SAMPLE SIZE DETERMINATION FOR MULTIPLE COMPARISONS WITH COMPONENTS OF A LINEAR FUNCTION OF MEAN VECTORS

REFERENCES

• Tukey , J. W. 1953 . “ The Problem of Multiple Comparisons ” . In Mimeographed monograph
   Google Scholar
• Hsu , J. C. 1984 . Constrained simultaneous confidence intervals for multiple comparisons with the best . Ann. Statist. , 12 : 1136–1144
   Google Scholar
• Dunnett , C. W. 1955 . A multiple comparison procedure for comparing several treatments with a control . J. Amer. Statist. Assoc. , 50 : 1096 – 1121 .
   Web of Science ®Google Scholar
• Hartley , H. O. 1950 . The use of range in analysis of variance . Biometrika , 37 : 271 – 280 .
   PubMed Web of Science ®Google Scholar
• Huynh , H. and Feldt , L. S. 1970 . Conditions under which mean square ratios in repeated measurements designs have exact F-distributions . J. Amer. Statist. Assoc. , 65 : 1582 – 1589 .
   Google Scholar
• Hochberg , Y. 1974 . The distribution of the range in general balanced models . Amer. Statist. , 28 : 137 – 138 .
   Web of Science ®Google Scholar
• Hochberg , Y. and Tamhane , A. C. 1987 . Multiple Comparison Procedures New York : John Wiley & Sons, Inc. .
   Google Scholar
• Hsu , J. C. 1996 . Multiple Comparisons: Theory and methods New York : Chapman & Hall, Inc. .
   Google Scholar
• Hsu , J. C. 1988 . Sample size computation for designing multiple comparison experiments . Comp. Statist. & Data Anal. , 7 : 79 – 91 .
   Web of Science ®Google Scholar
• Bhargava , R. P. and Srivastava , M. S. 1973 . On Tukey's confidence intervals for the contrasts in the means of the intraclass correlation model . J. Roy. Statist. Soc. Ser. B , 35 : 147 – 152 .
   Google Scholar
• Chow , Y. S. and Robbins , H. 1965 . On the asymptotic theory of fixed–width sequential confidence intervals for the mean . Ann. Math. Statist. , 36 : 457 – 462 .
   Google Scholar
• Nelson , B. L. and Matejcik , F. J. 1995 . Using common random numbers for indifference–zone selection and multiple comparisons in simulation . Manage. Sci. , 41 : 1935 – 1945 .
   Web of Science ®Google Scholar
• Stein , C. 1945 . A two–sample test for a linear hypothesis whose power is independent of the variance . Ann. Math. Statist. , 16 : 243 – 258 .
   Google Scholar
• Aoshima , M. and Mukhopadhyay , N. 1998 . Fixed–width simultaneous confidence intervals for multinormal means in several intraclass correlation models . J. Multiv. Anal. , 66 : 46 – 63 .
   Web of Science ®Google Scholar
• Bechhofer , R. E. 1954 . A single–sample multiple decision procedure for ranking means of normal populations with known variances . Ann. Math. Statist. , 25 : 16 – 39 .
   Google Scholar
• Takada , Y. and Aoshima , M. 1997 . Two-stage procedures for estimating a linear function of multinormal mean vectors, Seq . Anal. , 16 : 353 – 362 .
   Google Scholar
• Aoshima , M. 1998 . A two-stage procedure for fixed–size confidence region when covariance matrices have some structures . J. Japan Statist. Soc. , 28 : 59 – 67 .
   Google Scholar
• Hyakutake , H. 1999 . Selecting the component based on the difference of two multinormal means . Abstract of 67th Annual Meeting of Japan Statist. Soc. (Japanese) . 1999 . pp. 246 – 247 .
   Google Scholar
• Mukhopadhyay , N. and Duggan , W. T. 1997 . Can a two-stage procedure enjoy second–order properties? . Sankhya, Series A , 59 : 435 – 448 .
   Google Scholar
• Aoshima , M. and Takada , Y. 2000 . Second–order properties of a two-stage procedure for comparing several treatments with a control . J. J. Statist. Soc. , 30 : 27 – 41 .
   Google Scholar
• Aoshima , M. , Takada , Y. and Srivastava , M. S. in press . A two-stage procedure for estimating a linear function of kmultinormal mean vectors when covariance matrices are unknown . J. Statist. Plan. Inference ,
   Google Scholar
• Brown , L. D. 1984 . “ A note on the Tukey–Kramer procedure for pairwise comparisons of correlated means ” . In Design of Experiments: Ranking and Selection (Essays in Honor of Robert E. Bechhofer) Edited by: Santner , T. J. and Tamhane , A. C. 1 – 6 . New York : Marcel Dekker .
   Google Scholar
• Hayter , A. J. 1984 . A proof of the conjecture that the Tukey–Kramer multiple comparisons procedure is conservative . Ann. Statist. , 12 : 61 – 75 .
   Web of Science ®Google Scholar
• Hayter , A. J. 1989 . Pairwise comparisons of generally correlated means . J. Amer. Statist. Assoc. , 84 : 208 – 213 .
   Web of Science ®Google Scholar
• Mukhopadhyay , N. 1999 . Second–order properties of a two-stage fixed–size confidence region for the mean vector of a multivariate normal distribution . J. Multiv. Anal. , 68 : 250 – 263 .
   Web of Science ®Google Scholar
• Aoshima , M. 2000 . Second–order properties of improved two-stage procedure for a multivariate normal distribution . Commun. Statist.: Theory and Methods , 29 : 611 – 622 .
   Web of Science ®Google Scholar
• Aoshima , M. and Mukhopadhyay , N. 1999 . Second–order properties of a two-stage fixed–size confidence region when the covariance matrix has a structure . Commun. Statist.: Theory and Methods , 28 : 839 – 855 .
   Web of Science ®Google Scholar
• Nelson , B. L. 1993 . Robust multiple comparisons under common tandom numbers . ACM Trans. Model. Comp. Simu. , 3 : 225 – 243 .
   Google Scholar