메뉴 건너뛰기




Volumn 37, Issue 6 B, 2009, Pages 4184-4213

Decomposition tables for experiments I. A chain of randomizations

Author keywords

Analysis of variance; Balance; Decomposition table; Design of experiments; Efficiency factor; Multiphase experiments; Multitiered experiments; Orthogonal decomposition; Pseudofactor; Structure; Tier

Indexed keywords


EID: 73949092785     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/09-AOS717     Document Type: Article
Times cited : (13)

References (40)
  • 1
    • 0000945592 scopus 로고
    • A unified approach to design of experiments
    • MR0625801
    • BAILEY, R. A. (1981). A unified approach to design of experiments. J. Roy. Statist. Soc. Ser. A 144 214-223. MR0625801
    • (1981) J. Roy. Statist. Soc. Ser. A , vol.144 , pp. 214-223
    • BAILEY, R.A.1
  • 2
    • 25444510980 scopus 로고
    • Block structures for designed experiments
    • R. J. Wilson, ed, Shiva, Nantwich
    • BAILEY, R. A. (1982). Block structures for designed experiments. In Applications of Combinatorics (R. J. Wilson, ed.) 1-18. Shiva, Nantwich.
    • (1982) Applications of Combinatorics , pp. 1-18
    • BAILEY, R.A.1
  • 3
    • 0040557903 scopus 로고
    • Contribution to the discussion of "Analysis of variance models in orthogonal designs" by T. Tjur
    • MR0967202
    • BAILEY, R. A. (1984). Contribution to the discussion of "Analysis of variance models in orthogonal designs" by T. Tjur. Internat. Statist. Rev. 52 65-77. MR0967202
    • (1984) Internat. Statist. Rev , vol.52 , pp. 65-77
    • BAILEY, R.A.1
  • 4
    • 73949118328 scopus 로고    scopus 로고
    • BAILEY, R. A. (1989). Designs: mappings between structured sets. In Surveys in Combinatorics, 1989 (J. Siemons, ed.). Lond. Math. Soc. Lect. Note Ser. 141 22-51. Cambridge Univ. Press, Cambridge. MR1036750
    • BAILEY, R. A. (1989). Designs: mappings between structured sets. In Surveys in Combinatorics, 1989 (J. Siemons, ed.). Lond. Math. Soc. Lect. Note Ser. 141 22-51. Cambridge Univ. Press, Cambridge. MR1036750
  • 5
    • 73949085206 scopus 로고    scopus 로고
    • BAILEY, R. A. (1994). General balance: artificial theory or practical relevance? In Proceedings of the International Conference on Linear Statistical Inference LINSTAT '93 (T. Caliński and R. Kala, eds.) 171-184. Kluwer, Dordrecht. MR1333664
    • BAILEY, R. A. (1994). General balance: artificial theory or practical relevance? In Proceedings of the International Conference on Linear Statistical Inference LINSTAT '93 (T. Caliński and R. Kala, eds.) 171-184. Kluwer, Dordrecht. MR1333664
  • 6
    • 0002309888 scopus 로고    scopus 로고
    • Orthogonal partitions in designed experiments
    • MR1393974
    • BAILEY, R. A. (1996). Orthogonal partitions in designed experiments. Des. Codes Cryptogr. 8 45-77. MR1393974
    • (1996) Des. Codes Cryptogr , vol.8 , pp. 45-77
    • BAILEY, R.A.1
  • 7
    • 73949095846 scopus 로고    scopus 로고
    • BAILEY, R. A. (2004). Association Schemes: Designed Experiments, Algebra and Combinatorics. Cambridge Univ. Press, Cambridge. MR2047311
    • BAILEY, R. A. (2004). Association Schemes: Designed Experiments, Algebra and Combinatorics. Cambridge Univ. Press, Cambridge. MR2047311
  • 8
    • 73949127463 scopus 로고    scopus 로고
    • BAILEY, R. A. (2004). Principles of designed experiments in J. A. Nelder's papers. In Methods and Models in Statistics: In Honour of Professor John Nelder FRS (N. M. Adams, M. J. Crowder, D. J. Hand and D. A. Stephens, eds.) 171-194. Imperial College Press, London. MR2211790
    • BAILEY, R. A. (2004). Principles of designed experiments in J. A. Nelder's papers. In Methods and Models in Statistics: In Honour of Professor John Nelder FRS (N. M. Adams, M. J. Crowder, D. J. Hand and D. A. Stephens, eds.) 171-194. Imperial College Press, London. MR2211790
  • 9
    • 84926227962 scopus 로고    scopus 로고
    • BAILEY, R. A. (2008). Design of Comparative Experiments. Cambridge Univ. Press, Cambridge. MR2422352
    • BAILEY, R. A. (2008). Design of Comparative Experiments. Cambridge Univ. Press, Cambridge. MR2422352
  • 10
    • 73949161306 scopus 로고    scopus 로고
    • BIRKHOFF, G. and MACLANE, S. (1965). A Survey of Modern Algebra, 3rd ed. Macmillan, New York. MR0177992
