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John W. Tukey’s contributions to multiple comparisons. (English) Zbl 1029.01010

In 1953 John W. Tukey (1915-2000) accomplished a mimeograph paper “The problem of multiple comparisons”, which did much to shape the philosophy, mathematical development and practical applications of multiple inference. No other work or writer has had comparable influence. The proper treatment of multiplicity, which should take into account the “trade-off between extracting belief from data and payment of error” (Tukey 1991) is regarded by many as a critical component in a disciplined program of scientific research. Confidence intervals are identified with indication and significance tests with sanctification and action. He resumed intensive activity in this field during ihe last decade of his life. He introduced the notions of higher criticism and of Wholly significant difference and he was concerned with two forces: efficiency and robustness of Tukey’s conjecture on unbalanced pairwise comparison problem. L. D. Brown (1979) proved the conjecture for the cases 3, 4, and 5. A. J. Hayter (1984) was able to prove the 31-years-old conjecture for all \(k\).
Tukey’s long running debate with David B. Duncan (1916) was more philosophical. His disagreement with Ronald A. Fisher (1890-1962) on the use of least significant difference was more methodological and concerned with the extraction of maximum useful information from the data at hand for a given simultaneous error-rate. His continuing argument with Henry Scheffé (1907-1977) on the use of \(F\)-projections had both philosophical and methodological components. Tukey was convinced that Statistics is a part of science and not a branch of mathematics only. 54 references.
Reviewer: H.Grimm (Jena)

MSC:

01A60 History of mathematics in the 20th century
01A70 Biographies, obituaries, personalia, bibliographies
62-03 History of statistics
62F03 Parametric hypothesis testing
01-02 Research exposition (monographs, survey articles) pertaining to history and biography
62M15 Inference from stochastic processes and spectral analysis
65T50 Numerical methods for discrete and fast Fourier transforms

Biographic References:

