GRAECO-LATIN SQUARE DESIGN ON THE OPTIMIZATION OF CROP NUTRIENT BY APPLICATION OF FERTILIZER TO THE SOIL
Abstract
This study investigates the optimization of crop nutrient application using the Graeco-Latin Square Design (GLSD), with a focus on four different varieties of guinea corn cultivated on Phanadam Farm in Bwari, Abuja, over four harvest seasons (2020–2023). The research assessed the effects of crop variety, soil type, cropping system, and fertilizer type on crop yield. Employing a GLSD of order 4, the design efficiently controlled for three sources of variability, allowing for a robust analysis of the four treatment factors. Data were obtained from secondary sources and analyzed using Analysis of Variance (ANOVA). Results indicated that there were no statistically significant differences in yield attributable to crop variety, soil type, cropping system, or fertilizer type, as the F-calculated values were consistently lower than the F-tabulated value of 9.28. These findings suggest that although these factors may intuitively affect yield, uniform application of fertilizers can standardize yield across different conditions. The study recommends the consistent use of fertilizers in guinea corn production, regardless of variety or environmental factors, to enhance agricultural productivity
Keywords:
Graeco-Latin Square Design, Crop Nutrient Optimization, Guinea Corn Yield, Experimental Design, Fertilizer TypesDownloads
Published
DOI:
https://doi.org/10.5281/zenodo.15849440Issue
Section
How to Cite
License
Copyright (c) 2025 Oseni Halimat Olajumoke, Adenomon Monday Osagie, Abubakar Muhammad Auwal , Nweze Nwaze Obini
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
References
Abebe Z, Sharma JJ, Dechassa N, Kanampiu F. The effect of integrated organic and inorganic fertilizer rates on soybean and maize component crop performance in a soybean/maize mixture in Bako, Western Ethiopia. Afr J Agric Res. 2021; 8(29):3921–9.Search in Google Scholar
Alhasan KFH, Smarandache F. Neutrosophic Weibull distribution and neutrosophic family Weibull distribution. 2019: Infinite Study.
Andersen, L. D. (2013). Latin squares. In R. Wilson and J. J. Watkins (Eds.), Combinatorics: Ancient and modern (pp. 251–284). Oxford, UK: Oxford University Press, 2004.
Armitage P, Berry G. (2004). Statistical models in medical research (3rd Edition). Blackwell publishers.
Aslam M. A new attribute sampling plan using the neutrosophic statistical interval method. Complex Intel Syst. 2019; 5(4):365–70.
Aslam M. Neutrosophic analysis of variance: application to university students. Complex Intel Syst. 2019; 5(4):403–7 Simulation, 2022: p. 1–19.
Aslam M, Albassam M. Post hoc multiple comparison tests under neutrosophic statistics. J King Saud Univ-Sci. 2020; 32(6):2728–32.
"Archived copy". Archived from the original on February 19, 2010. Retrieved 2010-02-10. Retrieved Jan. 2010 "Liebig's law of the minimum". Oxford Reference.
Bose C. R., and Marvel B. (1984) “Introduction to Combinatorial Theory”. 135- 149(Ch.7). John Wiley & Sons, Inc.
Brunk, M.E., W.T. Federer (2003): Experimental Designs and probability sampling in marketing research. J. Amer. Statist. Assoc. 48.
Byers, J. (2001) “Basic Algorithms for Random Sampling and Treatment Randomization.
Cox, D.R. (2008). “The Interpretation of the effects of non-additivity in the Latin Square, “Biometrics, 45, 69-73
Cox (2007) “Planning of experiments” Published by Wiley and Sons INC.
Cochran, W. G. (2008). Recent work on the analysis of variance. Journal of the Royal Statistical Society, 101, 434–449. Doi:10.2307/2980213
Cochran, W. G. and Cox M. (2007). Experimental Design. John Wiley and Sons Ltd, New York.
Colton, J. A. (2012): “Avoiding Mean Square Error Bias in Designed Experiment” published under MiniTab Inc.
Dénes J, Keedwell A. Latin squares and their applications. Budapest: Académiai Kiado; 2004.
Dodge Y, Shah K. Estimation of parameters in Latin squares and Graeco-Latin squares with missing observations. Commun Stat-Theory Methods. 2007;6(15):1465–72.
Emanuel Epstein (2002). Mineral Nutrition of Plants: Principles and Perspectives. New York, Wiley. ISBN 9780471243403.
Effanga, E. O., & Offong, N. E. (2016). International Journal of Innovative research and advanced studies. Vol. 3 Issue 9, pp. 84–87.
Emanouilidis, E. (2005). Latin and magic squares. International Journal of Mathematical Education in Science and Technology 36, 546–549. Doi:10.1080/00207390412331336201
Geary, S., Disney (2006). “On bullwhip in supply chains-Historical review, present and expected future impact”. International Journal of Production Economics, 101(1),2-18.
Hicks C. R. and Turner K. V. (1973). Fundamental Concepts in the Design of Experiment. Oxford University Press, UK.
Holf, P. D. (2009): STA 502 lecture notes.
Hirel B, Tétu T, Lea PJ, Dubois F. Improving nitrogen use efficiency in crops for sustainable useagriculture. Sustainability. 2011;3(9):1452–85.10.3390/su3091452Search in Google Scholar
Hoshmand R. Design of experiments for agriculture and the natural sciences. CRC: Chapman and Hall, 2018.
