Combined Analysis of Sudoku Square Designs with Same Treatments

Authors: A. Danbaba

Abstract:

Several experiments are conducted at different environments such as locations or periods (seasons) with identical treatments to each experiment purposely to study the interaction between the treatments and environments or between the treatments and periods (seasons). The commonly used designs of experiments for this purpose are randomized block design, Latin square design, balanced incomplete block design, Youden design, and one or more factor designs. The interest is to carry out a combined analysis of the data from these multi-environment experiments, instead of analyzing each experiment separately. This paper proposed combined analysis of experiments conducted via Sudoku square design of odd order with same experimental treatments.

Keywords: Sudoku designs, combined analysis, multi-environment experiments, common treatments.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1124027

References:

[1] Gomes, F. F. and Guimares, R. F. (1958). Joint analysis of experiments incomplete randomized blocks with some common treatments. Biometrics 14, 521-526.
[2] Pavate, M. V. (1961). Combined Analysis of Balanced Incomplete Block Designs with Some Common Treatments, Biometrics, 17(1), 111-119.
[3] Giri, N. C. (1963) Note: On the Combined Analysis of Youden Squares and of Latin Square Designs with Some Common Treatments. Biometrics, 19 (1), 171-174.
[4] McIntosh, M. S. 1983. Analysis of combined experiments. Agron. J. 75:153–155.
[5] Blouin D. C., Webster E. P., and Bond J. A. (2011). On the Analysis of Combined Experiments. Weed Technology 2011 25(1), 165–169.
[6] Moore K. J. and Dixon P. M. (2015). Analysis of Combined Experiments Revisited, Agronomy Journal, 107(2), 763 – 771.
[7] Schabenberger, O. and F. J. Pierce. 2002. Contemporary statistical models for the plant and soil sciences. New York: CRC Press.
[8] Yang, R. C. 2007. Mixed-model analysis of crossover genotype- environment interactions. Crop Sci. 47:1051–1062.
[9] Snedecor G. W. and W. G. Cocharn (1967) Statistical Methods. Iowa State University Press, Ames.
[10] Hui-Dong, M. and Ru-Gen, X. (2008). Sudoku Square — a New Design in Field Experiment, ActaAgron Sin, 34(9), 1489–1493.
[11] Subramani, J. and Ponnuswamy, K.N. (2009). Construction and analysis of Sudoku designs, Model Assisted Statistics and Applications, 4(4), 287-301.
[12] Hocking, R.R. 1985. The analysis of linear models. Brooks/Cole, Monterey, CA.
[13] Donovan, D., Haaland B. and Nott D.J (2015). A Simple Approach to Constructing Quasi-Sudoku-based Sliced Space-Filling Designs. arxiv.1502.05522v1.
[14] Michael F. A. S. and Bikas K. S. (2014). SudoKu as an Experimental Design - Beyond the Traditional Latin Square Design, Statistics and Applications, 12 (1&2), 15-20.
[15] Okagbue, H. I., Adamu M.O., Oguntunde P.E., and Opanuga A. A. (2015), Some Notes on the 3-Factor Analysis of 9×9 Sudoku, Research Journal of Applied Sciences, 10(7), 284 – 286.
[16] Varun, S. B. (2015). Sudoku Squares as Experimental Designs, International Journal of Engineering Trends and Technology, 28(5), 229 – 235.
[17] Lorch, J. (2009), Mutually orthogonal families of linear sudoku solutions, J. Austral. Math. Soc., 87,409-420.
[18] Fontana, R. (2014). Random Latin squares and Sudoku designs generation, Electronic Journal of Statistics, 8, 883–893.
[19] A. Danbaba (2013). A Study on Treatment Tests from Sudoku Square Designs. International Journal of Statistics and Systems, 8(2), 131 – 136.
[20] Dahl G. (2009). Permutation matrices related to Sudoku, Linear Algebra and its Applications, 430, 2457–2463.
[21] Bailey, R. A., Cameron, P. J. and Connelly, R. (2008). Sudoku, gerechte designs, resolutions, affine space, spreads, reguli, and Hamming codes. Amer. Math. Monthly 115 383–404.
[22] Keedwell, A (2007), On sudoku squares’, Bulletin of Institute of Combinatoric. and Applications, 50, 52-60.