    • BIRKHOFF, G. and MACLANE, S. (1965). A Survey of Modern Algebra, 3rd ed. Macmillan, New York. MR0177992
  • 11
    • 0020975099 scopus 로고
    • Analysis of variance tables based on experimental structure
    • BRIEN, C. J. (1983). Analysis of variance tables based on experimental structure. Biometrics 39 51-59.
    • (1983) Biometrics , vol.39 , pp. 51-59
    • BRIEN, C.J.1
  • 12
    • 0040163810 scopus 로고
    • A model comparison approach to linear models
    • MR1030789
    • BRIEN, C. J. (1989). A model comparison approach to linear models. Util. Math. 36 225-254. MR1030789
    • (1989) Util. Math , vol.36 , pp. 225-254
    • BRIEN, C.J.1
  • 13
    • 84963495603 scopus 로고
    • Adelaide, Adelaide, South Australia. Available at, accessed July 9, 2008
    • BRIEN, C. J. (1992). Factorial linear model analysis. Ph. D. thesis, Dept. Plant Science, Univ. Adelaide, Adelaide, South Australia. Available at http://thesis.library.adelaide.edu.au/adt-SUA/public/adt- SUA20010530.175833/index.html (accessed July 9, 2008).
    • (1992) Factorial linear model analysis. Ph. D. thesis, Dept. Plant Science, Univ
    • BRIEN, C.J.1
  • 15
    • 0039697018 scopus 로고    scopus 로고
    • Tiers, structure formulae and the analysis of complicated experiments
    • BRIEN, C. J. and PAYNE, R. W. (1999). Tiers, structure formulae and the analysis of complicated experiments. The Statistician 48 41-52.
    • (1999) The Statistician , vol.48 , pp. 41-52
    • BRIEN, C.J.1    PAYNE, R.W.2
  • 17
    • 73949138302 scopus 로고    scopus 로고
    • COX, D. R. (1958). Planning of Experiments. Wiley, New York. MR0095561
    • COX, D. R. (1958). Planning of Experiments. Wiley, New York. MR0095561
  • 18
    • 0016788270 scopus 로고
    • Connectedness and orthogonality in multifactor designs
    • MR0381176
    • ECCLESTON, J. A. and RUSSELL, K. G. (1975). Connectedness and orthogonality in multifactor designs. Biometrika 62 341-345. MR0381176
    • (1975) Biometrika , vol.62 , pp. 341-345
    • ECCLESTON, J.A.1    RUSSELL, K.G.2
  • 19
    • 73949124113 scopus 로고    scopus 로고
    • FEDERER, W. T. (1975). The misunderstood split plot. In Applied Statistics (R. P. Gupta, ed.) 9-39. North Holland, Amsterdam. MR0391429
    • FEDERER, W. T. (1975). The misunderstood split plot. In Applied Statistics (R. P. Gupta, ed.) 9-39. North Holland, Amsterdam. MR0391429
  • 20
    • 0007284597 scopus 로고
    • Contribution to the discussion of "Complex experiments" by F. Yates
    • FISHER, R. A. (1935). Contribution to the discussion of "Complex experiments" by F. Yates. J. Roy. Statist. Soc. Suppl. 2 229-231.
    • (1935) J. Roy. Statist. Soc. Suppl , vol.2 , pp. 229-231
    • FISHER, R.A.1
  • 22
    • 85103058359 scopus 로고    scopus 로고
    • HEIBERGER, R. M. (1989). Computation for the Analysis of Designed Experiments. Wiley, New York. MR1019831
    • HEIBERGER, R. M. (1989). Computation for the Analysis of Designed Experiments. Wiley, New York. MR1019831
  • 23
    • 73949133506 scopus 로고    scopus 로고
    • HINKELMANN, K. and KEMPTHORNE, O. (2008). Design and Analysis of Experiments: I: Introduction to Experimental Design, 2nd ed. Wiley, New York. MR2363107
    • HINKELMANN, K. and KEMPTHORNE, O. (2008). Design and Analysis of Experiments: Volume I: Introduction to Experimental Design, 2nd ed. Wiley, New York. MR2363107
  • 24
    • 0001518974 scopus 로고
    • Balance in designed experiments with orthogonal block structure
    • MR0720254
    • HOUTMAN, A. M. and SPEED, T. P. (1983). Balance in designed experiments with orthogonal block structure. Ann. Statist. 11 1069-1085. MR0720254
    • (1983) Ann. Statist , vol.11 , pp. 1069-1085
    • HOUTMAN, A.M.1    SPEED, T.P.2
  • 25
    • 73949105761 scopus 로고    scopus 로고
    • INSIGHTFUL CORPORATION, Insightful Corporation, Seattle, Washington
    • INSIGHTFUL CORPORATION. (2007). S-PLUS 8.0 for Windows. Insightful Corporation, Seattle, Washington.
    • (2007) S-PLUS 8.0 for Windows
  • 26
    • 0011696825 scopus 로고
    • Factorization of the residual operator and canonical decomposition of nonorthogonal factors in the analysis of variance
    • MR0334423
