On a new approach to the analysis of variance for experiments with orthogonal block structure. III. Experiments in row-column designs

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

Euler L. (1782): Recherches sur une nouvelle espèce de quarrés magiques. Verh. Zeeuwach Genootschap Wetenschappen Vlissengen 9: 85-239.Search in Google Scholar

Gawęcki J., Wagner W. (1984): Podstawy Metodologii Badań Doświadczalnych w Nauce o Żywieniu i Żywności. Państwowe Wydawnictwo Naukowe, Warszawa - Poznań.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

John J.A. (1987): Cyclic Designs. Chapman and Hall, London.10.1007/978-1-4899-3326-3Search 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

Kozłowska M., Łacka A., Krawczyk R., Kozłowski R.J. (2011): Some block designs with nested rows and columns for research on pesticide dose limitation. Environmetrics 22: 781–788.10.1002/env.1070Search in Google Scholar

Kozłowska M., Łacka A., Skorupska A. (2012): Block designs with nested rows and columns for research on food acceptability limitation. Communications in Statistics – Theory and Methods 41, 2456-2464.10.1080/03610926.2011.617481Search in Google Scholar

Mejza I., Mejza S. (1994). Model building and analysis for block designs with nested rows and columns. Biometrical Journal 36: 327-340.10.1002/bimj.4710360311Search 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: 147-178.10.1098/rspa.1965.0012Search 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

Przybyłowski J., Walkowiak R. (1977): Kwadrat łaciński i związane z nim inne układy wierszowo-kolumnowe. Siódme Colloquium Metodologiczne z Agro-Biometrii. Polska Akademia Nauk, 354-369.Search in Google Scholar

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

Rao C.R. (1974): Projectors, generalized inverses and the BLUEs. 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., Kleffe J. (1988): Estimation of Variance Components and Applications. North-Holland, Amsterdam.Search 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

Siatkowski I. (2004): Analiza układów wierszowo-kolumnowych. Rozprawy Naukowe 356, Roczniki Akademii Rolniczej w Poznaniu.Search in Google Scholar

Singh M., Dey A. (1978): Two-way elimination of heterogeneity. Journal of the Royal Statistical Society, Series B 40: 58-63.10.1111/j.2517-6161.1978.tb01648.xSearch in Google Scholar

Singh M., Dey A. (1979): Block designs with nested rows and columns. Biometrika 66: 321-326.10.1093/biomet/66.2.321Search 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