Keedwell, A. D., & Dénes, J. (2015). Latin squares and their applications (2nd ed.). Amsterdam: North-Holland
Martin RJ, Nadarajah S. G. Raeco and L. Atin Square Designs. Encyclopedia of Biostatistics, 2005; 3.
Macronutrients and Micronutrients". Soilsfacstaff.cals.wisc.edu. Retrieved 2022-07-15.
Marschner, Petra, ed. (2012). Marcher’s mineral nutrition of higher plants (3rd ed.). Amsterdam: Elsevier/Academic Press. ISBN 9780123849052.
Montgomery DC. Design and analysis of experiments. John wiley & sons; 2017.
Nagarajan D et al. Analysis of neutrosophic multiple regression. Neutrosophic Sets Syst. 2021; 43:44–53.
Norman P. A. Huner; William Hopkins (2008-11-07). "3 & 4". Introduction to Plant Physiology 4th Edition. John Wiley & Sons, Inc. ISBN 978-0-470-24766-2.
Laekemariam F, Gidago G. Response of maize (Zea mays L.) to integrated fertilizer application in Wolaita, South Ethiopia. Adv Life Sci Technol. 2022;5(11):21–30.Search in Google Scholar
Onyiah LC. Design and analysis of experiments: classical and regression approaches with SAS. CRC Press; 2008.
Panhwar QA, Ali A, Naher UA, Memon MY. Fertilizer management strategies to enhance
Nutrient use efficiency and sustainable wheat production. In Organic farming. Amsterdam,Netherlands: Elsevier; 2019. p. 17–39.10.1016/B978-0-12-813272-2.00002-1Search in Google Scholar
Patro S, Smarandache F. The neutrosophic statistical distribution, more problems, more solutions. 2016: Infinite Study.
Perret, P., Bailleux, C., & Dauvier, B. (2011). The influence of relational complexity and strategy selection on children’s reasoning in the Latin Square Task. Cognitive Development, 26, 127–141. doi:10.1016/j.cogdev.2010.12.003
Preece D. Non-orthogonal Graeco-Latin designs. In: Combinatorial Mathematics IV. Springer; 2006. pp. 7–26.
Poulton, E. C. (1982). Influential companions: Effects of one strategy on another in within-subjects designs of cognitive psychology. Psychological Bulletin, 91, 673–690. doi:10.1037/0033-2909.91.3.673
Randive K, Raut T, Jawadand S. An overview of global fertilizer trends and India’s position in 2020. Miner Econ. 2021; 34:1–14. doi: 10.1007/s13563-020-00246-zSearch in Google Scholar
Street DJ. Graeco-Latin and nested row and column designs. In: Combinatorial Mathematics VIII. Springer; 2001. pp. 304–13.
Seberry J. A note on orthogonal Graeco-Latin designs. 2009.
Sapam S, Sinha BK. Graeco Latin square design with neighbor effects. J Stat Theory Pract. 2021; 15(1):1–10.
Smarandache F. Neutrosophic logic: A generalization of the intuitionistic fuzzy logic. Multispecies and multistructure Neutrosophic transdisciplinarity. 2010; 4:396.
Smarandache F. Introduction to neutrosophic statistics: infinite study. Columbus: Romania-Educational Publisher; 2014.
Salama A, Khaled O, Mahfouz K. Neutrosophic correlation and simple linear regression. Neutrosophic Sets Syst. 2014; 5:3–8.
RAK Sherwani, et al. Analysis of COVID-19 data using neutrosophic Kruskal–Wallis H test. BMC Med Res Methodol. 2021; 21(1):1–7.
RAK Sherwani , et al. A new neutrosophic sign test: an application to COVID-19 data. PLoS ONE. 2021; 16(8): e0255671.
Smarandache F. Indeterminacy in Neutrosophic Theories and their Applications. 2021: Infinite Study.
Tahat MM, Alananbeh KM, Othman YA, Leskovar DI. Soil health and sustainable agriculture.
Tabachnick, B. G., & Fidell, L. S. (2007). Experimental designs using ANOVA. Belmont, CA: Thomson Brooks/Cole.
Sustainability. 2020; 12(12):4859.10.3390/su12124859Search in Google Scholar
Wanless, I.: Transversals in Latin Squares: A Survey, p. 403–437. Cambridge University Press (Jun 2011). https://doi.org/10.1017/cbo9781139004114.010
Willner-Reid, J., Whitaker, D., Epstein, D. H., Phillips, K. A., Pulaski, A. R., Preston, K. L., & Willner, P. (2016). Cognitive-behavioral therapy for heroin and cocaine use: Ecological momentary assessment of homework simplification and compliance. Psychology and Psychotherapy, 89(2), 276–293. doi:10.1111/papt.12080
Yates F, Mather K. Ronald Aylmer Fisher, 2002. The Royal Society London. 2003.
Zahoor I, Mushtaq A. Water pollution from agricultural activities: A critical global review. Int J Chem Biochem Sci. 2023; 23(1):164–76.Search in Google Scholar
Zia, A. (2000): “Reducing Error in Informal Sector Survey” Published under Australlia Bureau of Statistics, Australia
