Henry K. Beecher. New York: Oxford University Press, 1959. pp. 73–91.
P43 In Studies in Mathematical Learning Theory, edited by Robert R. Bush and William K. Estes. Stanford Mathematical Studies in the Social Sci- ences, III. Stanford: Stanford University Press, 1959. • Chapter 12. Maurice Tatsuoka and Frederick Mosteller. “A commuting- operator model.” pp. 228–247. • Chapter 15. Robert R. Bush and Frederick Mosteller. “A comparison of eight models.” pp. 293–307. P44 Frederick Mosteller and Maurice Tatsuoka. “Ultimate choice between two attractive goals: Predictions from a model.” Psychometrika, 25 (1960), pp. 1–17. Reprinted in Readings in Mathematical Psychology, I,editedbyR. Duncan Luce, Robert R. Bush, and Eugene Galanter. New York: Wiley, 1963. pp. 498–514. P45 Richard Cohn, Frederick Mosteller, John W. Pratt, and Maurice Tatsuoka. “Maximizing the probability that adjacent order statistics of samples from several populations form overlapping intervals.” Annals of Mathematical Statistics, 31 (1960), pp. 1095–1104.
P46 Frederick Mosteller. “Optimal length of play for a binomial game.” The Mathematics Teacher, 54 (1961), pp. 411–412.
P47 Frederick Mosteller and Cleo Youtz. “Tables of the Freeman-Tukey trans- formations for the binomial and Poisson distributions.” Biometrika, 48 (1961), pp. 433–440.
P48 Gordon W. Allport, Paul H. Buck, Frederick Mosteller, and Talcott Par- sons, Chairman. “Samuel Andrew Stouffer,” Memorial Minute adopted by the Faculty of Arts and Sciences, Harvard University. Harvard University Gazette, April 29, 1961, pp. 197–198.
P49 Frederick Mosteller. “Understanding the birthday problem.” The Mathe- matics Teacher, 55 (1962), pp. 322–325. Bibliography 25
P50 Frederick Mosteller and David L. Wallace. “Notes on an authorship prob- lem.” In Proceedings of a Harvard Symposium on Digital Computers and Their Applications, 3–6 April 1961. Cambridge, MA: Harvard University Press, 1962. pp. 163–197.
P51 Reports on Continental Classroom’s TV course in probability and statis- tics. • Frederick Mosteller. “Continental Classroom’s TV course in probabil- ity and statistics.” The American Statistician, 16, No. 5 (December 1962), pp. 20–25. • Frederick Mosteller. “The U.S. Continental Classroom’s TV course in probability and statistics.”Quality, 7, No. 2 (1963), pp. 36–39. Abbreviated version. • Frederick Mosteller. “Continental Classroom’s TV course in probabil- ity and statistics.” The Mathematics Teacher, 56 (1963), pp. 407–413. • Frederick Mosteller. “Continental Classroom’s television course in probability and statistics.” Review of the International Statistical In- stitute, 31 (1963), pp. 153–162. P52 Frederick Mosteller and David L. Wallace. “Inference in an authorship problem: A comparative study of discrimination methods applied to the authorship of the disputed Federalist papers.” Journal of the American Statistical Association, 58 (1963), pp. 275–309.
P53 Frederick Mosteller. “Samuel S. Wilks: Statesman of Statistics.” The American Statistician, 18, No. 2 (April 1964), pp. 11–17.
P54 Frederick Mosteller. “Contributions of secondary school mathematics to social science.” In Proceedings of the UICSM Conference on the Role of Applications in a Secondary School Mathematics Curriculum, edited by Dorothy Friedman. Urbana, Illinois: University of Illinois Committee on School Mathematics, 1964. pp. 85–111.
P55 Frederick Mosteller. “John Davis Williams, 1909–1964, In Memoriam.” The Memorial Service, Santa Monica Civic Auditorium, Santa Monica, CA, December 6, 1964, pp. 3–13.
P56 Arthur P. Dempster and Frederick Mosteller. “A model for the weighting of scores.” Appendix C in Staff Leadership in Public Schools: A Socio- logical Inquiry, edited by Neal Gross and Robert E. Herriott. New York: Wiley, 1965. pp. 202–216.
P57 Frederick Mosteller. “His writings in applied statistics,” pp. 944–953 in “Samuel S. Wilks,” by Frederick F. Stephan, John W. Tukey, Frederick Mosteller, Alex M. Mood, Morris H. Hansen, Leslie E. Simon, and W.J. 26 Bibliography
Dixon. Journal of the American Statistical Association, 60 (1965), pp. 938–966.
P58 John P. Gilbert and Frederick Mosteller. “Recognizing the maximum of a sequence.” Journal of the American Statistical Association, 61 (1966), pp. 35–73.
P59 Gene Smith, Lawrence D. Egbert, Robert A. Markowitz, Frederick Mos- teller, and Henry K. Beecher. “An experimental pain method sensitive to morphine in man: The submaximum effort tourniquet technique.” Journal of Pharmacology and Experimental Therapeutics, 154 (1966), pp. 324–332.
P60 Subcommittee on the National Halothane Study of the Committee on Anesthesia, National Academy of Sciences—National Research Council. “Summary of the National Halothane Study: Possible association between halothane anesthesia and postoperative hepatic necrosis.” Journal of the American Medical Association, 197 (1966), pp. 775–788.
P61 Frederick Mosteller. Contribution to “Tribute to Walter Shewhart.” In- dustrial Quality Control, 24, No. 2 (1967), p. 117.
P62 Conrad Taeuber, Frederick Mosteller, and Paul Webbink. “Social Sci- ence Research Council Committee on Statistical Training.” The American Statistician, 21, No. 5 (December 1967), pp. 10–11. Reprinted from Social Science Research Council Items, 21,De- cember 1967, pp. 49–51. P63 Frederick Mosteller. “What has happened to probability in the high school?” The Mathematics Teacher, 60 (1967), pp. 824–831.
P64 Frederick Mosteller, Cleo Youtz, and Douglas Zahn. “The distribution of sums of rounded percentages.” Demography, 4 (1967), pp. 850–858.
P65 Frederick Mosteller. “Statistical comparisons of anesthetics: The National Halothane Study.” Bulletin of the International Statistical Institute,Pro- ceedings of the 36th Session, Sydney, 1967, XLII, Book 1, pp. 428–438.
P66 Lincoln E. Moses and Frederick Mosteller. “Institutional differences in postoperative death rates: Commentary on some of the findings of the National Halothane Study.” Journal of the American Medical Associa- tion, 203 (1968), pp. 492–494.
P67 Frederick Mosteller. “Association and estimation in contingency tables.” Journal of the American Statistical Association, 63 (1968), pp. 1–28. Bibliography 27
P68 Frederick Mosteller. “Errors: Nonsampling errors.” In International En- cyclopedia of the Social Sciences, Vol. 5, edited by David L. Sills. New York: Macmillan and Free Press, 1968, pp. 113–132. A slightly expanded version appeared in International Encyclo- pedia of Statistics, edited by William H. Kruskal and Judith M. Tanur. New York: The Free Press, 1978, pp. 208–229. P69 Frederick Mosteller. “S.S. Wilks.” In International Encyclopedia of the Social Sciences, Vol. 16, edited by David L. Sills. New York: Macmillan and Free Press, 1968. pp. 550–553.
P70 Frederick Mosteller and John W. Tukey. “Data analysis, including statis- tics.” Chapter 10 in Vol. 2 of The Handbook of Social Psychology, Second edition, edited by Gardner Lindzey and Elliot Aronson. Reading, MA: Addison-Wesley, 1968. pp. 80–203.
P71 Barry H. Margolin and Frederick Mosteller. “The expected coverage to the left of the ith order statistic for arbitrary distributions.” Annals of Mathematical Statistics, 40 (1969), pp. 644–647.
P72 Frederick Mosteller. “Progress report of the Joint Committee of the Amer- ican Statistical Association and the National Council of Teachers of Math- ematics.” The Mathematics Teacher, 63 (1970), pp. 199–208.
P73 Frederick Mosteller. “Progress report of the Joint Committee of the Amer- ican Statistical Association and the National Council of Teachers of Math- ematics.” The American Statistician 24, No. 3 (June 1970), pp. 8–12.
P74 Frederick Mosteller. Discussion of “Statistical aspects of rain stimulation— problems and prospects,” by Jeanne L. Lovasich, Jerzy Neyman, Elizabeth L. Scott, and Jerome A. Smith. Review of the International Statistical In- stitute, 38 (1970), pp. 169–170.
P75 Frederick Mosteller. “Collegiate football scores, U.S.A.” Journal of the American Statistical Association, 65 (1970), pp. 35–48. An abridged version appeared in Optimal Strategies in Sports, edited by Shaul P. Ladany and Robert E. Machol. Amsterdam: North-Holland/American Elsevier, 1977, pp. 97–105. P76 Frederick Mosteller. “The mathematical sciences at work with the social sciences: Learning with irregular rewards.” In “Mathematical sciences and social sciences: Excerpts from the Report of a Panel of the Behavioral and Social Sciences Survey,” selected by William H. Kruskal. Social Science Research Council Items, 24, September 1970, pp. 25–28. Also in The American Statistician, 25, No. 1 (February 1971), pp. 27–30. 28 Bibliography
P77 Frederick Mosteller with the aid of Frank Restle. “The mathematical sciences at work with the social sciences: Learning with irregular re- wards.” Chapter 1 in Mathematical Sciences and Social Sciences, edited by William H. Kruskal. Englewood Cliffs, NJ: Prentice-Hall, 1970. pp. 5– 19.
P78 Frederick Mosteller with the extensive aid of Margaret Martin and Conrad Taeuber. “The profession of social statistician.” Chapter 3 in Mathemati- cal Sciences and Social Sciences, edited by William H. Kruskal. Englewood Cliffs, NJ: Prentice-Hall, 1970. pp. 35–47.
P79 Robert R. Bush and Frederick Mosteller. “Mathematical or stochastic models for learning.” Chapter 14 in Psychology of Learning: Systems, Models, and Theories, by William S. Sahakian. Chicago: Markham Pub- lishing Company, 1970. pp. 280–294.
P80 Gudmund R. Iversen, Willard H. Longcor, Frederick Mosteller, John P. Gilbert, and Cleo Youtz. “Bias and runs in dice throwing and recording: a few million throws.” Psychometrika, 36 (1971), pp. 1–19.
P81 Frederick Mosteller. “Some considerations on the role of probability and statistics in the school mathematics programs of the 1970’s.” In Report of a Conference on Responsibilities for School Mathematics in the 70’s by School Mathematics Study Group, copyright by The Board of Trustees of the Leland Stanford Junior University, 1971. pp. 87–93.
P82 Frederick Mosteller. “The jackknife.” Review of the International Statis- tical Institute, 39 (1971), pp. 363–368.
