Abstract
The aim of the paper is to present a randomization model, statistical properties and their consequences for an analysis of some three factor experiments set up in resolvable split-plot × splitblock designs. To control several sources of local variation, nested blocking structure is applied. The designs considered are incomplete with respect to all the factors which levels are arranged in resolvable block designs.
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References
Ambroży, K., Mejza, I., 2003. Some split-plot × split-block designs. Colloquium Biometryczne, 33, 83–96.
Ambroży, K., Mejza, I., 2004. Split-plot × split-block type three factors designs. In: Proc. of the 19th International Workshop on Statistical Modelling, 291–295.
Ambroży, K., Mejza, I., 2006. GD PBIBD(2)s in incomplete Split-Plot × Split-Block type experiments. Metodološki zvezki — Advances in Methodology and Statistics, Vol. 3 No. 1, 39–48.
Caliński, T., Kageyama, S., 2000. Block Designs: A Randomization Approach, Volume I: Analysis. Lecture Notes in Statistics 150, Springer-Verlag, New York.
Caliński, T., Kageyama, S., 2003. Block Designs: A Randomization Approach, Volume II: Design. Lecture Notes in Statistics 170, Springer-Verlag, New York.
Gupta, S.C., 1985. On Kronecker block designs for factorial experiments. J. Statist. Plann. Infer. 52, 359–374.
Gupta, S., Mukerjee, R., 1989. A calculus for factorial arrangements. Lecture Notes in Statistics 59, Springer-Verlag.
Hedges, L.V., Olkin, I., 1985. Statistical Methods for Meta-Analysis. Academic Press Limited, London.
Houtman, A.M., Speed, T.P., 1983. Balance in designed experiments with orthogonal block structure. Ann. Statist., 11, 1069–1085.
Kachlicka, D., Mejza, S., 1990. Incomplete split-plot experiments — whole-plot treatments in a row-column design. Computational Statistics & Data Analysis, 9, 135–146.
Kachlicka, D., Mejza, S., 1996. Repeated row-column designs with split units. Computational Statistics & Data Analysis, 21, 293–305.
LeClerg, E.L., Leonard, W.H., Clark, A.G., 1962. Field plot technique. Burgess, Minneapolis.
Mejza, I., Mejza, S., 1984. Incomplete split-plot designs. Statist. Probab. Lett. 2., 327–332.
Mejza, I., Mejza, S., 1994. Model Building and Analysis for Block designs with Nested Rows and Columns. Biom. J. 36, 327–340.
Mejza, S., 1992. On some aspects of general balance in designed experiments. Statistica 52, 263–278.
Nelder, J.A., 1965a. The analysis of randomized experiments with orthogonal block structure. 1. Block structure and the null analysis of variance. Proc. of the Royal Soc. of Lond. Ser. A, 283, 147–162.
Nelder, J.A., 1965b. The analysis of randomized experiments with orthogonal block structure. 2. Treatment structure and general analysis of variance. Proc. of the Royal Soc. of Lond. Ser. A, 283, 163–178.
Pearce, S.C., 1983. The Agricultural Field Experiment. A Statistical Examination of Theory and Practice. John Wiley & Sons, Chichester.
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Mejza, I., Ambroży, K. Resolvable Incomplete Split-Plot × Split-Block Designs. J Stat Theory Pract 1, 405–416 (2007). https://doi.org/10.1080/15598608.2007.10411849
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DOI: https://doi.org/10.1080/15598608.2007.10411849