LATIN SQUARE DESIGN: A METHODOLOGICAL INNOVATION IN EDUCATIONAL RESEARCH FOR IMPROVED TEACHING AND LEARNING
DOI:
https://doi.org/10.33003/fjs-2025-0905-3686Keywords:
Latin Square Design, Educational Research, Experimental Design, Statistical Analysis, Student Learning OutcomesAbstract
A Latin square design (LSD) is a specific arrangement of integers, letters, or symbols, where each element appears exactly once in each row and column. Latin squares have long fascinated mathematicians, with a rich history and various applications in mathematics and other fields. It is more efficient and hence more powerful than reasonable alternatives such as Completely Randomized Design (CRD) or Randomized Complete Block Design (RCBD). Educational researchers also realized that Latin squares could be used in their work, but Latin-square designs do not appear to have been adopted in education anywhere near as often as in medical research. The review of how educational researchers have made use of Latin-square designs in their experiments. This work focuses on the performance of students of six classes in six different subjects by six different teachers using six different methods of teaching. A 6 × 6 Latin square design was employed. The descriptive statistics tables shows that SS3 students perform better with minimum average of failure (21.33%), all classes perform better in Ahmadu’s subjects that is Biology and Basic Science with minimum average failure (22.67%) and Method C (i.e. Deductive method) yield better result with minimum average failure (22.17%). From the Analysis of Variance, the p-value obtained for the three variables; Classes, Teachers and Methods of teaching given as 0.556, 0.612 and 0.842 respectively indicates that the null hypotheses are accepted and conclude that the differences between classes, teachers and method of teachings are not significant.
References
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Madhusudanan, G., Senthilkumar, S., Anand, I., & Sanjeevikumar, P. (2018). A shade dispersion scheme using Latin square arrangement to enhance power production in solar photovoltaic array under partial shading conditions. Journal of Renewable and Sustainable Energy, 10(5). https://doi.org/10.1063/1.5046366
Peng, Q., & Yuan, H. (2024). Using Latin Square Methodology to Test Vocabulary through Story Reading. Advances in Humanities and Modern Education Research, 1(1), 72-77.
Rankovic, N., Rankovic, D., Lukic, I., Savic, N., & Jovanovic, V. (2023). Ensemble model for predicting chronic non-communicable diseases using Latin square extraction and fuzzy-artificial neural networks from 2013 to 2019. Heliyon, 9(11). https://doi.org/10.1016/j.heliyon.2023.e22561
Richardson, J. T. (2018). The use of Latin-square designs in educational and psychological research. Educational Research Review, 24, 84-97. https://doi.org/10.1016/j.edurev.2018.03.003
Saurabh, S. and Singh, M. K. (2022). A Note on the Construction of Latin Square Type Designs. Communications in Statistics-Theory and Methods, 51(10), 3434-3437.https://doi.org/10.1080/03610926.2020.1734837
Sapam, S., Mandal, N., & Sinha, B. (2021). Latin square designs with neighbor effects-part II. Communications in Statistics-Theory and Methods, 50(14), 3371-3379. https://doi.org/10.1080/03610926.2019.1702694
Zeuch, N., Holling, H., & Kuhn, J. T. (2011). Analysis of the Latin Square Task with linear logistic test models. Learning and Individual Differences, 21(5), 629-632. www.elsevier.com/locate/lindif
Zhang, J., Zhu, Y., Abdelraheem, A., ElkinsArce, H. D., Dever, J., Wheeler, T., ... & Wedegaertner, T. (2022). Use of a Latin square design to assess experimental errors in field evaluation of cotton for resistance to Fusarium wilt race 4. Crop Science, 62(2), 575-591. https://doi.org/10.1002/csc2.20673
Zolfaghari, B., & Bibak, K. (2022). Combinatorial cryptography and Latin squares. In Perfect Secrecy in IoT: A Hybrid Combinatorial-Boolean Approach (pp. 37-55). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-031-13191-2_3
Adedoyin, A., Enebe, F. O., Oyekunle, R. A., & Balogun, N. A. (2023). Design and implementation of an online teaching and learning management system. FUDMA Journal of Sciences, 7(1), 148-155. DOI: https://doi.org/10.33003/fjs-2023-0701-1266
AlAita, A., Aslam, M., Al Sultan, K., & Saleem, M. (2024). Analysis of Graeco-Latin square designs in the presence of uncertain data. Journal of Big Data, 11(1), 109 https://doi.org/10.1186/s40537-024-00970-1.
Alexander, R. (2020). Using the latin square design model in the prioritization of network security threats: a quantitative study. Journal of Information Security, 11(02), 92. https://doi.org/10.4236/jis.2020.112006
Assuah, C. K. (2019). Using a Latin Square Design to Determine the Most Effective Mathematics Teaching Method. International Journal of New Technology and Research, 5(7), 64-69. https://doi.org/10.31871/ijntr.5.7.14
Beall, G. (1971). Change-over experiments in practice. Educational Testing Service Princeton, New Jersey.
Chen, Y., Huang, H., Tang, C., & Wei, W. (2024). A novel adaptive image privacy protection method based on Latin square. Nonlinear Dynamics, 112(12), 10485-10508. https://doi.org/10.21203/rs.3.rs-3702841/v1
Feldt, L. S. (1979). Everet F. Lindquist 19011978 a Retrospective Review of his Contributions to Educational Research. Journal of Educational Statistics, 4(1), 4-13. https://doi.org/10.3102/10769986004001004
Fisher, R. A. (1971). The design of experiments (8th ed., p. 216). New York: Hafner.