P83 Francis J. Anscombe, David H. Blackwell, and Frederick Mosteller (Chair- man). “Report of the Evaluation Committee on the University of Chicago Department of Statistics.” The American Statistician, 25, No. 3 (June 1971), pp. 17–24.
P84 Frederick Mosteller. “The Joint American Statistical Association—National Council of Teachers of Mathematics Committee on the Curriculum in Statistics and Probability.” Review of the International Statistical Insti- tute, 39 (1971), pp. 340–342.
P85 Frederick Mosteller. “A data-analytic look at Goldbach counts.” Statistica Neerlandica, 26 (1972), pp. 227–242.
P86 Frederick Mosteller. “An empirical study of the distribution of primes and litters of primes.” Paper 15 in Statistical Papers in Honor of George W. Snedecor, edited by T.A. Bancroft with the assistance of Susan Alice Bibliography 29
Brown, Ames, IA: The Iowa State University Press, 1972. pp. 245–257.
P87 William Fairley and Frederick Mosteller. “Trial of an adversary hearing: Public policy in weather modification.” International Journal of Mathe- matical Education in Science and Technology, 3 (1972), pp. 375–383.
P88 Frederick Mosteller. “Chairman’s Introduction.” In Statistics at the School Level, edited by Lennart R˚ade. Stockholm, Sweden: Almqvist and Wiksell International. New York: Wiley. 1973. pp. 23–37.
P89 Frederick Mosteller and David C. Hoaglin. “Statistics.” In the Encyclopae- dia Britannica, Fifteenth edition, 17 (1974), pp. 615–624.
P90 Frederick Mosteller. “The role of the Social Science Research Council in the advance of mathematics in the social sciences.” Social Science Re- search Council Items, 28, June 1974, pp. 17–24.
P91 William B. Fairley and Frederick Mosteller. “A conversation about Collins.” The University of Chicago Law Review, 41, No. 2 (Winter 1974), pp. 242– 253.
P92 Frederick Mosteller. “Robert R. Bush. Early Career.” Journal of Mathe- matical Psychology, 11 (1974), pp. 163–178.
P93 C.F. Mosteller, E.B. Newman, B.F. Skinner, and R.J. Herrnstein, Chair- man. “Stanley Smith Stevens,” Memorial Minute adopted by the Faculty of Arts and Sciences, Harvard University, April 9, 1974. Harvard Univer- sity Gazette, June 13, 1974.
P94 John P. Gilbert, Richard J. Light, and Frederick Mosteller. “Assessing social innovations: An empirical base for policy.” Chapter 2 in Evalua- tion and Experiment: Some Critical Issues in Assessing Social Programs, edited by Carl A. Bennett and Arthur A. Lumsdaine. New York: Aca- demic Press, 1975. pp. 39–193.
P95 John P. Gilbert, Richard J. Light, and Frederick Mosteller. “Assessing social innovations: An empirical base for policy.” Chapter 1 in Benefit– Cost and Policy Analysis 1974, an Aldine Annual on forecasting, decision- making, and evaluation. Edited by Richard Zeckhauser, Arnold C. Har- berger, Robert H. Haveman, Laurence E. Lynn, Jr., William A. Niskanen, and Alan Williams. Chicago: Aldine Publishing Company, 1975. pp. 3–65.
P96 Frederick Mosteller. “Comment by Frederick Mosteller.” On David K. Cohen’s “The Value of Social Experiments.” In Planned Variation in Ed- ucation: Should We Give Up or Try Harder?, edited by Alice M. Rivlin 30 Bibliography
and P. Michael Timpane. Washington, D.C.: The Brookings Institution, 1975. pp. 169–172.
P97 Frederick Mosteller, John P. Gilbert, and Bucknam McPeek. “Measuring the quality of life.” In Surgery in the United States: A Summary Report of the Study on Surgical Services for the United States, sponsored jointly by The American College of Surgeons and The American Surgical Asso- ciation, Volume III. Chicago: The College, 1976. pp. 2283–2299.
P98 John P. Gilbert, Frederick Mosteller, and John W. Tukey. “Steady social progress requires quantitative evaluation to be searching.” In The Evalu- ation of Social Programs, edited by Clark C. Abt. Beverly Hills, CA: Sage Publications, 1976. pp. 295–312.
P99 Persi Diaconis, Frederick Mosteller, and Hironari Onishi. “Second-order terms for the variances and covariances of the number of prime factors— includingthesquarefreecase.”Journal of Number Theory, 9 (1977), pp. 187–202.
P100 Committee on Community Reactions to the Concorde, Assembly of Be- havioral and Social Sciences, National Research Council. “Community reactions to the Concorde: An assessment of the trial period at Dulles Airport.” Washington, D.C.: National Academy of Sciences, 1977. Committee members: Angus Campbell, Chairman, William Bau- mol, Robert F. Boruch, James A. Davis, Elizabeth A. Deakin, Kenneth M. Eldred, Henning E. von Gierke, Amos H. Hawley, C. Frederick Mosteller, and H. Wayne Rudmose. P101 John P. Gilbert, Bucknam McPeek, and Frederick Mosteller. “Statistics and ethics in surgery and anesthesia.” Science, 198 (1977), pp. 684–689. Reprinted in Solutions to Ethical and Legal Problems in Social Research, edited by Robert F. Boruch and Joe S. Cecil. New York: Academic, 1983. pp. 65–82. P102 Frederick Mosteller. “Experimentation and innovations.” Bulletin of the International Statistical Institute, Proceedings of the 41st Session, New Delhi, 1977, XLVII, Book 1, pp. 559–572.
P103 Frederick Mosteller (with others). “Calendar Year 1977 Report,” National Advisory Council on Equality of Educational Opportunity, March 31, 1978. (Includes “Report of the Task Force on Evaluation,” pp. 15–24, and “Final Report of the Task Force on Evaluation,” pp. 25–38, by Jacquelyne J. Jackson, Haruko Morita, and Frederick Mosteller.) Bibliography 31
P104 Oliver Cope, John Hedley-Whyte, Richard J. Kitz, C. Frederick Mosteller, Henning Pontoppidan, William H. Sweet, Leroy D. Vandam, and Myron B. Laver, Chairman. “Henry K. Beecher,” Memorial Minute adopted by the Faculty of Medicine, Harvard University, June 1, 1977. Harvard Uni- versity Gazette, January 13, 1978. p. 9.
P105 Frederick Mosteller. “Dilemmas in the concept of unnecessary surgery.” Journal of Surgical Research, 25 (1978), pp. 185–192.
P106 Frederick Mosteller. “A resistant analysis of 1971 and 1972 professional football.” In Sports, Games, and Play: Social and Psychological View- points, edited by Jeffrey H. Goldstein. Hillsdale, NJ: Lawrence Erlbaum Associates, 1979. pp. 371–399.
P107 Frederick Mosteller. Comment on “Field experimentation in weather mod- ification,” by Roscoe R. Braham, Jr. Journal of the American Statistical Association, 74 (1979), pp. 88–90.
P108 Frederick Mosteller. “Problems of omissions in communications.” Clini- cal Pharmacology and Therapeutics, 25, No. 5, Part 2 (1979), pp. 761–764.
P109 Frederick Mosteller and Gale Mosteller. “New statistical methods in pub- lic policy. Part I: Experimentation.” Journal of Contemporary Business, 8, No. 3 (1979), pp. 79–92.
P110 Frederick Mosteller and Gale Mosteller. “New statistical methods in pub- lic policy. Part II: Exploratory data analysis.” Journal of Contemporary Business, 8, No. 3 (1979), pp. 93–115.
P111 William H. Kruskal and Frederick Mosteller. “Representative sampling, I: Non-scientific literature.” International Statistical Review, 47 (1979), pp. 13–24.
P112 William H. Kruskal and Frederick Mosteller. “Representative sampling, II: Scientific literature, excluding statistics.” International Statistical Re- view, 47 (1979), pp. 111–127.
P113 William H. Kruskal and Frederick Mosteller. “Representative sampling, III: The current statistical literature.” International Statistical Review, 47 (1979), pp. 245–265.
P114 William H. Kruskal and Frederick Mosteller. “Representative sampling, IV: The history of the concept in statistics, 1895–1939.” International Statistical Review, 48 (1980), pp. 169–195. 32 Bibliography
P115 Frederick Mosteller. “Classroom and platform performance.” The Amer- ican Statistician, 34 (1980), pp. 11–17. Reprinted in Amstat News, September 2002, pp. 15–20.
P116 Frederick Mosteller, Bucknam McPeek, and John P. Gilbert. “The clini- cian’s responsibility for the decision process.” CAHP News Letter (Center for the Analysis of Health Practices, Harvard School of Public Health), Winter 1980, pp. 2–4.
P117 Bucknam McPeek, John P. Gilbert, and Frederick Mosteller. “The clini- cian’s responsibility for helping to improve the treatment of tomorrow’s patients.” New England Journal of Medicine, 302 (1980), pp. 630–631.
P118 Clark C. Abt and Frederick Mosteller. “Presentation and acceptance of the Lazarsfeld Prize to Frederick Mosteller.” In Problems in American So- cial Policy Research, edited by Clark C. Abt. Cambridge, MA: Abt Books, 1980. pp. 273–276.
P119 Frederick Mosteller, John P. Gilbert, and Bucknam McPeek. “Reporting standards and research strategies for controlled trials: Agenda for the ed- itor. Controlled Clinical Trials, 1 (1980), pp. 37–58.
P120 Frederick Mosteller. “Clinical trials methodology: Hypotheses, designs, and criteria for success or failure.” In Medical Advances through Clinical Trials: A Symposium on Design and Ethics of Human Experimentation, May 31 and June 1, 1979. Edmonton, Alberta, Canada, edited by John B. Dossetor, 1980. pp. 12–26.
P121 Stephen Lagakos and Frederick Mosteller. “A case study of statistics in the regulatory process: The FD&C Red No. 40 experiments.” Journal of the National Cancer Institute, 66 (1981), pp. 197–212.
P122 Frederick Mosteller. “Innovation and evaluation.” Science, 211 (27 Febru- ary 1981), pp. 881–886. Presidential address, annual meeting of the American Association for the Advancement of Science in Toronto, Ontario, Canada, 6 January 1981. P123 Frederick Mosteller. “Leonard Jimmie Savage memorial service tribute.” Yale University, March 18, 1972. Published in The Writings of Leonard Jimmie Savage—A Memorial Selection, edited by a committee. Wash- ington, D.C.: The American Statistical Association and The Institute of Mathematical Statistics, 1981, pp. 25–28. Bibliography 33
P124 Arthur P. Dempster and Frederick Mosteller. “In memoriam: William Gemmell Cochran, 1909–1980.” The American Statistician, 35 (1981), p. 38.
