## Bibliography

**Included in the supplementary materials for Brien (2017c) is a full bibliography of multiphase experiments up to the end of 2017.**

Bailey, R.A. and Brien, C.J. . (2016) Randomization-based models for multitiered experiments: I. A chain of randomizations. *Annals of Statistics*, **44**, 1131-1164. published manuscript or Definitive published version at projecteuclid.org or Definitive published version at arXiv

Box, G.E.P. and Jones, S. (1992). Split-plot designs for robust product experimentation. *Journal of Applied Statistics*, **19**, 3-26.

Brien, C.J. (1980) *Patterns in correlation matrices arising in wine-tasting
and other experiments*. M.Ag.Sc. thesis (in a PDF file), University of Adelaide.

Brien, C.J. (1983). Analysis of variance tables based on experimental structure. *Biometrics*, **39**, 133-139.

Brien, C.J. (1989) A model comparison approach to linear models. *Utilitas Mathematica*, **36**, 225-254.

Brien, C.J. (1992) *Factorial Linear Model Analysis*. PhD thesis (in a PDF file or a Postscript file), University of Adelaide.

Brien, C. J. (2017a). dae: functions useful in the design and ANOVA of experiments. R package version 3.0-12. http://CRAN.R-project.org/package=dae, last accessed January 5, 2018.

Brien, C. J. (2017b). ACANONICAL procedure. In *GenStat Release 19 Reference Manual* **Part 3: Procedure Library**, 23-â€“25. Ed. by VSN International. Hemel Hempstead: VSN International.

Brien, C.J. (2017c) Multiphase experiments in practice: A look back. *Australian & New Zealand Journal of Statistics*, **59**, 327-352. Accepted version or Definitive published version at onlinelibrary.wiley.com.

Brien, C.J. (2018) Multiphase experiments with at least one later laboratory phase. II. Nonorthogonal designs. In preparation.

Brien, C.J. and Bailey, R.A. (2006) Multiple randomizations (with discussion). *Journal of the Royal Statistical Society, Series B*, **68**, 571-609. Accepted version (without discussion) or Definitive published version at www.blackwell-synergy.com.

Brien, C.J. and Bailey, R.A. (2009) Decomposition tables for multitiered experiments. I. A chain of randomizations. *Annals of Statistics*, **37**, 4184-4213. published manuscript or Definitive published version at projecteuclid.org or Definitive published version at arXiv.

Brien, C.J. and Bailey, R.A. (2010) Decomposition tables for multitiered experiments. II. Two-one randomizations. *Annals of Statistics*, **38**, 3164-3190. published manuscript or Definitive published version at projecteuclid.org or Definitive published version at arXiv

Brien, C.J., and Demétrio, C.G.B. (1998a), Using the randomization in specifying the ANOVA model and table for properly and improperly replicated grazing trials. *Australian Journal of Experimental Agriculture*, **38**, 325-334.

Brien, C.J., and Demétrio, C.G.B. (1998b) Using the randomization in specifying the ANOVA model and table for grazing trials. unpublished manuscript in a PDF file or a postscript file.

Brien, C.J., and Demétrio, C.G.B. (2009) Formulating mixed models for experiments, including longitudinal experiments. *Journal of Agricultural, Biological and Environmental Sciences*, **14(3)**, 253-80. Accepted version or Definitive published version at SpringerLink.

Brien, C.J., Harch, B.D., Correll, R.L. and Bailey, R.A. (2011) Multiphase experiments with at least one later laboratory phase. I. Orthogonal designs. *Journal of Agricultural, Biological and Environmental Sciences*, **16(3)**, 422-450. Accepted version or Definitive published version at SpringerLink and supplementals at Springerlink.

Brien, C.J., May, P. and Mayo, O. (1987) Analysis of judge performance in wine-quality evaluations. *Journal of Food Science*, **52**, 1273-1279.

Brien, C.J. and Payne, R.W. (1999), Tiers, structure formulae and the analysis of complicated experiments. *The Statistician*, **48**, 41-52.

Brien, C.J. and Payne, R.W. (2006) AMTIER Procedure. in *GenStat Reference Manual Release 9*, **Part 3, Procedure Library PL 17**, 73-75. Ed. by R.W. Payne and P.W. Lane. VSN International: Hemel Hempstead.

Butler, D. G., Tan, M. K. and Cullis, B. R. (2009) Improving the accuracy of selection for late maturity alpha-amylase in wheat using multi-phase designs. *Crop and Pasture Science*, **60**, 1202-8.

Butler, D. G. (2014) od: generate optimal designs for comparative experiments. Version 0.75.

Cox, D.R. (1958) *Planning of Experiments*. Wiley: New York.

