Abstract
The paper deals with experiments laid out in a complete or an incomplete split-plot design in which one control (standard) treatment occurs in addition to the usual treatments. Usually the control (standard) treatment has been treated as one specific factor level. In this paper, in contrast to others in this area, the control (standard) may not be strictly connected with treatment combinations. The new incomplete split-plot designs with control satisfy all generally accepted methodological requirements, with special reference to the problems of randomisation. Moreover, tools are described which allow checking of the general balance or efficiency of the design, as well as performance of experiments with inference.
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References
Bailey R (1995) General balance: artificial theory or practical relevance. In: Proceedings of the international conference on linear statistical inference, LINSTAT’93. Mathematics and applications, vol 306. Kluwer, Dordrecht, pp 171–184
Bingham D, Sitter RS (1999) Some theoretical results for fractional factorial split-plot designs. Ann Stat 27: 1240–1255
Calinski T, Kageyama S (2000) Block designs: a randomization approach, vol I. Analysis. Lecture notes in statistics 150. Springer, New York
Cochran WG, Cox GM (1957) Experimental designs. Wiley, New York
Federer WT, King F (2007) Variations on split plot and split block experiment designs. Wiley, New Jersey
Gomez KA, Gomez AA (1984) Statistical procedures for agricultural research. Wiley, New York
Goos P (2002) The optimal design of blocked and split-plot experiments. Lecture notes in statistics, vol 164, Springer, New York
Hinkelman K, Kempthorne O (2007a) Design and analysis of experiments: introduction to experimental design, vol 1. Wiley, New York
Hinkelman K, Kempthorne O (2007b) Design and analysis of experiments: advanced experimental design, vol 2. Wiley, New York
Houtman AM, Speed TP (1983) Balance in designed experiments with orthogonal block structure. Ann Stat 11: 1069–1085
Kachlicka D, Mejza I (1998) Supplemented block designs with split units. Colloq Biomet 28: 77–90
Kachlicka D, Mejza I (2002) Modelling and analysis of a resolvable split-plot design with supplemented whole plots. FOLIA Facultatis Scientarium Naturalium Universitatis Masarykianae, pp 83–90
Kempthorne O (1952) The design and analysis of experiments. Wiley, New York
Kowalski SM, Vinning GG (2001) Split-plot experimentation for process and quality improvement. Front Stat Qual Control 6: 335–350
Kowalski SM, Parker PA, Vinning GG (2007) Tutorial: industrial split-plot experiments. Qual Eng 19: 1–16
Mejza I (1996) Control treatments in incomplete split-plot designs. Tatra Mountains Math Publ 7: 69–77
Mejza I, Mejza S (1984) Incomplete split-plot designs. Stat Probab Lett 2: 327–332
Mejza I, Mejza S (1996) Incomplete split-plot generated by GDPBIB(2). Calcutta Stat Assoc Bull 46: 117–127
Mejza I, Kuriki S, Mejza S (2001) Balanced square lattice designs in split-plot designs. Colloq Biomet 31: 97–103
Mejza S (1985) A split-plot design with whole plot treatments in an incomplete block design. In: Caliński T, Klonecki W (eds) Lecture notes in statistics, vol 35. Linear statistical inference. Springer, New York, pp 211–222
Mejza S (1987) Experiments in incomplete split-plot designs. In: Pukkila T, Puntanen S (eds) Proceedings second int. Tampere conf. in statistics, University of Tampere, pp 575–584
Mejza S (1992) On some aspects of general balance in designed experiments. Statistica, anno LII, vol 2, pp 263–278
Montgomery DC (1997) Design and analysis of experiments. Wiley, New York
Nelder JN (1965) The analysis of experiments with orthogonal block structure. Proc R Soc Lond A 283: 147–178
Nelder JN (1968) The combination of information in generally balanced designs. J R Stat Soc B 30: 303–311
Neyman J, Iwaszkiewicz K, Kolodziejczyk S (1935) Statistical problems in agricultural experimentation. J R Stat Soc Suppl 2: 107–180
Ozawa K, Mejza S, Jimbo M, Mejza I, Kuriki S (2004) Incomplete split-plot designs generated by some resolvable balanced designs. Stat Probab Lett 68: 9–15
Patterson HN, Williams ER (1976) A new class of resolvable incomplete block designs. Biometrika 63: 83–92
Pearce SC (1983) The agricultural field experiment. A statistical examination of theory and practice. Wiley, New York
Pearce SC, Calinski T, de Marshall TFC (1974) The basic contrasts of an experimental design with special reference to the analysis of data. Biometrika 54: 449–460
Rao CR, Mitra SK (1971) Generalized inverse of matrices and its applications. Wiley, New York
Robinson TJ, Brenneman WA, Myers WR (2009) An intuitive graphical approach to understanding the split-plot experiment. J Stat Edu 17/1: 1–17
Spilke J, Piepho HP, Meyer U (2004) Approximating the degrees of freedom for contrasts of genotypes laid out as subplots an alpha-design in a split-plot experiment. Plant Breed 123: 193–197
White RF (1975) Randomization in the analysis of variance. Biometrics 31: 555–571
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Aastveit, A.H., Almøy, T., Mejza, I. et al. Individual control treatment in split-plot experiments. Stat Papers 50, 697–710 (2009). https://doi.org/10.1007/s00362-009-0253-5
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DOI: https://doi.org/10.1007/s00362-009-0253-5