P125 Frederick Mosteller. “Evaluation: Requirements for scientific proof.” Chap- ter 8 in Coping with the Biomedical Literature: A Primer for the Scientist and the Clinician, edited by Kenneth S. Warren. New York: Praeger, 1981. pp. 103–121.
P126 Frederick Mosteller, Andrew F. Siegel, Edward Trapido, and Cleo Youtz. “Eye fitting straight lines.” The American Statistician, 35 (1981), pp. 150–152.
P127 Frederick Mosteller. “Foreword.” Milbank Memorial Fund Quarterly/Health and Society, 59, No. 3 (1981), pp. 297–307. This introduces and discusses a special issue devoted to medical experimentation and social policy. P128 William Kruskal and Frederick Mosteller. “Ideas of representative sam- pling.” In New Directions for Methodology of Social and Behavioral Sci- ence: Problems with Language Imprecision, edited by Donald W. Fiske. San Francisco: Jossey-Bass, 1981. pp. 3–24.
P129 Thomas A. Louis, Frederick Mosteller, and Bucknam McPeek. “Timely topics in statistical methods for clinical trials.” Annual Review of Bio- physics and Bioengineering, 11 (1982), pp. 81–104.
P130 Bucknam McPeek, Cornelia McPeek, and Frederick Mosteller. “In memo- riam: John Parker Gilbert (1926–1980).” The American Statistician, 36 (1982), p. 37.
P131 Frederick Mosteller. “Foreword.” In Contributions to Statistics: William G. Cochran, compiled by Betty I.M. Cochran. New York: Wiley, 1982. pp. vii–xiii.
P132 Rebecca DerSimonian, L. Joseph Charette, Bucknam McPeek, and Fred- erick Mosteller. “Reporting on methods in clinical trials.” New England Journal of Medicine, 306 (1982), pp. 1332–1337.
P133 Frederick Mosteller and John W. Tukey. “Combination of results of stated precision: I. The optimistic case.” Utilitas Mathematica, 21A (1982), pp. 155–179.
P134 Arthur Dempster, Margaret Drolette, Myron Fiering, Nathan Keyfitz, David D. Rutstein, and Frederick Mosteller, Chairman. “William Gemmell 34 Bibliography
Cochran,” Memorial Minute adopted by the Faculty of Arts and Sciences, Harvard University, November 9, 1982. Harvard University Gazette,De- cember 3, 1982, p. 4.
P135 Frederick Mosteller. “The role of statistics in medical research.” Chapter 1inStatistics in Medical Research: Methods and Issues, with Applications in Cancer Research,editedbyValerieMik´e and Kenneth E. Stanley. New York: Wiley, 1983. pp. 3–20.
P136 J.L. Hodges, Jr., Frederick Mosteller, and Cleo Youtz. “Allocating loss of precision in the sample mean to wrong weights and redundancy in sampling with replacement from a finite population.” In A Festschrift for Erich L. Lehmann in Honor of His Sixty-Fifth Birthday,editedbyPeterJ. Bickel, Kjell A. Doksum, and J.L. Hodges, Jr. Belmont, CA: Wadsworth, 1983. pp. 239–248.
P137 Frederick Mosteller. “The changing role of the statistician: Getting into the mainstream with policy decisions.” Section Newsletter, Statistics, American Public Health Association, February 1983. Talk given at luncheon in honor of Joel Kleinman, the Spiegel- man Award winner, American Public Health Association Annual Meeting, Montreal, Quebec, Canada, November 16, 1982. P138 Frederick Mosteller. Comment on “Ethical Guidelines for Statistical Prac- tice: Historical Perspective, Report of the ASA Ad Hoc Committee on Pro- fessional Ethics, and Discussion.” The American Statistician, 37 (1983), pp. 10–11.
P139 Frederick Mosteller, John P. Gilbert, and Bucknam McPeek. “Controver- sies in design and analysis of clinical trials.” In Clinical Trials: Issues and Approaches, edited by Stanley H. Shapiro and Thomas A. Louis. New York: Marcel Dekker, 1983. pp. 13–64.
P140 John D. Emerson, Bucknam McPeek, and Frederick Mosteller. “Reporting clinical trials in general surgical journals.” Surgery, 95 (1984), pp. 572– 579.
P141 Frederick Mosteller. “Biography of John W. Tukey.” In The Collected Works of John W. Tukey, Volume I, Time Series: 1949–1964, edited by David R. Brillinger. Belmont, CA: Wadsworth Advanced Books and Soft- ware, 1984. pp. xv–xvii.
P142 Frederick Mosteller and John W. Tukey. “Combination of results of stated precision: II. A more realistic case.” In W.G. Cochran’s Impact on Statis- tics, edited by Poduri S.R.S. Rao and Joseph Sedransk. New York: Wiley, Bibliography 35
1984. pp. 223–252.
P143 Frederick Mosteller. “Selection of papers by quality of design, analysis, and reporting.” Chapter 6 in Selectivity in Information Systems: Survival of the Fittest, edited by Kenneth S. Warren. New York: Praeger, 1985. pp. 98–116.
P144 Thomas A. Louis, Harvey V. Fineberg, and Frederick Mosteller. “Findings for public health from meta-analysis.” Annual Review of Public Health, 6 (1985), pp. 1–20.
P145 Frederick Mosteller and Milton C. Weinstein. “Toward evaluating the cost- effectiveness of medical and social experiments.” Chapter 6 in Social Ex- perimentation, edited by Jerry A. Hausman and David A. Wise. Chicago: University of Chicago Press, 1985. pp. 221–249.
P146 Frederick Mosteller and David C. Hoaglin. “Description or prediction?” 1984 Proceedings of the Business and Economic Statistics Section.Wash- ington, D.C.: American Statistical Association, 1985. pp. 11–15.
P147 Judy O’Young, Bucknam McPeek, and Frederick Mosteller. “The clin- ician’s role in developing measures for quality of life in cardiovascular disease.” Quality of Life and Cardiovascular Care, 1 (1985), pp. 290–296.
P148 B. McPeek, M. Gasko, and F. Mosteller. “Measuring outcome from anes- thesia and operation.” Theoretical Surgery, 1 (1986), pp. 2–9.
P149 Augustine Kong, G. Octo Barnett, Frederick Mosteller, and Cleo Youtz. “How medical professionals evaluate expressions of probability.” New Eng- land Journal of Medicine, 315 (1986), pp. 740–744. Response to comments: New England Journal of Medicine, 316 (1987), p. 551. [Comments, pp. 549–551.] P150 Stephen W. Lagakos and Frederick Mosteller. “Assigned shares in compen- sation for radiation-related cancers.” Risk Analysis, 6 (1986), pp. 345–357. Response to comments, pp. 377–380. [Comments, pp. 363–375.] P151 M.F. McKneally, D.S. Mulder, A. Nachemson, F. Mosteller, and B. McPeek. “Facilitating scholarship: Creating the atmosphere, setting, and teamwork for research.” Chapter 5 in Principles and Practice of Research: Strategies for Surgical Investigators, edited by Hans Troidl, Walter O. Spitzer, Bucknam McPeek, David S. Mulder, and Martin F. McKneally. New York: Springer-Verlag, 1986. pp. 36–42. 36 Bibliography
P152 Frederick Mosteller. “A statistical study of the writing styles of the au- thors of The Federalist papers.” Proceedings of the American Philosophical Society, 131 (1987), pp. 132–140.
P153 Morris Hansen and Frederick Mosteller. “William Gemmell Cochran, July 15, 1909—March 29, 1980.” In Biographical Memoirs, 56. Washington, D.C.: National Academy Press, 1987. pp. 60–89.
P154 Kathryn Lasch, Alesia Maltz, Frederick Mosteller, and Tor Tosteson. “A protocol approach to assessing medical technologies.” International Jour- nal of Technology Assessment in Health Care, 3 (1987), pp. 103–122.
P155 Frederick Mosteller. “Implications of measures of quality of life for policy development.” Journal of Chronic Diseases, 40 (1987), pp. 645–650.
P156 Frederick Mosteller. “Assessing quality of institutional care.” American Journal of Public Health, 77 (1987), pp. 1155–1156.
P157 Frederick Mosteller. “Compensating for radiation-related cancers by prob- ability of causation or assigned shares.” Bulletin of the International Sta- tistical Institute, Proceedings of the 46th Session, Tokyo, 1987, LII,Book 4, pp. 571–577.
P158 W. H. Kruskal and F. Mosteller. “Representative sampling.” In Encyclo- pedia of Statistical Sciences, 8, edited by Samuel Kotz and Norman L. Johnson. New York: Wiley, 1988. pp. 77–81.
P159 John C. Bailar III and Frederick Mosteller. “Guidelines for statistical re- porting in articles for medical journals: Amplifications and explanations,” Annals of Internal Medicine, 108 (1988), pp. 266–273.
P160 Frederick Mosteller. “Broadening the scope of statistics and statistical ed- ucation.” The American Statistician, 42 (1988), pp. 93–99.
P161 “Frederick Mosteller and John W. Tukey: A conversation.” Moderated by Francis J. Anscombe. Statistical Science, 3 (1988), pp. 136–144.
P162 Graham A. Colditz, James N. Miller, and Frederick Mosteller. “The effect of study design on gain in evaluations of new treatments in medicine and surgery.” Drug Information Journal, 22 (1988), pp. 343–352.
P163 Graham A. Colditz, James N. Miller, and Frederick Mosteller. “Measur- ing gain in the evaluation of medical technology.” International Journal of Technology Assessment in Health Care, 4 (1988), pp. 637–642. Bibliography 37
P164 Nan Laird and Frederick Mosteller. Discussion of “Publication bias: A problem in interpreting medical data,” by Colin B. Begg and Jesse A. Berlin. Journal of the Royal Statistical Society, Series A, 151 (1988), p. 456.
P165 Frederick Mosteller. “Growth and advances in statistics.” Response to “Should mathematicians teach statistics?” by David S. Moore. College Mathematics Journal, 19 (1988), pp. 15–16.
P166 Frederick Mosteller. “‘The muddiest point in the lecture’ as a feedback device.” On Teaching and Learning: The Journal of the Harvard-Danforth Center, 3 (April 1989), pp. 10–21. Also in Medianen 1992 (newsletter of the Education Committee of the Swedish Statistical Association), pp. 1–12. P167 Frederick Mosteller and Elisabeth Burdick. “Current issues in health care technology assessment.” International Journal of Technology Assessment in Health Care, 5 (1989), pp. 123–136.
P168 The LORAN Commission. “The LORAN Commission: A summary re- port.” In Harvard Community Health Plan, 1988 Annual Report, pp. 3–6, 9–14, 17–22, 25–30. (Published in 1989.) Members of the Commission: David Banta, Robert Cushman, Douglas Fraser, Robert Freeman, Betty Friedan, Benjamin Ka- plan, Frederick Mosteller, David Nathan, Albert Rees, Hays Rock- well, Robert Sproull, Marshall Wolf, and John Paris. P169 Frederick Mosteller, John E. Ware, Jr., and Sol Levine. “Finale panel: Comments on the conference on advances in health status assessment.” Medical Care, 27, No. 3 Supplement (1989), pp. S282–S294.