Cullis, B.R., Smith, A.B., Panozzo, J.F. and Lim, P. (2003) Barley malting quality: are we selecting the best? *Australian Journal of Agricicultural Research*, **54**, 1261-75.

Curnow, R.N. (1959) The analysis of a two phase experiment. *Biometrics*, **15**, 60-73.

Eccleston, J.A. and Russell, K. (1975) Connectedness and orthogonality in multi-factor designs. *Biometrika*, **62**, 341-345.

Federer, W.T. (1975) The misunderstood split plot. In Gupta, R.P., *Applied Statistics*, 9-39. North Holland: Amsterdam.

Heiberger, R.M. (1989) *Computation for the Analysis of Designed Experiments*. Wiley: New York.

Jarrett, R. G. and K. Ruggiero (2008) Design and Analysis of Two-Phase Experiments for Gene Expression Microarraysâ€”Part I. *Biometrics*, **64(1)**, 208-216.

Kerr, M.K. (2003) Design Considerations for Efficient and Effective Microarray Studies. *Biometrics*, **59**, 822-828.

Lewis, S.M. (2006) Discussion on ‘Multiple randomizations’ (by C.J. Brien and R.A. Bailey). *Journal of the Royal Statistical Society, Series B*, **68**, 602. Definitive published version at www.blackwell-synergy.com.

McIntyre, G.A. (1955) Design and analysis of two phase experiments.
*Biometrics*, **11**, 324-34.

Mee, R.W. and Bates, R.L. (1998) Split-lot designs: experiments for multi-stage batch processes. *Technometrics*, **40**,
127-140.

Miller, A. (1997) Strip-plot configurations of fractional factorials. *Technometrics*, **39**, 153-161.

Monod, H. and Bailey, R.A. (1992) Pseudofactors: Normal use to improve dessign and facilitate analysis. *Appl. Statist.*, **41**, 317-36.

Payne, R.W., Harding, S.A.. Murray, D.A., Soutar, D.M., Baird, D.B., Welham, S.J., Kane, A. F., Gilmour, A. R., Thompson, R., Webster, R. and Tunnicliffe Wilson, G. (2006) *The Guide to GenStat Release 9, Part 2 Statistics*. VSN International. Hemel Hempstead.

Preece, D.A. (1991) Contribution to the discussion of
‘Strata for randomized experiments’ by R.A. Bailey, *Journal of the Royal Statistical Society, B*, **53**, 67-68.

R Development Core Team. (2018) *R: A Language and Environment for Statistical Computing*. R Foundation for Statistical Computing: Vienna, Austria. http://www.r-project.org/, last accessed January, 2018.

SAS~Institute~Inc. (2015) *SAS/QC® 14.1 User's Guide*. SAS Institute Inc.: Cary, NC. http://support.sas.com/documentation/cdl/en/qcug/68161/HTML/default/viewer.htm#qcug_optex_toc.htm, last accessed June 19, 2016.

Smith, A.B., Cullis, B.R., Appels, R., Campbell, A.W., Cornish, G.B., Martin, D. and Allen, H.M. (2001) The statistical analysis of quality traits in plant improvement programs with application to the mapping of milling yield in wheat. *Australian Journal of Agricultural Research*, **52**, 1207-1219.

Smith, A.B., Lim, P. and Cullis, B.R. (2006) The design and analysis of multi-phase plant breeding experiments. *The Journal of Agricultural Science*, **144(05)**, 393-409.

Smith, A.B., Thompson, R., Butler, D. G. and Cullis, B. R. (2011) The design and analysis of variety trials using mixtures of composite and individual plot samples. *Journal of the Royal Statistical Society: Series C (Applied Statistics)*, **60**, 437-455.

Smith, A. B., Butler, D. G., Cavanagh, C. R. and Cullis, B. R. (2015) Multi-phase variety trials using both composite and individual replicate samples: a model-based design approach. *Journal of Agricultural Science*, **153(6)**, 1017-1029.

White, R.F. (1975) Randomization and the analysis of variance. *Biometrics*, **31**, 552-572.

Wilkinson G.N. and Rogers, C. E. (1973) Symbolic description of factorial models for analysis of variance. *Appl. Statist.*, **22**, 392-9.

Wilkinson, R.I., Frisina, C., Partington, D., Franz, P.R., Thomson, F., Brien, C.J., Tomkins, R.B. and Faragher, J.D. (2008) Effects of 1-methylcyclopropene on firmness and flesh browning of Australian Pink Lady^{TM} apples. *Journal of Horticultural Science and Technology*, **83**, 165-170.

Wood, J.T., Williams, E.R. and Speed, T.P. (1988) Non-orthogonal block structure in two-phase designs. *Austral. J. Statist.*, **30A**, 225-37.