Use of α-resolvable designs in the construction of two-factor experiments of split-plot type
By: Kazuhiro Ozawa, Shinji Kuriki and Stanisław Mejza
References
- 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.), Kluwer, Dordrecht: 171–184. Springer Netherlands.
- Bailey R.A., Monod H., Morgan J.P. (1995): Construction and optimality of affine-resolvable designs. Biometrika 82(1): 187–200.
- Bhargava R.P., Shah K.R. (1975): Analysis of some mixed models for block and split-plot designs. Annals of the Institute of Statistical Mathematics 27: 365–375.
- Caliński T., Czajka S., Kaczmarek Z., Krajewski P., Pilarczyk W. (2005): Analyzing multi-environment variety trials using randomization-derived mixed models. Biometrics 61(2): 448–455.
- Caliński T., Czajka S., Kaczmarek Z., Krajewski P., Pilarczyk W. (2009a): Analyzing the genotype-by-environment interactions under a randomization-derived mixed model. Journal of Agricultural, Biological, and Environmental Statistics 14(2): 224–241.
- Caliński T., Czajka S., Pilarczyk W. (2009b): On the application of affine resolvable designs to variety trials. Journal of Statistics and Applications 4(2-3): 201–224.
- Caliński T., Czajka S., Kaczmarek Z., Krajewski P., Pilarczyk W., Siatkowski I., Siatkowski M. (2015): On a mixed model analysis of multi-environment variety trials: a reconsideration of the one-stage and the two-stage models and analyses. Statistical Papers: 1–33. DOI: 10.1007/s00362-015-0706-y.
- Caliński T., Kageyama S. (2000): Block Designs: A Randomization Approach, Volume I: Analysis. Lecture Notes in Statistics 150, New York, Springer.
- Caliński T., Kageyama S. (2003): Block Designs: A Randomization Approach, Volume II: Design. Lecture Notes in Statistics 170, New York, Springer.
- Gomez K.A., Gomez A.A. (1984): Statistical procedures for agricultural research, 2nd edition. New York, John Wiley & Sons.
- Houtman A.M., Speed T.P. (1983): Balance in designed experiments with orthogonal block structure. The Annals of Statistics 11: 1069–1085.
- Kadowaki S., Kageyama S. (2009): Existence of affine α-resolvable PBIB designs with some constructions. Hiroshima Mathematical Journal 39: 293–326.
- Kageyama S. (1973): On µ-resolvable and affine µ-resolvable balanced incomplete block designs. The Annals of Statistics 1: 195–203.
- Hinkelmann K., Kempthorne O. (2007): Design and Analysis of Experiments, Introduction to Experimental Design (Volume 1), 2nd edition. Hoboken, John Wiley & Sons.
- Hinkelmann K., Kempthorne O. (2005): Design and Analysis of Experiments, Advanced Experimental Design (Volume 2). Hoboken, John Wiley & Sons.
- Hinkelmann K. eds. (2012): Design and Analysis of Experiments, Special Designs and Applications (Volume 3). Hoboken, John Wiley & Sons.
- Little M.T., Hills F.J. (1978): Agricultural Experimentation: Design and Analysis. New York, John Wiley & Sons.
- Khatri C.G., Rao C.R. (1968): Solutions to some functional equations and their applications to characterization of probability distributions. Sankhyā A 30: 167–180.
- Kuriki S., Nakajima K. (2007): Square lattice designs in incomplete split-plot designs. Journal of Statistical Theory and Practice 1(3-4): 417–426.
- Mejza S. (1992). On some aspects of general balance in designed experiments. Statistica 52(2): 263–278.
- Mejza I., Kuriki S., Mejza S. (2001): Balanced square lattice designs in split-block designs. Colloquium Biometricum 31: 97–103.
- Mejza I., Mejza S. (1984): Incomplete split plot designs. Statistics & Probability Letters 2: 327–332.
- Mejza I., Mejza S. (1996): Incomplete split-plot designs generated by GDPBIBD(2). Calcutta Statistical Association Bulletin 46: 117–127.
- Mejza S. (1987): Experiments in incomplete split-plot designs. In Pukkila, T. and Puntanen, S. (Eds.), Proceeding of Second International Tampere Conference in Statistics. University of Tampere, 575–584.
- Nelder J.A. (1965a): The analysis of randomized experiments with orthogonal block structure. I. Block structure and the null analysis of variance. Proceedings of the Royal Society. London, A 283: 147–162.
- Nelder J.A. (1965b): The analysis of randomized experiments with orthogonal block structure. II. Treatment structure and the general analysis of variance. Proceedings of the Royal Society. London, A 283: 163–178.
- Ozawa K., Kuriki S. (2006): Incomplete split-plot designs generated from α-resolvable designs. Statistics & Probability Letters 76: 1245–1254.
- Ozawa K., Mejza S., Jimbo M., Mejza I., Kuriki S. (2004): Incomplete split-plot designs generated by some resolvable balanced designs. Statistics & Probability Letters 68: 9–15.
- Pearce S.C., Caliński T., Marshall T.F. de C. (1974): The basic contrasts of an experimental design with special reference to the analysis of data. Biometrika 61: 449–460.
- Rees H.D. (1969): The analysis of variance of some non-orthogonal designs with split-plot. Biometrika 56: 43–54.
- Robinson J. (1967a): Incomplete split-plot designs. Biometrics 21: 793–802.
- Robinson J. (1967b): Blocking in incomplete split-plot designs. Biometrika 57: 347–350.
Language: English
Page range: 105 - 118
Published on: Dec 10, 2016
Published by: Polish Biometric Society
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year
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© 2016 Kazuhiro Ozawa, Shinji Kuriki, Stanisław Mejza, published by Polish Biometric Society
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.