P170 Graham A. Colditz, James N. Miller, and Frederick Mosteller. “How study design affects outcomes in comparisons of therapy. I: Medical.” Statistics in Medicine, 8 (1989), pp. 441–454.
P171 James N. Miller, Graham A. Colditz, and Frederick Mosteller. “How study design affects outcomes in comparisons of therapy. II: Surgical.” Statistics in Medicine, 8 (1989), pp. 455–466.
P172 Robert Timothy Reagan, Frederick Mosteller, and Cleo Youtz. “Quan- titative meanings of verbal probability expressions.” Journal of Applied Psychology, 74 (1989), pp. 433–442.
P173 Bucknam McPeek, Frederick Mosteller, and Martin McKneally. “Random- ized clinical trials in surgery.” International Journal of Technology Assess- 38 Bibliography
ment in Health Care, 5 (1989), pp. 317–332.
P174 Persi Diaconis and Frederick Mosteller. “Methods for studying coinci- dences.” Journal of the American Statistical Association, 84 (1989), pp. 853–861. 1987 R.A. Fisher Memorial Lecture.
P175 Frederick Mosteller and Cleo Youtz. “Quantifying probabilistic expres- sions” and “Rejoinder” to Comments. Statistical Science, 5 (1990), pp. 2–12, 32–34.
P176 Frederick Mosteller. “Improving research methodology: An overview.” Summary in Lee Secrest, Edward Perrin, and John Bunker, editors, Re- search Methodology: Strengthening Causal Interpretations of Nonexperi- mental Data, Agency for Health Care Policy and Research Conference Proceedings, U.S. Department of Health and Human Services, May 1990, pp. 221–230.
P177 Nan M. Laird and Frederick Mosteller. “Some statistical methods for com- bining experimental results.” International Journal of Technology Assess- ment in Health Care, 6 (1990), pp. 5–30.
P178 Frederick Mosteller. “Summing up.” Chapter 16 in The Future of Meta– Analysis, Kenneth W. Wachter and Miron L. Straf, editors. Proceedings of a workshop convened by the Committee on National Statistics, National Research Council, October 1986, Hedgesville, West Virginia. New York: Russell Sage Foundation, 1990. pp. 185–190.
P179 J.D. Emerson, E. Burdick, D.C. Hoaglin, F. Mosteller, and T.C. Chalmers. “An empirical study of the possible relation of treatment differences to quality scores in controlled randomized clinical trials.” Controlled Clini- cal Trials, 11 (1990), pp. 339–352.
P180 Frederick Mosteller and fellow members of National Cancer Institute Ex- tramural Committee to Assess Measures of Progress Against Cancer. “Special report: Measurement of progress against cancer.” Journal of the National Cancer Institute, 82, No. 10 (1990), pp. 825–835.
P181 H. Troidl et al., editors. Principles and Practice of Research: Strategies for Surgical Investigators, second edition. New York: Springer-Verlag, 1991. • Chapter I5. A.S. Wechsler, M.F. McKneally, C.M. Balch, F. Mosteller, B. McPeek, and D.S. Mulder. “Strengthening the research environ- ment.” pp. 31–40. • Chapter II11. R.E. Pollack, C.M. Balch, J. Roth, B. McPeek, and F. Mosteller. “Formulating an initial research plan.” pp. 88–90. Bibliography 39
• Chapter II14. B. McPeek, F. Mosteller, M.F. McKneally, and E.A.M. Neugebauer. “Experimental methods: Clinical trials.” pp. 114–125.
P182 In Elisabeth Burdick, Marie A. McPherson, and Frederick Mosteller, guest editors. “Special section: The contribution of medical registries to tech- nology assessment.” International Journal of Technology Assessment in Health Care, 7, No. 2 (Spring 1991). • Alexia Antczak-Bouckoms, Elisabeth Burdick, Sidney Klawansky, and Frederick Mosteller. “Introduction: Using medical registries and data sets for technology assessment.” pp. 123–128. • Grace Wyshak, Elisabeth Burdick, and Frederick Mosteller. “Technol- ogy assessment in the Connecticut Tumor Registry.” pp. 129–133. • Sidney Klawansky, Alexia Antczak-Bouckoms, Judith Barr, Elisabeth Burdick, Mark S. Roberts, Grace Wyshak, and Frederick Mosteller. “Using medical registries and data sets for technology assessment: An overview of seven case studies.” pp. 194–199. P183 Frederick Mosteller. “The contributions of firms: A fresh movement in medicine.” Medical Care, 29, No. 7, Supplement (July 1991), pp. JS3–JS4.
P184 Frederick Mosteller. “Comment” on Jessica Utts, “Replication and meta- analysis in parapsychology.” Statistical Science, 6, No. 4 (1991), pp. 395– 396.
P185 Frederick Mosteller. “From the President of the ISI.” ISI Newsletter, 16, No. 1 (January 1992), p. 2.
P186 J.D. Bentkover, R.H. Sheshinski, J. Hedley-Whyte, C.A. Warfield, and F. Mosteller. “Lower back pain: Laminectomies, spinal fusions, demograph- ics, and socioeconomics.” International Journal of Technology Assessment in Health Care, 8, No. 2 (1992), pp. 309–317.
P187 Elliott M. Antman, Joseph Lau, Bruce Kupelnick, Frederick Mosteller, and Thomas C. Chalmers. “A comparison of results of meta-analyses of randomized control trials and recommendations of clinical experts: treat- ments for myocardial infarction.” Journal of the American Medical Asso- ciation, 268, No. 2 (July 8, 1992), pp. 240–248.
P188 Robert D. Morris, Anne-Marie Audet, Italo F. Angelillo, Thomas C. Chalmers, and Frederick Mosteller. “Chlorination, chlorination by-prod- ucts, and cancer: A meta-analysis.” American Journal of Public Health, 82, No. 7 (July 1992), pp. 955–963.
P189 Joseph Lau, Elliott M. Antman, Jeanette Jimenez-Silva, Bruce Kupelnick, Frederick Mosteller, and Thomas C. Chalmers. “Cumulative meta-analysis 40 Bibliography
of therapeutic trials for myocardial infarction.” New England Journal of Medicine, 327, No. 4 (July 23, 1992), pp. 248–254.
P190 Frederick Mosteller and Thomas C. Chalmers. “Some progress and prob- lems in meta-analysis of clinical trials.” Statistical Science, 7, No. 2 (1992), pp. 227–236.
P191 Frederick Mosteller. “Message from the President.” ISI Newsletter, 16, No. 3 (October 1992), p. 2.
P192 Harris Cooper, Kristina M. DeNeve, and Frederick Mosteller. “Predict- ing professional sports game outcomes from intermediate game scores.” Chance, 5, No. 3–4 (1992), pp. 18–22.
P193 Harris Cooper and Frederick Mosteller. “The fourth quarter of the Super Bowl.” National Academy of Sciences, Office of News and Public Infor- mation, January 22, 1993.
P194 Frederick Mosteller. “Message from the President.” ISI Newsletter, 17, No. 1 (January 1993), p. 2.
P195 Wafaie W. Fawzi, Thomas C. Chalmers, M. Guillermo Herrera, and Frederick Mosteller. “Vitamin A supplementation and child mortality: A meta-analysis.” Journal of the American Medical Association, 269, No. 7 (February 17, 1993), pp. 898–903.
P196 Miriam E. Adams, Alexia Antczak-Bouckoms, Howard S. Frazier, Joseph Lau, Thomas C. Chalmers, and Frederick Mosteller. “Assessing the effec- tiveness of ambulatory cardiac monitoring for specific clinical indications, introduction.” International Journal of Technology Assessment in Health Care, 9, No. 1 (1993), pp. 97–101.
P197 Frederick Mosteller and Cleo Youtz. “Professional golf scores are Poisson on the final tournament days.” 1992 Proceedings of the Section on Statis- tics in Sports. Alexandria, VA: American Statistical Association (1992), pp. 39–51.
P198 Debra R. Milamed, Carol A. Warfield, John Hedley-Whyte, and Frederick Mosteller. “Laminectomy and the treatment of lower-back pain in Mas- sachussetts.” International Journal of Technology Assessment in Health Care, 9, No. 3 (1993), pp. 426–439.
P199 Frederick Mosteller and Cleo Youtz. “Where eagles fly.” Chance, 6, No. 2 (1993), pp. 37–42. Bibliography 41
P200 Frederick Mosteller. “Message from the President.” ISI Newsletter, 17, No. 2 (May 1993), p. 2.
P201 Jane C. Ballantyne, Daniel B. Carr, Thomas C. Chalmers, Keith B. G. Dear, Italo F. Angelillo, and Frederick Mosteller. “Postoperative patient- controlled analgesia: Meta-analyses of initial randomized control trials.” Journal of Clinical Anesthesiology, 5 (May/June 1993), pp. 182–193.
P202 Dennis L. Kasper, Ramzi S. Cotran, Frederick Mosteller, Peter V. Tish- ler, Stephen Zinner, Sir Kenneth Stuart, Frank E. Speizer, Michelene Matthews–Roth, James O. Taylor, Thomas H. Weller, Jeffrey Parson- net, and Richard Platt. Edward H. Kass memorial minute adopted by the Faculty of Medicine, Harvard University, May 26, 1993. Harvard Gazette (July 9, 1993), pp. 11–12.
P203 Frederick Mosteller and Howard S. Frazier. “Improving the contributions of technology assessment to the health care system of the U.S.A.” Journal of the Italian Statistical Society, 1, No. 3 (1992), pp. 297–310.
P204 Frederick Mosteller. “The prospect of data-based medicine in the light of ECPC.” The Milbank Quarterly, 71, No. 3 (1993), pp. 523–532.
P205 Judith A. Hall, Linda Tickle-Degnen, Robert Rosenthal, and Frederick Mosteller. “Hypotheses and problems in research synthesis.” Chapter 2 in The Handbook of Research Synthesis, Harris Cooper and Larry V. Hedges, editors. New York: Russell Sage Foundation, 1994. pp. 17–28.
P206 Sidney Klawansky, Catherine Berkey, Nirav Shah, Frederick Mosteller, and Thomas C. Chalmers. “Survival from localized breast cancer: Vari- ability across trials and registries.” International Journal of Technology Assessment in Health Care, 9, No. 4 (1993), pp. 539–553.