Tukey, J. W.
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[1] ALMOND, R. G., LEWIS, C., TUKEY, J. W. and YAN, D. (2000). Display s for comparing a given state to many others. Amer. Statist. 54 89-93.
[2] ANDREWS, D. F., BICKEL, P. J., HAMPEL, F. R., HUBER, P. J., ROGERS, W. H. and TUKEY, J. W.
[3] . Robust Estimates of Location: Survey and Advances. Princeton Univ. Press. · Zbl 0254.62001
[4] BASFORD, K. E. and TUKEY, J. W. (1997). Graphical profiles as an aid to understanding plant breeding experiments. J. Statist. Plann. Inference 57 93-107. · Zbl 0900.62028 · doi:10.1016/S0378-3758(96)00038-9
[5] BASFORD, K. E. and TUKEY, J. W. (1998). Graphical Analy sis of Multiresponse Data. Chapman and Hall, London.
[6] BEGUN, J. and GABRIEL, K. R. (1981). Closure of the Newman-Keuls multiple comparisons procedure. J. Amer. Statist. Assoc. 76 241-245. · doi:10.2307/2287817
[7] BENJAMINI, Y. and HOCHBERG, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. J. Roy. Statist. Soc. Ser. B 57 289-300. JSTOR: · Zbl 0809.62014
[8] BENJAMINI, Y., HOCHBERG, Y. and KLING, Y. (1993). False discovery rate control in pairwise comparisons. Working Paper 93-2, Dept. Statistics and O.R., Tel Aviv Univ.
[9] BENJAMINI, Y., HOCHBERG, Y. and STARK, P. B. (1998). Confidence intervals with more power to determine the sign: Two ends constrain the means. J. Amer. Statist. Assoc. 93 309-317. JSTOR: · Zbl 1068.62509 · doi:10.2307/2669627
[10] BERRY, D. A. and HOCHBERG, Y. (1999). Bayesian perspectives on multiple comparisons. J. Statist. Plann. Inference 82 215-227. · Zbl 1063.62527 · doi:10.1016/S0378-3758(99)00044-0
[11] BRAUN, H. I. and TUKEY, J. W. (1983). Multiple comparisons through orderly partitions: The maximum subrange procedure. In Principals of Modern Psy chological Measurement: A Festschrift for Frederic M. Lord (H. Wainer and S. Messick, eds.) 55-65. Erlbaum, Hillsdale, NJ.
[12] BRILLINGER, D. R., FERNHOLZ, L. T. and MORGENTHALER, S., eds. (1997). The Practice of Data Analy sis. Princeton Univ. Press. · Zbl 0907.62003
[13] BROWN, L. D. (1979). A proof that the Tukey-Kramer multiple comparison procedure for differences between treatment means is level for 3, 4, or 5 treatments. Technical report, Dept. Mathematics, Cornell Univ.
[14] BROWN, L. D. (1984). A note on the Tukey-Kramer procedure for pairwise comparisons of correlated means. In Design of Experiments: Ranking and Selection (Essay s in Honor of Robert E. Beckhofer) (T. J. Santner and A. C. Tamhane, eds.) 1-6. Dekker, New York. · Zbl 0559.62059
[15] BROWN, L. D., CASELLA, G. and HWANG, J. T. G. (1995). Optimal confidence sets, bioequivalence, and the limaçon of Pascal. J. Amer. Statist. Assoc. 90 880-889. JSTOR: · Zbl 0842.62089 · doi:10.2307/2291322
[16] CURRAN-EVERETT, D. (2001). Multiple comparisons: Philosophies and illustrations. Amer. J. physiology: Regulatory Integrative and Comparative physiology 279 R1-R8.
[17] DONOHO, D. L. and JOHNSTONE, I. M. (1994). Ideal spatial adaptation by wavelet shrinkage. Biometrika 81 425-455. JSTOR: · Zbl 0815.62019 · doi:10.1093/biomet/81.3.425
[18] DUNN, O. J. (1974). On multiple tests and confidence intervals. Comm. Statist. 3 101-103. · Zbl 0283.62025 · doi:10.1080/03610927408827108
[19] DUNNETT, C. W. (1980). Pairwise multiple comparisons in the homogeneous variance, unequal sample size case. J. Amer. Statist. Assoc. 75 789-795.
[20] HAy TER, A. J. (1984). A proof of the conjecture that the Tukey-Kramer multiple comparisons procedure is conservative. Ann. Statist. 12 61-75. · Zbl 0545.62047 · doi:10.1214/aos/1176346392
[21] HAy TER, A. J. (1989). Pairwise comparisons of generally correlated means. J. Amer. Statist. Assoc. 84 208-213. JSTOR: · Zbl 0684.62047 · doi:10.2307/2289865
[22] HAy TER, A. and HSU, J. (1994). On the relationship between stepwise decision procedures and confidence sets. J. Amer. Statist. Assoc. 89 128-136. · Zbl 0800.62182 · doi:10.2307/2291208
[23] HOAGLIN, D. C., MOSTELLER, F. and TUKEY, J. W., eds. (1991). Fundamentals of Exploratory Analy sis of Variance. Wiley, New York.
[24] HOCHBERG, Y. (1974). The distribution of the range in general balanced models. Amer. Statist. 28 137-138. JSTOR: · Zbl 0319.62031 · doi:10.2307/2683339
[25] HOCHBERG, Y. (1975). An extension of the t-method to general unbalanced models of fixed effects. J. Roy. Statist. Soc. Ser. B 37 426-433. JSTOR: · Zbl 0352.62074
[26] HOCHBERG, Y. and TAMHANE, A. C. (1987). Multiple Comparison Procedures. Wiley, New York. · Zbl 0731.62125
[27] HSU, J. C. (1996). Multiple Comparisons: Theory and Methods. Chapman and Hall, London. · Zbl 0898.62090
[28] JONES, L. V., LEWIS, C. and TUKEY, J. W. (2001). Hy pothesis tests, multiplicity of. In International Ency clopedia of the Social and Behavioral Sciences (N. J. Smelser and P. B. Baltes, eds.) 7127-7133. Elsevier, London.
[29] JONES, L. V. and TUKEY, J. W. (2000). A sensible formulation of the significance test. Psy chological Methods 5 411-414.
[30] KESELMAN, H. J., CRIBBIE, R. and HOLLAND, B. (1999). The pairwise multiple comparison multiplicity problem: An alternative approach to family wise and comparisonwise ty pe I error control. Psy chological Methods 4 58-69.