    • JAMES, A. T. and WILKINSON, G. N. (1971). Factorization of the residual operator and canonical decomposition of nonorthogonal factors in the analysis of variance. Biometrika 58 279-294. MR0334423
    • (1971) Biometrika , vol.58 , pp. 279-294
    • JAMES, A.T.1    WILKINSON, G.N.2
  • 27
    • 0007805056 scopus 로고
    • Design and analysis of two phase experiments
    • MCINTYRE, G. A. (1955). Design and analysis of two phase experiments. Biometrics 11 324-334.
    • (1955) Biometrics , vol.11 , pp. 324-334
    • MCINTYRE, G.A.1
  • 28
    • 0001234954 scopus 로고
    • The analysis of randomized experiments with orthogonal block structure. I. Block structure and the null analysis of variance
    • MR0176576
    • NELDER, J. A. (1965). The analysis of randomized experiments with orthogonal block structure. I. Block structure and the null analysis of variance. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 283 147-162. MR0176576
    • (1965) Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci , vol.283 , pp. 147-162
    • NELDER, J.A.1
  • 29
    • 0001234954 scopus 로고
    • The analysis of randomized experiments with orthogonal block structure. II. Treatment structure and the general analysis of variance
    • MR0174156
    • NELDER, J. A. (1965). The analysis of randomized experiments with orthogonal block structure. II. Treatment structure and the general analysis of variance. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 283 163-178. MR0174156
    • (1965) Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci , vol.283 , pp. 163-178
    • NELDER, J.A.1
  • 30
    • 0000423624 scopus 로고
    • The combination of information in generally balanced designs
    • MR0234582
    • NELDER, J. A. (1968). The combination of information in generally balanced designs. J. Roy. Statist. Soc. Ser. B 30 303-311. MR0234582
    • (1968) J. Roy. Statist. Soc. Ser. B , vol.30 , pp. 303-311
    • NELDER, J.A.1
  • 31
    • 0002534858 scopus 로고
    • A reformulation of linear models
    • MR0458743
    • NELDER, J. A. (1977). A reformulation of linear models. J. Roy. Statist. Soc. Ser. A 140 48-76. MR0458743
    • (1977) J. Roy. Statist. Soc. Ser. A , vol.140 , pp. 48-76
    • NELDER, J.A.1
  • 33
    • 0002073116 scopus 로고
    • General balance, combination of information and the analysis of covariance
    • MR1172964
    • PAYNE, R. W. and TOBIAS, R. D. (1992). General balance, combination of information and the analysis of covariance. Scand. J. Statist. 19 3-23. MR1172964
    • (1992) Scand. J. Statist , vol.19 , pp. 3-23
    • PAYNE, R.W.1    TOBIAS, R.D.2
  • 36
    • 5344244656 scopus 로고    scopus 로고
    • R CORE DEVELOPMENT TEAM , R Foundation for Statistical Computing, Vienna
    • R CORE DEVELOPMENT TEAM (2008). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna.
    • (2008) R: A Language and Environment for Statistical Computing
  • 37
    • 0002868387 scopus 로고
    • Analysis of variance models in orthogonal designs
    • MR0967202
    • TJUR, T. (1984). Analysis of variance models in orthogonal designs. Internat. Statist. Rev. 52 33-81. MR0967202
    • (1984) Internat. Statist. Rev , vol.52 , pp. 33-81
    • TJUR, T.1
  • 38
    • 1542506776 scopus 로고
    • Some aspects of the analysis of factorial experiments in a completely randomized design
    • MR0087283
    • WILK, M. B. and KEMPTHORNE, O. (1956). Some aspects of the analysis of factorial experiments in a completely randomized design. Ann. Math. Statist. 27 950-985. MR0087283
    • (1956) Ann. Math. Statist , vol.27 , pp. 950-985
    • WILK, M.B.1    KEMPTHORNE, O.2
  • 39
    • 0041122237 scopus 로고
    • A general recursive procedure for analysis of variance
    • WILKINSON, G. N. (1970). A general recursive procedure for analysis of variance. Biometrika 57 19-46.
    • (1970) Biometrika , vol.57 , pp. 19-46
    • WILKINSON, G.N.1
  • 40
    • 0007847052 scopus 로고
    • Non-orthogonal block structure in two-phase designs
    • WOOD, J. T., WILLIAMS, E. R. and SPEED, T. P. (1988). Non-orthogonal block structure in two-phase designs. Aust. J. Stat. 30A 225-237.
    • (1988) Aust. J. Stat , vol.30 A , pp. 225-237
    • WOOD, J.T.1    WILLIAMS, E.R.2    SPEED, T.P.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.