P207 Graham A. Colditz, Timothy F. Brewer, Catherine S. Berkey, Mary E. Wilson, Elisabeth Burdick, Harvey V. Fineberg, and Frederick Mosteller. “Efficacy of BCG vaccine in the prevention of tuberculosis: meta-analysis of the published literature.” Journal of the American Medical Association, 271, No. 9 (March 2, 1994), pp. 698–702.
P208 Les Irwig, Anna N. A. Tosteson, Constantine Gatsonis, Joseph Lau, Gra- ham Colditz, Thomas C. Chalmers, and Frederick Mosteller. “Guide- lines for meta-analyses evaluating diagnostic tests.” Annals of Internal Medicine, 120, No. 8 (April 15, 1994), pp. 667–676.
P209 John P. Bunker, Howard S. Frazier, and Frederick Mosteller. “Improving health: Measuring effects of medical care.” The Milbank Quarterly, 72, 42 Bibliography
No. 2 (1994), pp. 225–258.
P210 Frederick Mosteller. “Introduction.” In “The Moriguti report on the role of statisticians: A discussion.” International Statistical Institute Occasional Paper Series #4, Voorburg, Netherlands, 1994. p. 1.
P211 John D. Emerson, David C. Hoaglin, and Frederick Mosteller. “A modi- fied random-effect procedure for combining risk difference in sets of 2 × 2 tables from clinical trials.” Journal of the Italian Statistical Society, 2, No. 3 (1993), pp. 269–290.
P212 C.S. Berkey, D.C. Hoaglin, F. Mosteller, and G.A. Colditz. “A random- effects regression model for meta-analysis.” Statistics in Medicine, 14 (1995), pp. 395–411.
P213 Vic Hasselblad, Frederick Mosteller, Benjamin Littenberg, Thomas C. Chalmers, Maria G.M. Hunink, Judith A. Turner, Sally C. Morton, Paula Diehr, John B. Wong, and Neil R. Powe. “A survey of current problems in meta-analysis: Discussion from the Agency for Health Care Policy and Research Inter-PORT Work Group on Literature Review/Meta-Analysis.” Medical Care, 33, No. 2 (1995), pp. 202–220.
P214 C.S. Berkey, A. Antczak-Bouckoms, D.C. Hoaglin, F. Mosteller, and B.L. Pihlstrom. “Multiple-outcomes meta-analysis of treatments for periodon- tal disease.” Journal of Dental Research, 74, No. 4 (April 1995), pp. 1030– 1039.
P215 Graham A. Colditz, Catherine S. Berkey, Frederick Mosteller, Timothy F. Brewer, Mary E. Wilson, Elisabeth Burdick, and Harvey V. Fineberg. “The efficacy of Bacillus Calmette-Gu´erin vaccination of newborns and infants in the prevention of tuberculosis: Meta-analyses of the published literature.” Pediatrics, 96, No. 1 (July 1995), pp. 29–35.
P216 Graham A. Colditz, Elisabeth Burdick, and Frederick Mosteller. “Hetero- geneity in meta-analysis of data from epidemiologic studies: A commen- tary.” American Journal of Epidemiology, 142, No. 4 (August 15, 1995), pp. 371–382.
P217 Elon Eisenberg, Catherine S. Berkey, Daniel B. Carr, Frederick Mosteller, and Thomas C. Chalmers. “Efficacy and safety of nonsteroidal anti- inflammatory drugs for cancer pain: A meta-analysis.” Journal of Clinical Oncology, 12, No. 12 (December 1994), pp. 2756–2765.
P218 Frederick Mosteller. “The Tennessee study of class size in the early school grades.” The Future of Children, 5, No. 2 (Summer/Fall 1995), pp. 113– Bibliography 43
127.
P219 John P. Bunker, Howard S. Frazier, and Frederick Mosteller. “The role of medical care in determining health: Creating an inventory of benefits.” Chapter 10 in Society and Health,BenjaminC.AmickIII,SolLevine, Alvin R. Tarlov, and Diana Chapman Walsh, editors. New York: Oxford University Press, 1995. pp. 305–341.
P220 Frederick Mosteller. “Expansion of notes of the vaccine group.” Clinical Research and Regulatory Affairs, Special Issue on the First National Meet- ing on Research Synthesis: Applications to Drug Regulatory Policy and Health Care Policy, 13, No. 1 (1996), pp. 51–56.
P221 Frederick Mosteller. “Editorial: The promise of risk-based allocation trials in assessing new treatments.” American Journal of Public Health, 86, No. 5 (May 1996), pp. 622–623.
P222 Frederick Mosteller and Graham A. Colditz. “Understanding research syn- thesis (meta-analysis).” Annual Review of Public Health, 17 (1996), pp. 1–23.
P223 Frederick Mosteller and fellow members of the National Institutes of Health Technology Assessment Panel on Integration of Behavioral and Relaxation Approaches into the Treatment of Chronic Pain and Insomnia. “Integration of behavioral and relaxation approaches into the treatment of chronic pain and insomnia.” Journal of the American Medical Associ- ation, 276, No. 4 (July 24/31, 1996), pp. 313–318.
P224 John D. Emerson, David C. Hoaglin, and Frederick Mosteller. “Simple robust procedures for combining risk differences in sets of 2 × 2 tables.” Statistics in Medicine, 15, No. 14 (1996), pp. 1465–1488.
P225 Frederick Mosteller. “Discussant comments on ‘So what? The implica- tions of new analytic methods for designing NCES surveys,’ by Robert F. Boruch and George Terhanian.” From Data to Information. New Di- rections for the National Center for Education Statistics, National Center for Education Statistics Conference Proceedings, U.S. Department of Ed- ucation, NCES 96-901, August 1996, pp. 4-116–4-118.
P226 Catherine S. Berkey, Frederick Mosteller, Joseph Lau, and Elliott M. Antman. “Uncertainty of the time of first significance in random effects cumulative meta-analysis.” Controlled Clinical Trials, 17, No. 5 (1996), pp. 357–371. 44 Bibliography
P227 Frederick Mosteller, Richard J. Light, and Jason A. Sachs. “Sustained in- quiry in education. Lessons from skill grouping and class size.” Harvard Educational Review, 66, No. 4 (Winter 1996), pp. 797–842.
P228 Bernard Rosner, Frederick Mosteller, and Cleo Youtz. “Modeling pitcher performance and the distribution of runs per inning in Major League Base- ball.” The American Statistician, 50, No. 4 (1996), pp. 352–360.
P229 Jane C. Ballantyne, Daniel B. Carr, Catherine S. Berkey, Thomas C. Chalmers, and Frederick Mosteller. “Comparative efficacy of epidural, subarachnoid, and intracerebroventricular opioids in patients with pain due to cancer.” Regional Anesthesia, 21, No. 6 (1996), pp. 542–556.
P230 Edward J. Miech, Bill Nave, and Frederick Mosteller. “On CALL: A review of computer-assisted language learning in U.S. colleges and universities.” Educational Media and Technology Yearbook 1997, Robert Maribe Branch and Barbara B. Minor, editors. Englewood, CO: Libraries Unlimited, Inc., 22 (1997), pp. 61–84. The complete report of this study with five appendices is available in ERIC as ED 394 525. P231 Lincoln E. Moses and Frederick Mosteller. “Experimentation: Just do it!” Chapter 12 in Statistics and Public Policy (Festschrift in honor of I. Richard Savage), Bruce D. Spencer, editor. New York: Oxford Univer- sity Press, 1997. pp. 212–232.
P232 Frederick Mosteller. “Project report: The Tennessee study of class size in the early school grades.” Bulletin of the American Academy of Arts and Sciences, L, No. 7 (1997), pp. 14–25.
P233 Frederick Mosteller. “Lessons from sports statistics.” 1996 Proceedings of the Section on Statistics in Sports. Alexandria, VA: American Statistical Association, 1996. pp. 1–8.
P234 Frederick Mosteller. “Smaller classes do make a difference in the early grades.” The Harvard Education Letter (July/August 1997), pp. 5–7.
P235 Frederick Mosteller. “Lessons from sports statistics.” The American Statis- tician, 51, No. 4 (1997), pp. 305–310. Reprinted in Anthology of Statistics in Sports (ASA-SAIM Series on Statistics and Applied Probability, Vol. 16), edited by Jim Al- bert, Jay Bennett, and James J. Cochran. Philadelphia: Society for Industrial and Applied Mathematics, 2005. pp. 245–250. Bibliography 45
P236 In H. Troidl, M.F. McKneally, D.S. Mulder, A.S. Wechsler, B. McPeek, and W.O. Spitzer, editors. Surgical Research: Basic Principles and Clini- cal Practice, third edition. New York: Springer-Verlag, 1998. • Chapter 26. M.F. McKneally, B. McPeek, F. Mosteller, and E.A.M. Neugebauer. “Clinical trials.” pp. 197–209. • Chapter 36. F. Mosteller and B. Rosner. “Introductory biostatistics texts: Selected annotated bibliography.” pp. 321–327. • Chapter 40. R.E. Pollock, C.M. Balch, J. Roth, B. McPeek, and F. Mosteller. “Formulating an initial research plan.” pp. 363–365. P237 John D. Emerson and Frederick Mosteller. “Interactive multimedia in col- lege teaching. Part I: A ten-year review of reviews.” In Educational Media and Technology Yearbook 1998, Robert Maribe Branch and Mary Ann Fitzgerald, editors. Englewood, CO: Libraries Unlimited, Inc. 23 (1998), pp. 43–58.
P238 John D. Emerson and Frederick Mosteller. “Interactive multimedia in col- lege teaching. Part II: Lessons from research in the sciences.” In Educa- tional Media and Technology Yearbook 1998, Robert Maribe Branch and Mary Ann Fitzgerald, editors. Englewood, CO: Libraries Unlimited, Inc. 23 (1998), pp. 59–75.
P239 Lincoln E. Moses and Frederick Mosteller. “Frontiers of biostatistics.” En- cyclopedia of Biostatistics, Peter Armitage and Theodore Colton, editors. Chichester, England: Wiley, 1998. pp. 1590–1597.
P240 Frederick Mosteller. “The Tennessee study of class size in the early school grades.” In The Practice of Data Analysis: Essays in Honor of John W. Tukey, D.R. Brillinger, L.T. Fernholz, and S. Morgenthaler, editors. Princeton, NJ: Princeton University Press, 1997. pp. 261–277.
P241 J.C. Ballantyne, D.B. Carr, S. DeFerranti, T. Suarez, J. Lau, T.C. Chalmers, I.F. Angelillo, and F. Mosteller. “The comparative effects of postoperative analgesic therapies on pulmonary outcome: cumulative meta-analysis of randomized controlled trials.” Anesthesia & Analgesia, 86, No. 3 (1998), pp. 598–612.
P242 C.S. Berkey, D.C. Hoaglin, A. Antczak-Bouckoms, F. Mosteller, and G.A. Colditz. “Meta-analysis of multiple outcomes by regression with random effects.” Statistics in Medicine, 17 (1998), pp. 2537–2550.