[31] KRAMER, C. Y. (1956). Extension of multiple range tests to group means with unequal numbers of replications. Biometrics 12 307-310. JSTOR: · doi:10.2307/3001469
[32] KURTZ, T. E. (1956). An extension of a multiple comparisons procedure. Ph.D. dissertation, Princeton Univ.
[33] LEWIS, C. and TUKEY, J. W. (2001). Improved multiple comparison procedures for controlling the false discovery rate. Unpublished manuscript.
[34] MARCUS, R., PERITZ, E. and GABRIEL, K. R. (1976). On closed testing procedures with special reference to ordered analysis of variance. Biometrika 63 655-660. JSTOR: · Zbl 0353.62037 · doi:10.1093/biomet/63.3.655
[35] MAY, J. M. (1952). Extended and corrected tables of the upper percentage points of the ”Studentized” range. Biometrika 39 192-193. JSTOR: · Zbl 0046.35803
[36] MCGILL, R., TUKEY, J. W. and LARSEN, W. O. (1978). Variations on box plots. Amer. Statist. 32 12-16.
[37] MILLER, R. G. (1966). Simultaneous Statistical Inference. McGraw-Hill, New York. · Zbl 0192.25702
[38] OTTENBACHER, K. J. (1998). Quantitative evaluation of multiplicity in epidimiology and public health research. Amer. J. Epidimiology 147 615-619.
[39] RAMSEY, P. H. (1981). Power of univariate pairwise multiple comparison procedures. Psy chological Bulletin 90 352-366.
[40] SEO, T., MANO, S. and FUJIKOSHI, Y. (1994). A generalized Tukey conjecture for multiple comparisons among mean vectors. J. Amer. Statist. Assoc. 89 676-679. JSTOR: · Zbl 0801.62060 · doi:10.2307/2290870
[41] SHAFFER, J. P. (1995). Multiple hy pothesis testing: A review. Annual Review of Psy chology 46 561-584.
[42] SPJØTVOLL, E. and STOLINE, M. R. (1973). An extension of the T -method of multiple comparison to include the cases with unequal sample sizes. J. Amer. Statist. Assoc. 68 975-978. · Zbl 0271.62101 · doi:10.2307/2284534
[43] TUKEY, J. W. (1951). Reminder sheets for ”Discussion of paper on multiple comparisons by Henry Scheffé.” In The Collected Works of John W. Tukey VIII. Multiple Comparisons: 1948- 1983 469-475. Chapman and Hall, New York.
[44] TUKEY, J. W. (1953). The problem of multiple comparisons. Unpublished manuscript. In The Collected Works of John W. Tukey VIII. Multiple Comparisons: 1948-1983 1-300. Chapman and Hall, New York.
[45] TUKEY, J. W. (1960). A survey of sampling from contaminated distributions. In Contributions to Probability and Statistics: Essay s in Honor of Harold Hotelling (I. Olkin, S. G. Ghury e, W. Hoeffding, W. G. Madow and H. B. Mann, eds.) 448-485. Stanford Univ. Press. · Zbl 0201.52803
[46] TUKEY, J. W. (1977a). Some thoughts on clinical trials, especially problems of multiplicity. Science 198 679-684.
[47] TUKEY, J. W. (1977b). Higher criticism for individual significances in several tables or parts of tables. Internal working paper 89-9, Princeton Univ.
[48] TUKEY, J. W. (1991). The philosophy of multiple comparisons. Statist. Sci. 6 100-116.
[49] TUKEY, J. W. (1993a). Graphic comparisons of several linked aspects: Alternatives and suggested principles (with discussion). J. Comput. Graph. Statist. 2 1-49. JSTOR: · doi:10.2307/1390951
[50] TUKEY, J. W. (1993b). Where should multiple comparisons go next? In Multiple Comparisons, Selection, and Applications in Biometry (F. M. Hoppe, ed.) 187-207. Dekker, New York. · Zbl 0829.62069
[51] TUKEY, J. W. (1994). The Collected Works of John W. Tukey VIII. Multiple Comparisons: 1948- 1983. Chapman and Hall, New York. · Zbl 0807.01035
[52] TUKEY, J. W. (1995). Controlling the proportion of false discoveries for multiple comparisonFuture directions. In Perspectives on Statistics for Educational Research: Proceedings of a Workshop (V. S. Williams, L. V. Jones and I. Olkin, eds.). Technical Report 35, National Institute of Statistical Sciences, Research Triangle Park, NC.
[53] TUKEY, J. W., BLOOMFIELD, P., BRAUN, H. I. and MCNEILL, D. R. (1978). Advances in data analysis. Unpublished manuscript.
[54] TUKEY, J. W., CIMINERA, J. L. and HEy SE, J. F. (1985). Testing the statistical certainty of a response to increasing doses of a drug. Biometrics 41 295-301. · Zbl 0613.62131 · doi:10.2307/2530666
[55] WELSCH, R. E. (1977). Stepwise multiple comparison procedures. J. Amer. Statist. Assoc. 72 566- 575. JSTOR: · Zbl 0369.62081 · doi:10.2307/2286218
[56] WILKINSON, L. (1999). Statistical methods in psy chology journals-guidelines and explanations. American Psy chology 54 594-604.
[57] WILLIAMS, V. S. L., JONES, L. V. and TUKEY, J. W. (1994). Controlling error in multiple comparisons, with special attention to the National Assessment of Educational Progress. Technical Report 33, National Institute of Statistical Sciences, Research Triangle Park, NC.
[58] WILLIAMS, V. S. L., JONES, L. V. and TUKEY J. W. (1999). Controlling error in multiple comparisons, with examples from state-to-state differences in educational achievement. Journal of Educational and Behavioral Statistics 24 42-69.
[59] YEKUTIELI, D. (2001). Controlling the false discovery rate under dependency. Ph.D. dissertation, Dept. Statistics, Tel Aviv Univ. (in Hebrew). · Zbl 1041.62061
[60] PRINCETON, NEW JERSEY 08541 E-MAIL: hbraun@ets.org
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