1. bookVolume 57 (2020): Issue 2 (December 2020)
Journal Details
License
Format
Journal
eISSN
2199-577X
First Published
17 Aug 2013
Publication timeframe
2 times per year
Languages
English
access type Open Access

On a new approach to the analysis of variance for experiments with orthogonal block structure. IV. Experiments in split-plot designs

Published Online: 31 Dec 2020
Volume & Issue: Volume 57 (2020) - Issue 2 (December 2020)
Page range: 151 - 175
Journal Details
License
Format
Journal
eISSN
2199-577X
First Published
17 Aug 2013
Publication timeframe
2 times per year
Languages
English
Summary

This paper provides estimation and hypothesis testing procedures for experiments in split-plot designs. These experiments have been shown to have a convenient orthogonal block structure when properly randomized. Due to this property, the analysis of experimental data can be carried out in a relatively simple manner. Relevant simplification procedures are indicated. According to the adopted approach, the analysis of variance and hypothesis testing procedures can be performed directly, rather than by combining the results of analyses based on some stratum submodels. The practical application of the presented theory is illustrated by examples of real experiments in appropriate split-plot designs. The present paper is the fourth in the planned series of publications on the analysis of experiments with orthogonal block structure.

Keywords

Bailey, R. A. (2008): Design of Comparative Experiments. Cambridge University Press.10.1017/CBO9780511611483Search in Google Scholar

Brzeskwiniewicz H. (1994): Experiment with split-plot generated by PBIB designs. Biometrical Journal 36: 557-570.10.1002/bimj.4710360508Search in Google Scholar

Caliński T., Kageyama S. (2000): Block Designs: A Randomization Approach, Vol. I: Analysis. Lecture Notes in Statistics 150, Springer, New York.10.1007/978-1-4612-1192-1Search in Google Scholar

Caliński T., Siatkowski I. (2017): On a new approach to the analysis of variance for experiments with orthogonal block structure. I. Experiments in proper block designs. Biometrical Letters 54: 91-122.10.1515/bile-2017-0006Search in Google Scholar

Caliński T., Siatkowski I. (2018): On a new approach to the analysis of variance for experiments with orthogonal block structure. II. Experiments in nested block designs. Biometrical Letters 55: 147-178.10.2478/bile-2018-0011Search in Google Scholar

Caliński T., Łacka A., Siatkowski I. (2019): On a new approach to the analysis of variance for experiments with orthogonal block structure. III. Experiments in row-column designs. Biometrical Letters 56: 183-213.10.2478/bile-2019-0014Search in Google Scholar

Elandt R. (1964): Statystyka matematyczna w zastosowaniu do doświadczalnictwa rolniczego. Państwowe Wydawnictwo Naukowe, Warszawa, Poland.Search in Google Scholar

Hinkelmann K., Kempthorne O. (2008): Design and Analysis of Experiments, Vol. 1: Introduction to Experimental Design, 2nd ed. Wiley, Hoboken, New Jersey.Search in Google Scholar

Houtman A.M., Speed T.P. (1983): Balance in designed experiments with orthogonal block structure. Annals of Statistics 11: 1069-1085.10.1214/aos/1176346322Search in Google Scholar

Johnson N.L., Kotz S., Balakrishnan N. (1995): Continuous Univariate Distributions, Vol. 2, 2nd ed. Wiley, New York.Search in Google Scholar

Kala R. (2019): A new look at combining information from stratum submodels. In: Ahmed S., Carvalho F., Puntanen S. (eds.) Matrices, Statistics and Big Data. IWMS 2016. Contributions to Statistics. Springer: 35-49.10.1007/978-3-030-17519-1_3Search in Google Scholar

Mejza I. (1996): Control treatments in incomplete split-plot designs. Tatra Mountains Mathematical Publications 7: 69-77.Search in Google Scholar

Mejza S. (1986): Doświadczenia w układach blokowych niekompletnych o jednostkach rozszczepionych. Rozprawy Naukowe 150, Roczniki Akademii Rolniczej w Poznaniu.Search in Google Scholar

Nelder J.A. (1965): The analysis of randomized experiments with orthogonal block structure. Proceedings of the Royal Society of London, Series A 283: 147-178.Search in Google Scholar

Nelder J.A. (1968): The combination of information in generally balanced designs. Journal of the Royal Statistical Society, Series B 30: 303-311.10.2307/2343525Search in Google Scholar

Pearce S.C. (1983): The Agricultural Field Experiment: A Statistical Examination of Theory and Practice. Wiley, New York.Search in Google Scholar

Rao C.R. (1971): Unified theory of linear estimation. Sankhyā, Series A 33: 371-394.Search in Google Scholar

Rao C.R. (1974): Projectors, generalized inverses and the BLUE’s. Journal of the Royal Statistical Society, Series B 36: 442-448.10.1111/j.2517-6161.1974.tb01019.xSearch in Google Scholar

Rao C.R., Mitra S.K. (1971): Generalized Inverse of Matrices and its Applications. Wiley, New York.Search in Google Scholar

R Core Team (2017): R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.Search in Google Scholar

Volaufova J. (2009): Heteroscedastic ANOVA: old p values, new views. Statistical Papers 50: 943-962.10.1007/s00362-009-0262-4Search in Google Scholar

Yates F. (1933): The principles of orthogonality and confounding in replicated experiments. Journal of Agricultural Science 23: 108-145.10.1017/S0021859600052916Search in Google Scholar

Yates F. (1935): Complex experiments. Supplement to the Journal of the Royal Statistical Society 2: 181-247.10.2307/2983638Search in Google Scholar

Yates F. (1939): The recovery of inter-block information in variety trials arranged in three-dimensional lattices. Annals of Eugenics 9: 136-156.10.1111/j.1469-1809.1939.tb02203.xSearch in Google Scholar

Yates F. (1940): The recovery of inter-block information in balanced incomplete block designs. Annals of Eugenics 10: 317-325.10.1111/j.1469-1809.1940.tb02257.xSearch in Google Scholar

Recommended articles from Trend MD

Plan your remote conference with Sciendo