P243 Frederick Mosteller, Richard J. Light, and Jason A. Sachs. “Sustained in- quiry in education: Lessons from skill grouping and class size.” In Cool Thinking on Hot Topics: A Research Guide for Educators. Cambridge, 46 Bibliography
MA: Harvard Educational Review, 1998. pp. 67–113.
P244 Graham A. Colditz, Catherine S. Berkey, and Frederick Mosteller. “Meta- analysis of randomized trials.” Chapter 6 in Charles H. Hennekens, Julie E. Buring, JoAnn E. Manson, and Paul M. Ridker, editors. Clinical Trials in Cardiovascular Disease: A Companion to Braunwald’s Heart Disease. Philadelphia: W.B. Saunders Company, 1999. pp. 43–51.
P245 Frederick Mosteller. “The case for smaller classes and for evaluating what works in the schoolroom.” Harvard Magazine, 101, No. 5 (1999), pp. 34– 35.
P246 Frederick Mosteller. “How does class size relate to achievement in schools?” Chapter 6 in Earning and Learning, Susan E. Mayer and Paul E. Peter- son, editors. Washington, D.C.: Brookings Institute Press and Russell Sage Foundation, 1999. pp. 117–129.
P247 Jennifer Taylor and Frederick Mosteller. “Runaways: A review of the lit- erature.” Boston, MA: American Academy of Arts and Sciences, 1999.
P248 John D. Emerson and Frederick Mosteller. “Development programs for college faculty: Preparing for the twenty-first century.” In R.M. Branch and M.A. Fitzgerald, editors. Educational Media and Technology Year- book, Englewood, CO: Libraries Unlimited, Inc., 25, 2000. pp. 26–42.
P249 John D. Emerson, Frederick Mosteller, and Cleo Youtz. “Students can help improve college teaching: A review for an agenda for the statistics profession.” In C.R. Rao and G. Szekely, editors. Statistics for the 21st Century. New York: Marcel Dekker, 2000. pp. 145–172.
P250 Bill Nave, Edward J. Miech, and Frederick Mosteller. “A lapse in stan- dards: Linking standards-based reform with student achievement.” Phi Delta Kappan, 82, No. 2 (2000), pp. 128–133.
P251 Bill Nave, Edward J. Miech, and Frederick Mosteller. “The role of field trials in evaluating school practices: A rare design.” In Daniel L. Stuffle- beam, George F. Madaus, Thomas Kellaghan, editors. Evaluation Models: Viewpoints on Educational and Human Services Evaluation, second edi- tion. Boston, MA: Kluwer Academic Publishers, 2000. pp. 145–161.
P252 Edward J. Miech, Bill Nave, and Frederick Mosteller. “Large-scale profes- sional development for schoolteachers: Cases from Pittsburgh, New York City, and the National School Reform Faculty.” Chapter 7 in Richard J. Light, editor. Evaluation Findings That Surprise, New Directions in Eval- Bibliography 47
uation, No. 90. San Francisco: Jossey-Bass, 2001. pp. 83–99.
P253 Lincoln E. Moses, Frederick Mosteller, and John H. Buehler. “Compar- ing results of large clinical trials to those of meta-analyses.” Statistics in Medicine, 21, No. 6 (2002), pp. 793–800.
P254 John D. Emerson, Lisa Boes, and Frederick Mosteller. “Critical thinking in college students: Critical issues in empirical research.” In Educational Media and Technology Yearbook, M.A. Fitzgerald, M. Orey, and R.M. Branch, editors. Englewood, CO: Libraries Unlimited, Inc., 27, 2002. pp. 52–71.
P255 Mosteller, F., Nave, B., and Miech, E.J. “Why we need a structured ab- stract in education research.” Educational Researcher, 33, no. 1 (2004), 29–34.
P256 John D. Emerson and Frederick Mosteller. “Cooperative learning in schools and colleges: I. Teamwork in college mathematics.” Educational Media and Technology Yearbook, M. Orey, M.A. Fitzgerald, and R.M. Branch, editors. Westport, CT: Libraries Unlimited, Inc., 29, 2004. pp. 132–147.
P257 John D. Emerson and Frederick Mosteller. “Cooperative learning in schools and colleges: II. A review of reviews.” Educational Media and Technology Yearbook, M. Orey, M.A. Fitzgerald, and R.M. Branch, edi- tors. Westport, CT: Libraries Unlimited, Inc., 29, 2004. pp. 148–162.
P258 Edward J. Miech, Bill Nave, and Frederick Mosteller. “The 20,000 article problem: How a structured abstract could help practitioners sort out ed- ucational research.” Phi Delta Kappan, 86, No. 5 (2005), pp. 396–400.
P259 Frederick Mosteller. “Biographical Memoirs: John W. Tukey.” Proceedings of the American Philosophical Society, 149, No. 4 (2005), pp. 626–630.
MISCELLANEOUS
M1–M6 Articles on magic.
M1 Frederick Mosteller. “Encore.” Part I. In My Best,editedbyJ.G.Thomp- son, Jr. Philadelphia: Charles H. Hopkins & Co., 1945. pp. 103–104. Related to M3. M2–M6 Appeared in The Phoenix, a two–sheet biweekly publication. Is- sues 1 through 73 were edited by Walter Gibson and Bruce Elliott; later 48 Bibliography
issues were edited by Bruce Elliott. All issues were published by Louis Tannen.
Issues have now been bound into sets of 50 (1–50, 50–100, etc.) and dis- tributed by Louis Tannen Inc., New York, NY.
M2 “Bravo.” Issue 49, December 3, 1943, pp. 200–201.
M3 “Encore.” Issue 58, April 14, 1944, pp. 236–237.
M4 “The Back Room.” Issue 87, p. 355.
M5 “Ambiguous.” Issue 117, January 10, 1947, p. 470.
M6 “Thesis.” Issue 118, January 24, 1947, p. 475.
M7 and M8 are in “Letters from Readers.” In The Bridge World, edited by Ely Culbertson et al.
M7 Frederick Mosteller. “Anti Zankl.” 17, No. 8, May 1946, pp. 2–3.
M8 Frederick Mosteller. “Eight points.” 17, No. 12, September 1946, p. 2.
M9 Frederick Mosteller. Contribution to Standard Sampling Procedures. Ma- terial Inspection Service, U.S.N. Administration Manual, 1945.
M10 Frederick Mosteller and John W. Tukey. Binomial probability graph paper (No. 32,298). Norwood, MA: Codex Book Company, 1946.
M11 Frederick Mosteller. “School finances questioned.” Letter in Carnegie Alumnus, 33, No. 1, September 1947, pp. 1–2.
M12 Frederick Mosteller. Editor of “Questions and Answers.” In The American Statistician, October 1947–December 1951. Questions 1–30.
M13 Frederick Mosteller. “Can you be a successful gambler?” TV Guide,May 13–19, 1961, pp. 6–7.
M14 Frederick Mosteller. “Textbook supplements.” In Gottfried E. Noether, Guide to Probability and Statistics, especially prepared for Continental Classroom. Reading, MA: Addison-Wesley, 1961. pp. 43–51.
M15 Frederick Mosteller. “Foreword.” In Probability and Statistics—An Intro- duction Through Experiments, by Edmund C. Berkeley. New York: Science Bibliography 49
Materials Center, 1961. pp. v–vii.
M16 Frederick Mosteller, contributor. Goals for School Mathematics. The Re- port of the Cambridge Conference on School Mathematics. Educational Services Incorporated. Boston: Houghton Mifflin, 1963.
M17 Frederick Mosteller. “Foreword.” In Math and After Math, by Robert Hooke and Douglas Shaffer. New York: Walker and Company, 1965. pp. ix–xii.
M18 Frederick Mosteller. “Age of achievement.” Letter in The Wall Street Jour- nal, July 6, 1967.
M19 Frederick Mosteller. “The President Reports: Three Major ASA Actions.” The American Statistician, 21 (4), 1967, pp. 2–4.
M20 Coeditor of Reports of the National Assessment of Educational Progress. A Project of the Education Commission of the States. Report 2. Citizenship: National Results. November 1970. Wash- ington, D.C.: Superintendent of Documents, U.S. Government Printing Office.
Report 3. 1969–1970 Writing: National Results. November 1970. Washington, D.C.: Superintendent of Documents, U.S. Govern- ment Printing Office.
Report 2–1. Citizenship: National Results. November 1970. Ed- ucation Commission of the States, Denver, Colorado and Ann Ar- bor, Michigan.
Report 4. 1969–1970 Science: Group Results for Sex, Region, and Size of Community. April 1971. Washington, D.C.: Superin- tendent of Documents, U.S. Government Printing Office.
Report 5. 1969–1970 Writing: Group Results for Sex, Region, and Size of Community (Preliminary Report). April 1971. Educa- tion Commission of the States, Denver, Colorado and Ann Arbor, Michigan.
Report 7. 1969–1970 Science: Group and Balanced Group Re- sults for Color, Parental Education, Size and Type of Community and Balanced Group Results for Region of the Country, Sex. De- cember 1971. Education Commission of the States, Denver, Col- orado. 50 Bibliography
Report 8. National Results—Writing Mechanics. February 1972. Washington, D.C.: Superintendent of Documents, U.S. Govern- ment Printing Office.
Report 9. Citizenship: 1969–1970 Assessment: Group Results for Parental Education, Color, Size and Type of Community. May 1972. Education Commission of the States, Denver, Colorado.
Report 02-GIY. Reading and Literature: General Information Yearbook. May 1972. Education Commission of the States, Denver, Colorado. M21 Frederick Mosteller. “Introduction.” In Structural and Statistical Problems for a Class of Stochastic Processes, The First Samuel Stanley Wilks Lec- ture at Princeton University, March 17, 1970, by Harald Cram´er. Prince- ton, NJ: Princeton University Press, 1971. pp. 1–2.
M22 Frederick Mosteller. A page on subject matter at secondary level. In De- velopments in Mathematical Education, Proceedings of the Second Inter- national Congress on Mathematical Education,editedbyA.G.Howson. Cambridge: The University Press, 1973. p. 27.
M23 Frederick Mosteller. “Foreword.” In Social Statistics in Use, by Philip M. Hauser. New York: Russell Sage Foundation, 1975. pp. vii–viii.
M24 Frederick Mosteller. “Report of the President.” In “Officers’ Reports, 1975.” The Institute of Mathematical Statistics Bulletin, 4 (1975), pp. 207–208.
M25 Frederick Mosteller. Research Resources Evaluation Panel, coordinated by Bolt, Beranek, and Newman. Assuring the Resources for Biomedical Re- search: an Evaluation of the Scientific Mission of the Division of Research Resources, National Institutes of Health. October 1976.