Fisher, R. A. (1925). Statistical methods for research workers. Edinburgh, Scotland: Oliver & Boyd. Retrieved from http://psychclassics.yorku.ca/Fisher/Methods/
Gao, Z., Sun, P., Li, M., Jeon, S. W., & Jin, H. (2023). Orthogonal Latin Square Based Particle Swarm Optimization: A Dynamic Approach for Continues Functions Optimization. International Conference on Advanced Computational Intelligence (ICACI) (pp. 1-6). IEEE. https://doi.org/10.1109/icaci58115.2023.10146187
Hartung, J., Goecke, B., Schroeders, U., Schmitz, F., & Wilhelm, O. (2022). Latin square tasks: A multi-study evaluation. Intelligence, 94, 101683.
Higham, J., & Richardson, J. T. (2021). Corrigendum to The use of Latin-square designs in educational and psychological research[Educational Research Review 24 (2018) 8497]. Educational Research Review, 32, 100378. https://doi.org/10.1016/j.edurev.2018.03.003
Horsham, C., Baade, P., Kou, K., O'Hara, M., Sinclair, C., Loescher, L. J., ... & Janda, M. (2021). Optimizing texting interventions for melanoma prevention and early detection: A Latin square crossover RCT. American Journal of Preventive Medicine, 61(3), 348-356. ACTRN12618001299291.
Hua, Z., Li, J., Chen, Y., & Yi, S. (2021). Design and application of an S-box using complete Latin square. Nonlinear Dynamics, 104(1), 807-825.
Jahnavi, A., & Anithaashri, T. P. (2024). Improvisation of crime detection system in car parking space using novel randomized block design analytics over Latin square design. In AIP Conference Proceedings (Vol. 2871, No. 1). AIP Publishing. https://doi.org/10.1063/5.0227962
Keedwell, A. D., & Dnes, J. (2015). Latin Squares and Their Applications: Latin Squares and Their Applications. Elsevier.
Kumar, P., Moazzamigodarzi, M., & Rahimi, M. (2024). Neutrosophic Analysis of Experimental Data Using Neutrosophic Graeco-Latin Square Design. Axioms, 13(8), 559.https://doi.org/10.3390/axioms13080559
Livingston Jr, G. C., and Rayner, J. C. W. (2024). Rank tests for the Latin square design. Communications in Statistics-Theory and Methods, 1-14.https://doi.org/10.1080/03610926.2024.2387249
Madhusudanan, G., Senthilkumar, S., Anand, I., & Sanjeevikumar, P. (2018). A shade dispersion scheme using Latin square arrangement to enhance power production in solar photovoltaic array under partial shading conditions. Journal of Renewable and Sustainable Energy, 10(5). https://doi.org/10.1063/1.5046366
Peng, Q., & Yuan, H. (2024). Using Latin Square Methodology to Test Vocabulary through Story Reading. Advances in Humanities and Modern Education Research, 1(1), 72-77.
Rankovic, N., Rankovic, D., Lukic, I., Savic, N., & Jovanovic, V. (2023). Ensemble model for predicting chronic non-communicable diseases using Latin square extraction and fuzzy-artificial neural networks from 2013 to 2019. Heliyon, 9(11). https://doi.org/10.1016/j.heliyon.2023.e22561
Richardson, J. T. (2018). The use of Latin-square designs in educational and psychological research. Educational Research Review, 24, 84-97. https://doi.org/10.1016/j.edurev.2018.03.003
Saurabh, S. and Singh, M. K. (2022). A Note on the Construction of Latin Square Type Designs. Communications in Statistics-Theory and Methods, 51(10), 3434-3437.https://doi.org/10.1080/03610926.2020.1734837
Sapam, S., Mandal, N., & Sinha, B. (2021). Latin square designs with neighbor effects-part II. Communications in Statistics-Theory and Methods, 50(14), 3371-3379. https://doi.org/10.1080/03610926.2019.1702694
Zeuch, N., Holling, H., & Kuhn, J. T. (2011). Analysis of the Latin Square Task with linear logistic test models. Learning and Individual Differences, 21(5), 629-632. www.elsevier.com/locate/lindif
Zhang, J., Zhu, Y., Abdelraheem, A., ElkinsArce, H. D., Dever, J., Wheeler, T., ... & Wedegaertner, T. (2022). Use of a Latin square design to assess experimental errors in field evaluation of cotton for resistance to Fusarium wilt race 4. Crop Science, 62(2), 575-591. https://doi.org/10.1002/csc2.20673
Zolfaghari, B., & Bibak, K. (2022). Combinatorial cryptography and Latin squares. In Perfect Secrecy in IoT: A Hybrid Combinatorial-Boolean Approach (pp. 37-55). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-031-13191-2_3
Published
2025-05-31
How to Cite
Sule, A. S., Lantana, B., Nuhu, U. M., Nasir, U., & Amina, A. N. (2025). LATIN SQUARE DESIGN: A METHODOLOGICAL INNOVATION IN EDUCATIONAL RESEARCH FOR IMPROVED TEACHING AND LEARNING. FUDMA JOURNAL OF SCIENCES, 9(5), 328 - 334. https://doi.org/10.33003/fjs-2025-0905-3686
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Research Articles
FUDMA Journal of Sciences