M26 Frederick Mosteller. “Swine Flu: Quantifying the ‘Possibility.’ ” Letter in Science, 192 (25 June 1976), pp. 1286 and 1288.
M27 Frederick Mosteller. “Who Said It?” Letter in Royal Statistical Society News & Notes, 5, No. 2, October 1978, p. 5.
M28 Frederick Mosteller. Testimony by Frederick Mosteller. In “Kenneth Pre- witt, Frederick Mosteller, and Herbert A. Simon testify at National Sci- ence Foundation Hearings.” Social Science Research Council Items, 34 (March 1980), pp. 4–5. All testimonies pp. 1–7. Bibliography 51
M29 Frederick Mosteller. “Regulation of social research.” Editorial in Science, 208 (13 June 1980), p. 1219.
M30 Frederick Mosteller. “The next 100 years of Science.” In “Science Centen- nial 3 July 1980 to 4 July 1980.” Centennial Issue of Science, edited by Philip H. Abelson and Ruth Kulstad. 209 (4 July 1980), pp. 21–23.
M31 Frederick Mosteller. “Social programs.” Transaction/Social Science and Modern Society, 17, No. 6 (September/October 1980), pp. 10–12.
M32 Frederick Mosteller. “Taking science out of social science.” Editorial in Science, 212 (17 April 1981), p. 291.
M33 Frederick Mosteller. “Improving the precision of clinical trials.” Editorial in American Journal of Public Health, 72 (May 1982), p. 430.
M34 Frederick Mosteller. “The imperfect science of victim compensation.” Washington, D.C.: The Washington Times, June 4, 1985. p. 12A.
M35 Frederick Mosteller. Abstract of talk on “Assigned Shares: Probability of radiation as a cause of cancer.” Final Report, ASA Conference on Ra- diation and Health, Coolfont V. Washington, D.C.: American Statistical Association, 1985. pp. 21–22.
M36 In Data: A Collection of Problems from Many Fields for the Student and Research Worker, edited by D.F. Andrews and A.M. Herzberg. New York: Springer-Verlag, 1985. • S.W. Lagakos and F. Mosteller. “Time to death and type of death in mice receiving various doses of Red Dye No. 40.” pp. 239–243. • F. Mosteller and D.L. Wallace. “Disputed authorship: The Federalist Papers.” pp. 423–425. M37 Frederick Mosteller. “Foreword.” In New Developments in Statistics for Psychology and the Social Sciences,editedbyA.D.Lovie,Londonand New York: The British Psychological Society and Methuen, 1986. pp. vii– ix.
M38 Barbara J. Culliton and Frederick Mosteller. “How big is ‘big,’ how rare is ‘rare?’ Inquiring minds want to know.” The Newsletter of the National Association of Science Writers, 34, No. 3 (September 1986), p. 13.
M39 Frederick Mosteller. “Foreword.” In News & Numbers: A Guide to Report- ing Statistical Claims and Controversies in Health and Related Fields,by Victor Cohn. Ames, IA: Iowa State University Press, 1989. pp. ix–x. 52 Bibliography
M40 Frederick Mosteller. “A word of welcome.” Ad Hoc, 49th Session of the ISI, August 25, 1993, pp. 1–2.
M41 Frederick Mosteller, Contributor to The Milbank Memorial Fund at 90. New York: Milbank Memorial Fund, 1995. pp. 73–74
REVIEWS R1 Guide for Quality Control and Control Chart Method of Analyzing Data. American War Standards, Z1.1–1941 and Z1.2–1941. New York: Ameri- can Standards Association, 1941, and Control Chart Method of Control- ling Quality During Production. American War Standards, Z1.3-1942. New York: American Standards Association, 1942.
Frederick Mosteller. Journal of the American Statistical Association, 40 (1945), pp. 379–380.
R2 Ledyard R. Tucker. “Maximum validity of a test with equivalent items.” Psychometrika, 11 (1946), pp. 1–13.
F. Mosteller. Mathematical Reviews, 7 (1946), pp. 463–464.
R3 Frederick E. Croxton and Dudley J. Cowden. “Tables to facilitate com- putation of sampling limits of s, and fiducial limits of sigma.” Industrial Quality Control, 3 (July 1946), pp. 18–21.
Frederick Mosteller. Mathematical Tables and Other Aids to Computation, II, No. 18, April 1947. National Research Council. p. 258.
R4 Hans Zeisel (Introduction by Paul F. Lazarsfeld). Say It with Figures.New York: Harper and Brothers, 1947.
Frederick Mosteller. Public Opinion Quarterly, 11 (Fall 1947), pp. 468– 469.
R5 Quinn McNemar. “Opinion-attitude methodology.” Psychological Bul- letin, 43, No. 4 (July 1946), pp. 289–374. Washington, D.C.: American Psychological Association.
Frederick Mosteller. Journal of the American Statistical Association, 42 (1947), pp. 192–195.
R6 Paul G. Hoel. Introduction to Mathematical Statistics. New York: Wiley, 1947. Bibliography 53
Frederick Mosteller. The Journal of Business of the University of Chicago, 20 (1947), pp. 176–177.
R7 George W. Snedecor. Statistical Methods. Ames, IA: The Iowa State Col- lege Press, 1946.
Frederick Mosteller. Annals of Mathematical Statistics, 19 (1948), pp. 124–126.
R8 Abraham Wald. Sequential Analysis. New York: Wiley, 1947.
Frederick Mosteller. Journal of Applied Mechanics, 15 (1948), pp. 89–90.
R9 Palmer O. Johnson. Statistical Methods in Research. New York: Prentice– Hall, 1949.
Frederick Mosteller. Journal of the American Statistical Association, 44 (1949), pp. 570–572.
R10 Norbert Wiener. Cybernetics, or Control and Communication in the An- imal and the Machine. New York: Wiley, 1948.
Frederick Mosteller. Journal of Abnormal and Social Psychology, 44 (1949), pp. 558–560.
R11 N. Rashevsky. Mathematical Theory of Human Relations: An Approach to a Mathematical Biology of Social Phenomena. Mathematical Biophysics Monograph Series No. 2. Bloomington, IN: Principia Press, 1948.
Frederick Mosteller. Journal of the American Statistical Association, 44 (1949), pp. 150–155.
R12 S.S. Wilks. Elementary Statistical Analysis. Princeton, NJ: Princeton Uni- versity Press, 1948.
Frederick Mosteller. Psychometrika, 15 (1950), pp. 73–76.
R13 Frank Yates. Sampling Methods for Censuses and Surveys. London: Charles Griffin and Company, 1949.
Frederick Mosteller. The Review of Economics and Statistics, 32 (1950), pp. 267–268.
R14 W.E. Deming. Some Theory of Sampling. New York: Wiley, 1950. 54 Bibliography
Frederick Mosteller. Psychological Bulletin, 48 (1951), pp. 454–455.
R15 Gamma Globulin in the Prophylaxis of Poliomyelitis: An evaluation of the efficacy of gamma globulin in the prophylaxis of paralytic poliomyelitis as used in the United States 1953. Public Health Monograph No. 20. Report of the National Advisory Committee for the Evaluation of Gamma Globu- lin in the Prophylaxis of Poliomyelitis, Public Heatlh Publication No. 358, U.S. Department of Health, Education, and Welfare. Washington, D.C.: Superintendent of Documents, U.S. Government Printing Office, 1954.
Frederick Mosteller. Journal of the American Statistical Association, 49 (1954), pp. 926–927.
R16 Paul F. Lazarsfeld, editor. Mathematical Thinking in the Social Sciences. Glencoe, IL: The Free Press, 1954.
Frederick Mosteller. American Anthropologist, 58 (1956), pp. 736–739.
R17 John Cohen and Mark Hansel. Risk and Gambling: The Study of Subjec- tive Probability. London: Longmans, Green, and Co., 1956.
Frederick Mosteller. Econometrica, 27 (1959), pp. 505–506.
R18 Herbert A. Simon. Models of Man: Social and Rational. Mathematical Es- says on Rational Human Behavior in a Social Setting. New York: Wiley, 1957.
Frederick Mosteller. American Sociological Review, 24 (1959), pp. 409– 413. Contains some original data illustrating the changing values of a parameter of a stochastic model—the probability of a new word— as the number of words in the text so far increases. R19 Raoul Naroll. Data Quality Control—A New Research Technique. Prole- gomena to a Cross–Cultural Study of Culture Stress. New York: The Free Press, 1962.
Frederick Mosteller and E.A. Hammel. Journal of the American Statistical Association, 58 (1963), pp. 835–836.
R20 Herbert Solomon, editor. Studies in Item Analysis and Prediction. Stan- ford Mathematical Studies in the Social Sciences, VI. Stanford, CA: Stan- ford University Press, 1961. Bibliography 55
Frederick Mosteller. Journal of the American Statistical Association, 58 (1963), pp. 1180–1181.
R21 L. R˚ade, editor. The Teaching of Probability and Statistics. Stockholm: Almqvist & Wiksell, 1970. Proceedings of the first CSMP International Conference co-sponsored by Southern Illinois University and Central Mid- western Regional Educational Laboratory.
F. Mosteller. Review of the International Statistical Institute, 39, No. 3 (1971), pp. 407–408.
R22 Frederick Mosteller, Gale Mosteller, and Keith A. Soper. “Knowledge be- yond achievement. A seventies perspective on school effects—a review symposium on The Enduring Effects of Education,byHerbertHyman, Charles Wright, and John Reed.” School Review, 84 (1976), pp. 265–283.
R23 Anthony C. Atkinson and Stephen E. Fienberg, editors. A Celebration of Statistics (The ISI Centenary Volume). New York: Springer-Verlag, 1985.
Frederick Mosteller. Journal of the American Statistical Association, 81 (1986), pp. 1118–1119.
R24 Hans Zeisel. Say it with Figures, Sixth Edition. New York: Harper & Row, 1985.
Frederick Mosteller. Public Opinion Quarterly, 52 (1988), pp. 274–275.
R25 W.S. Peters. Counting for Something: Statistical Principles and Person- alities. New York: Springer-Verlag, 1987.
Frederick Mosteller. Metrika, 36 (1989), pp. 61–62.
R26 A. Hawkins, editor. Training Teachers to Teach Statistics, Proceedings of the International Statistical Institute Round Table Conference, Budapest, Hungary, 23–27 July 1988. Voorburg, The Netherlands: International Sta- tistical Institute, 1990.
Frederick Mosteller. Short Book Reviews, International Statistical Insti- tute, 11, No. 1 (April 1991), pp. 2–3. Reprinted from The Annals of Mathematical Statistics (1946), 17, pp. 13–23
1. Unbiased Estimates for Certain Binomial Sampling Problems with Applications
M.A. Girshick, Frederick Mosteller, and L.J. Savage
U.S. Department of Agriculture; Statistical Research Group, Princeton University; and Statistical Research Group, Columbia University
1. Introduction. The purpose of this paper is to present some theorems with applications concerning unbiased estimation of the parameter p (frac- tion defective) for samples drawn from a binomial distribution. The estimate constructed is applicable to samples whose items are drawn and classified one at a time until the number of defectives i, and the number of nondefectives j, simultaneously agree with one of a set of preassigned number pairs. When this agreement takes place, the sampling operation ceases and an unbiased estimate of the proportion p of defectives in the population may be made. Some examples of this kind of sampling are ordinary single sampling in which n items are observed and classified as defective or nondefective; curtailed sin- gle sampling where it is desired to cease sampling as soon as the decision regarding the lot being inspected can be made, that is as soon as the number of defectives or nondefectives attain one of a fixed pair of preassigned values; double, multiple, and sequential sampling. In the cases of double and multiple sampling the subsamples may be curtailed when a decision is reached, while for sequential sampling the process may be truncated, i.e. an upper bound may be set on the amount of sampling to be done. In section 3 expressions are given for the unique unbiased estimates of p for single, curtailed single, curtailed double, and sequential sampling. One or two of the illustrative examples of section 3 may be of interest because their rather bizarre results suggest that some estimate other than an unbiased estimate may be preferable; but the discussion of estimates other than unbiased ones is outside the scope of this paper. This paper was originally written by Mosteller and Savage. A communication from M.A. Girshick revealed that he had independently discovered for the sequential probability ratio test the estimatep ˆ(α) given here and demonstrated its uniqueness. For purposes of publication it seemed appropriate to present the results in a single paper. 58 M.A. Girshick, Frederick Mosteller, and L.J. Savage
2. The estimate of pˆ. For the purposes of the present paper the word point will refer only to points in the xy-plane with nonnegative integral coor- dinates. We shall need the following nomenclature. A region R is a set of points containing (0, 0). The point (x2,y2)isimmediately beyond (x1,y1)ifeither x2 = x1 +1, y2 = y1 or x2 = x1, y2 = y1 +1.A path in R from the point α0 to the point αn is a finite sequence of points α0,α1, ··· ,αn such that αi(i>0) is immediately beyond αi−1 and αjR with the possible exception of αn.A boundary point, that is, an element of the boundary B of R,isapointnot in R which is the last point αn of a path from the origin. Accessible points are the points in R which can be reached by paths from the origin, while inaccessible points are the points which cannot be reached by any path from the origin. All points are thus divided into three mutually exclusive categories: accessible, inaccessible, and boundary points. The index of a point is the sum of its coordinates, and the index of a region is the least upper bound of the indices of its accessible points. A finite region is a region for which the indices of the accessible points are less than some number n. In particular a region containing only a finite number of points is finite. Paths may be thought of as arising by a random process such that a path reaching αi =(x, y),αiR, will be extended to αi+1 =(x, y +1)with − probability p or to αi+1 =(x+1,y) with probability q =1 p. We exclude p = 0, 1 unless these values are specifically mentioned. When a path is extended to a boundary point of R the process ceases. It is clear from the definitions that for a finite region R, paths from the origin cannot include more points than n +2wheren is the index of the region. This means that a path from the origin cannot escape from a finite region and that the probability that it strikes some boundary point is unity. It is clear that each path from the origin to a boundary point or an accessible point has probability pyqx,ifthe point has coordinates (x, y). We will need the following statements which are immediate consequences of the discussion above: A. The probability of a boundary point or an accessible point being included in a path from the origin is P (α)=k(α)pyqx, where k(α) is the number of paths from the origin to the point. We shall call P (α) the probability of the point. B. For a finite region P (α)=1, i.e. the sum of the probabilities of the αB boundary points is unity. Any region for which P (α) = 1 will be called a closed region. αB Of course, all finite regions are closed; but it is convenient to have a condi- tion such as that supplied by the following theorem guaranteeing the closure of some infinite regions as well. 1 Unbiased Estimates 59
1 Theorem 1. A√ sufficient condition that a region R be closed is that lim infn→∞ A(n)/ n =0, where A(n) is the number of accessible points of index n. Proof. We consider the ascending sequence of finite regions Rn, each consisting of the points of R whose indices are less than n. The boundary Bn of Rn can be written as the set theoretic union Kn An,whereKn is Bn B, and An are the accessible points of R of index n.IfαBn and Pn(α) is the probability of α with respect to Rn, it is easily seen that for αKn,Pn(α)= P (α). Since every point of B is ultimately contained in the ascending sequence Kn, P (α) = lim P (α) = lim Pn(α) ≤ 1, n→∞ n→∞ αB αKn αKn the inequality being a consequence of statement B. But Pn(α) is mono- αAn tonically decreasing because Pn(α) is monotonically increasing with n αKn while Pn(α) = 1, from statement B. αBn If we can show lim Pn(α) = 0 under the condition of the theorem, n→∞ αAn y n−y the proof is complete.√ For any point αAn,Pn(α)=√kn(α)p q which for fixed p is O(1/ n). The sum over An is O(A(n√)/ n) and therefore since the hypothesis of the theorem implies that A(n)/ n attains arbitrarily small values for arbitrarily large values of n, the sum in question decreases mono- tonically to zero. Corollary. If the number of accessible points of R of index n is bounded, the region is closed. That the condition given in Theorem 1 is not a necessary condition may be seen by examining the region R consisting of all points except points of the form (2x +1, 2y + 1) and (3, 0) and (0, 3). Theorem 2. If R is closed and R contains S, S is closed. Proof. The proof is essentially similar to that of Theorem 1. Any reasonable estimate of p will be a function defined on the boundary points, because the boundary points constitute, so to speak, a sufficient statis- tic for p. That is, the probability of any path from (0, 0) given the boundary point α at which it terminates is independent of p, and is in fact 1/k(α). We shall construct an unbiased estimate of p for closed regions R,thatisa 2 functionp ˆ(α),αB, such that αB pˆ(α)P (α)=p (absolutely convergent). Construction. Let k∗(α) be the number of paths in R from the point (0, 1) to the boundary point α,andletpˆ(α)=k∗(α)/k(α). We remark that the definitions imply k∗((0, 1)) = 1, when (0,1) is a boundary point. 1If it is desired to admit p =0, 1, the existence of boundary points (x, 0) or (0,y) respectively must be postulated. 2Even if such a sum were p for a region which was not closed, we would not call the estimate an unbiased estimate. 60 M.A. Girshick, Frederick Mosteller, and L.J. Savage
Theorem 3. For any closed region R pˆ(α) is an unbiased estimate of p. Proof: k∗(α) pˆ(α)P (α)= k(α)pyqx k(α) αB αB = k∗(α)pyqx. αB
If (0, 1) is a boundary point, then k∗((0, 1)) = 1 and k∗(α)=0,α=(0 , 1), in which case the sum in question consists of the single term p. If (0, 1) is not a boundary point, consider the region R obtained by deleting (0, 1) from R, and k (α), the number of paths in R from the origin to the boundary point α of R. k∗(α)=k(α) − k (α) k∗(α)pyqx = k(α)pyqx − k (α)pyqx αB αB αB =1− k (α)pyqx. αB
Now R is closed (Theorem 2); except for (0, 1) every boundary point of R is easily seen to be a boundary point of R;andk (α) vanishes except for the boundary points of R . Therefore p + k (α)pyqx =1, αB and the proof is complete. It is clear from the construction that 0 ≤ pˆ(α) ≤ 1; this is rather satisfying, since an estimate of p outside of these bounds would be received with some misgivings. Theorem 3 may be generalized to yield unbiased estimates of linear com- binations of functions of the form ptqu provided the points (u, t)arenot inaccessible points. We need only let the point (u, t) play the role of (0, 1). Even though the point (u, t) is inaccessible it may be possible to represent ptqu as a polynomial, none of whose terms correspond to inaccessible points. It is clear from Theorem 1 thatp ˆ(α) is an unbiased estimate of p for the usual sequential binomial tests, but the computation may be quite heavy. It should be noted that the coordinate system used here differs slightly from the coordinate system customarily used in sequential analysis. The custom is to let the x coordinate represent the number of items inspected, whereas we use it to represent the number of nondefectives; this is the only difference between the coordinates. We understand that in applications the customary procedure seems preferable, but we find the present coordinates more convenient for the purposes of this article. 1 Unbiased Estimates 61
In generalp ˆ is not the only unbiased estimate of p. A necessary condition for uniqueness is that the region be simple,thatisthatallthepointsbetween any two accessible points on the line x + y = n be accessible points. In other words no accessible points of index n shall be separated on the line x + y = n by inaccessible points or boundary points. Theorem 4. A necessary condition that the estimate pˆ be the unique un- biased estimate for the closed region R is that R be simple. Proof. For a region that is not simple we shall construct a function m(α) not identically zero, such that m(α)P (α)=0. (1) αB
Butp ˆ(α)+m(α) will be an unbiased estimate of p different fromp ˆ. Suppose we have a closed region R which is not simple. We consider the lowest index n where the accessible points are separated. There will be at least one uninterrupted sequence of points between some pair of accessible points that are not accessible points. It is easy to see that all the points of this uninterrupted sequence are boundary points of R. Let this sequence be the points αi =(x0 − i, y0 + i),i =0, 1, ··· ,t,x0 + y0 = n. To begin the j construction of m(α)letm(αj)=(−1) /k(α), 0 ≤ j ≤ t. The coordinates of the point α above the top point of the sequence are (x0 − t, y0 + t + 1), and the number of paths from α to any point on the boundary is l (α), where if α is a boundary point the number of paths l (α ) = 1; similarly α =(x0 +1,y0)andl (α) is the number of paths from α to the boundary point α with the same convention if α is a boundary point. To complete the construction of m(α), let m(α)=−[l (α)+(−1)tl (α)]/k(α) for boundary points not members of the sequence under consideration. Before proceeding to check equation (1), we show that − l (α)pyqx = py0 qx0+1 ; l (α)pyqx = py0+t+1qx0 t. (2) αB αB Because of symmetry we need only carry out the demonstration for the first sum. If α is a boundary point l (α ) = 1, and for all other points αl (α)=0, and the sum is the single term py0 qx0+1.Ifα is not a boundary point consider the region obtained by deleting α from R and the corresponding k (α), the number of paths from (0,0) to the boundary points of the new closed region R . Every boundary of R except α is a boundary point of R. Let us extend the definition of k (α) to the whole boundary of R by defining k (α)=0for α not in the boundary B of R . Then it is easy to see that
k(α)=k (α )l (α)+k (α).
Now 62 M.A. Girshick, Frederick Mosteller, and L.J. Savage 1= k(α)pyqx αB = k (α ) l (α)pyqx + k (α)pyqx αB αB = k (α ) l (α)pyqx +1− k (α )py0 qx0+1 αB establishing equation (2). We now check that m(α) satisfies equation (1):